diff --git a/PackageInfo.g b/PackageInfo.g index a64a409..6b4d42a 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -1,9 +1,9 @@ SetPackageInfo( rec( PackageName := "loops", Subtitle := "Computing with quasigroups and loops in GAP", -Version := "3.3.0", -Date := "26/10/2016", -ArchiveURL := "http://www.math.du.edu/loops/loops-3.3.0", +Version := "3.4.0", +Date := "27/10/2017", +ArchiveURL := "http://www.math.du.edu/loops/loops-3.4.0", ArchiveFormats := "-win.zip .tar.gz", Persons := [ @@ -83,7 +83,7 @@ Dependencies := rec( ), AvailabilityTest := ReturnTrue, -BannerString := "This version of LOOPS is ready for GAP 4.7.\n", +BannerString := "This version of LOOPS is ready for GAP 4.8.\n", Autoload := false, # false for deposited packages TestFile := "tst/testall.g", diff --git a/data/automorphic.tbl b/data/automorphic.tbl index fe9d6fc..15007cb 100644 --- a/data/automorphic.tbl +++ b/data/automorphic.tbl @@ -2,39 +2,21 @@ ## #W automorphic.tbl Automorphic loops G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: automorphic.tbl, v 3.3.0 2016/10/20 gap Exp $ +#H @(#)$Id: automorphic.tbl, v 3.4.0 2017/10/23 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) ## -############################################################################# -## Binding global variables -## LOOPS_automorphic_cocycles -## LOOPS_automorphic_bases -## LOOPS_automorphic_coordinates - -# Many small automorphic loops are represtented by encoded Cayley tables. -# -# Commutative automorphic loops of order 243 are represtented as central -# extensions of the cyclic group of order 3. -# The necessary data is only loaded on demand and consists of: -# - LOOPS_automorphic_cocycles, a list of encoded bases of the -# space of cocycles modulo coboundaries for every factor loop F needed. -# - LOOPS_automorphic_coordinates, a list that for every loop -# points to the factor loop and gives coordinates of the required cocycle -# with respect to the relevant basis. - LOOPS_automorphic_data := [ #implemented orders -[3,6,8,9,10,12,14,15,27,81,243], +[3,6,8,9,10,12,14,15,27,81], #number of nonassociative loops of given order -[1,1,7,2,3,2,5,2,7,72,118451], +[1,1,7,2,3,2,5,2,7,72], #the loops [ -#order 3 (Z_3) +#order 3 (Z_3, use left Bruck loops, placeholder only) [ -"201" ], #order 6 [ @@ -50,10 +32,8 @@ LOOPS_automorphic_data := [ "0325476301675421076455760132467102374523106543201", "0325476310674520176545761023467013275432106452301" ], -#order 9 (two abelian groups) +#order 9 (two abelian groups, use left Bruck loops, placeholder only) [ -"204537861534867678012861207201345534", -"204537861534867678120862017012453345" ] , #order 10 @@ -80,20 +60,13 @@ LOOPS_automorphic_data := [ "234068597BDAEC340189675DEBCA401297856ECDAB012375968CAEBD6897ADECB041328975DCABE430215689EABDC102439756CBDEA324107568BECAD21304BDEC0413258976DECA4302187569ABDE1024395687ECAB3241076895CABD2130469758", "234067895BCDEA340178956CDEAB401289567DEABC012395678EABCD7968ADBEC012348579ECADB340129685DBECA123405796CADBE401236857BECAD23401DBEC0432156789ECAD3210478956ADBE1043295678BECA4321067895CADB2104389567" ], -#order 27 (commutative only, placeholder) +#order 27 (commutative only, use left Bruck loops, placeholder) [ ] , -#order 81 (commutative only, placeholder) -[ -] -, -#order 243 (commutative only, placeholder) +#order 81 (commutative only, use left Bruck loops, placeholder) [ ] ] ]; -LOOPS_automorphic_cocycles := []; -LOOPS_automorphic_bases := []; -LOOPS_automorphic_coordinates := []; diff --git a/data/automorphic/automorphic_cocycles.tbl b/data/automorphic/automorphic_cocycles.tbl deleted file mode 100644 index 60562c5..0000000 --- a/data/automorphic/automorphic_cocycles.tbl +++ /dev/null @@ -1,8058 +0,0 @@ -############################################################################# -## -#W automorphic_cocycles.tbl G. P. Nagy / P. Vojtechovsky -## -#H @(#)$Id: automorphic_cocycles.tbl, v 3.3.0 2016/10/20 gap Exp $ -## -#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), -#Y P. Vojtechovsky (University of Denver, USA) -## - -# cocycles for commutative automorphic loops of order 243 - -LOOPS_automorphic_cocycles := -# for factors of order 9 -[ -[ -"6`5[M.,", -"U$R^,", -"3#QhY9l4=", -"2'pwq", -"3#QhS<]EA" -], -# for factor of order 27 -[ -"5d+2q'HlX4t)<>QwA6RA;PcK{`B>Jzd&XJ8<[:|']|8=%7/2QP#1VG^d", -"2]^4fQntIt?>N%/8;t_[ur^-Lyqd6KiYSWCQkuoTw|", -"WPDx-a|zBO7,R+rye^37#LH:+efo[&eaOb~UEv/V0", -"2Fn}rAZjS5%1++ZJQ=]$[rHW:=|k`14E4B`YHv+I:tF<;RbSf(BhdC~~x-q3tt=.zK0UWZWrq", -"N%;}mF{1E%jOj)8%JQ8#aRdLn.+WufO{*aiM'+-z[ob2X29)wzd_4kJ(ZeV[kA$k7r.D@:9p~", -"VZc6~t.-(2>-hi;oj4Rzw^`:($,jmkT@YZ4a#U6:B.d1Lehl1}/1{TR=#^HBNlV56-", -"j:wiQj0ig=Kql1Cf&}V,^%``Z7Z+&m7?4uLMT[}+ekhIalTmD1RE-ktl=F*5{`d2,*", -"3+>{Vcp]dqM`8mMowcqc5.7P~aqHi&[DnG{8M`}O{MJY&;u'a8.4wa-tR%t:qic`UkjsTQw2Rzo%6Mhft|Pv9GO=x}}|O_S2|+*OFC2]}dCf8W&", -"WLzl(Wb)+FavH+NyHD3H^m@~ZmWu~M(]1+q)TlH.&", -"2Fn}rAZjS5%1++ZJQ=]$[rHW:=|k`14E44FV{vleOG?HDkycql}DTzo{rNK{449-dI|`]P$~d", -"12.W./ADP*t:.tkW}cA50,w,lViI;q+2X/xlnaF,#}?)usJa?7.Uud4V[.2u@Y(BdR9yYl86YUXC(/jSDs4l'&", -"5d+2q'HlX4t)<>QwA6RA;PcK{`B>Jzd&XJ8<[:|']|8=%7/2QP#1VG^d", -"2Fn}rAZjS5%1++ZJQ=]$[rHW:=|k`14E4B`YHv+I:tF<;RbSf(BhdC~~x-q3tt=.zK0UWZWrq", -"3@1Aju?P%w:;@a,0x-#3WF%=<0|[/XeKIur8%Myq", -"5d+2q'HlX4t)<>QwA6RA;PcK{`B>Jzd&XJ8<[:|']|8=%7/2QP#1VG^d", -"WPDx-a|zBO7,R+rye^37#LH:+efo[&eaOb~UEv/V0", -"12.W./ADP*t:.tzo:SH>)sYG#t5nqzGr8ye0WlPIZI1jP*EA,rCty.IOG?QM,J|f=d<0{ydaS-C5Fm", -"3@1Aju?P%w:;@a,0x-#3WF%=<0|[/XeKIur8%Myq", -"5d+2q'HlX4t)<>QwA6RA;PcK{`B>Jzd&XJ8<[:|']|8=%7/2QP#1VG^d", -"WPDx-a|zBO7,R+rye^37#LH:+efo[&eaOb~UEv/V0", -"3@1Aju?P%w:;@a,0x-#3WF%=<0|[/XeKIur8%Myq", -"5d+2q'HlX4t)<>QwA6RA;PcK{`B>Jzd&XJ8<[:|']|8=%7/2QP#1VG^d", -"WPDx-a|zBO7,R+rye^37#LH:+efo[&eaOb~UEv/V0", -"3@1Aju?P%w:;@a,0x-#3WF%=<0|[/XeKIur8%Myq", -"12.W./ADP*t:.tzo:SH>)sYG#t5nqzGr8ye0W=}K~[OYfHfX^iHk%Mg,CV_1Jv(O{&V]'3zx\ -brDb|rlAt]#CA.=*w4?M}_<*Q?dyZr`x,l{IbP.]],D+qt5Va9@F+PocOgPXQ/aa_&})AtC$(Ktsj:Pl-fw15KGH>eq", - 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-# ordered bases for the space of cocycles modulo coboundaries -# the indices point to the above list of cocycles - -LOOPS_automorphic_bases := -[ -# for factors of order 9 -[ -[ 1, 2, 3, 4], -[ 5 ] -], -# for factors of order 27 -[ -[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ], -[ 12, 13, 14, 15 ], -[ 16, 17, 18 ], -[ 19, 20, 21, 22 ], -[ 23, 24, 25 ], -[ 26, 27, 28 ], -[ 29 ] -], -# for factors of order 81 -[ -[ 53, 60, 21, 24, 56, 19, 54, 13, 2, 26, 66, 14, 63, 38, 35, 3, 57, 4, 20, 51, 32, 22, 40, 1 ], -[ 52, 59, 23, 55, 19, 13, 25, 65, 62, 33, 39 ], -[ 53, 58, 24, 56, 19, 13, 26, 66, 35, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 43, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 16, 13, 66, 63, 35, 1 ], -[ 53, 60, 24, 56, 15, 13, 1, 65, 62, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 1, 25, 65, 62, 33 ], -[ 53, 60, 24, 56, 19, 63, 26, 66, 35, 1 ], -[ 53, 60, 24, 56, 19, 62, 26, 66, 1, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 63, 13, 26, 66, 35, 1 ], -[ 53, 60, 24, 56, 62, 13, 26, 66, 1, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 63, 13, 26, 66, 35, 1 ], -[ 53, 60, 24, 56, 62, 13, 26, 66, 1, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 7, 26, 63, 35, 1 ], -[ 53, 60, 24, 56, 19, 8, 26, 64, 1, 33 ], -[ 53, 60, 24, 56, 19, 9, 26, 62, 1, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 28, 13, 63, 66, 35, 1 ], -[ 53, 60, 24, 56, 27, 13, 64, 66, 1, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 29, 13, 62, 66, 1, 33 ], -[ 53, 60, 24, 56, 19, 11, 26, 1, 62, 33 ], -[ 53, 60, 24, 56, 19, 12, 26, 1, 62, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 60, 24, 56, 19, 9, 26, 62, 1, 33 ], -[ 53, 60, 24, 56, 19, 10, 26, 63, 35, 1 ], -[ 53, 60, 24, 56, 19, 6, 26, 63, 35, 1 ], -[ 53, 60, 24, 56, 19, 5, 26, 1, 62, 33 ], -[ 53, 60, 24, 56, 19, 13, 26, 66, 63, 1 ], -[ 53, 31, 24, 56, 17, 13, 63, 66, 35, 1 ], -[ 53, 30, 24, 56, 18, 13, 64, 66, 1, 33 ], -[ 52, 23, 55, 42 ], -[ 52, 23, 46, 34 ], -[ 52, 55, 61, 34 ], -[ 52, 23, 55 ], -[ 52, 23, 41, 34 ], -[ 52, 23, 47, 34 ], -[ 23, 55, 48, 34 ], -[ 52, 23, 55 ], -[ 52, 23, 55 ], -[ 52, 23, 34 ], -[ 56, 49, 37, 1 ], -[ 1, 55 ], -[ 1, 55, 50 ], -[ 53, 1 ], -[ 53, 1 ], -[ 53, 24, 1 ], -[ 53, 24, 45, 1 ], -[ 53, 24, 1 ], -[ 53, 24, 1 ], -[ 1, 23, 36 ], -[ 53, 24, 1 ], -[ 53, 24, 1 ], -[ 53, 24, 1 ], -[ 23, 1 ], -[ 44 ] -] -]; - -# data for reconstruction of commutative automorphic loops -# -# For each order n (of factor loop), the list is firts processed -# with SplitString(...," "), resulting in a list ls. -# -# Every entry of ls is a string s. The first character of s determines the -# id of the factor loop of order n. The remainder of s contains coded -# coordinates of the cocycle with respect to the above basis. - -LOOPS_automorphic_coordinates := -[ -# for factors of order 9 -"1 11 19 1C 1D 1F 2", -# for factors of order 27 -"1 11 19 1C 1D 1F 1@ 1] 1^ 1_ 12# 12+ 12- 184 187 18A 18C 18D 18H 18J 18K 18M\ - 18O 18Q 18b 18c 18d 18e 18i 190 191 193 195 197 19A 19J 19K 19L 19P 1WI 1Wg \ -1W( 1?b 1?c 11Di 13}Y 13}Z 21 23 29 2A 2C 2F 2R 2S 2T 2U 39 3A 3B 3C 3D 43 4C\ - 4D 4F 4T 4U 4V 4W 6F 71", -# for factors of order 81 -"2 21 23 29 2A 2C 2F 2R 2S 2T 2U 2@ 2[ 2^ 22z 22# 22+ 22, 23p 23q 23s 284 287 \ -28A 28B 28D 28G 28J 28K 28M 28P 28S 28T 28U 28V 28Y 28b 28c 28d 28e 28h 28k 2\ -8l 28m 28n 28q 28_ 28| 290 291 293 296 299 29A 29C 29F 29I 29J 29K 29L 29O 29\ -R 29S 29T 29U 29X 29a 29g 2OC 2OU 2O{ 2Q. 2Rs 2Tb 2Th 2Tk 2Tn 2UR 2WG 2WM 2WP\ - 2WS 2WY 2We 2Wh 2Wk 2Wn 2Wq 2Wt 2W( 2W+ 2W. 2W; 2W> 2W[ 2X3 2X6 2X9 2XC 2XF \ -2XI 2XL 2XO 2XR 2XU 2XX 2Xa 2-a 2-b 2-c 2-d 2=U 2=V 2=W 2?M 2?P 2?b 2?c 2?d 2\ -?e 2?h 2?% 2?+ 2@j 2@p 215d 21Ba 21Bd 21Dh 21Tg 21bk 22YR 22YS 22YU 22ZK 22a7\ - 22a8 22aA 22aY 22aZ 22aa 22ab 22ae 22wX 22yG 22yb 22^G 22^e 23}Y 23}Z 23}b 2\ -3}q 23}r 23}s 23}t 24Mt 27CH 27CI 27CK 29k, 29k- 29k/ 3 39 3A 3B 3D 3E 3R 3U \ -3@ 3[ 31H 31I 31i 31j 32z 32# 32$ 32% 32& 32' 32( 32) 32* 32+ 32, 32- 32. 32/\ - 32: 32; 32< 32= 32> 32? 32@ 32[ 32] 32^ 32_ 32` 32{ 32| 32} 32~ 330 331 332 \ -333 334 335 336 337 338 339 33A 33B 33C 33D 33E 33F 33G 33H 33I 33J 33K 33L 3\ -3M 33N 38A 38S 38T 38V 38W 38X 38t 38w 38[ 38] 39I 39J 39j 39k 39- 39. 39: 39\ -; 39< 3A8 3A9 3AB 3AC 3AD 3AZ 3Ac 3A# 3A$ 3A% 3A& 3A' 3A( 3A) 3A* 3A+ 3A, 3A-\ - 3A. 3A/ 3A: 3A; 3A< 3A= 3A> 3A? 3A@ 3A[ 3A] 3A^ 3A_ 3A` 3A{ 3A| 3A} 3A~ 3B0 \ -3B1 3B2 3B3 3B4 3B5 3B6 3B7 3B8 3B9 3BA 3BB 3BC 3BD 3BE 3BF 3BG 3BH 3BI 3BJ 3\ -BK 3BL 3BM 3BN 3BO 3BP 3BQ 3BR 3BS 3BT 3BU 3BV 3BW 3BX 3BY 3BZ 3Ba 3Bb 3Bc 3B\ -d 3Be 3Bf 3Bg 3Bh 3Bi 3Bj 3Bk 3Bl 3Bm 3Bn 3Bo 3Bp 3O3 3O6 3OC 3OF 3Ov 3Ow 3Oy\ - 3Oz 3O^ 3O_ 3PK 3PL 3Pl 3Pm 3P/ 3P: 3QA 3QB 3Qb 3Qc 3Q% 3Q& 3Q' 3Q( 3Q) 3Q* \ -3Q+ 3Q, 3Q- 3Q. 3Q/ 3Q: 3Q; 3Q< 3Q= 3Q> 3Q? 3Q@ 3Q[ 3Q] 3Q^ 3Q_ 3Q` 3Q{ 3Q| 3\ -Q} 3Q~ 3R0 3R1 3R2 3R3 3R4 3R5 3R6 3R7 3R8 3R9 3RA 3RB 3RC 3RD 3RE 3RF 3RG 3R\ -H 3RI 3RJ 3RK 3RL 3RM 3RN 3RO 3RP 3RQ 3RR 3RS 3RT 3RU 3RV 3RW 3RX 3RY 3RZ 3Ra\ - 3Rb 3Rc 3Rd 3Re 3Rf 3Rg 3Rh 3Ri 3Rj 3Rk 3Rl 3Rm 3Rn 3Ro 3Rp 3Rq 3Rr 3W4 3W5 \ -3WD 3WE 3WF 3Ww 3Wz 3W_ 3W` 3XL 3XM 3Xm 3Xn 3X: 3X= 3YB 3YC 3YE 3YF 3YG 3Yc 3\ -Yd 3Yf 3Yg 3Yh 3Y& 3Y' 3Y( 3Y) 3Y* 3Y+ 3Y, 3Y- 3Y. 3Y/ 3Y: 3Y; 3Y< 3Y= 3Y> 3Y\ -? 3Y@ 3Y[ 3Y] 3Y^ 3Y_ 3Y` 3Y{ 3Y| 3Y} 3Y~ 3Z0 3Z1 3Z2 3Z3 3Z4 3Z5 3Z6 3Z7 3Z8\ - 3Z9 3ZA 3ZB 3ZC 3ZD 3ZE 3ZF 3ZG 3ZH 3ZI 3ZJ 3ZK 3ZL 3ZM 3ZN 3ZO 3ZP 3ZQ 3ZR \ -3ZS 3ZT 3ZU 3ZV 3ZW 3ZX 3ZY 3ZZ 3Za 3Zb 3Zc 3Zd 3Ze 3Zf 3Zg 3Zh 3Zi 3Zj 3Zk 3\ -Zl 3Zm 3Zn 3Zo 3Zp 3Zq 3Zr 3Zs 3e5 3eE 3e` 3e} 3fM 3fP 3fn 3fo 3fq 3fr 3fs 3f\ -; 3f< 3gC 3gD 3gd 3ge 3g' 3g( 3g) 3g* 3g+ 3g, 3g- 3g. 3g/ 3g: 3g; 3g< 3g= 3g>\ - 3g? 3g@ 3g[ 3g] 3g^ 3g_ 3g` 3g{ 3g| 3g} 3g~ 3h0 3h1 3h2 3h3 3h4 3h5 3h6 3h7 \ -3h8 3h9 3hA 3hB 3hC 3hD 3hE 3hF 3hG 3hH 3hI 3hJ 3hK 3hL 3hM 3hN 3hO 3hP 3hQ 3\ -hR 3hS 3hT 3hU 3hV 3hW 3hX 3hY 3hZ 3ha 3hb 3hc 3hd 3he 3hf 3hg 3hh 3hi 3hj 3h\ -k 3hl 3hm 3hn 3ho 3hp 3hq 3hr 3hs 3ht 3-9 3-C 3-a 3-b 3-d 3-e 3-$ 3-' 3-- 3-:\ - 3-= 3.? 3.@ 3/G 3/H 3/h 3/i 3?A 3?D 3?b 3?e 3?% 3?& 3?. 3?/ 3?: 3@@ 3@[ 3@^ \ -3@_ 3[H 3[I 3[K 3[L 3[M 3[i 3[l 3|B 3|C 3|E 3|F 3|G 3|& 3|/ 3}[ 3}] 3~I 3~J 3\ -~j 3~k 315C 315D 315F 315G 315d 315g 316] 316^ 317k 317l 31DD 31DG 31De 31Df \ -31Dh 31Di 31Dj 31E^ 31E_ 31E{ 31E| 31Fl 31Fo 31Lf 31Li 31M_ 31M` 31Nm 31Nn 31\ -T* 31T+ 31T- 31T. 31T= 31T> 31T? 31T@ 31T[ 31T] 31U` 31U{ 31b+ 31b> 31c{ 31c|\ - 31c~ 31d0 31k| 31k} 32YR 32YT 32YU 32YV 32YW 32Ya 32Yb 32Yc 32Yd 32Ye 32Yf 3\ -2Yj 32Yk 32Yl 32Ym 32Yn 32Yo 32ZH 32ZI 32ZJ 32ZK 32ZL 32ZM 32ZN 32ZO 32ZP 32Z\ -Q 32ZR 32ZS 32ZT 32ZU 32ZV 32ZW 32ZX 32ZY 32ZZ 32Za 32Zb 32Zc 32Zd 32Ze 32Zf \ -32Zg 32Zh 32a| 32a} 32a~ 32b0 32b1 32b2 32b3 32b4 32b5 32b6 32b7 32b8 32b9 32\ -bA 32bB 32bC 32bD 32bE 32bF 32bG 32bH 32bI 32bJ 32bK 32bL 32bM 32bN 32bO 32bP\ - 32bR 32bS 32bU 32bV 32bX 32bY 32bZ 32ba 32bb 32bc 32bd 32be 32bf 32gS 32gT 3\ -2gV 32gW 32gX 32gb 32gc 32gd 32ge 32gf 32gg 32gk 32gl 32gm 32gn 32go 32gp 32h\ -I 32hJ 32hK 32hL 32hM 32hN 32hO 32hP 32hQ 32hR 32hS 32hT 32hU 32hV 32hW 32hX \ -32hY 32hZ 32ha 32hb 32hc 32hd 32he 32hf 32hg 32hh 32hi 32i8 32i9 32iA 32iB 32\ -iC 32iD 32iE 32iF 32iG 32iH 32iI 32iJ 32iK 32iL 32iM 32iN 32iO 32iP 32iQ 32iR\ - 32iS 32iT 32iU 32iV 32iW 32iX 32iY 32i} 32i~ 32j0 32j1 32j2 32j3 32j4 32j5 3\ -2j6 32j7 32j8 32j9 32jA 32jB 32jC 32jD 32jE 32jF 32jG 32jH 32jI 32jJ 32jK 32j\ -L 32jM 32jN 32jO 32jP 32jS 32jT 32jV 32jW 32jY 32jZ 32ja 32jb 32jc 32jd 32je \ -32jf 32jg 32jq 32jr 32js 32jt 32ju 32jv 32jw 32jx 32jy 32jz 32j# 32j$ 32j% 32\ -j& 32j' 32j( 32j) 32j* 32j+ 32j, 32j- 32j. 32j/ 32j: 32j; 32j< 32j= 32z0 32z1\ - 32z3 32z4 32z6 32z7 32z9 32zA 32zB 32zC 32zD 32zE 32zF 32zG 32zH 32zR 32zT 3\ -2zU 32zW 32zX 32zZ 32za 32zb 32zc 32zd 32ze 32zf 32zg 32zh 32zi 32*1 32*2 32*\ -3 32*4 32*5 32*6 32*7 32*8 32*9 32*A 32*B 32*C 32*D 32*E 32*F 32*G 32*H 32*I \ -32*J 32*K 32*L 32*M 32*N 32*O 32*P 32*Q 32*R 32*S 32*T 32*V 32*W 32*Y 32*Z 32\ -*b 32*c 32*d 32*e 32*f 32*g 32*h 32*i 32*j 32 4W? 4W@ 4W[ 4W] 4W^ 4W` 4W| 4W} 4X0 4X2 4X3 4\ -X5 4X6 4X7 4X9 4XA 4XC 4XD 4XF 4XH 4XI 4XJ 4XL 4XM 4XN 4XO 4XP 4XQ 4XR 4XS 4X\ -T 4XU 4XV 4XW 4XX 4XY 4XZ 4Xa 4Xb 4Xc 4Xd 4Xe 4Xf 4Xg 4Xh 4Xi 4Xj 4Xk 4Xl 4-a\ - 4/+ 4/, 4/> 4/@ 4:y 4:z 4 41b?\ - 41b@ 41b| 41b} 41b~ 41c6 41c7 41cF 41cH 41cO 41cP 41cX 41cY 41cZ 41cg 41ch 4\ -1ci 41cp 41cq 41cr 42YR 42YS 42YU 42YW 42ZH 42ZI 42ZK 42ZL 42a7 42aA 42aY 42a\ -b 42ae 42wU 42wV 42xK 42xM 42yA 42yD 42yG 42yH 42yJ 42yK 42yM 42yb 42yc 42yd \ -42ye 42yf 42yg 42^D 42^e 43}P 43}Y 43}Z 43}q 43}r 43}s 44MS 44Mt 47B] 47B^ 47\ -B~ 47C2 47C3 47C4 47C5 47CH 47CI 47CJ 47CK 47CL 47CM 47Ci 47Cj 47Ck 47Cl 47Cm\ - 47Cn 47Ep 47Eq 47Er 47Es 47Et 47Eu 47Ey 47Ez 47E# 47E$ 47E% 47E& 47E' 47E( 4\ -7E) 47E= 47E> 47E? 47E@ 47E[ 47E] 47E{ 47E| 47E} 47E~ 47F0 47F1 47F2 47F3 47F\ -4 47FE 47FF 47FG 47FH 47FI 47FJ 47FN 47FO 47FP 47FQ 47FR 47FS 47FT 47FU 47FV \ -47Z^ 47Z_ 47a2 47aK 47aL 47aM 47al 47am 47an 47cs 47ct 47cu 47c$ 47c% 47c& 47\ -c@ 47c[ 47c] 47c~ 47d0 47d1 47dH 47dI 47dJ 47dQ 47dR 47dS 47fO 47fP 47fQ 47fX\ - 47fY 47fZ 47fp 47fq 47fr 47fy 47fz 47f# 47f= 47f> 47f? 47f{ 47f| 47f} 49kH 4\ -9kI 49kJ 49kK 49kL 49kM 49ki 49kl 49km 49kn 49ko 49k# 49k$ 49k% 49k& 49k, 49k\ -- 49k. 49k/ 49k: 49k; 49+K 49+L 49+M 49+l 49+u 49+v 49+w 49+& 49+/ 49+: 49+; \ -5 5R 5T 5[ 51H 51N 51i 51l 52z 52# 52$ 52% 52& 52' 52( 52) 52* 52+ 52, 52- 52\ -. 52/ 52: 52; 52< 52= 52> 52? 52@ 52[ 52] 52^ 52_ 52` 52{ 52| 52} 530 531 532\ - 533 534 536 537 538 539 53A 53B 53C 53D 53E 53F 53G 53H 53I 53J 53K 53L 53M \ -53N 58A 58S 58T 58t 58v 58[ 58] 59I 59J 59j 59k 59. 59: 59; 59< 5A8 5A9 5AZ 5\ -Ab 5A# 5A$ 5A% 5A& 5A' 5A( 5A) 5A* 5A+ 5A, 5A- 5A. 5A/ 5A: 5A; 5A< 5A= 5A> 5A\ -? 5A@ 5A[ 5A] 5A^ 5A_ 5A` 5A{ 5A| 5A~ 5B0 5B1 5B2 5B3 5B4 5B5 5B6 5B7 5B8 5B9\ - 5BA 5BB 5BC 5BD 5BE 5BF 5BG 5BH 5BI 5BJ 5BK 5BL 5BM 5BN 5BO 5BP 5BQ 5BR 5BS \ -5BT 5BU 5BV 5BW 5BX 5BY 5BZ 5Ba 5Bb 5Bc 5Bd 5Be 5Bf 5Bg 5Bh 5Bi 5Bj 5Bk 5Bl 5\ -Bm 5Bn 5Bo 5Bp 5OC 5O^ 5O{ 5PK 5PL 5Pl 5Pm 5P/ 5P: 5QA 5QB 5Qb 5Qc 5Q% 5Q& 5Q\ -' 5Q( 5Q) 5Q* 5Q+ 5Q, 5Q- 5Q. 5Q/ 5Q: 5Q; 5Q< 5Q= 5Q> 5Q? 5Q@ 5Q[ 5Q] 5Q^ 5Q_\ - 5Q` 5Q{ 5Q| 5Q} 5Q~ 5R0 5R1 5R2 5R3 5R4 5R5 5R6 5R7 5R8 5R9 5RA 5RB 5RC 5RD \ -5RE 5RF 5RG 5RH 5RI 5RJ 5RK 5RL 5RM 5RN 5RO 5RP 5RQ 5RR 5RS 5RT 5RU 5RV 5RW 5\ -RX 5RY 5RZ 5Ra 5Rb 5Rc 5Rd 5Re 5Rf 5Rg 5Rh 5Ri 5Rj 5Rk 5Rl 5Rm 5Rn 5Ro 5Rp 5R\ -q 5Rr 5W7 5WD 5W_ 5W` 5XL 5XR 5Xm 5Xp 5X: 5X; 5YB 5YC 5YD 5YH 5YI 5Yc 5Yd 5Ye\ - 5Yf 5Yg 5Y& 5Y' 5Y( 5Y) 5Y* 5Y+ 5Y, 5Y- 5Y. 5Y/ 5Y: 5Y; 5Y< 5Y= 5Y> 5Y? 5Y@ \ -5Y[ 5Y] 5Y^ 5Y_ 5Y` 5Y{ 5Y| 5Y} 5Y~ 5Z0 5Z1 5Z2 5Z3 5Z4 5Z5 5Z6 5Z7 5Z8 5Z9 5\ -ZA 5ZB 5ZC 5ZD 5ZE 5ZF 5ZG 5ZH 5ZI 5ZJ 5ZK 5ZL 5ZM 5ZN 5ZO 5ZP 5ZQ 5ZR 5ZS 5Z\ -T 5ZU 5ZV 5ZW 5ZX 5ZY 5ZZ 5Za 5Zb 5Zc 5Zd 5Ze 5Zf 5Zg 5Zh 5Zi 5Zj 5Zk 5Zl 5Zm\ - 5Zn 5Zo 5Zp 5Zq 5Zr 5Zs 5e5 5eE 5e` 5e{ 5fM 5fN 5fn 5fo 5f; 5f> 5gC 5gD 5gd \ -5ge 5g' 5g( 5g) 5g* 5g+ 5g, 5g- 5g. 5g/ 5g: 5g; 5g< 5g= 5g> 5g? 5g@ 5g[ 5g] 5\ -g^ 5g_ 5g` 5g{ 5g| 5g} 5g~ 5h0 5h1 5h2 5h3 5h4 5h5 5h6 5h7 5h8 5h9 5hA 5hB 5h\ -C 5hD 5hE 5hF 5hG 5hH 5hI 5hJ 5hK 5hL 5hM 5hN 5hO 5hP 5hQ 5hR 5hS 5hT 5hU 5hV\ - 5hW 5hX 5hY 5hZ 5ha 5hb 5hc 5hd 5he 5hf 5hg 5hh 5hi 5hj 5hk 5hl 5hm 5hn 5ho \ -5hp 5hq 5hr 5hs 5ht 5-9 5-A 5-a 5-b 5-$ 5-- 5?A 5?B 5?b 5?d 5?% 5?( 5?. 5|B 5\ -|C 5|c 5|d 5|& 5|/ 515' 515: 51D( 51D; 51L) 51L, 51L< 51T* 51T- 51T. 51T= 51T\ -> 51T? 51b+ 51b> 51j, 51j? 52YT 52YU 52YX 52Ya 52Yb 52Yc 52Yj 52Yk 52Yl 52ZH \ -52ZI 52ZJ 52ZK 52ZL 52ZM 52ZN 52ZO 52ZP 52ZQ 52ZR 52ZS 52ZT 52ZU 52ZV 52ZW 52\ -ZX 52ZY 52ZZ 52Za 52Zb 52Zc 52Zd 52Ze 52Zf 52Zg 52Zh 52gS 52gV 52gY 52gb 52gc\ - 52gd 52gk 52gl 52gm 52hI 52hJ 52hK 52hL 52hM 52hN 52hO 52hP 52hQ 52hR 52hS 5\ -2hT 52hU 52hV 52hW 52hX 52hY 52hZ 52ha 52hb 52hc 52hd 52he 52hf 52hg 52hh 52h\ -i 52i8 52i9 52iA 52iB 52iC 52iD 52iE 52iF 52iG 52iH 52iI 52iJ 52iK 52iL 52iM \ -52iN 52iO 52iP 52iQ 52iR 52iS 52iT 52iU 52iV 52iW 52iX 52iY 53Fa 53Fb 53Fc 53\ -Fj 53Fm 53Fp 53Fq 53Fr 53Fs 53Ft 53Fu 53Nb 53Nc 53Nd 53Nk 53Nn 53No 53Np 53Nq\ - 53Nt 53Nu 53Nv 53Vc 53Vd 53Ve 53Vl 53Vm 53Vn 53Vo 53Vr 53Vu 53Vv 53Vw 6 6G 6\ -R 6T 6[ 61H 61I 61i 61j 62z 62# 62$ 62% 62& 62' 62( 62) 62* 62+ 62, 62- 62. 6\ -2/ 62: 62; 62< 62= 62> 62? 62@ 62[ 62] 62^ 62_ 62` 62{ 62| 62} 631 632 633 63\ -4 635 636 637 638 639 63A 63B 63C 63D 63E 63F 63G 63H 63I 63J 63K 63L 63M 63N\ - 68A 68S 68T 68t 68v 68[ 68] 69I 69O 69j 69k 69l 69m 69n 69. 69: 69< 6A8 6A9 \ -6AZ 6Ab 6A# 6A$ 6A% 6A& 6A' 6A( 6A) 6A* 6A+ 6A, 6A- 6A. 6A/ 6A: 6A; 6A< 6A= 6\ -A> 6A? 6A@ 6A[ 6A] 6A^ 6A_ 6A` 6A{ 6A| 6A~ 6B0 6B1 6B3 6B4 6B5 6B6 6B7 6B8 6B\ -9 6BA 6BB 6BC 6BD 6BE 6BF 6BG 6BH 6BI 6BJ 6BK 6BL 6BM 6BN 6BO 6BP 6BQ 6BR 6BS\ - 6BT 6BU 6BV 6BW 6BX 6BY 6BZ 6Ba 6Bb 6Bc 6Bd 6Be 6Bf 6Bg 6Bh 6Bi 6Bj 6Bk 6Bl \ -6Bm 6Bn 6Bo 6Bp 6OC 6Ov 6Ow 6O^ 6O_ 6PK 6PQ 6Pl 6Pm 6Pn 6Po 6Pp 6P/ 6P< 6QA 6\ -QB 6Qb 6Qc 6Q% 6Q& 6Q' 6Q( 6Q) 6Q* 6Q+ 6Q, 6Q- 6Q. 6Q/ 6Q: 6Q; 6Q< 6Q= 6Q> 6Q\ -? 6Q@ 6Q[ 6Q] 6Q^ 6Q_ 6Q` 6Q{ 6Q| 6Q} 6Q~ 6R0 6R1 6R2 6R3 6R4 6R5 6R6 6R7 6R8\ - 6R9 6RA 6RB 6RC 6RD 6RE 6RF 6RG 6RH 6RI 6RJ 6RK 6RL 6RM 6RN 6RO 6RP 6RQ 6RR \ -6RS 6RT 6RU 6RV 6RW 6RX 6RY 6RZ 6Ra 6Rb 6Rc 6Rd 6Re 6Rf 6Rg 6Rh 6Ri 6Rj 6Rk 6\ -Rl 6Rm 6Rn 6Ro 6Rp 6Rq 6Rr 6WD 6WE 6WF 6Ww 6Wx 6W_ 6W| 6XL 6XM 6Xm 6Xn 6X: 6X\ -; 6YB 6YC 6YD 6YH 6YI 6Yc 6Yd 6Ye 6Yf 6Yg 6Y& 6Y' 6Y( 6Y) 6Y* 6Y+ 6Y, 6Y- 6Y.\ - 6Y/ 6Y: 6Y; 6Y< 6Y= 6Y> 6Y? 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91h@ 91h[ 91h] 91h^ 91h_ 91h` 91h{ 91h| 91h~ \ -91i0 91i2 91i3 91i4 91i5 91i6 91i7 91i8 91i9 91iA 91iB 91iC 91iD 91iF 91iG 91\ -iH 91iI 91iJ 91iK 91iM 91iN 91iO 91iP 91iQ 91iS 91iT 91iV 91iW 91iX 91iY 91iZ\ - 91ia 91ib 91ic 91id 91if 91ig 91ih 91ii 91ij 91ik 91il 91im 91in 91ip 91iq 9\ -1ir 91is 91it 91iv 91iw 91iy 91iz 91i# 91i$ 91i% 91i& 91i( 91i) 91i+ 91i, 91i\ -- 91i. 91i/ 91i: 91i; 91i< 91i= 91i> 91i? 91i@ 91i] 91i^ 91i_ 91i` 91i{ 91i} \ -91i~ 91j0 91j1 91j2 91j3 91j4 91j6 91j7 91j8 91j9 91jA 91jC 91jD 91jF 91jG 92\ -YU 92YV 92YW 92Ya 92Yb 92Yc 92Yd 92Ye 92Yf 92Y' 92Y( 92Y) 92Y* 92Y+ 92Y, 92Y-\ - 92Y. 92Y/ 92Y: 92Y; 92Y< 92Y= 92Y> 92Y? 92ZI 92ZJ 92ZK 92ZL 92ZM 92ZQ 92ZS 9\ -2ZT 92ZU 92ZV 92ZZ 92Za 92Zb 92Zc 92Zd 92Ze 92Zi 92Zj 92Zk 92Zl 92Zm 92Zn 92Z\ -o 92Zp 92Zq 92Zr 92Zt 92Zu 92Zv 92Zw 92Zx 92Zy 92Zz 92Z# 92Z$ 92Z% 92Z& 92Z' \ -92Z( 92Z) 92Z* 92Z+ 92a7 92a8 92a9 92aA 92aB 92aC 92aG 92aI 92aJ 92aK 92aL 92\ -aP 92aQ 92aR 92aS 92aT 92aU 92aY 92aZ 92aa 92ab 92ac 92ad 92ae 92af 92ag 92ah\ - 92ai 92aj 92ak 92al 92am 92an 92ao 92ap 92aq 92at 92au 92av 92aw 92ax 92ay 9\ -2a~ 92b0 92b1 92b2 92b4 92b5 92b6 92b7 92b8 92bA 92bB 92bC 92bD 92bE 92bG 92b\ -H 92bI 92bJ 92bK 92bL 92bM 92bN 92bP 92bQ 92bR 92bS 92bT 92bV 92bW 92bX 92bY \ -92bZ 92bb 92bc 92bd 92be 92bf 92bh 92bi 92bj 92bk 92bl 92bm 92bn 92bo 92bs 92\ -bt 92bu 92bw 92bx 92by 92bz 92b# 92b% 92b& 92b' 92b( 92b) 92b+ 92b, 92b- 92b.\ - 92b/ 92b: 92b; 92b< 92b= 92b> 92b? 92b[ 92b] 92b^ 92b_ 92b` 92b| 92b~ 92c0 9\ -2c1 92c2 92c3 92c4 92c6 92c7 92c8 92c9 92cA 92cC 92cD 92cE 92cF 92cG 92cI 92c\ -J 92cK 92cL 92cM 92cO 92cP 92cQ 92cR 92cS 92cT 92cU 92cV 92cX 92cY 92cZ 92ca \ -92cb 92cd 92ce 92cf 92ch 92cj 92ck 92cl 92cm 92cn 92cp 92cq 92cr 92cs 92ct 92\ -cu 92cv 92cw 92cy 92cz 92c# 92c$ 92c% 92c' 92c( 92c* 92c+ 92c, 92c- 92c. 92c:\ - 92c; 92c< 92c= 92c> 92c@ 92c[ 92c] 92c^ 92c_ 92c{ 92c} 92c~ 92d0 92d1 92d2 9\ -2d3 92d5 92d6 92d7 92d8 92d9 92dB 92dC 92dD 92dF 92dH 92dI 92dJ 92dK 92dL 92d\ -N 92dO 92dP 92dQ 92dR 92dS 92dT 92dU 92dW 92dX 92dY 92dZ 92da 92dc 92dd 92de \ -92df 92di 92dj 92dk 92dl 92dm 92dp 92dq 92dr 92ds 92dt 92du 92dv 92gV 92gW 92\ -gX 92ge 92gf 92gg 92gk 92gl 92gm 92gn 92go 92gp 92gt 92gv 92gx 92gy 92g# 92g$\ - 92g% 92g& 92g' 92g( 92g) 92g* 92g+ 92g, 92g- 92g. 92g/ 92g: 92g; 92g< 92g= 9\ -2g> 92g? 92g@ 92hJ 92hK 92hL 92hM 92hN 92hR 92hS 92hT 92hU 92hV 92hW 92ha 92h\ -b 92hc 92hd 92he 92hf 92hj 92hl 92hm 92hn 92ho 92hp 92hq 92hr 92ht 92hv 92hw \ -92hx 92hy 92hz 92h# 92h$ 92h% 92h& 92h' 92h( 92h) 92h* 92h+ 92h, 92i8 92i9 92\ -iA 92iB 92iC 92iD 92iI 92iJ 92iK 92iL 92iM 92iQ 92iR 92iS 92iT 92iU 92iV 92iZ\ - 92ia 92ib 92ic 92id 92ie 92if 92ig 92ih 92ii 92ij 92ik 92il 92im 92in 92io 9\ -2ip 92iq 92is 92it 92iu 92iv 92iw 92ix 92iy 92iz 92j1 92j2 92j3 92j4 92j5 92j\ -6 92j7 92j8 92j9 92jA 92jB 92jC 92jD 92jE 92jF 92jG 92jH 92jI 92jJ 92jK 92jL \ -92jM 92jN 92jO 92jP 92jR 92jS 92jT 92jU 92jV 92jW 92jX 92jY 92jZ 92ja 92jb 92\ -jc 92je 92jf 92jg 92ji 92jj 92jk 92jl 92jm 92jn 92jo 92jp 92js 92jt 92ju 92jv\ - 92jw 92jx 92jy 92jz 92j# 92j$ 92j& 92j' 92j( 92j) 92j* 92j+ 92j, 92j- 92j. 9\ -2j/ 92j: 92j; 92j< 92j= 92j> 92j? 92j@ 92j[ 92j] 92j^ 92j_ 92j` 92j{ 92j} 92j\ -~ 92k0 92k1 92k2 92k3 92k4 92k5 92k6 92k7 92k9 92kA 92kB 92kC 92kD 92kE 92kF \ -92kI 92kJ 92kK 92kL 92kM 92kN 92kO 92kP 92kQ 92kR 92kS 92kT 92kU 92kV 92kW 92\ -kX 92kY 92ka 92kb 92kc 92kd 92ke 92kf 92kg 92kh 92ki 92kj 92kk 92kl 92km 92kn\ - 92ko 92kp 92kr 92ks 92kt 92ku 92kv 92kw 92kx 92ky 92kz 92k$ 92k% 92k& 92k( 9\ -2k) 92k+ 92k, 92k- 92k. 92k/ 92k: 92k; 92k< 92k> 92k? 92k@ 92k[ 92k] 92k^ 92k\ -_ 92k` 92k{ 92k} 92k~ 92l0 92l1 92l2 92l3 92l4 92l6 92l7 92l8 92l9 92lA 92lB \ -92lC 92lD 92lE 92lF 92lG 92lH 92lI 92lJ 92lK 92lL 92lM 92lN 92lP 92lQ 92lR 92\ -lS 92lT 92lU 92lV 92lX 92lY 92lZ 92la 92lb 92lc 92ld 92lf 92lg 92lh 92li 92lj\ - 92lk 92ll 92lm 92ln 92lo 92lp 92lr 92ls 92lt 92lu 92lv 92lw 92oW 92oX 92oc 9\ -2od 92oe 92of 92og 92oh 92ol 92om 92on 92oo 92op 92oq 92ou 92ov 92ox 92oy 92o\ -$ 92o% 92o) 92o* 92o+ 92o, 92o- 92o. 92o/ 92o; 92o< 92o= 92o> 92o? 92o@ 92o[ \ -92pK 92pL 92pM 92pN 92pO 92pS 92pT 92pU 92pV 92pW 92pX 92pb 92pc 92pd 92pe 92\ -pf 92pg 92pk 92pl 92pm 92pn 92po 92pp 92pq 92pr 92ps 92pu 92pv 92pw 92px 92py\ - 92pz 92p# 92p$ 92p% 92p& 92p' 92p( 92p) 92p* 92p+ 92p, 92p- 92q9 92qA 92qB 9\ -2qC 92qD 92qE 92qI 92qJ 92qL 92qM 92qN 92qS 92qT 92qU 92qV 92qW 92qa 92qb 92q\ -c 92qd 92qe 92qf 92qg 92qh 92qi 92qk 92ql 92qm 92qn 92qo 92qp 92qq 92qr 92qs \ -92qu 92qv 92qw 92qx 92qy 92qz 92q# 92r0 92r2 92r3 92r4 92r5 92r6 92r7 92r8 92\ -r9 92rA 92rB 92rC 92rD 92rE 92rF 92rG 92rH 92rI 92rJ 92rK 92rL 92rM 92rN 92rO\ - 92rP 92rQ 92rR 92rT 92rU 92rV 92rW 92rX 92rY 92rZ 92ra 92rb 92rd 92re 92rf 9\ -2rg 92rh 92ri 92rj 92rk 92rl 92rm 92rn 92ro 92rp 92rq 92rr 92ru 92rv 92rw 92r\ -x 92ry 92rz 92r# 92r$ 92r% 92r& 92r( 92r) 92r* 92r+ 92r- 92r. 92r/ 92r: 92r; \ -92r< 92r= 92r> 92r@ 92r[ 92r] 92r^ 92r_ 92r` 92r{ 92r| 92r} 92s0 92s1 92s2 92\ -s3 92s4 92s5 92s6 92s7 92s9 92sA 92sB 92sC 92sD 92sE 92sF 92sG 92sH 92sI 92sJ\ - 92sK 92sL 92sM 92sN 92sO 92sQ 92sR 92sS 92sT 92sU 92sV 92sW 92sX 92sY 92sa 9\ -2sb 92sc 92sd 92sf 92sg 92sh 92si 92sj 92sk 92sl 92sm 92sn 92so 92sp 92sr 92s\ -t 92su 92sv 92sw 92sx 92sy 92sz 92s$ 92s% 92s& 92s' 92s( 92s) 92s* 92s, 92s- \ -92s. 92s/ 92s: 92s; 92s= 92s> 92s? 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92*@ 92*[ 92*] 92*^ 92*_ 92*\ -` 92*{ 92*| 92*} 92*~ 92+0 92+1 92+2 92+4 92+5 92+6 92+7 92+8 92+9 92+A 92+B \ -92+C 92+D 92+E 92+F 92+G 92+H 92+I 92+J 92+K 92+L 92+N 92+O 92+P 92+Q 92+R 92\ -+T 92+U 92+V 92+W 92+X 92+Y 92+Z 92+a 92+b 92+c 92+d 92+e 92+f 92+g 92+h 92+j\ - 92+k 92+l 92+m 92+n 92+o 92+p 92+q 92+r 92+s 92+t 92+u 92+v 92+w 92+x 92+y 9\ -2+z 92+# 92+% 92+& 92+' 92+( 92+) 92+* 92+, 92+- 92+. 92+/ 92+: 92+; 92+< 92+\ -= 92+> 92+? 92+@ 92+[ 92+] 92+^ 92+_ 92+` 92+{ 92+| 92+~ 92,0 92,1 92,2 92,3 \ -92,4 92,5 92,6 92,7 92,8 92,9 92,A 92,B 92,C 92,E 92,F 92,G 92,H 92,I 92,J 92\ -,K 92,L 92,M 92,N 92,O 92,P 92,Q 92,R 92,S 92,T 92,U 92,V 92,W 92,X 92,Z 92,a\ - 92,b 92,d 92,e 92,f 92,g 92,h 92,i 92,j 92,l 92,m 92,n 92,o 92,p 92,q 92,r 9\ -2,s 92,t 92,u 92,v 92,w 92,x 92,y 92,z 92/Z 92/a 92/b 92/f 92/g 92/h 92/i 92/\ -j 92/k 92/o 92/p 92/q 92/r 92/s 92/t 92/x 92/z 92/$ 92/% 92/' 92/( 92/) 92/* \ -92/+ 92/, 92/- 92/. 92/< 92/= 92/> 92/? 92/@ 92/] 92/^ 92:M 92:N 92:O 92:P 92\ -:Q 92:R 92:W 92:X 92:Y 92:Z 92:a 92:e 92:f 92:g 92:h 92:i 92:j 92:n 92:o 92:p\ - 92:q 92:r 92:s 92:t 92:u 92:v 92:w 92:x 92:y 92:z 92:# 92:$ 92:% 92:& 92:' 9\ -2:( 92:) 92:* 92:+ 92:, 92:. 92:/ 92:: 92;D 92;E 92;F 92;G 92;H 92;L 92;M 92;\ -N 92;P 92;Q 92;U 92;V 92;W 92;X 92;Y 92;Z 92;d 92;f 92;g 92;h 92;i 92;j 92;k \ -92;l 92;m 92;n 92;o 92;p 92;q 92;r 92;s 92;t 92;u 92;v 92;w 92;x 92;y 92;z 92\ -;# 92;$ 92;% 92;& 92<3 92<5 92<6 92<7 92<8 92<9 92 92 92=? 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932[ 932] 932^ 932` 932{ 932| 932} 932~ 9330 \ -9331 9332 9333 9334 9335 9336 9337 9338 933A 933B 933C 933D 933E 933F 933I 93\ -3J 933K 933L 933M 933N 933O 933P 933Q 933S 933T 933U 933V 933W 933X 933Y 933Z\ - 933a 933b 933c 933d 933e 933f 933h 933i 933j 933k 933l 933m 933n 933o 933p 9\ -33q 933r 933s 933t 933u 933v 933w 933x 933y 933z 933# 933$ 933% 933& 933' 933\ -( 933) 933* 933+ 933- 933. 933/ 933; 933< 933= 933> 933? 933@ 933] 933^ 933_ \ -933` 933{ 933} 933~ 9340 9341 9342 9343 9344 9345 9346 9347 9348 9349 934A 93\ -4B 934C 934D 934E 934F 934G 934I 934J 934K 934L 934M 934N 934O 934P 934Q 934R\ - 934S 934T 934V 934X 934Y 934Z 934a 934b 934c 934d 934f 934g 934h 934i 934j 9\ -34k 934l 934m 934n 934o 934p 934q 934r 934s 934t 934u 934v 934w 934x 934y 934\ -z 934# 934$ 934% 937c 937d 937i 937j 937k 937l 937m 937n 937r 937s 937t 937u \ -937v 937w 937$ 937% 937& 937( 937* 937+ 937, 937- 937. 937< 937= 937> 937? 93\ -7[ 937^ 937_ 937{ 937| 938P 938Q 938R 938S 938T 938U 938Y 938Z 938a 938b 938c\ - 938d 938h 938i 938k 938l 938m 938q 938r 938s 938t 938u 938v 938x 938y 938z 9\ -38# 938$ 938% 938& 938' 938( 938) 938* 938+ 938, 938- 938. 938/ 938: 938; 938\ -< 938= 939F 939G 939H 939J 939K 939O 939P 939Q 939R 939S 939T 939Y 939Z 939a \ -939b 939c 939g 939h 939i 939j 939l 939m 939n 939o 939p 939q 939r 939s 939t 93\ -9u 939v 939w 939x 939y 939z 939# 939$ 939% 939& 939' 939( 939) 93A7 93A8 93A9\ - 93AA 93AB 93AC 93AD 93AE 93AF 93AG 93AH 93AI 93AJ 93AK 93AL 93AN 93AO 93AP 9\ -3AQ 93AS 93AT 93AU 93AV 93AW 93AX 93AZ 93Aa 93Ab 93Ad 93Ae 93Af 93Ag 93Ah 93A\ -i 93Aj 93Ak 93Al 93Am 93An 93Ao 93Ap 93Aq 93Ar 93As 93At 93Au 93Av 93Aw 93Ax \ -93A# 93A$ 93A% 93A& 93A' 93A( 93A) 93A* 93A+ 93A, 93A- 93A. 93A/ 93A; 93A< 93\ -A= 93A> 93A? 93A@ 93A[ 93A] 93A^ 93A_ 93A{ 93A| 93A} 93A~ 93B0 93B1 93B3 93B4\ - 93B5 93B6 93B7 93B8 93B9 93BA 93BB 93BC 93BD 93BE 93BF 93BG 93BI 93BJ 93BK 9\ -3BL 93BM 93BN 93BO 93BP 93BQ 93BR 93BS 93BT 93BU 93BV 93BW 93BX 93BY 93BZ 93B\ -a 93Bb 93Bc 93Bd 93Be 93Bf 93Bg 93Bi 93Bj 93Bk 93Bl 93Bm 93Bn 93Bo 93Bp 93Bq \ -93Br 93Bs 93Bt 93Bu 93Bv 93Bw 93Bx 93By 93Bz 93B# 93B$ 93B& 93B' 93B( 93B) 93\ -B* 93B, 93B- 93B. 93B/ 93B: 93B< 93B= 93B> 93B? 93B@ 93B[ 93B] 93B^ 93B_ 93B`\ - 93B{ 93B| 93B} 93B~ 93C0 93C1 93C2 93C3 93C4 93C5 93C6 93C7 93C8 93C9 93CA 9\ -3CB 93CC 93CD 93CE 93CF 93CG 93CH 93CJ 93CK 93CL 93CM 93CN 93CO 93CP 93CR 93C\ -S 93CT 93CU 93CV 93CX 93CY 93CZ 93Ca 93Cb 93Cc 93Cd 93Ce 93Cf 93Cg 93Ch 93Ci \ -93Cj 93Ck 93Cm 93Cn 93Co 93Cp 93Cq 93Cr 93Cs 93Ct 93Cu 93Cv 93Cw 93Cx 93Cy 93\ -Cz 93C$ 93C% 93C& 93Fj 93Fk 93Fl 93Fm 93Fn 93Fo 93Fp 93Fq 93Fr 93Fs 93Ft 93Fu\ - 93Fv 93Fw 93Fx 93Fy 93Fz 93F# 93F- 93F. 93F/ 93F: 93F; 93F< 93F= 93F> 93F? 9\ -3F@ 93F[ 93F] 93F^ 93F_ 93F` 93F{ 93F| 93F} 93F~ 93G0 93G1 93G2 93G3 93G4 93G\ -5 93G6 93G7 93G8 93G9 93GA 93GB 93GC 93GD 93GE 93GF 93GG 93GQ 93GR 93GS 93GT \ -93GU 93GV 93GW 93GX 93GY 93GZ 93Ga 93Gb 93Gc 93Ge 93Gf 93Gg 93Gh 93Gj 93Gk 93\ -Gl 93Gm 93Gn 93Go 93Gq 93Gr 93Gs 93Gt 93Gu 93Gv 93Gw 93Gx 93Gy 93Gz 93G# 93G$\ - 93G% 93G& 93G' 93G( 93G) 93G* 93G+ 93G, 93G- 93G/ 93G: 93G; 93G< 93G= 93G> 9\ -3G? 93G@ 93G[ 93G] 93G^ 93G_ 93G` 93G{ 93G| 93G} 93G~ 93H0 93H1 93H3 93H4 93H\ -5 93H6 93H8 93H9 93HA 93HB 93HC 93HD 93HE 93HF 93HG 93HH 93HI 93HJ 93HK 93HL \ -93HM 93HN 93HO 93HP 93HQ 93HR 93HS 93HT 93HU 93HW 93HX 93HY 93HZ 93Ha 93Hb 93\ -Hc 93Hd 93He 93Hf 93Hg 93Hh 93Hi 93Hj 93Hk 93Hl 93Hn 93Ho 93Hp 93Hq 93Hr 93Hs\ - 93Ht 93Hu 93Hv 93Hw 93Hy 93Hz 93H# 93H$ 93H% 93H& 93H' 93H( 93H) 93H* 93H+ 9\ -3H, 93H- 93H. 93H/ 93H: 93H; 93H< 93H= 93H? 93H@ 93H[ 93H] 93H^ 93H_ 93H{ 93H\ -| 93H} 93H~ 93I0 93I1 93I2 93I3 93I4 93I5 93I8 93IA 93IB 93ID 93IE 93IG 93IH \ -93II 93IJ 93IK 93IL 93IM 93IN 93IO 93IP 93IQ 93IR 93IS 93IT 93IV 93IW 93IX 93\ -IY 93IZ 93Ie 93If 93Ih 93Ii 93Ij 93Ik 93Il 93Im 93In 93Io 93Ip 93Iq 93Ir 93Is\ - 93It 93Iu 93Iw 93Ix 93Iy 93Iz 93I% 93I& 93I( 93I) 93I+ 93I, 93I- 93I. 93I/ 9\ -3I: 93I; 93I< 93I= 93I> 93I? 93I@ 93I[ 93I] 93I_ 93I` 93I| 93I} 93I~ 93J0 93J\ -1 93J3 93J4 93J5 93J6 93J7 93J9 93JA 93JB 93JC 93JF 93JG 93JH 93JI 93JJ 93JK \ -93JL 93JM 93JO 93JP 93JQ 93JR 93JS 93JU 93JV 93JW 93JX 93JY 93Ja 93Jb 93Jc 93\ -Jd 93Je 93Jg 93Jh 93Ji 93Jj 93Jk 93Jl 93Jm 93Jn 93Jp 93Jq 93Jr 93Js 93Jt 93Jv\ - 93Jw 93Jx 93Jy 93Jz 93J$ 93J% 93J& 93J( 93J* 93J+ 93J, 93J- 93J/ 93J: 93J; 9\ -3J< 93J= 93J> 93J? 93J@ 93J[ 93J_ 93J` 93J{ 93J| 93J~ 93K0 93K1 93K2 93K3 93K\ -5 93K6 93K8 93K9 93KA 93KB 93KC 93KD 93KE 93KF 93KG 93KH 93KI 93KK 93KL 93KN \ -93KO 93KQ 93KR 93KS 93KT 93KU 93KW 93KX 93KZ 93Ka 93Kb 93Kc 93Kd 93Ke 93Kf 93\ -Kg 93Kh 93Ki 93Kj 93Kl 93Km 93Kn 93Ko 93Kp 93Kr 93Ks 93Kt 93Ku 93Kv 93Kx 93Ky\ - 93K# 93K$ 93K% 93K& 93K' 93K( 93K) 93K* 93K+ 93K, 93K. 93K/ 93K: 93K; 93K< 9\ -3K= 93K> 93K? 93K@ 93K[ 93K] 93K` 93K{ 93K| 93K} 93K~ 93L0 93L1 93L2 93L3 93L\ -4 93L5 93L6 93L7 93LB 93LC 93LD 93LE 93LF 93LG 93LH 93LJ 93LK 93LL 93LM 93LN \ -93LO 93LP 93LQ 93LR 93LS 93LT 93LU 93LV 93LW 93LY 93LZ 93La 93Lb 93Lc 93Ld 93\ -Le 93Lf 93Lg 93Lh 93Li 93Lj 93Ll 93Lm 93Ln 93Lo 93Lp 93Lq 93Lr 93Ls 93Lt 93Lu\ - 93Lw 93Lx 93Ly 93Lz 93L# 93L$ 93L% 93L& 93L' 93L( 93L) 93L* 93L+ 93L, 93L- 9\ -3L. 93L/ 93L: 93L; 93L< 93L= 93L> 93L@ 93L[ 93L^ 93L_ 93L` 93L{ 93L| 93L} 93L\ -~ 93M0 93M1 93M4 93M5 93M6 93M8 93M9 93MA 93MB 93MC 93MD 93ME 93MF 93MG 93MI \ -93MJ 93MK 93ML 93MM 93MN 93MO 93MP 93MQ 93MR 93MS 93MU 93MV 93MW 93MX 93MY 93\ -MZ 93Ma 93Mb 93Mc 93Md 93Me 93Mg 93Mi 93Mk 93Mm 93Mn 93Mo 93Mp 93Mq 93Mr 93Ms\ - 93Mt 93Mu 93Mv 93Mw 93Mx 93Mz 93M# 93M$ 93M% 93M& 93M' 93M( 93M) 93M* 93M+ 9\ -3M, 93M- 93M: 93M; 93M< 93M= 93M> 93M? 93M@ 93M[ 93M] 93M^ 93M_ 93M` 93M{ 93M\ -| 93M} 93M~ 93N1 93N2 93N3 93N4 93N5 93N6 93N8 93N9 93NA 93NB 93NC 93ND 93NE \ -93NF 93NG 93NH 93NI 93NJ 93NK 93NL 93NN 93NO 93NP 93NQ 93NR 93NS 93NT 93NU 93\ -NV 93NW 93NX 93NY 93Na 93Nc 93Nd 93Nf 93Nh 93Nk 93Nl 93Nm 93Nn 93No 93Np 93Nq\ - 93Nr 93Ns 93Nu 93Nv 93Nw 93Ny 93N# 93N$ 93N% 93N& 93N' 93N( 93N) 93N+ 93N, 9\ -3N- 93N. 93N/ 93N: 93N; 93N< 93N= 93N> 93N? 93N@ 93N[ 93N^ 93N` 93N{ 93N} 93N\ -~ 93O0 93O1 93O2 93O3 93O4 93O5 93O6 93O7 93O8 93O9 93OA 93OB 93OC 93OD 93OE \ -93OF 93OG 93OH 93OI 93OJ 93OK 93OL 93OM 93ON 93OO 93OP 93OQ 93OR 93OS 93OT 93\ -OU 93OV 93OW 93OX 93OY 93OZ 93Oa 93Ob 93Oc 93Oe 93Of 93Og 93Oh 93Oi 93Ok 93Ol\ - 93Om 93On 93Oo 93Oq 93Or 93Os 93Ot 93Ou 93Ov 93Ow 93Ox 93Oy 93Oz 93O# 93O$ 9\ -3O% 93O& 93O' 93O( 93O* 93O+ 93O, 93O- 93O/ 93O: 93O; 93O< 93O= 93O> 93O? 93O\ -@ 93O[ 93O] 93O^ 93O_ 93O` 93O{ 93O| 93O} 93O~ 93P0 93P1 93P2 93P3 93P5 93P6 \ -93P7 93P9 93PA 93PB 93PC 93PD 93PE 93PF 93PG 93PH 93PI 93PJ 93PK 93PL 93PM 93\ -PN 93PO 93PP 93PQ 93PR 93PS 93PT 93PU 93PV 93PW 93PX 93PZ 93Pa 93Pb 93Pc 93Pd\ - 93Pe 93Pf 93Pg 93Ph 93Pi 93Pj 93Pk 93Pl 93Pm 93Pn 93Po 93Pp 93Pq 93Ps 93Pt 9\ -3Pu 93Pv 93Pw 93Px 93Py 93Pz 93P# 93P$ 93P% 93P& 93P' 93P( 93P) 93P* 93P+ 93P\ -, 93P- 93P. 93P: 93P; 93P< 93P= 93P> 93P? 93P@ 93P[ 93P] 93P^ 93P_ 93P` 93P{ \ -93P| 93P} 93P~ 93Q0 93Q1 93Q2 93Q3 93Q4 93Q5 93Q6 93Q8 93Q9 93QA 93QB 93QC 93\ -QD 93QE 93QG 93QH 93QI 93QJ 93QK 93QL 93QM 93QN 93QO 93QP 93QQ 93QR 93QS 93QT\ - 93QU 93QW 93QX 93QY 93QZ 93Qa 93Qb 93Qe 93Qf 93Qh 93Qi 93Qj 93Qk 93Ql 93Qm 9\ -3Qn 93Qo 93Qp 93Qq 93Qr 93Qs 93Qt 93Qu 93Qv 93Qw 93Qx 93Qy 93Qz 93Q# 93Q$ 93Q\ -% 93Q' 93Q( 93Q) 93Q+ 93Q, 93Q- 93Q. 93Q/ 93Q: 93Q; 93Q< 93Q= 93Q> 93Q? 93Q@ \ -93Q[ 93Q] 93Q^ 93Q_ 93Q{ 93Q} 93Q~ 93R0 93R1 93R2 93R3 93R4 93R5 93R6 93R7 93\ -R8 93R9 93RB 93RC 93RD 93RF 93RG 93RI 93RJ 93RK 93RL 93RM 93RN 93RP 93RQ 93RR\ - 93RS 93RT 93RU 93RV 93RW 93RX 93RY 93RZ 93Ra 93Rb 93Rd 93Re 93Rf 93Rg 93Ri 9\ -3Rk 93Rl 93Rm 93Rn 93Ro 93Rq 93Rr 93Rs 93Rt 93Ru 93Rv 93Rw 93Rx 93Ry 93Rz 93R\ -# 93R$ 93R% 93R& 93R' 93R) 93R* 93R+ 93R, 93R- 93R. 93R/ 93R: 93R; 93R< 93R= \ -93R> 93R? 93R@ 93R[ 93R] 93R^ 93R_ 93R` 93R{ 93R| 93R} 93S0 93S1 93S2 93S3 93\ -S4 93S5 93S6 93S8 93SA 93SB 93SC 93SD 93SE 93SF 93SG 93SH 93SI 93SJ 93SL 93SM\ - 93SN 93SO 93SP 93SQ 93SR 93ST 93SU 93SV 93SW 93SX 93SY 93SZ 93Sb 93Sc 93Sd 9\ -3Se 93Sf 93Sg 93Sh 93Si 93Sj 93Sk 93Sl 93Sm 93Sn 93Sp 93Sq 93Sr 93Ss 93St 93S\ -u 93Sv 93Sw 93Sx 93Sy 93Sz 93S# 93S% 93S& 93S' 93S( 93S) 93S* 93S+ 93S- 93S. \ -93S/ 93S: 93S; 93S< 93S= 93S> 93S? 93S@ 93S[ 93S] 93S^ 93S_ 93S` 93S{ 93S| 93\ -S} 93S~ 93T0 93T1 93T2 93T3 93T4 93T5 93T6 93T7 93T8 93T9 93TB 93TC 93TD 93TE\ - 93TF 93TG 93TH 93TI 93TJ 93TL 93TM 93TN 93TO 93TP 93TQ 93TR 93TS 93TT 93TU 9\ -3TV 93TW 93TX 93Ta 93Tb 93Tc 93Td 93Te 93Tf 93Tg 93Th 93Ti 93Tj 93Tk 93Tm 93T\ -o 93Tp 93Tq 93Tr 93Ts 93Tt 93Tu 93Tv 93Tw 93Tx 93Ty 93Tz 93T# 93T$ 93T% 93T& \ -93T' 93T( 93T) 93T* 93T, 93T- 93T. 93T/ 93T: 93T; 93T< 93T= 93T> 93T@ 93T] 93\ -T^ 93T` 93T{ 93T| 93T} 93T~ 93U0 93U1 93U2 93U4 93U5 93U7 93U8 93U9 93UA 93UB\ - 93UC 93UD 93UE 93UF 93UG 93UH 93UI 93UJ 93UL 93UM 93UN 93UO 93UP 93UQ 93UR 9\ -3US 93UT 93UV 93UX 93UY 93UZ 93Ua 93Ub 93Uc 93Ud 93Ue 93Uf 93Ug 93Uh 93Ui 93U\ -j 93Uk 93Ul 93Un 93Uo 93Up 93Uq 93Ur 93Us 93Ut 93Uu 93Uv 93Uw 93Ux 93Uy 93Uz \ -93U# 93U$ 93U% 93U& 93U' 93U( 93U) 93U* 93U+ 93U, 93U- 93U. 93U/ 93U: 93U; 93\ -U< 93U= 93U> 93U? 93U@ 93U[ 93U] 93U^ 93U_ 93U` 93U{ 93U| 93U~ 93V1 93V2 93V3\ - 93V4 93V5 93V6 93V7 93V9 93VB 93VC 93VD 93VE 93VF 93VG 93VH 93VI 93VJ 93VK 9\ -3VL 93VM 93VN 93VO 93VP 93VS 93VT 93VU 93VV 93VW 93VX 93VY 93VZ 93Va 93Vb 93V\ -d 93Ve 93Vf 93Vh 93Vj 93Vk 93Vl 93Vm 93Vn 93Vo 93Vp 93Vq 93Vr 93Vs 93Vt 93Vu \ -93Vv 93Vy 93Vz 93V# 93V$ 93V& 93V' 93V( 93V* 93V+ 93V, 93V- 93V. 93V/ 93V: 93\ -V; 93V< 93V= 93V> 93V? 93V@ 93V[ 93V^ 93V_ 93V` 93V{ 93V} 93V~ 93W2 93W3 93W5\ - 93W6 93W7 93W9 93WA 93WB 93WC 93WD 93WE 93WF 93WG 93WH 93WI 93WJ 93WK 93WL 9\ -3WM 93WN 93WO 93WP 93WQ 93WR 93WS 93WT 93WU 93WV 93WW 93WX 93WY 93WZ 93Wa 93W\ -b 93Wc 93Wd 93We 93Wf 93Wg 93Wh 93Wi 93Wj 93Wk 93Wl 93Wm 93Wn 93Wo 93Wp 93Wq \ -93Wr 93Wt 93Wu 93Wv 93Ww 93Wx 93Wy 93Wz 93W# 93W$ 93W% 93W& 93W' 93W( 93W) 93\ -W* 93W+ 93W, 93W- 93W/ 93W: 93W; 93W< 93W= 93W> 93W? 93W@ 93W[ 93W] 93W^ 93W_\ - 93W` 93W{ 93W| 93W} 93W~ 93X0 93X1 93X2 93X4 93X5 93X6 93X7 93X8 93X9 93XA 9\ -3XB 93XC 93XD 93XE 93XF 93XG 93XH 93XI 93XJ 93XK 93XL 93XN 93XO 93XP 93XQ 93X\ -S 93XT 93XU 93XV 93XW 93XX 93XZ 93Xa 93Xb 93Xc 93Xd 93Xe 93Xf 93Xg 93Xh 93Xi \ -93Xj 93Xk 93Xl 93Xm 93Xn 93Xo 93Xp 93Xq 93Xr 93Xs 93Xt 93Xu 93Xv 93Xw 93Xx 93\ -Xz 93X# 93X$ 93X% 93X& 93X' 93X( 93X) 93X* 93X+ 93X, 93X- 93X. 93X/ 93X: 93X;\ - 93X< 93X= 93X> 93X? 93X@ 93X[ 93X] 93X^ 93X_ 93X` 93X| 93X} 93X~ 93Y0 93Y1 9\ -3Y2 93Y3 93Y4 93Y5 93Y6 93Y7 93Y9 93YB 93YC 93YD 93YE 93YG 93YI 93YJ 93YK 93Y\ -L 93YM 93YN 93YO 93YP 93YQ 93YR 93YS 93YT 93YU 93YV 93YW 93YX 93YZ 93Yb 93Yd \ -93Ye 93Yf 93Yh 93Yi 93Yj 93Yk 93Yl 93Ym 93Yn 93Yo 93Yp 93Yq 93Yr 93Ys 93Yt 93\ -Yu 93Yv 93Yw 93Yx 93Yy 93Yz 93Y# 93Y$ 93Y% 93Y& 93Y' 93Y) 93Y+ 93Y, 93Y- 93Y.\ - 93Y/ 93Y: 93Y; 93Y< 93Y= 93Y> 93Y? 93Y@ 93Y[ 93Y] 93Y^ 93Y_ 93Y{ 93Y| 93Y~ 9\ -3Z0 93Z1 93Z2 93Z3 93Z4 93Z5 93Z6 93Z7 93Z8 93Z9 93ZA 93ZB 93ZD 93ZE 93ZF 93Z\ -G 93ZI 93ZJ 93ZL 93ZM 93ZN 93ZO 93ZQ 93ZR 93ZS 93ZT 93ZU 93ZV 93ZW 93ZX 93ZY \ -93ZZ 93Za 93Zb 93Zc 93Zd 93Zf 93Zg 93Zh 93Zi 93Zj 93Zk 93Zl 93Zn 93Zo 93Zp 93\ -Zr 93Zs 93Zt 93Zu 93Zv 93Zw 93Zy 93Zz 93Z# 93Z$ 93Z% 93Z' 93Z( 93Z) 93Z* 93Z+\ - 93Z, 93Z. 93Z/ 93Z: 93Z; 93Z< 93Z= 93Z> 93Z? 93Z@ 93Z[ 93Z] 93Z^ 93Z_ 93Z` 9\ -3Z{ 93Z} 93Z~ 93a0 93a1 93a2 93a3 93a4 93a5 93a6 93a7 93a8 93a9 93aA 93aC 93a\ -D 93aE 93aF 93aG 93aH 93aI 93aJ 93aK 93aM 93aN 93aO 93aP 93aQ 93aR 93aT 93aU \ -93aV 93aW 93aZ 93aa 93ab 93ad 93ae 93af 93ag 93ah 93ai 93aj 93ak 93al 93am 93\ -an 93ap 93aq 93ar 93at 93au 93av 93aw 93ax 93ay 93az 93a# 93a$ 93a% 93a' 93a(\ - 93a) 93a* 93a+ 93a, 93a- 93a/ 93a: 93a; 93a< 93a= 93a> 93a? 93a@ 93a[ 93a] 9\ -3a^ 93a_ 93a` 93a{ 93a| 93a} 93a~ 93b0 93b1 93b2 93b3 93b4 93b5 93b6 93b7 93b\ -8 93b9 93bA 93bC 93bE 93bF 93bG 93bH 93bI 93bJ 93bL 93bM 93bO 93bP 93bQ 93bR \ -93bS 93bT 93bU 93bV 93bW 93bX 93bY 93ba 93bc 93bd 93be 93bf 93bg 93bh 93bi 93\ -bj 93bk 93bm 93bn 93bo 93bp 93bq 93br 93bs 93bt 93bu 93bv 93bw 93bx 93by 93bz\ - 93b# 93b$ 93b% 93b& 93b' 93b( 93b* 93b+ 93b, 93b- 93b. 93b/ 93b: 93b; 93b< 9\ -3b= 93b> 93b@ 93b[ 93b] 93b^ 93b_ 93b` 93b{ 93b| 93b} 93b~ 93c0 93c1 93c2 93c\ -3 93c4 93c5 93c6 93c7 93c9 93cA 93cB 93cC 93cD 93cE 93cF 93cH 93cJ 93cL 93cO \ -93cP 93cQ 93cR 93cS 93cT 93cU 93cV 93cW 93cX 93cY 93ca 93cb 93cc 93cd 93ce 93\ -cf 93cg 93ch 93ci 93cj 93cl 93cm 93co 93cp 93cq 93cr 93cs 93ct 93cu 93cv 93cw\ - 93cx 93cy 93cz 93c# 93c% 93c& 93c' 93c( 93c) 93c* 93c+ 93c, 93c- 93c/ 93c; 9\ -3c< 93c= 93c> 93c? 93c@ 93c[ 93c] 93c^ 93c_ 93c` 93c{ 93c| 93c} 93c~ 93d1 93d\ -2 93d3 93d4 93d5 93d6 93d7 93d8 93d9 93dA 93dB 93dD 93dE 93dF 93dG 93dH 93dI \ -93dJ 93dK 93dL 93dM 93dN 93dP 93dQ 93dR 93dS 93dT 93dU 93dV 93dW 93dX 93dY 93\ -dZ 93da 93db 93dc 93dm 93dn 93do 93dp 93dq 93dr 93ds 93dt 93du 93dv 93dw 93dx\ - 93dy 93dz 93d# 93d$ 93d% 93d& 93d: 93d; 93d< 93d= 93d> 93d? 93d@ 93d[ 93d] 9\ -3d^ 93d_ 93d` 93d{ 93d| 93d} 93d~ 93e0 93e1 93e2 93e3 93e4 93e5 93e6 93e7 93e\ -8 93e9 93eA 93eB 93eC 93eD 93eE 93eF 93eG 93eH 93eI 93eJ 93eU 93eV 93eW 93eX \ -93eY 93eZ 93eb 93ec 93ed 93ee 93ef 93eg 93eh 93ei 93ej 93ek 93el 93em 93en 93\ -eo 93eq 93er 93es 93et 93eu 93ev 93ex 93ey 93ez 93e$ 93e% 93e& 93e' 93e( 93e)\ - 93e* 93e+ 93e, 93e- 93e. 93e/ 93e: 93e; 93e< 93e= 93e> 93e? 93e@ 93e[ 93e^ 9\ -3e_ 93e` 93e{ 93e| 93e} 93e~ 93f0 93f1 93f2 93f3 93f4 93f5 93f6 93f7 93f8 93f\ -9 93fA 93fB 93fC 93fD 93fF 93fG 93fH 93fI 93fK 93fL 93fM 93fN 93fO 93fQ 93fR \ -93fS 93fT 93fU 93fV 93fW 93fX 93fY 93fZ 93fa 93fb 93fc 93fd 93fe 93ff 93fg 93\ -fh 93fi 93fj 93fk 93fl 93fm 93fn 93fo 93fp 93fr 93fs 93ft 93fu 93fv 93fw 93fx\ - 93fy 93fz 93f# 93f$ 93f% 93f& 93f' 93f) 93f* 93f+ 93f, 93f- 93f. 93f/ 93f: 9\ -3f; 93f< 93f= 93f> 93f? 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93u@ 93u[ 93u] 93u^ 93u_ 93u` \ -93u{ 93u| 93u} 93u~ 93v0 93v1 93v2 93v3 93v4 93v5 93v6 93v7 93v8 93v9 93vA 93\ -vB 93vC 93vD 93vE 93vF 93vG 93vI 93vJ 93vK 93vM 93vN 93vO 93vP 93vQ 93vR 93vT\ - 93vU 93vV 93vW 93vX 93vY 93vZ 93va 93vb 93vc 93vd 93ve 93vf 93vg 93vi 93vj 9\ -3vk 93vl 93vm 93vn 93vo 93vp 93vq 93vr 93vt 93vu 93vv 93vw 93vx 93vy 93vz 93v\ -# 93v$ 93v% 93v& 93v' 93v( 93v) 93v+ 93v, 93v- 93v. 93v/ 93v: 93v; 93v= 93v> \ -93v? 93v[ 93v] 93v^ 93v_ 93v` 93v{ 93v| 93v} 93v~ 93w0 93w1 93w2 93w3 93w4 93\ -w6 93w7 93w8 93w9 93wA 93wC 93wD 93wE 93wF 93wH 93wI 93wJ 93wK 93wL 93wM 93wN\ - 93wO 93wP 93wQ 93wR 93wS 93wT 93wU 93wV 93wW 93wX 93wY 93wZ 93wa 93wb 93wc 9\ -3wd 93we 93wf 93wi 93wj 93wk 93wl 93wn 93wo 93wp 93wq 93wr 93ws 93wt 93wu 93w\ -v 93ww 93wx 93wy 93wz 93w# 93w$ 93w& 93w' 93w( 93w) 93w+ 93w, 93w- 93w. 93w/ \ -93w: 93w< 93w= 93w> 93w? 93w@ 93w[ 93w] 93w^ 93w_ 93w` 93w{ 93w| 93w} 93w~ 93\ -x0 93x2 93x3 93x4 93x5 93x6 93x7 93x8 93x9 93xA 93xB 93xC 93xD 93xE 93xF 93xG\ - 93xH 93xI 93xJ 93xK 93xL 93xM 93xN 93xO 93xQ 93xR 93xS 93xT 93xU 93xV 93xX 9\ -3xY 93xZ 93xa 93xd 93xe 93xf 93xg 93xh 93xi 93xj 93xk 93xl 93xm 93xn 93xo 93x\ -p 93xr 93xs 93xt 93xx 93xy 93xz 93x# 93x$ 93x% 93x& 93x' 93x( 93x) 93x* 93x+ \ -93x, 93x- 93x. 93x/ 93x: 93x; 93x< 93x= 93x> 93x@ 93x] 93x^ 93x_ 93x` 93x{ 93\ -x| 93x} 93x~ 93y0 93y1 93y2 93y3 93y4 93y5 93y7 93y8 93y9 93yA 93yB 93yC 93yD\ - 93yF 93yG 93yH 93yI 93yJ 93yL 93yM 93yN 93yO 93yP 93yQ 93yR 93yS 93yT 93yU 9\ -3yV 93yW 93yX 93yY 93yZ 93ya 93yb 93yc 93ye 93yf 93yh 93yj 93yk 93yl 93yn 93y\ -o 93yp 93yq 93yr 93ys 93yt 93yu 93yv 93yw 93yx 93yy 93yz 93y# 93y$ 93y% 93y& \ -93y' 93y( 93y) 93y* 93y, 93y. 93y/ 93y; 93y< 93y= 93y> 93y? 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A~@ A~[ A~] A~^ A~_ A~` A\ -~{ A~| A~} A~~ A100 A101 A102 A103 A104 A105 A106 A107 A108 A10A A10E A10F A1\ -0G A10H A10I A10J A10K A10L A10M A10N A10O A10P A10Q A10R A10S A10T A10U A10V\ - A10W A10X A10Y A10Z A10a A10b A10e A10f A10g A10h A10i A10j A10k A10l A10m A\ -10n A10o A10p A10q A10r A10s A10t A10u A10v A10w A10x A10y A10z A10# A10$ A10\ -% A10& A10' A10( A10) A10, A10- A10. A10/ A10; A10< A10= A10> A10? A10@ A10[ \ -A10] A10^ A10_ A10` A10{ A10| A10} A10~ A110 A111 A112 A113 A115 A116 A117 A1\ -18 A119 A11A A11B A11C A11D A11E A11F A11G A11H A11I A11J A11K A11L A11M A11P\ - A11Q A11R A11S A11T A11U A11V A11W A11X A11Y A11Z A11a A11c A11e A11f A11g A\ -11h A11i A11j A11k A11l A11m A11o A11p A11q A11r A11s A11t A11u A11v A11w A11\ -x A11y A11z A11$ A11% A11& A11' A11( A11) A11* A11+ A11, A11- A11. A11/ A11: \ -A11< A11@ A11[ A11] A11^ A11_ A11` A11{ A11| A11} A11~ A120 A121 A122 A123 A1\ -24 A125 A126 A127 A128 A129 A12A A12B A12C A12E A12F A12G A12I A12J A12K A12L\ - A12M A12N A12P A12R A12S A12T A12U A12V A12W A12X A12Y A12Z A12a A12b A12c A\ -12d A12e A12f A12g A12h A12i A12l A12m A12o A12p A12q A12r A12s A12t A12u A12\ -v A12w A12x A12y A12z A12# A12$ A12% A12& A12' A12( A12) A12* A12+ A12, A12- \ -A12. A12= A12> A12? A12@ A12[ A12] A12^ A12_ A12` A12{ A12| A12} A12~ A130 A1\ -31 A132 A133 A134 A135 A136 A137 A13B A13C A13D A13E A13F A13G A13H A13I A13J\ - A13K A13L A13M A13N A13O A13P A13Q A13R A13S A13T A13U A13V A13X A13Y A13Z A\ -13a A13b A13c A13d A13e A13f A13g A13h A13i A13j A13k A13l A13m A13n A13q A13\ -r A13s A13t A13u A13v A13w A13x A13# A13$ A13% A13& A13' A13( A13) A13* A13+ \ -A13- A13. A13/ A13: A13; A13< A13= A13> A13? A13@ A13[ A13] A13^ A13_ A13` A1\ -3{ A13| A13} A13~ A140 A141 A142 A143 A144 A145 A146 A147 A14A A14B A14C A14D\ - A14E A14G A14H A14I A14J A14K A14L A14M A14N A14O A14P A14Q A14R A14T A14V A\ -14W A14X A14Y A14Z A14a A14b A14c A14d A14e A14f A14h A14i A14j A14k A14l A14\ -m A14n A14o A14p A14q A14r A14s A14t A14u A14v A14w A14x A14y A14z A14# A14$ \ -A14% A14& A14* A14+ A14, A14- A14. A14/ A14: A14; A14< A14= A14> A14? A14@ A1\ -4[ A14^ A14_ A14` A14{ A14| A14} A14~ A152 A153 A154 A155 A156 A157 A158 A159\ - A15A A15B A15( A15* A15- A15. A15; A15= A15@ A15[ A15_ A15{ A15~ A160 A163 A\ -164 A165 A166 A167 A168 A169 A16A A16B A16C A16D A16E A16G A16H A16I A16J A16\ -K A16L A16M A16N A16O A16P A16Q A16R A16T A16U A16W A16X A16Y A16Z A16a A16b \ -A16c A16d A16e A16g A16h A16i A16j A16k A16l A16m A16n A16o A16p A16q A16r A1\ -6t A16u A16w A16x A16y A16z A16# A16$ A16% A16& A16' A16( A16) A16* A16, A16-\ - A16. A16/ A16: A16; A16< A16= A16> A16@ A16[ A16] A16_ A171 A173 A17C A17P A\ -17Q A17Y A17) A17; A17= A17> A17? A17@ A17[ A17] A17^ A17_ A17` A17{ A17| A17\ -} A17~ A180 A181 A182 A183 A184 A185 A186 A187 A188 A189 A18A A18B A18F A18G \ -A18H A18I A18J A18K A18L A18M A18N A18O A18P A18Q A18R A18S A18T A18U A18V A1\ -8W A18X A18Y A18Z A18a A18c A18f A18g A18h A18i A18j A18k A18l A18m A18n A18o\ - A18p A18q A18r A18s A18t A18u A18v A18w A18x A18y A18z A18# A18$ A18% A18& A\ -18' A18( A18) A18* A18+ A18, A18- A18. A18/ A18: A18; A18< A18> A18? A18] A18\ -^ A18_ A18` A18{ A18| A18} A18~ A190 A192 A193 A194 A195 A196 A197 A198 A199 \ -A19A A19B A19C A19D A19E A19H A19I A19J A19K A19L A19M A19N A19O A19P A19S A1\ -9T A19U A19V A19W A19X A19Y A19Z A19a A19b A19c A19d A19e A19f A19g A19h A19i\ - A19j A19l A19m A19n A19o A19p A19q A19r A19s A19t A19u A19v A19w A19x A19y A\ -19z A19# A19$ A19% A19& A19' A19( A19+ A19, A19- A19. A19/ A19: A19< A19= A19\ -> A19? A19@ A19[ A19] A19^ A19_ A19{ A19| A19} A19~ A1A0 A1A1 A1A2 A1A3 A1A4 \ -A1A6 A1A7 A1A8 A1A9 A1AC A1AD A1AE A1AF A1AG A1AH A1AI A1AJ A1AK A1AL A1AM A1\ -AP A1AQ A1AR A1AS A1AT A1AU A1AV A1AW A1AY A1AZ A1Aa A1Ab A1Ac A1Ad A1Ae A1Af\ - A1Ag A1Ah A1Ai A1Aj A1An A1Ao A1Ap A1Aq A1Ar A1As A1At A1Au A1Av A1Aw A1Ax A\ -1Ay A1Az A1A# A1A$ A1A% A1A& A1A' A1A( A1A) A1A* A1A+ A1A, A1A- A1A. A1A/ A1A\ -> A1A? A1A@ A1A[ A1A] A1A^ A1A_ A1A` A1A{ A1A| A1A} A1A~ A1B0 A1B1 A1B2 A1B3 \ -A1B4 A1B5 A1B6 A1B7 A1B8 A1BC A1BE A1BF A1BG A1BH A1BI A1BJ A1BK A1BL A1BM A1\ -BN A1BO A1BP A1BQ A1BR A1BS A1BT A1BU A1BV A1BW A1BX A1BY A1BZ A1Ba A1Bb A1Bc\ - A1Bd A1Bf A1Bh A1Bj A1Bk A1Bl A1Bm A1Bn A1Bo A1Bp A1Bq A1Br A1Bs A1Bt A1Bu A\ -1Bv A1Bw A1Bx A1By A1Bz A1B# A1B$ A1B% A1B& A1B' A1B( A1B) A1B* A1B, A1B- A1B\ -. A1B/ A1B: A1B; A1B< A1B= A1B> A1B? A1B@ A1B[ A1B] A1B^ A1B{ A1B| A1B} A1B~ \ -A1C0 A1C1 A1C3 A1C5 A1C6 A1C7 A1C8 A1C9 A1CA A1CB A1CC A1CD A1CE A1CF A1CG A1\ -CH A1CI A1CJ A1CL A1CM A1CO A1CP A1CQ A1CR A1CS A1CT A1CU A1CV A1CW A1CX A1CY\ - A1CZ A1Ca A1Cb A1Cc A1Cd A1Ce A1Cf A1Cg A1Ch A1Cj A1Cl A1Cm A1Cn A1Co A1Cp A\ -1Cq A1Cr A1Cs A1Ct A1Cu A1Cv A1Cw A1Cy A1C# A1C$ A1C% A1C& A1C' A1C( A1C) A1C\ -* A1C+ A1C, A1C. A1C/ A1C: A1C; A1C< A1C? A1C@ A1C[ A1C] A1C^ A1C_ A1C` A1C| \ -A1C} A1C~ A1D0 A1D1 A1D2 A1D3 A1D4 A1D5 A1D6 A1D7 A1D8 A1D9 A1DA A1DB A1DC A1\ -DE A1DF A1DG A1DI A1DJ A1DK A1DM A1DN A1DP A1DQ A1DS A1DT A1DV A1DW A1DX A1DY\ - A1DZ A1Da A1Db A1Dc A1Dd A1Df A1Dg A1Di A1Dj A1Dl A1Dm A1Dn A1Do A1Ds A1Dt A\ -1Dv A1Dw A1Dx A1Dy A1Dz A1D# A1D% A1D& A1D' A1D( A1D) A1D* A1D+ A1D, A1D- A1D\ -. A1D/ A1D: A1D; A1D< A1D= A1D> A1D? A1D@ A1D[ A1D] A1D^ A1D_ A1D{ A1D| A1E2 \ -A1E4 A1E5 A1E6 A1E7 A1E8 A1E9 A1EA A1EB A1EC A1ED A1EE A1EF A1EG A1EI A1EJ A1\ -EK A1EL A1EM A1EN A1EO A1EP A1EQ A1ER A1ET A1EU A1EV A1EX A1EY A1EZ A1Ea A1Eb\ - A1Ec A1Ed A1Ee A1Ef A1Eg A1Ei A1Ej A1Ek A1El A1Em A1En A1Eo A1Ep A1Eq A1Er A\ -1Et A1Eu A1Ev A1Ex A1Ey A1Ez A1E# A1E$ A1E% A1E& A1E' A1E( A1E) A1E+ A1E, A1E\ -- A1E. A1E/ A1E: A1E; A1E< A1E= A1E> A1E? A1E@ A1E[ A1E^ A1E_ A1E` A1E{ A1E| \ -A1E} A1E~ A1F0 A1F1 A1F2 A1F3 A1F4 A1F5 A1F6 A1F7 A1F9 A1FA A1FB A1FC A1FD A1\ -FE A1FF A1FG A1FH A1FI A1FJ A1FK A1FL A1FN A1FO A1FP A1FQ A1FR A1FS A1FT A1FU\ - A1FV A1FW A1FX A1FY A1FZ A1Fa A1Fb A1Fc A1Fd A1Fe A1Ff A1Fg A1Fh A1Fi A1Fj A\ -1Fk A1Fl A1Fn A1Fp A1Fq A1Fr A1Fs A1Fv A1Fw A1Fx A1Fy A1F# A1F% A1F& A1F' A1F\ -) A1F+ A1F- A1F. A1F< A1F> A1F? A1F@ A1F[ A1F] A1F^ A1F_ A1F` A1F{ A1F| A1F} \ -A1F~ A1G0 A1G1 A1G2 A1G3 A1G4 A1G5 A1G6 A1G7 A1G8 A1G9 A1GA A1GB A1GG A1GH A1\ -GI A1GJ A1GK A1GL A1GM A1GN A1GO A1GP A1GQ A1GR A1GS A1GT A1GU A1GV A1GW A1GX\ - A1GY A1GZ A1Ga A1Gb A1Gc A1Gd A1Gh A1Gi A1Gj A1Gk A1Gl A1Gm A1Gn A1Go A1Gp A\ -1Gq A1Gr A1Gs A1Gt A1Gu A1Gv A1Gw A1Gx A1Gy A1Gz A1G# A1G$ A1G& A1G' A1G( A1G\ -) A1G* A1G+ A1G, A1G- A1G. A1G/ A1G: A1G; A1G< A1G= A1G? A1G[ A1G^ A1G_ A1G` \ -A1G{ A1G| A1G} A1G~ A1H2 A1H3 A1H4 A1H5 A1H6 A1H7 A1H8 A1H9 A1HA A1HB A1HC A1\ -HD A1HE A1HF A1HH A1HI A1HJ A1HK A1HL A1HM A1HN A1HO A1HP A1HQ A1HR A1HS A1HU\ - A1HV A1HW A1HX A1HY A1HZ A1Ha A1Hb A1Hc A1Hd A1He A1Hf A1Hg A1Hh A1Hi A1Hk A\ -1Hm A1Hn A1Ho A1Hp A1Hq A1Hr A1Hs A1Ht A1Hu A1Hv A1Hw A1Hx A1Hy A1H$ A1H% A1H\ -& A1H' A1H( A1H) A1H* A1H+ A1H- A1H. A1H/ A1H; A1H< A1H= A1H> A1H? A1H@ A1H[ \ -A1H] A1H^ A1H_ A1H` A1H| A1H} A1H~ A1I0 A1I1 A1I2 A1I3 A1I4 A1I6 A1I8 A1I9 A1\ -IA A1IB A1IC A1ID A1IE A1IF A1IG A1IH A1II A1IJ A1IK A1IL A1IM A1IN A1IO A1IP\ - A1IQ A1IR A1IS A1IT A1IU A1IV A1IW A1IY A1IZ A1Ia A1Ib A1Ic A1If A1Ig A1Ih A\ -1Ii A1Ij A1Ik A1In A1Io A1Ip A1Ir A1Is A1It A1Iu A1Iv A1Iw A1Ix A1Iy A1Iz A1I\ -# A1I$ A1I% A1I& A1I' A1I( A1I) A1I* A1I+ A1I, A1I- A1I. A1I/ A1I; A1I? A1I@ \ -A1I[ A1I] A1I^ A1I_ A1I` A1I{ A1I| A1I} A1I~ A1J0 A1J1 A1J2 A1J3 A1J4 A1J5 A1\ -J6 A1J7 A1J8 A1J9 A1JD A1JE A1JF A1JG A1JH A1JI A1JJ A1JK A1JL A1JM A1JN A1JO\ - A1JP A1JQ A1JR A1JS A1JT A1JU A1JV A1JW A1JX A1JY A1JZ A1Ja A1Jb A1Jc A1Jd A\ -1Jf A1Jh A1Ji A1Jk A1Jl A1Jm A1Jn A1Jo A1Jp A1Jq A1Jr A1Js A1Jt A1Ju A1Jv A1J\ -w A1Jx A1Jy A1Jz A1J# A1J$ A1J% A1J& A1J' A1J( A1J) A1J* A1J- A1J. A1J/ A1J: \ -A1J; A1J< A1J= A1J> A1J? A1J@ A1J[ A1J] A1J^ A1J_ A1J` A1J| A1J} A1J~ A1K0 A1\ -K1 A1K2 A1K3 A1K5 A1K6 A1K7 A1K8 A1K9 A1KA A1KB A1KC A1KD A1KE A1KF A1KG A1KH\ - A1KI A1KJ A1KK A1KN A1KP A1KQ A1KR A1KS A1KT A1KU A1KV A1KW A1KX A1Ka A1Kb A\ -1Kc A1Kd A1Ke A1Kf A1Kg A1Kh A1Ki A1Kj A1Kk A1Kl A1Km A1Kn A1Ko A1Kp A1Ks A1K\ -t A1Ku A1Kv A1Kw A1Kx A1Ky A1Kz A1K# A1K$ A1K% A1K& A1K' A1K( A1K) A1K* A1K+ \ -A1K, A1K- A1K. A1K: A1K; A1K< A1K= A1K> A1K@ A1K[ A1K] A1K^ A1K_ A1K` A1K| A1\ -K} A1K~ A1L0 A1L1 A1L2 A1L3 A1L4 A1L5 A1L6 A1L7 A1LA A1LB A1LC A1LD A1LF A1LG\ - A1LH A1LI A1LK A1LM A1LN A1LO A1LP A1LQ A1LR A1LS A1LT A1LU A1LV A1LW A1LY A\ -1La A1Lb A1Lc A1Ld A1Lf A1Lg A1Li A1Lk A1Lm A1Ln A1Lo A1Lp A1Lq A1Ls A1Lt A1L\ -u A1Lv A1Lw A1Lx A1Ly A1L# A1L' A1L( A1L) A1L* A1L+ A1L, A1L- A1L. A1L/ A1L: \ -A1L; A1L> A1L@ A1L] A1L` A1L{ A1L| A1L} A1L~ A1M0 A1M1 A1M2 A1M3 A1M5 A1M6 A1\ -M7 A1M8 A1M9 A1MA A1MB A1MC A1MD A1ME A1MF A1MH A1MI A1MJ A1MK A1ML A1MM A1MN\ - A1MO A1MP A1MQ A1MR A1MT A1MU A1MV A1MW A1MY A1MZ A1Ma A1Mb A1Mc A1Md A1Me A\ -1Mf A1Mg A1Mh A1Mi A1Mk A1Ml A1Mm A1Mn A1Mo A1Mp A1Mq A1Mr A1Ms A1Mt A1Mu A1M\ -w A1My A1Mz A1M# A1M$ A1M% A1M& A1M' A1M( A1M) A1M* A1M+ A1M- A1M. A1M/ A1M: \ -A1M; A1M< A1M= A1M> A1M? A1M@ A1M[ A1M^ A1M_ A1M` A1M{ A1M| A1M} A1M~ A1N0 A1\ -N1 A1N3 A1N4 A1N5 A1N6 A1N7 A1N8 A1NA A1NB A1NC A1ND A1NE A1NF A1NG A1NH A1NI\ - A1NK A1NL A1NN A1NO A1NP A1NQ A1NR A1NS A1NT A1NU A1NV A1NX A1NY A1NZ A1Na A\ -1Nb A1Nc A1Ne A1Nf A1Ng A1Nh A1Ni A1Nj A1Nk A1Nl A1Nn A1No A1Nq A1Nr A1Ns A1N\ -t A1Nu A1Nv A1Nw A1Nx A1Ny A1N# A1N$ A1N& A1N' A1N( A1N) A1N* A1N+ A1N- A1N. \ -A1N/ A1N= A1N> A1N? A1N@ A1N[ A1N] A1N^ A1N_ A1N` A1N{ A1N| A1N} A1N~ A1O0 A1\ -O1 A1O2 A1O3 A1O4 A1O5 A1O6 A1O7 A1O8 A1O9 A1OA A1OB A1OC A1OD A1OH A1OI A1OJ\ - A1OK A1OL A1OM A1ON A1OO A1OP A1OQ A1OR A1OS A1OT A1OU A1OV A1OW A1OX A1OY A\ -1OZ A1Oa A1Ob A1Oc A1Od A1Oe A1Og A1Oh A1Oi A1Oj A1Ok A1Ol A1Om A1On A1Oo A1O\ -p A1Oq A1Or A1Os A1Ot A1Ou A1Ov A1Ow A1Ox A1Oy A1Oz A1O# A1O$ A1O% A1O& A1O' \ -A1O) A1O* A1O+ A1O, A1O- A1O. A1O/ A1O: A1O; A1O< A1O= A1O> A1O? A1O@ A1O[ A1\ -O] A1O^ A1O_ A1O` A1O{ A1O| A1O} A1O~ A1P0 A1P2 A1P3 A1P4 A1P5 A1P6 A1P7 A1P8\ - A1P9 A1PA A1PB A1PC A1PD A1PE A1PF A1PG A1PH A1PI A1PK A1PL A1PM A1PN A1PO A\ -1PP A1PQ A1PR A1PS A1PU A1PV A1PW A1PX A1PY A1PZ A1Pa A1Pb A1Pc A1Pd A1Pe A1P\ -f A1Pg A1Ph A1Pi A1Pk A1Pl A1Pm A1Pn A1Po A1Pp A1Pq A1Pr A1Ps A1Pt A1Pu A1Pv \ -A1Pw A1Px A1Py A1Pz A1P# A1P$ A1P% A1P& A1P' A1P( A1P) A1P* A1P+ A1P- A1P. A1\ -P/ A1P: A1P; A1P= A1P> A1P? A1P@ A1P[ A1P] A1P^ A1P_ A1P` A1P{ A1P} A1P~ A1Q0\ - A1Q1 A1Q2 A1Q3 A1Q4 A1Q5 A1Q6 A1Q7 A1Q9 A1QA A1QB A1QC A1QD A1QE A1QF A1QG A\ -1QH A1QI A1QJ A1QK A1QL A1QM A1QN A1QO A1QP A1QQ A1QR A1QS A1QT A1QU A1QV A1Q\ -W A1QY A1QZ A1Qa A1Qb A1Qc A1Qd A1Qe A1Qf A1Qg A1Qh A1Qi A1Qj A1Qk A1Ql A1Qm \ -A1Qn A1Qp A1Qq A1Qr A1Qs A1Qt A1Qu A1Qv A1Qw A1Qx A1Qy A1Qz A1Q# A1Q$ A1Q% A1\ -Q& A1Q' A1Q( A1Q) A1Q* A1Q+ A1Q, A1Q- A1Q. A1Q/ A1Q: A1Q; A1Q< A1Q@ A1Q[ A1Q]\ - A1Q^ A1Q_ A1Q` A1Q{ A1Q| A1Q} A1Q~ A1R0 A1R1 A1R2 A1R3 A1R4 A1R5 A1R6 A1R7 A\ -1R8 A1R9 A1RA A1RE A1RF A1RG A1RH A1RI A1RJ A1RK A1RL A1RM A1RN A1RO A1RP A1R\ -Q A1RR A1RS A1RT A1RU A1RV A1RW A1RX A1RY A1RZ A1Ra A1Rb A1Rc A1Rd A1Re A1Rf \ -A1Rg A1Rh A1Ri A1Rj A1Rk A1Rl A1Rm A1Rn A1Ro A1Rp A1Rq A1Rr A1Rs A1Rt A1Ru A1\ -Rv A1Rw A1Rx A1Rz A1R# A1R$ A1R% A1R& A1R' A1R( A1R) A1R+ A1R, A1R- A1R. A1R/\ - A1R: A1R; A1R< A1R= A1R> A1R? A1R@ A1R[ A1R] A1R^ A1R_ A1R` A1R{ A1R} A1R~ A\ -1S0 A1S1 A1S2 A1S3 A1S4 A1S5 A1S6 A1S8 A1S9 A1SA A1SB A1SC A1SD A1SE A1SF A1S\ -G A1SH A1SI A1SJ A1SK A1SL A1SN A1SO A1SQ A1SR A1SS A1ST A1SU A1SV A1SW A1SX \ -A1SY A1SZ A1Sa A1Sb A1Sc A1Sd A1Se A1Sf A1Sg A1Sh A1Si A1Sj A1Sk A1Sl A1Sm A1\ -Sn A1So A1Sp A1Sq A1Ss A1St A1Su A1Sv A1Sw A1Sx A1Sy A1Sz A1S# A1S$ A1S% A1S&\ - A1S' A1S( A1S) A1S* A1S+ A1S, A1S- A1S/ A1S: A1S; A1S< A1S= A1S> A1S? A1S[ A\ -1S] A1S^ A1S_ A1S` A1S{ A1S| A1S} A1T0 A1T1 A1T2 A1T3 A1T4 A1T5 A1T6 A1T7 A1T\ -8 A1T9 A1TA A1TB A1TC A1TD A1TE A1T+ A1T- A1T< A1T? A1T^ A1T{ A1V@ A1V[ A1V] \ -A1V_ A1V{ A1V| A1W0 A1W1 A1W2 A1W3 A1W4 A1W7 A1W9 A1WA A1WB A1WD A1WE A1WI A1\ -WJ A1WL A1WN A1WR A1WS A1WT A1WU A1WV A1WY A1Wa A1Wb A1Wc A1We A1Wf A1Wi A1Wj\ - A1Wk A1Wm A1Wo A1Wp A1Ws A1Wt A1Wu A1Wv A1Ww A1W$ A1W% A1W& A1W( A1W) A1W, A\ -1W- A1W. A1W/ A1W: A1W< A1W= A1W@ A1W[ A1W] A1W^ A1W_ A1W| A1W~ A1X1 A1X3 A1X\ -7 A1X8 A1X9 A1XA A1XB A1XD A1XE A1XH A1XI A1XJ A1XK A1XL A1XO A1XQ A1XS A1XV \ -A1XY A1XZ A1Xa A1Xb A1Xc A1Xe A1Xf A1Xi A1Xj A1Xk A1Xl A1Xm A1Xp A1Xr A1Xt A1\ -Xv A1Xw A1Xz A1X# A1X$ A1X% A1X& A1X( A1X) A1X- A1X. A1X/ A1X: A1X= A1X? A1X@\ - A1X[ A1X_ A1X| A1X} A1X~ A1Y0 A1Y1 A1Y3 A1Y4 A1Y8 A1Y9 A1YA A1YB A1YE A1YG A\ -1YH A1YI A1YK A1YO A1YP A1YQ A1YR A1YS A1YU A1YV A1YZ A1Ya A1Yb A1Yc A1Yf A1Y\ -h A1Yi A1Yj A1Yl A1Ym A1Yo A1Yr A1Ys A1Yt A1Yu A1Yv A1Yy A1Yz A1Y$ A1Y% A1Y& \ -A1Y' A1Y( A1Y+ A1Y, A1Y/ A1Y: A1Y< A1Y[ A1Y] A1Y^ A1Y{ A1Y| A1Y~ A1Z0 A1Z1 A1\ -Z2 A1Z6 A1Z7 A1ZA A1ZB A1ZG A1ZH A1ZI A1ZJ A1ZK A1ZO A1ZQ A1ZR A1ZS A1ZT A1ZU\ - A1ZX A1ZY A1Zb A1Zc A1Ze A1Zh A1Zi A1Zj A1Zk A1Zl A1Zo A1Zp A1Zr A1Zs A1Zt A\ -1Zu A1Zv A1Zz A1Z% A1Z& A1Z( A1Z+ A1Z, A1Z- A1Z. A1Z/ A1Z< A1Z= A1Z? A1Z@ A1Z\ -[ A1Z] A1Z^ A1Z{ A1Z| A1a0 A1a1 A1a3 A1a6 A1a7 A1a8 A1a9 A1aA A1aD A1aE A1aG \ -A1aH A1aI A1aJ A1aK A1aN A1aR A1aS A1aU A1aX A1aY A1aZ A1aa A1ab A1ae A1ah A1\ -ai A1aj A1ak A1al A1ao A1ap A1as A1at A1av A1ay A1az A1a# A1a$ A1a% A1a( A1a)\ - A1a+ A1a, A1a- A1a. A1a/ A1a< A1a= A1a@ A1a[ A1a^ A1a{ A1a| A1a} A1a~ A1b0 A\ -1b3 A1b4 A1b7 A1b8 A1b9 A1bA A1bD A1bE A1bH A1bI A1bK A1bL A1bN A1bO A1bP A1b\ -Q A1bT A1bU A1bV A1bX A1bY A1bZ A1ba A1bb A1bd A1be A1bf A1bg A1bh A1bj A1bk \ -A1bl A1bo A1bp A1bq A1bs A1bv A1bw A1by A1bz A1b# A1b$ A1b% A1b' A1b( A1b) A1\ -b* A1b+ A1b, A1b- A1b. A1b/ A1b: A1b; A1b< A1b= A1b> A1b? A1b@ A1b] A1b^ A1b_\ - A1b` A1b{ A1b} A1c0 A1c3 A1c4 A1c7 A1c8 A1c9 A1cA A1cC A1cD A1cE A1cF A1cG A\ -1cK A1cL A1cM A1cN A1cO A1cP A1cQ A1cR A1cT A1cU A1cV A1cX A1cY A1cZ A1cb A1c\ -e A1cf A1cg A1ch A1ci A1ck A1cl A1cm A1co A1cq A1cs A1cu A1cv A1cw A1cx A1cy \ -A1c# A1c$ A1c% A1c( A1c) A1c* A1c, A1c- A1c/ A1c: A1c< A1c= A1c> A1c? A1c@ A1\ -c^ A1c_ A1c` A1c| A1c} A1d0 A1d3 A1d4 A1d5 A1d7 A1dA A1dB A1dD A1dE A1dF A1dH\ - A1dK A1dL A1dN A1dP A1dQ A1dR A1dU A1dV A1dW A1dX A1da A1db A1dc A1de A1dg A\ -1dh A1di A1dk A1dl A1dm A1do A1dp A1dq A1dr A1ds A1du A1dv A1dw A1dx A1dy A1d\ -z A1d% A1d& A1d' A1d( A1d) A1d* A1d+ A1d, A1d- A1d/ A1d: A1d; A1d? A1d@ A1d] \ -A1d_ A1d{ A1d| A1d~ A1e1 A1e2 A1e3 A1e4 A1e5 A1e8 A1eA A1eB A1eC A1eD A1eE A1\ -eF A1eJ A1eL A1eM A1eO A1eQ A1eS A1eT A1eU A1eV A1eX A1eb A1ec A1ed A1ee A1ef\ - A1eg A1ej A1ek A1em A1en A1eo A1ep A1eq A1et A1eu A1ev A1ew A1ex A1ey A1e$ A\ -1e% A1e& A1e' A1e) A1e* A1e+ A1e. A1e/ A1e: A1e= A1e@ A1e[ A1e] A1e^ A1e_ A1e\ -{ A1e} A1e~ A1f1 A1f2 A1f3 A1f4 A1f9 A1fA A1fB A1fC A1fD A1fE A1fG A1fI A1fJ \ -A1fK A1fL A1fM A1fS A1fT A1fU A1fW A1fZ A1fa A1fb A1fc A1fd A1fe A1ff A1fg A1\ -fj A1fk A1fl A1fm A1fn A1fo A1ft A1fu A1fw A1fx A1f$ A1f% A1f& A1f( A1f) A1f+\ - A1f- A1f. A1f: A1f; A1f< A1f= A1f@ A1f[ A1f] A1f^ A1f` A1f{ A1f} A1f~ A1g0 A\ -1g1 A1g2 A1g3 A1g4 A1g5 A1g8 A1g9 A1gB A1gC A1gD A1gH A1gI A1gJ A1gK A1gL A1g\ -Q A1gR A1gS A1gT A1gV A1gX A1gZ A1ga A1gc A1gg A1gh A1gi A1gj A1gk A1gm A1gn \ -A1gq A1gr A1gs A1gt A1gu A1gv A1gw A1g# A1g% A1g& A1g' A1g( A1g, A1g. A1g: A1\ -g; A1g< A1g> A1g] A1g^ A1g_ A1g` A1g~ A1h0 A1h1 A1h2 A1h3 A1h5 A1h7 A1hB A1hC\ - A1hG A1hH A1hJ A1hK A1hL A1hM A1hQ A1hR A1hS A1hT A1hU A1hW A1hY A1hZ A1ha A\ -1hc A1hd A1hg A1hh A1hi A1hk A1hl A1hm A1hn A1hp A1hq A1hr A1hs A1ht A1hu A1h\ -v A1hx A1hz A1h# A1h& A1h' A1h* A1h, A1h. A1h/ A1h: A1h; A1h@ A1h[ A1h] A1h^ \ -A1h` A1h| A1h~ A1i1 A1i2 A1i4 A1i5 A1i6 A1i7 A1i8 A1i9 A1iA A1iB A1iC A1iG A1\ -iH A1iI A1iJ A1iK A1iM A1iQ A1iS A1iT A1iW A1iX A1iY A1ia A1ib A1ic A1id A1ig\ - A1ih A1ij A1ik A1il A1im A1in A1ip A1ir A1it A1iu A1ix A1iz A1i# A1i$ A1i% A\ -1i& A1i' A1i) A1i+ A1i, A1i- A1i. A1i/ A1i; A1i< A1i= A1i> A1i? A1i[ A1i] A1i\ -` A1i{ A1i| A1i~ A1j0 A1j1 A1j2 A1j7 A1j8 A1j9 A1jA A1jC A1jE A1jJ A1jK A1jO \ -A1jQ A1jS A1jT A1jX A1jY A1jZ A1ja A1jc A1jd A1jf A1jg A1jj A1jk A1jn A1jp A1\ -jr A1js A1jt A1ju A1jw A1jx A1jy A1jz A1j$ A1j) A1j, A1j- A1j. A1j: A1j; A1j<\ - A1j= A1j> A1j? A1j| A1j} A1j~ A1k2 A1k4 A1k6 A1k8 A1k9 A1kC A1kD A1kE A1kG A\ -1kI A1kJ A1kN A1kO A1kP A1kQ A1kT A1kV A1kX A1kZ A1ka A1kd A1kf A1kh A1kj A1k\ -k A1kp A1kq A1kr A1ku A1kw A1kz A1k# A1k$ A1k& A1k' A1k( A1k) A1k* A1k+ A1k, \ -A1k- A1k. A1k; A1k< A1k= A1k> A1k? A1k@ A1k[ A1k] A1k_ A1k` A1k{ A1k} A1k~ A1\ -l2 A1l3 A1l4 A1l6 A1l7 A1l8 A1l9 A1lE A1lF A1lG A1lJ A1lL A1lM A1lN A1lP A1lQ\ - A1lT A1lV A1lW A1lX A1lZ A1la A1lc A1le A1lf A1lg A1lh A1li A1lk A1lm A1lo A\ -1lq A1lr A1lu A1lv A1lw A1ly A1l# A1l$ A1l' A1l( A1l) A1l* A1l+ A1l. A1l: A1l\ -[ A1l_ A1l` A1l{ A1l} A1m2 A1m3 A1m4 A1m6 A1mB A1mC A1mD A1mE A1mF A1mG A1mL \ -A1mM A1mN A1mO A1mS A1mT A1mU A1mV A1mW A1mX A1mZ A1mc A1md A1me A1mg A1mh A1\ -mj A1mm A1mn A1mo A1mq A1mt A1mu A1mv A1mw A1mx A1my A1mz A1m# A1m& A1m' A1m(\ - A1m* A1m+ A1m- A1m/ A1m: A1m; A1m< A1m= A1m> A1m[ A1m] A1m^ A1m_ A1m{ A1m| A\ -1m} A1n1 A1n2 A1n4 A1n5 A1n8 A1nA A1nB A1nC A1nD A1nF A1nI A1nJ A1nK A1nL A1n\ -M A1nN A1nP A1nS A1nT A1nX A1nZ A1nb A1nc A1nd A1ne A1nj A1nk A1nl A1nm A1nn \ -A1no A1nq A1nt A1nu A1nx A1ny A1n# A1n% A1n& A1n' A1n( A1n- A1n. A1n: A1n< A1\ -n> A1n[ A1n] A1n^ A1n_ A1n{ A1n} A1o0 A1o1 A1o2 A1o3 A1o5 A1o8 A1o9 A1oB A1oC\ - A1oD A1oE A1oF A1oI A1oJ A1oK A1oM A1oP A1oR A1oS A1oT A1oU A1oV A1oW A1oZ A\ -1oa A1oc A1od A1oe A1og A1oj A1ok A1ol A1on A1oo A1os A1ou A1ov A1ow A1ox A1o\ -$ A1o% A1o' A1o( A1o) A1o, A1o. A1o; A1o< A1o= A1o^ A1o_ A1o` A1o~ A1p2 A1p3 \ -A1p4 A1p7 A1p9 A1pA A1pC A1pD A1pH A1pJ A1pK A1pL A1pM A1pO A1pQ A1pR A1pT A1\ -pU A1pV A1pa A1pb A1pd A1pe A1pf A1pi A1pk A1pl A1pm A1pn A1pr A1ps A1pu A1pv\ - A1pw A1p% A1p' A1p( A1p. A1p/ A1p: A1p; A1p? A1p@ A1p] A1p^ A1p_ A1p| A1p~ A\ -1q0 A1q2 A1q3 A1q7 A1q9 A1qA A1qB A1qC A1qE A1qG A1qJ A1qK A1qL A1qO A1qQ A1q\ -T A1qU A1qY A1qa A1qb A1qc A1qd A1qh A1qk A1ql A1qm A1qp A1qr A1qs A1qu A1qv \ -A1qw A1q$ A1q% A1q& A1q' A1q) A1q+ A1q, A1q. A1q/ A1q: A1q? A1q] A1q^ A1q| A1\ -q~ A1r0 A1r1 A1r2 A1r7 A1r9 A1rA A1rB A1rG A1rH A2YU A2YV A2YW A2YX A2YY A2YZ\ - A2Ya A2Yb A2Yc A2Yd A2Ye A2Yf A2Yg A2Yh A2Yi A2Y' A2Y( A2Y) A2Y* A2Y+ A2Y, A\ -2Y- A2Y. A2Y/ A2Y: A2Y; A2Y< A2Y= A2Y> A2Y? A2Z2 A2Z3 A2Z4 A2Z5 A2Z6 A2Z7 A2Z\ -8 A2Z9 A2ZA A2ZB A2ZC A2ZD A2ZE A2ZF A2ZG A2ZI A2ZJ A2ZK A2ZL A2ZM A2ZN A2ZO \ -A2ZP A2ZR A2ZT A2ZU A2ZV A2ZW A2ZX A2ZY A2ZZ A2Za A2Zb A2Zc A2Zd A2Ze A2Zf A2\ -Zg A2Zh A2Zi A2Zk A2Zl A2Zm A2Zn A2Zo A2Zp A2Zq A2Zt A2Zu A2Zv A2Zw A2Zx A2Zy\ - A2Zz A2Z# A2Z$ A2Z% A2Z& A2Z' A2Z( A2Z) A2Z* A2Z+ A2Z, A2Z. A2Z/ A2Z: A2Z; A\ -2Z< A2Z= A2Z> A2Z] A2Z^ A2Z_ A2Z` A2Z{ A2Z| A2Z} A2Z~ A2a0 A2a1 A2a2 A2a3 A2a\ -4 A2a5 A2a6 A2a7 A2a8 A2a9 A2aA A2aB A2aC A2aD A2aE A2aF A2aG A2aI A2aJ A2aK \ -A2aL A2aM A2aN A2aO A2aS A2aT A2aU A2aV A2aW A2aX A2aY A2aZ A2aa A2ab A2ac A2\ -ad A2ae A2af A2ag A2ah A2ai A2ak A2al A2am A2an A2ao A2ap A2ar A2at A2au A2av\ - A2aw A2ax A2ay A2az A2a# A2a$ A2a% A2a& A2a' A2a( A2a) A2a* A2a+ A2a, A2a. A\ -2a/ A2a: A2a; A2a< A2a= A2a> A2a@ A2a[ A2a] A2a^ A2a_ A2a` A2a{ A2b0 A2b1 A2b\ -2 A2b3 A2b4 A2b6 A2b7 A2b8 A2b9 A2bA A2bC A2bD A2bE A2bF A2bG A2bI A2bJ A2bK \ -A2bL A2bM A2bN A2bP A2bR A2bS A2bT A2bV A2bW A2bX A2bY A2bZ A2bb A2bc A2bd A2\ -be A2bf A2bh A2bi A2bj A2bk A2bl A2bm A2bn A2bo A2bs A2bt A2bu A2bv A2bx A2by\ - A2bz A2b# A2b$ A2b& A2b' A2b( A2b) A2b* A2b, A2b- A2b. A2b/ A2b: A2b; A2b< A\ -2b= A2b> A2b? A2b@ A2b] A2b^ A2b_ A2b` A2b{ A2b~ A2c0 A2c1 A2c2 A2c3 A2c4 A2c\ -5 A2c7 A2c8 A2c9 A2cA A2cB A2cD A2cF A2cG A2cH A2cI A2cK A2cL A2cM A2cN A2cQ \ -A2cR A2cS A2cT A2cU A2cV A2cW A2cX A2cZ A2ca A2cb A2cc A2cd A2cg A2cj A2ck A2\ -cl A2cm A2cn A2cp A2cq A2cr A2cs A2ct A2cu A2cv A2cw A2cy A2cz A2c# A2c$ A2c%\ - A2c' A2c( A2c* A2c+ A2c, A2c- A2c. A2c: A2c; A2c< A2c= A2c> A2c@ A2c[ A2c] A\ -2c^ A2c_ A2c| A2c} A2c~ A2d0 A2d1 A2d2 A2d3 A2d4 A2d6 A2d7 A2d8 A2d9 A2dA A2d\ -C A2dD A2dF A2dG A2dI A2dJ A2dK A2dL A2dM A2dP A2dQ A2dR A2dS A2dT A2dU A2dV \ -A2dW A2dY A2dZ A2da A2db A2dc A2dg A2dh A2di A2dk A2dl A2dm A2dn A2dq A2dr A2\ -ds A2dt A2du A2dv A2dz A2d# A2d% A2d& A2d' A2d( A2d) A2d* A2d+ A2d, A2d- A2d/\ - A2d: A2d; A2d= A2d> A2d? A2d@ A2d[ A2d] A2d^ A2d| A2d~ A2e0 A2e1 A2e2 A2e3 A\ -2e4 A2e5 A2e6 A2e7 A2e8 A2e9 A2eA A2eD A2eE A2eF A2eG A2eH A2eI A2eJ A2eK A2e\ -M A2eP A2eQ A2eR A2eS A2eT A2eU A2eV A2eW A2eX A2eY A2eZ A2ea A2ec A2ed A2ee \ -A2eg A2eh A2ei A2ej A2ek A2el A2en A2eo A2ep A2eq A2er A2es A2eu A2ev A2ew A2\ -ey A2ez A2e# A2e$ A2e% A2e& A2e' A2e( A2e+ A2e, A2e- A2e. A2e/ A2e: A2e= A2e>\ - A2e? A2e[ A2e] A2e` A2e{ A2e| A2e} A2e~ A2f0 A2f1 A2f2 A2f4 A2f5 A2f6 A2f8 A\ -2f9 A2fA A2fB A2fC A2fE A2fF A2fG A2fH A2fI A2fN A2fO A2fP A2fQ A2fR A2fS A2f\ -U A2fV A2fW A2fY A2fZ A2fa A2fb A2fd A2fe A2ff A2fh A2fi A2fj A2fk A2fl A2fm \ -A2fn A2fo A2fp A2fq A2fr A2fs A2fx A2fy A2fz A2f# A2f$ A2f% A2f& A2f' A2f* A2\ -f+ A2f, A2f- A2f. A2f: A2f< A2f= A2f> A2f? A2f[ A2f] A2f^ A2f` A2f{ A2f| A2f}\ - A2f~ A2g0 A2g1 A2g3 A2g4 A2g5 A2g7 A2g8 A2g9 A2gB A2gC A2gD A2gE A2gF A2gH A\ -2gI A2gL A2gM A2gN A2gO A2gP A2gQ A2gR A2gV A2gW A2gX A2gY A2gZ A2ga A2ge A2g\ -f A2gg A2gh A2gi A2gj A2gk A2gl A2gm A2gn A2go A2gp A2gq A2gr A2gs A2g% A2g& \ -A2g' A2g( A2g) A2g* A2g+ A2g, A2g- A2g. A2g: A2g< A2g= A2g? A2g@ A2h0 A2h1 A2\ -h2 A2h3 A2h4 A2h5 A2h6 A2h7 A2h8 A2h9 A2hB A2hC A2hE A2hF A2hG A2hJ A2hK A2hL\ - A2hM A2hN A2hO A2hP A2hQ A2hU A2hV A2hW A2hX A2hY A2hZ A2ha A2hb A2hc A2hd A\ -2he A2hf A2hg A2hh A2hi A2hj A2hk A2hm A2hn A2ho A2hp A2hq A2hr A2hs A2ht A2h\ -v A2hw A2hx A2hy A2hz A2h# A2h$ A2h% A2h& A2h' A2h( A2h) A2h* A2h+ A2h, A2h- \ -A2h. A2h: A2h; A2h< A2h= A2h> A2h? A2h] A2h^ A2h_ A2h` A2h{ A2h| A2h} A2h~ A2\ -i0 A2i1 A2i2 A2i3 A2i4 A2i5 A2i6 A2i7 A2i8 A2i9 A2iA A2iB A2iC A2iD A2iE A2iF\ - A2iG A2iI A2iJ A2iK A2iL A2iM A2iN A2iO A2iP A2iT A2iU A2iV A2iW A2iX A2iY A\ -2iZ A2ia A2ib A2ic A2id A2ie A2if A2ig A2ih A2ii A2ik A2il A2im A2in A2io A2i\ -p A2iq A2it A2iu A2iv A2iw A2ix A2iy A2iz A2i# A2i$ A2i% A2i& A2i' A2i( A2i) \ -A2i* A2i+ A2i, A2i- A2i/ A2i: A2i; A2i< A2i= A2i> A2i? A2i@ A2i] A2i^ A2i_ A2\ -i` A2i{ A2i| A2j1 A2j2 A2j3 A2j4 A2j5 A2j6 A2j7 A2j8 A2j9 A2jA A2jD A2jE A2jF\ - A2jG A2jI A2jJ A2jK A2jL A2jM A2jN A2jO A2jP A2jS A2jT A2jU A2jW A2jY A2jZ A\ -2ja A2jc A2je A2jf A2jg A2ji A2jk A2jl A2jm A2jn A2jo A2jp A2jt A2ju A2jv A2j\ -w A2jx A2jy A2jz A2j# A2j$ A2j' A2j( A2j) A2j* A2j, A2j- A2j. A2j/ A2j: A2j; \ -A2j< A2j= A2j> A2j? A2j@ A2j[ A2j] A2j_ A2j` A2j{ A2k0 A2k1 A2k2 A2k3 A2k4 A2\ -k5 A2k7 A2k8 A2k9 A2kA A2kB A2kC A2kE A2kF A2kI A2kJ A2kK A2kL A2kM A2kN A2kP\ - A2kR A2kS A2kT A2kU A2kV A2kW A2kX A2kZ A2ka A2kb A2kc A2kd A2ke A2kg A2ki A\ -2kk A2kl A2km A2kn A2ko A2kp A2kr A2ks A2kt A2ku A2kv A2kw A2kx A2ky A2kz A2k\ -$ A2k% A2k& A2k) A2k+ A2k, A2k- A2k. A2k/ A2k: A2k; A2k= A2k> A2k@ A2k[ A2k^ \ -A2k_ A2k` A2k{ A2k~ A2l0 A2l1 A2l2 A2l3 A2l4 A2l5 A2l7 A2l8 A2l9 A2lA A2lC A2\ -lD A2lE A2lG A2lH A2lI A2lJ A2lK A2lL A2lM A2lQ A2lR A2lS A2lT A2lU A2lV A2lW\ - A2lX A2lZ A2la A2lb A2le A2lf A2lg A2lh A2lj A2lk A2ll A2lm A2ln A2lr A2ls A\ -2lt A2lu A2lv A2lw A2l# A2l$ A2l% A2l& A2l' A2l( A2l) A2l* A2l+ A2l, A2l- A2l\ -. A2l: A2l< A2l> A2l? A2l@ A2l[ A2l] A2l^ A2l_ A2l} A2l~ A2m0 A2m1 A2m2 A2m3 \ -A2m4 A2m5 A2m6 A2m7 A2m8 A2m9 A2mA A2mD A2mE A2mG A2mH A2mI A2mJ A2mK A2mL A2\ -mN A2mQ A2mS A2mT A2mU A2mV A2mW A2mX A2mY A2mZ A2ma A2md A2me A2mf A2mh A2mi\ - A2mj A2mk A2ml A2mm A2mn A2mo A2mq A2mr A2ms A2mt A2mu A2mx A2mz A2m# A2m$ A\ -2m% A2m& A2m' A2m( A2m* A2m, A2m- A2m. A2m/ A2m: A2m< A2m= A2m> A2m? A2m@ A2m\ -] A2m^ A2m_ A2m| A2m} A2m~ A2n0 A2n1 A2n2 A2n4 A2n5 A2n7 A2n9 A2nA A2nB A2nE \ -A2nF A2nG A2nH A2nI A2nJ A2nK A2nL A2nO A2nP A2nQ A2nR A2nS A2nT A2nU A2nV A2\ -nX A2nZ A2na A2nb A2nc A2ne A2nf A2nh A2ni A2nj A2nk A2nl A2nm A2np A2nq A2nr\ - A2ns A2nu A2nv A2ny A2nz A2n# A2n$ A2n% A2n& A2n' A2n( A2n* A2n- A2n. A2n/ A\ -2n: A2n; A2n= A2n> A2n? A2n@ A2n[ A2n` A2n{ A2n| A2n} A2n~ A2o0 A2o1 A2o2 A2o\ -4 A2o5 A2o7 A2o8 A2o9 A2oA A2oB A2oC A2oD A2oE A2oF A2oG A2oH A2oI A2oJ A2oN \ -A2oO A2oP A2oQ A2oR A2oS A2oW A2oc A2od A2oe A2of A2og A2oh A2oi A2oj A2ok A2\ -ol A2om A2on A2oo A2op A2oq A2or A2os A2ot A2o) A2o* A2o+ A2o, A2o- A2o. A2o<\ - A2o> A2o? A2o[ A2p4 A2p5 A2p6 A2p7 A2p8 A2p9 A2pD A2pE A2pH A2pI A2pK A2pL A\ -2pM A2pN A2pO A2pP A2pQ A2pR A2pV A2pW A2pX A2pY A2pZ A2pa A2pb A2pc A2pd A2p\ -e A2pf A2pg A2ph A2pi A2pj A2pk A2pl A2pm A2pn A2po A2pp A2pq A2pr A2ps A2pv \ -A2pw A2px A2py A2pz A2p# A2p$ A2p% A2p& A2p' A2p( A2p) A2p* A2p+ A2p, A2p- A2\ -p. A2p; A2p< A2p= A2p> A2p? A2p@ A2p[ A2p_ A2p` A2p{ A2p| A2p} A2p~ A2q0 A2q1\ - A2q2 A2q3 A2q4 A2q5 A2q6 A2q7 A2q8 A2q9 A2qA A2qB A2qC A2qD A2qE A2qF A2qG A\ -2qH A2qI A2qJ A2qL A2qM A2qN A2qO A2qP A2qQ A2qR A2qU A2qV A2qW A2qX A2qY A2q\ -Z A2qa A2qb A2qc A2qd A2qe A2qf A2qg A2qh A2qi A2ql A2qm A2qn A2qo A2qp A2qq \ -A2qr A2qv A2qw A2qx A2qy A2qz A2q# A2q$ A2q% A2q& A2q' A2q( A2q) A2q* A2q+ A2\ -q, A2q/ A2q: A2q; A2q< A2q= A2q> A2q? A2q^ A2q_ A2q` A2q{ A2q| A2q} A2r2 A2r3\ - A2r4 A2r5 A2r6 A2r7 A2r8 A2r9 A2rA A2rC A2rE A2rF A2rG A2rI A2rK A2rL A2rM A\ -2rN A2rO A2rP A2rQ A2rR A2rT A2rU A2rV A2rY A2rZ A2ra A2rb A2re A2rf A2rg A2r\ -h A2rk A2rl A2rm A2rn A2ro A2rp A2rq A2ru A2rv A2rw A2rx A2ry A2rz A2r# A2r$ \ -A2r% A2r& A2r) A2r* A2r+ A2r, A2r/ A2r: A2r; A2r< A2r= A2r> A2r? A2r] A2r^ A2\ -r_ A2r` A2r{ A2r| A2s0 A2s1 A2s2 A2s3 A2s4 A2s5 A2s6 A2s7 A2s8 A2sA A2sB A2sC\ - A2sD A2sF A2sG A2sI A2sJ A2sL A2sM A2sN A2sO A2sS A2sT A2sU A2sV A2sW A2sX A\ -2sZ A2sa A2sb A2sc A2sd A2se A2si A2sj A2sl A2sm A2sn A2so A2sp A2sq A2st A2s\ -u A2sv A2sw A2sx A2sy A2sz A2s$ A2s% A2s& A2s' A2s) A2s* A2s, A2s- A2s. A2s/ \ -A2s: A2s; A2s> A2s? A2s[ A2s^ A2s_ A2s` A2s{ A2s| A2t0 A2t1 A2t2 A2t3 A2t4 A2\ -t5 A2t6 A2t8 A2t9 A2tA A2tB A2tC A2tD A2tJ A2tK A2tL A2tM A2tN A2tR A2tS A2tT\ - A2tU A2tV A2tW A2tX A2tY A2ta A2tb A2tc A2te A2tf A2th A2ti A2tj A2tk A2tl A\ -2tm A2tn A2to A2tr A2ts A2tt A2tu A2tv A2tw A2tx A2t$ A2t% A2t& A2t' A2t( A2t\ -) A2t* A2t+ A2t, A2t- A2t. A2t/ A2t< A2t= A2t@ A2t[ A2t] A2t^ A2t_ A2t` A2t~ \ -A2u0 A2u1 A2u2 A2u3 A2u4 A2u5 A2u6 A2u7 A2u8 A2u9 A2uA A2uC A2uG A2uH A2uI A2\ -uJ A2uK A2uL A2uM A2uN A2uS A2uT A2uU A2uV A2uW A2uX A2uY A2uZ A2ua A2ub A2uc\ - A2ug A2uh A2ui A2uj A2uk A2ul A2um A2un A2ur A2us A2ut A2uu A2uv A2uw A2ux A\ -2u# A2u$ A2u% A2u& A2u' A2u( A2u* A2u+ A2u- A2u. A2u/ A2u: A2u; A2u< A2u= A2u\ -? A2u@ A2u[ A2u^ A2u_ A2u} A2u~ A2v0 A2v1 A2v2 A2v3 A2v4 A2v5 A2v7 A2v8 A2vA \ -A2vB A2vC A2vE A2vF A2vG A2vH A2vI A2vJ A2vL A2vN A2vP A2vQ A2vR A2vS A2vT A2\ -vU A2vV A2vX A2va A2vb A2vc A2vd A2vf A2vg A2vi A2vk A2vl A2vm A2vn A2vp A2vq\ - A2vr A2vs A2vu A2vv A2vz A2v# A2v$ A2v% A2v& A2v' A2v( A2v) A2v+ A2v- A2v. A\ -2v/ A2v: A2v; A2v< A2v> A2v? A2v@ A2v[ A2v] A2v^ A2v_ A2v| A2v} A2v~ A2w0 A2w\ -1 A2w2 A2w3 A2w5 A2w7 A2w8 A2w9 A2wA A2wB A2wF A2wG A2wH A2wI A2wJ A2wM A2wO \ -A2wP A2wQ A2wR A2wS A2wT A2wX A2wY A2wZ A2wa A2wb A2wc A2wd A2we A2wf A2wg A2\ -wh A2wi A2wj A2wk A2wl A2w' A2w( A2w) A2w- A2w. A2w/ A2w: A2w; A2w< A2w= A2w>\ - A2w? A2w@ A2w[ A2w] A2x2 A2x3 A2x4 A2x5 A2x6 A2x7 A2xB A2xC A2xD A2xE A2xF A\ -2xG A2xH A2xI A2xJ A2xK A2xL A2xM A2xN A2xO A2xP A2xQ A2xR A2xS A2xT A2xV A2x\ -W A2xX A2xY A2xZ A2xa A2xb A2xc A2xd A2xe A2xg A2xh A2xi A2xk A2xl A2xm A2xn \ -A2xo A2xp A2xq A2xr A2xs A2xt A2xu A2xv A2xx A2xy A2xz A2x# A2x$ A2x% A2x& A2\ -x' A2x( A2x) A2x, A2x- A2x/ A2x: A2x; A2x< A2x= A2x> A2x? A2x@ A2x[ A2x] A2x^\ - A2x` A2x{ A2x| A2x} A2x~ A2y0 A2y1 A2y2 A2y3 A2y4 A2y6 A2y8 A2yB A2yC A2yD A\ -2yE A2yF A2yG A2yH A2yI A2yJ A2yK A2yL A2yN A2yO A2yP A2yR A2yS A2yT A2yU A2y\ -V A2yW A2yX A2yY A2yZ A2ya A2yb A2ye A2yf A2yg A2yh A2yi A2yj A2yk A2yl A2ym \ -A2yo A2yp A2yr A2ys A2yt A2yu A2yv A2yw A2yx A2yy A2yz A2y# A2y$ A2y% A2y( A2\ -y) A2y* A2y+ A2y, A2y- A2y. A2y/ A2y: A2y; A2y< A2y> A2y@ A2y[ A2y] A2y^ A2y_\ - A2y` A2y{ A2y| A2y} A2y~ A2z3 A2z4 A2z5 A2z6 A2z8 A2z9 A2zA A2zB A2zC A2zD A\ -2zE A2zH A2zI A2zJ A2zK A2zM A2zN A2zO A2zP A2zQ A2zR A2zU A2zV A2zW A2zZ A2z\ -a A2zb A2zc A2zd A2ze A2zf A2zi A2zj A2zk A2zl A2zm A2zo A2zp A2zq A2zr A2zv \ -A2zw A2zx A2zy A2zz A2z# A2z$ A2z% A2z& A2z' A2z( A2z) A2z* A2z+ A2z- A2z. A2\ -z/ A2z: A2z; A2z= A2z> A2z? A2z@ A2z[ A2z] A2z^ A2z_ A2z{ A2z| A2z} A2z~ A2#0\ - A2#2 A2#4 A2#5 A2#6 A2#7 A2#A A2#B A2#C A2#D A2#E A2#F A2#H A2#I A2#J A2#L A\ -2#M A2#N A2#O A2#P A2#R A2#S A2#V A2#W A2#X A2#Y A2#Z A2#a A2#c A2#d A2#e A2#\ -g A2#h A2#i A2#j A2#k A2#l A2#n A2#o A2#p A2#q A2#r A2#t A2#u A2#v A2#w A2#x \ -A2#y A2#z A2## A2#% A2#& A2#' A2#( A2#) A2#+ A2#, A2#- A2#. A2#; A2#< A2#= A2\ -#> A2#? A2#[ A2#] A2#^ A2#_ A2#` A2#{ A2#| A2#} A2#~ A2$0 A2$1 A2$2 A2$3 A2$4\ - A2$6 A2$7 A2$8 A2$9 A2$B A2$D A2$E A2$F A2$G A2$H A2$J A2$K A2$L A2$M A2$N A\ -2$P A2$Q A2$R A2$S A2$T A2$U A2$V A2$W A2$Y A2$Z A2$a A2$c A2$d A2$e A2$f A2$\ -g A2$i A2$j A2$k A2$l A2$m A2$n A2$q A2$r A2$s A2$t A2$u A2$v A2$x A2$y A2$% \ -A2$' A2$( A2$) A2$* A2$+ A2$, A2$- A2$. A2$; A2$< A2$= A2$> A2$? A2$@ A2$[ A2\ -$] A2$^ A2$_ A2$` A2%0 A2%1 A2%2 A2%3 A2%4 A2%5 A2%6 A2%7 A2%8 A2%A A2%B A2%C\ - A2%D A2%E A2%F A2%G A2%H A2%I A2%J A2%K A2%L A2%N A2%Q A2%T A2%U A2%V A2%W A\ -2%X A2%Y A2%Z A2%a A2%d A2%e A2%f A2%g A2%h A2%i A2%j A2%k A2%l A2%n A2%o A2%\ -p A2%q A2%r A2%s A2%t A2%u A2%w A2%x A2%y A2%# A2%$ A2%% A2%& A2%( A2%) A2%* \ -A2%- A2%. A2%: A2%; A2%< A2%= A2%> A2%? A2%@ A2%[ A2%] A2%^ A2%_ A2%| A2%} A2\ -%~ A2&0 A2&1 A2&2 A2&3 A2&4 A2&5 A2&6 A2&8 A2&A A2&B A2&C A2&D A2&E A2&F A2&G\ - A2&H A2&I A2&J A2&K A2&M A2&N A2&O A2&Q A2&R A2&S A2&U A2&X A2&Y A2&a A2&b A\ -2&c A2&d A2&e A2&f A2&g A2&h A2&i A2&j A2&k A2&l A2&o A2&p A2&r A2&s A2&t A2&\ -u A2&v A2&w A2&x A2&y A2&z A2&$ A2&% A2&& A2&' A2&( A2&) A2&* A2&+ A2&, A2&- \ -A2&. A2&: A2&; A2&< A2&> A2&? A2&] A2&^ A2&_ A2&` A2&{ A2&| A2&} A2&~ A2'1 A2\ -'2 A2'3 A2'4 A2'5 A2'6 A2'7 A2'8 A2'9 A2'A A2'E A2'F A2'G A2'H A2'J A2'K A2'L\ - A2'M A2'N A2'O A2'P A2'R A2'S A2'T A2'U A2'Y A2'Z A2'a A2'b A2'c A2'd A2'e A\ -2'f A2'g A2'n A2'o A2'p A2'q A2'r A2's A2't A2'u A2'v A2'( A2') A2'* A2'+ A2'\ -, A2'- A2'. 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A2|/ A2|: A2|; A2|< A2|= \ -A2|@ A2|[ A2|_ A2|{ A2|| A2|} A2|~ A2}0 A2}1 A2}3 A2}4 A2}5 A2}6 A2}7 A2}8 A2\ -}9 A2}A A2}B A2}C A2}D A2}H A2}J A2}L A2}M A2}N A2}O A2}P A2}Q A2}R A2}S A2}T\ - A2}U A2}W A2}X A2}Y A2}Z A2}a A2}b A2}c A2}d A2}e A2}j A2}k A2}m A2}o A2}p A\ -2}q A2}r A2}s A2}t A2}u A2}v A2}w A2}y A2}z A2}# A2}% A2}& A2}' A2}( A2}) A2}\ -, A2}. A2}/ A2}; A2}< A2}= A2}> A2}? A2}@ A2}[ A2}] A2}^ A2}_ A2}` A2}{ A2}~ \ -A2~0 A2~1 A2~2 A2~3 A2~4 A2~5 A2~8 A2~B A2~C A2~D A2~E A2~F A2~G A2~H A2~I A2\ -~J A2~K A2~L A2~M A2~O A2~P A2~Q A2~S A2~T A2~U A2~V A2~W A2~X A2~b A2~c A2~d\ - A2~e A2~f A2~g A2~h A2~i A2~j A2~q A2~r A2~s A2~t A2~u A2~v A2~w A2~x A2~y A\ -2~+ A2~, A2~- A2~. A2~/ A2~: A2~; A2~< A2~= A2~> A2~? A306 A307 A308 A309 A30\ -A A30B A30C A30D A30E A30F A30G A30O A30P A30Q A30S A30T A30V A30W A30X A30Y \ -A30Z A30a A30b A30c A30d A30e A30f A30h A30i A30j A30k A30l A30m A30n A30o A3\ -0p A30q A30r A30s A30u A30w A30x A30y A30z A30# A30$ A30% A30& A30' A30( A30)\ - A30* A30- A30. A30/ A30: A30; A30< A30= A30> A30? A30[ A30] A30^ A30` A30{ A\ -30| A30} A30~ A310 A311 A312 A313 A314 A315 A318 A319 A31A A31B A31C A31D A31\ -E A31F A31G A31H A31I A31K A31L A31N A31O A31P A31Q A31R A31S A31T A31U A31V \ -A31W A31X A31Z A31a A31b A31c A31d A31e A31f A31g A31h A31i A31k A31m A31n A3\ -1o A31p A31q A31r A31s A31t A31u A31v A31w A31x A31y A31z A31# A31$ A31% A31&\ - A31' A31( A31) A31* A31+ A31- A31. A31/ A31; A31< A31= A31> A31? A31@ A31[ A\ -31] A31^ A31_ A31` A31{ A31| A31} A31~ A320 A321 A322 A323 A327 A328 A329 A32\ -A A32B A32C A32D A32E A32F A32G A32H A32I A32K A32L A32M A32N A32O A32P A32Q \ -A32S A32T A32U A32V A32X A32Y A32Z A32a A32d A32e A32f A32g A32h A32i A32j A3\ -2k A32l A32n A32o A32p A32q A32r A32s A32t A32u A32v A32z A32# A32$ A32& A32'\ - A32( A32) A32* A32+ A32, A32- A32. A32: A32; A32< A32= A32> A32? A32[ A32] A\ -32^ A32` A32{ A32| A32} A32~ A330 A331 A332 A333 A334 A335 A336 A337 A338 A33\ -A A33C A33D A33E A33F A33G A33I A33J A33K A33M A33N A33O A33P A33Q A33S A33T \ -A33U A33V A33W A33X A33Y A33Z A33a A33b A33c A33d A33e A33f A33g A33j A33k A3\ -3l A33m A33n A33o A33p A33q A33r A33s A33t A33u A33v A33w A33x A33y A33z A33#\ - A33$ A33% A33& A33' A33( A33) A33+ A33- A33. A33/ A33; A33< A33= A33> A33? A\ -33[ A33] A33^ A33_ A33` A33| A33~ A340 A341 A342 A343 A345 A346 A347 A348 A34\ -9 A34A A34B A34C A34E A34F A34G A34J A34K A34L A34M A34N A34O A34P A34Q A34R \ -A34S A34T A34V A34W A34X A34Z A34a A34b A34e A34f A34g A34h A34j A34k A34l A3\ -4m A34n A34o A34p A34q A34r A34s A34t A34u A34v A34w A34x A34y A34z A34# A34$\ - A34% A34) A34* A34+ A34, A34- A34. A34/ A34: A34; A34< A34= A34? A34@ A34[ A\ -34] A34^ A34_ A34` A34{ A34| A34} A34~ A355 A356 A357 A358 A359 A35A A35B A35\ -C A35E A35F A35G A35H A35I A35J A35K A35L A35M A35N A35O A35P A35Q A35S A35T \ -A35X A35Y A35Z A35a A35b A35c A35d A35e A35g A35h A35i A35j A35k A35l A35m A3\ -5n A35o A35p A35q A35r A35s A35u A35v A35w A35x A35y A35z A35# A35$ A35% A35&\ - A35' A35* A35+ A35, A35- A35. A35/ A35: A35; A35< A35= A35> A35[ A35] A35^ A\ -35_ A35` A35{ A35| A35} A35~ A360 A361 A362 A363 A364 A365 A366 A367 A368 A36\ -9 A36A A36B A36C A36D A36E A36J A36K A36M A36N A36O A36P A36Q A36R A36S A36T \ -A36U A36V A36W A36X A36Y A36Z A36a A36b A36c A36d A36e A36f A36i A36k A36l A3\ -6n A36o A36p A36q A36r A36s A36t A36u A36v A36w A36x A36# A36$ A36& A36' A36(\ - A36) A36* A36+ A36, A36/ A36; A36= A36> A36? A36@ A36[ A36] A36^ A36_ A36` A\ -36{ A36| A36} A36~ A370 A371 A372 A373 A374 A375 A376 A377 A378 A379 A37D A37\ -E A37F A37G A37H A37I A37J A37K A37L A37M A37N A37O A37P A37R A37S A37T A37U \ -A37V A37W A37X A37d A37i A37j A37k A37l A37m A37n A37o A37p A37q A37r A37s A3\ -7t A37u A37v A37w A37x A37y A37z A37, A37- A37. A37< A37= A37> A387 A388 A389\ - A38A A38B A38C A38P A38Q A38R A38S A38T A38U A38V A38W A38X A38Y A38Z A38a A\ -38b A38c A38d A38e A38f A38g A38h A38i A38k A38l A38m A38n A38o A38p A38q A38\ -r A38s A38t A38u A38v A38x A38y A38z A38# A38$ A38% A38& A38' A38( A38) A38* \ -A38- A38. A38/ A38: A38; A38< A38= A38> A38? A38@ A38] A38^ A38_ A38` A38{ A3\ -8| A38} A38~ A390 A391 A392 A393 A394 A395 A398 A399 A39A A39B A39C A39D A39E\ - A39F A39G A39H A39I A39K A39L A39N A39O A39P A39Q A39R A39S A39T A39U A39V A\ -39W A39Y A39Z A39a A39b A39c A39d A39e A39f A39g A39h A39i A39k A39l A39n A39\ -p A39q A39r A39s A39t A39u A39v A39w A39x A39y A39z A39$ A39% A39& A39' A39( \ -A39) A39* A39+ A39, A39. A39; A39< A39= A39> A39? A39@ A39[ A39] A39^ A39_ A3\ -9` A39{ A39| A39~ A3A0 A3A1 A3A2 A3A3 A3A4 A3A8 A3A9 A3AA A3AB A3AC A3AD A3AE\ - A3AF A3AG A3AH A3AI A3AJ A3AL A3AM A3AN A3AO A3AP A3AQ A3AR A3AT A3AU A3AV A\ -3AX A3AY A3AZ A3Aa A3Ab A3Ad A3Ae A3Af A3Ag A3Ah A3Ai A3Aj A3Ak A3Al A3Am A3A\ -o A3Ap A3Aq A3Ar A3As A3At A3Au A3Av A3Aw A3A# A3A$ A3A% A3A& A3A' A3A( A3A) \ -A3A* A3A+ A3A, A3A- A3A. A3A/ A3A; A3A< A3A= A3A> A3A? A3A@ A3A] A3A^ A3A_ A3\ -A{ A3A| A3A} A3A~ A3B0 A3B3 A3B4 A3B5 A3B6 A3B7 A3B8 A3B9 A3BA A3BB A3BC A3BD\ - A3BE A3BF A3BJ A3BK A3BL A3BM A3BN A3BO A3BP A3BQ A3BR A3BT A3BU A3BV A3BW A\ -3BX A3BY A3BZ A3Ba A3Bb A3Bc A3Bd A3Be A3Bf A3Bg A3Bk A3Bl A3Bm A3Bo A3Bp A3B\ -q A3Br A3Bs A3Bt A3Bu A3Bv A3Bw A3Bx A3By A3Bz A3B# A3B$ A3B& A3B( A3B) A3B* \ -A3B+ A3B. A3B/ A3B: A3B< A3B= A3B> A3B? A3B@ A3B^ A3B_ A3B` A3B{ A3B| A3B} A3\ -B~ A3C0 A3C1 A3C2 A3C3 A3C4 A3C5 A3C6 A3C7 A3C9 A3CA A3CB A3CC A3CD A3CF A3CG\ - A3CH A3CJ A3CK A3CL A3CM A3CN A3CP A3CR A3CS A3CT A3CU A3CV A3CX A3CY A3CZ A\ -3Ca A3Cb A3Cc A3Cd A3Cf A3Cg A3Ch A3Ci A3Ck A3Cl A3Cm A3Cn A3Co A3Cp A3Cq A3C\ -r A3Cs A3Ct A3Cu A3Cv A3Cx A3Cz A3C$ A3C% A3C& A3C* A3C+ A3C, A3C- A3C. A3C/ \ -A3C: A3C; A3C< A3C= A3C> A3C@ A3C[ A3C] A3C^ A3C_ A3C` A3C{ A3C| A3C} A3C~ A3\ -D0 A3D5 A3D6 A3D7 A3D8 A3D9 A3DA A3DB A3DC A3DD A3DF A3DG A3DH A3DI A3DJ A3DK\ - A3DL A3DM A3DN A3DO A3DP A3DQ A3DR A3DV A3DX A3DY A3DZ A3Da A3Db A3Dc A3Dd A\ -3De A3Df A3Dh A3Di A3Dj A3Dk A3Dl A3Dm A3Dn A3Do A3Dp A3Dq A3Dr A3Ds A3Dt A3D\ -v A3Dw A3Dz A3D# A3D$ A3D% A3D& A3D' A3D( A3D) A3D* A3D+ A3D, A3D- A3D. A3D/ \ -A3D: A3D; A3D< A3D= A3D> A3D@ A3D^ A3D_ A3D` A3D{ A3D| A3D} A3D~ A3E0 A3E1 A3\ -E2 A3E3 A3E6 A3E7 A3E8 A3E9 A3EA A3EB A3EC A3ED A3EE A3EF A3EG A3EI A3EJ A3EK\ - A3EL A3EN A3EO A3EP A3EQ A3ER A3ES A3ET A3EU A3EV A3EW A3EX A3EY A3EZ A3Ea A\ -3Eb A3Ec A3Ed A3Ee A3Ef A3Eg A3Ei A3El A3Em A3Ep A3Eq A3Er A3Es A3Et A3Eu A3E\ -v A3Ew A3Ex A3Ey A3Ez A3E# A3E$ A3E% A3E& A3E' A3E( A3E) A3E* A3E+ A3E, A3E. \ -A3E: A3E< A3E= A3E> A3E? A3E@ A3E[ A3E] A3E^ A3E_ A3E` A3E{ A3E| A3E} A3E~ A3\ -F1 A3F2 A3F3 A3F4 A3F5 A3F7 A3F9 A3FA A3FD A3FF A3FG A3FH A3FI A3FJ A3FK A3FL\ - A3FM A3FN A3FQ A3FR A3FT A3FU A3FV A3FW A3FX A3FY A3FZ A3Fj A3Fk A3Fl A3Fm A\ -3Fn A3Fo A3Fp A3Fq A3Fr A3Fs A3Ft A3Fw A3Fx A3Fy A3Fz A3F- A3F. A3F/ A3F: A3F\ -; A3F< A3F= A3F> A3F? A3F@ A3F] A3F_ A3F` A3F| A3F} A3F~ A3G0 A3G1 A3G2 A3G3 \ -A3G5 A3G6 A3G7 A3G8 A3G9 A3GA A3GB A3GC A3GD A3GE A3GF A3GG A3GQ A3GR A3GS A3\ -GT A3GU A3GV A3GW A3GX A3GY A3GZ A3Ga A3Gb A3Gc A3Gd A3Gf A3Gg A3Gh A3Gi A3Gj\ - A3Gl A3Gm A3Gn A3Go A3Gq A3Gr A3Gs A3Gt A3Gu A3Gv A3Gw A3Gx A3Gy A3Gz A3G# A\ -3G$ A3G% A3G' A3G) A3G* A3G+ A3G- A3G/ A3G: A3G; A3G< A3G> A3G? A3G@ A3G[ A3G\ -] A3G^ A3G_ A3G` A3G{ A3G| A3G} A3G~ A3H0 A3H1 A3H3 A3H4 A3H5 A3H6 A3H7 A3HA \ -A3HB A3HC A3HE A3HF A3HG A3HH A3HI A3HJ A3HL A3HM A3HN A3HO A3HQ A3HR A3HS A3\ -HT A3HU A3HW A3HX A3HY A3HZ A3Ha A3Hb A3Hc A3Hd A3He A3Hf A3Hg A3Hh A3Hi A3Hj\ - A3Hk A3Hm A3Hn A3Ho A3Hp A3Hq A3Hs A3Ht A3Hu A3Hv A3Hx A3Hz A3H# A3H$ A3H% A\ -3H& A3H' A3H( A3H) A3H* A3H+ A3H, A3H- A3H/ A3H: A3H; A3H< A3H= A3H> A3H@ A3H\ -[ A3H] A3H^ A3H{ A3H| A3H} A3H~ A3I0 A3I1 A3I2 A3I3 A3I4 A3I5 A3I9 A3IC A3IE \ -A3IF A3IH A3II A3IJ A3IK A3IL A3IM A3IN A3IO A3IP A3IQ A3IR A3IS A3IT A3IU A3\ -IW A3IX A3IY A3Id A3Ie A3Ig A3Ih A3Ij A3Ik A3Il A3Im A3In A3Io A3Ip A3Iq A3Ir\ - A3Is A3It A3Iu A3Iv A3Iw A3Iy A3I# A3I% A3I& A3I( A3I) A3I+ A3I, A3I- A3I. A\ -3I/ A3I: A3I; A3I< A3I= A3I> A3I? A3I@ A3I[ A3I] A3I_ A3I` A3I| A3I} A3I~ A3J\ -0 A3J1 A3J3 A3J4 A3J5 A3J6 A3J7 A3J9 A3JA A3JD A3JF A3JG A3JH A3JI A3JJ A3JK \ -A3JL A3JM A3JN A3JP A3JQ A3JR A3JS A3JT A3JV A3JW A3JX A3JY A3JZ A3Jb A3Jc A3\ -Jd A3Jf A3Jh A3Ji A3Jk A3Jl A3Jm A3Jn A3Jo A3Jp A3Jr A3Js A3Jt A3Ju A3Jv A3Jx\ - A3Jy A3Jz A3J# A3J$ A3J& A3J( A3J) A3J* A3J. A3J/ A3J: A3J; A3J< A3J= A3J> A\ -3J? A3J@ A3J[ A3J^ A3J` A3J{ A3J} A3J~ A3K1 A3K2 A3K3 A3K4 A3K5 A3K7 A3K8 A3K\ -A A3KB A3KC A3KD A3KE A3KF A3KG A3KH A3KI A3KK A3KL A3KM A3KQ A3KR A3KS A3KT \ -A3KU A3KW A3KX A3KZ A3Ka A3Kb A3Kc A3Kd A3Ke A3Kf A3Kg A3Kh A3Ki A3Kj A3Km A3\ -Kn A3Ko A3Kp A3Kq A3Ks A3Kt A3Ku A3Kv A3Kw A3Ky A3Kz A3K$ A3K% A3K& A3K' A3K(\ - A3K) A3K* A3K, A3K. A3K/ A3K: A3K; A3K< A3K= A3K> A3K? A3K@ A3K] A3K^ A3K_ A\ -3K{ A3K| A3K} A3K~ A3L0 A3L1 A3L2 A3L3 A3L4 A3L5 A3L8 A3LC A3LD A3LE A3LF A3L\ -G A3LH A3LI A3LM A3LN A3LO A3LP A3LQ A3LR A3LS A3LT A3LU A3LV A3LW A3La A3Lc \ -A3Ld A3Le A3Lf A3Lg A3Lh A3Li A3Lj A3Lm A3Ln A3Lp A3Lq A3Lr A3Ls A3Lt A3Lu A3\ -Lv A3Lw A3Ly A3Lz A3L# A3L$ A3L% A3L& A3L) A3L, A3L- A3L. A3L/ A3L: A3L; A3L<\ - A3L= A3L> A3L] A3L^ A3L` A3L{ A3L| A3L} A3L~ A3M0 A3M1 A3M3 A3M5 A3M6 A3M8 A\ -3M9 A3MA A3MB A3MC A3MD A3ME A3MF A3MI A3MJ A3ML A3MM A3MN A3MO A3MP A3MQ A3M\ -R A3MS A3MU A3MV A3MY A3MZ A3Ma A3Mb A3Mc A3Md A3Me A3Mj A3Mm A3Mn A3Mo A3Mp \ -A3Mq A3Mr A3Ms A3Mt A3Mu A3Mv A3Mw A3Mx A3Mz A3M# A3M& A3M' A3M( A3M) A3M* A3\ -M+ A3M, A3M- A3M/ A3M< A3M= A3M> A3M? A3M@ A3M[ A3M] A3M^ A3M_ A3M{ A3M| A3M}\ - A3M~ A3N1 A3N2 A3N3 A3N4 A3N5 A3N6 A3N7 A3N9 A3NA A3ND A3NE A3NF A3NG A3NH A\ -3NI A3NJ A3NK A3NL A3NM A3NN A3NP A3NQ A3NR A3NS A3NT A3NU A3NV A3NW A3NX A3N\ -k A3Nl A3Nm A3Nn A3No A3Np A3Nq A3Nr A3Ns A3N% A3N( A3N) A3N- A3N. A3N/ A3N: \ -A3N; A3N< A3N= A3N> A3N? A3N@ A3N] A3N^ A3N_ A3N` A3N| A3N} A3O0 A3O1 A3O2 A3\ -O4 A3O5 A3O6 A3O7 A3O8 A3O9 A3OA A3OB A3OC A3OD A3OE A3OF A3OG A3OH A3OI A3OJ\ - A3OL A3OM A3OP A3OQ A3OR A3OS A3OT A3OU A3OV A3OW A3OX A3OY A3OZ A3Oa A3Ob A\ -3Oc A3Of A3Og A3Oh A3Oi A3Oj A3Om A3On A3Oo A3Oq A3Or A3Os A3Ot A3Ou A3Ov A3O\ -w A3Ox A3Oy A3Oz A3O# A3O$ A3O% A3O& A3O' A3O) A3O* A3O+ A3O, A3O/ A3O: A3O; \ -A3O< A3O= A3O? A3O@ A3O[ A3O] A3O^ A3O_ A3O` A3O{ A3O| A3O} A3O~ A3P0 A3P1 A3\ -P2 A3P3 A3P5 A3P6 A3P7 A3P8 A3PA A3PB A3PC A3PD A3PF A3PG A3PH A3PI A3PJ A3PK\ - A3PL A3PM A3PN A3PO A3PP A3PQ A3PR A3PS A3PT A3PU A3PV A3PW A3PX A3PZ A3Pa A\ -3Pb A3Pc A3Pd A3Pe A3Pf A3Pg A3Ph A3Pi A3Pj A3Pk A3Pl A3Pm A3Pn A3Po A3Pp A3P\ -q A3Ps A3Pt A3Pu A3Pv A3Pw A3Px A3P# A3P$ A3P% A3P& A3P' A3P( A3P) A3P* A3P+ \ -A3P, A3P- A3P. A3P: A3P; A3P< A3P= A3P> A3P? A3P@ A3P[ A3P] A3P^ A3P_ A3P{ A3\ -P} A3P~ A3Q0 A3Q1 A3Q2 A3Q3 A3Q4 A3Q5 A3Q6 A3QB A3QE A3QF A3QG A3QH A3QJ A3QK\ - A3QL A3QM A3QN A3QO A3QP A3QQ A3QR A3QS A3QT A3QU A3QV A3QY A3QZ A3Qe A3Qg A\ -3Qh A3Qi A3Qj A3Qk A3Ql A3Qm A3Qn A3Qo A3Qp A3Qq A3Qr A3Qs A3Qt A3Qu A3Qv A3Q\ -x A3Qz A3Q$ A3Q' A3Q( A3Q) A3Q, A3Q- A3Q. A3Q/ A3Q: A3Q; A3Q< A3Q= A3Q> A3Q? \ -A3Q@ A3Q[ A3Q] A3Q^ A3Q{ A3Q} A3Q~ A3R0 A3R1 A3R2 A3R3 A3R6 A3R7 A3R8 A3R9 A3\ -RD A3RE A3RF A3RI A3RJ A3RK A3RL A3RM A3RN A3RO A3RQ A3RR A3RS A3RT A3RU A3RV\ - A3RW A3RX A3RY A3RZ A3Rb A3Rd A3Re A3Rh A3Rk A3Rl A3Rm A3Rn A3Ro A3Rp A3Rq A\ -3Rs A3Rt A3Ru A3Rv A3Rw A3Rx A3Ry A3Rz A3R# A3R& A3R) A3R, A3R- A3R. A3R/ A3R\ -: A3R; A3R< A3R= A3R> A3R? A3R@ A3R[ A3R] A3R^ A3R` A3R{ A3R} A3R~ A3S2 A3S3 \ -A3S4 A3S5 A3S9 A3SA A3SB A3SC A3SD A3SE A3SF A3SG A3SH A3SI A3SJ A3SL A3SN A3\ -SO A3SP A3SR A3ST A3SU A3SV A3SW A3SX A3SZ A3Sb A3Sc A3Sd A3Se A3Sf A3Sg A3Sh\ - A3Si A3Sj A3Sk A3Sl A3Sm A3Sn A3So A3St A3Su A3Sv A3Sw A3Sy A3Sz A3S# A3S$ A\ -3S& A3S' A3S( A3S) A3S* A3S+ A3S- A3S/ A3S: A3S; A3S< A3S= A3S> A3S? A3S@ A3S\ -[ A3S] A3S` A3S{ A3S| A3S} A3S~ A3T0 A3T1 A3T2 A3T3 A3T4 A3T5 A3T6 A3T7 A3TD \ -A3TE A3TF A3TG A3TH A3TI A3TK A3TL A3TN A3TO A3TP A3TQ A3TR A3TS A3TT A3TU A3\ -TV A3TW A3TX A3Tb A3Tc A3Td A3Te A3Tf A3Tg A3Th A3Ti A3Tj A3Tk A3To A3Tp A3Tq\ - A3Tr A3Ts A3Tt A3Tu A3Tv A3Tw A3Tx A3Ty A3Tz A3T# A3T$ A3T% A3T& A3T' A3T( A\ -3T+ A3T, A3T. A3T/ A3T: A3T; A3T< A3T= A3T] A3T` A3T| A3T} A3T~ A3U0 A3U1 A3U\ -2 A3U3 A3U4 A3U7 A3U8 A3U9 A3UA A3UB A3UC A3UD A3UE A3UF A3UH A3UI A3UJ A3UL \ -A3UM A3UN A3UO A3UP A3UQ A3UR A3US A3UT A3UV A3UX A3UZ A3Ua A3Ub A3Uc A3Ud A3\ -Ue A3Uf A3Ug A3Ui A3Uj A3Uo A3Up A3Uq A3Ur A3Us A3Ut A3Uu A3Uv A3Uw A3Ux A3U#\ - A3U$ A3U% A3U& A3U' A3U( A3U) A3U* A3U+ A3U, A3U- A3U. A3U: A3U< A3U= A3U> A\ -3U? A3U@ A3U[ A3U] A3U^ A3U_ A3U` A3U| A3U} A3U~ A3V1 A3V2 A3V3 A3V4 A3V5 A3V\ -6 A3V7 A3VB A3VC A3VD A3VE A3VF A3VG A3VH A3VI A3VJ A3VK A3VL A3VM A3VN A3VO \ -A3VP A3VQ A3VT A3VU A3VV A3VW A3VX A3VY A3Va A3Vb A3Vl A3Vm A3Vn A3Vo A3Vp A3\ -Vq A3Vr A3Vs A3Vt A3Vv A3Vw A3Vx A3Vz A3V$ A3V% A3V& A3V( A3V* A3V+ A3V- A3V.\ - A3V/ A3V: A3V; A3V< A3V= A3V> A3V? A3V@ A3V[ A3WA A3WB A3WC A3WD A3WE A3WF A\ -3WG A3WH A3WI A3WJ A3WL A3WM A3WO A3WP A3WQ A3WS A3WT A3WU A3WV A3WW A3WX A3W\ -Y A3WZ A3Wa A3Wb A3Wc A3Wd A3We A3Wg A3Wh A3Wi A3Wj A3Wl A3Wn A3Wo A3Wp A3Wq \ -A3Wr A3Wt A3Wu A3Wv A3Ww A3Wx A3Wy A3Wz A3W# A3W$ A3W% A3W& A3W' A3W) A3W+ A3\ -W, A3W- A3W/ A3W: A3W; A3W< A3W= A3W? A3W@ A3W[ A3W] A3W^ A3W_ A3W` A3W{ A3W|\ - A3W} A3W~ A3X0 A3X1 A3X2 A3X4 A3X5 A3X6 A3X7 A3X8 A3XB A3XC A3XD A3XE A3XF A\ -3XG A3XH A3XI A3XJ A3XK A3XL A3XM A3XO A3XP A3XQ A3XR A3XS A3XU A3XV A3XW A3X\ -X A3XZ A3Xa A3Xb A3Xc A3Xd A3Xe A3Xf A3Xg A3Xh A3Xi A3Xj A3Xk A3Xl A3Xm A3Xn \ -A3Xp A3Xq A3Xr A3Xs A3Xt A3Xv A3Xw A3Xx A3X# A3X$ A3X% A3X& A3X' A3X( A3X) A3\ -X* A3X+ A3X, A3X- A3X. A3X/ A3X; A3X< A3X= A3X> A3X? A3X[ A3X] A3X^ A3X_ A3X`\ - A3X{ A3X~ A3Y0 A3Y1 A3Y2 A3Y3 A3Y4 A3Y5 A3Y6 A3Y7 A3YC A3YD A3YE A3YF A3YH A\ -3YJ A3YK A3YL A3YM A3YN A3YO A3YP A3YQ A3YR A3YS A3YT A3YU A3YV A3YY A3YZ A3Y\ -a A3Yg A3Yh A3Yi A3Yj A3Yk A3Yl A3Ym A3Yn A3Yo A3Yp A3Yq A3Yr A3Ys A3Yt A3Yu \ -A3Yv A3Yw A3Yx A3Y# A3Y% A3Y' A3Y) A3Y+ A3Y, A3Y- A3Y/ A3Y: A3Y; A3Y< A3Y= A3\ -Y> A3Y? A3Y@ A3Y[ A3Y] A3Y^ A3Y_ A3Y{ A3Y~ A3Z0 A3Z1 A3Z2 A3Z3 A3Z4 A3Z5 A3Z6\ - A3Z7 A3Z8 A3Z9 A3ZA A3ZE A3ZF A3ZG A3ZM A3ZN A3ZO A3ZP A3ZR A3ZS A3ZT A3ZU A\ -3ZW A3ZY A3ZZ A3Za A3Zc A3Ze A3Zf A3Zi A3Zk A3Zl A3Zn A3Zo A3Zp A3Zq A3Zr A3Z\ -t A3Zu A3Zv A3Zy A3Zz A3Z# A3Z$ A3Z' A3Z( A3Z* A3Z- A3Z. A3Z/ A3Z: A3Z; A3Z< \ -A3Z= A3Z> A3Z? A3Z@ A3Z[ A3Z] A3Z^ A3Z_ A3Z{ A3Z} A3Z~ A3a1 A3a3 A3a4 A3a5 A3\ -a7 A3a8 A3a9 A3aB A3aC A3aD A3aE A3aF A3aG A3aH A3aI A3aJ A3aK A3aN A3aO A3aP\ - A3aQ A3aT A3aU A3aV A3aW A3aZ A3aa A3ab A3ad A3ae A3af A3ag A3ah A3ai A3aj A\ -3ak A3al A3am A3ap A3aq A3ar A3as A3av A3aw A3ax A3ay A3a% A3a& A3a' A3a( A3a\ -) A3a* A3a+ A3a, A3a- A3a/ A3a: A3a; A3a= A3a> A3a? A3a@ A3a[ A3a] A3a^ A3a| \ -A3a} A3a~ A3b0 A3b1 A3b2 A3b3 A3b4 A3b5 A3b6 A3b7 A3b8 A3b9 A3bE A3bF A3bG A3\ -bH A3bI A3bJ A3bK A3bN A3bO A3bQ A3bR A3bS A3bT A3bU A3bV A3bW A3bX A3bY A3bc\ - A3bd A3be A3bf A3bg A3bh A3bi A3bj A3bk A3bm A3bn A3bo A3bp A3br A3bs A3bt A\ -3bu A3bv A3bw A3bx A3by A3bz A3b# A3b$ A3b% A3b& A3b' A3b( A3b) A3b+ A3b- A3b\ -. A3b/ A3b: A3b; A3b< A3b= A3b> A3b@ A3b[ A3b] A3b` A3b{ A3b| A3b} A3b~ A3c0 \ -A3c1 A3c2 A3c3 A3c4 A3c7 A3c9 A3cA A3cB A3cC A3cD A3cE A3cF A3cJ A3cL A3cM A3\ -cP A3cQ A3cR A3cS A3cT A3cU A3cX A3cY A3cZ A3cb A3cc A3cd A3ce A3cf A3cg A3ci\ - A3cj A3cm A3co A3cp A3cq A3cr A3cs A3ct A3cu A3cv A3cw A3cx A3cy A3cz A3c# A\ -3c% A3c& A3c' A3c( A3c) A3c* A3c+ A3c, A3c- A3c< A3c= A3c> A3c? A3c@ A3c[ A3c\ -] A3c^ A3c_ A3c` A3c{ A3c| A3c} A3c~ A3d1 A3d2 A3d3 A3d4 A3d5 A3d6 A3d7 A3d8 \ -A3d9 A3dB A3dF A3dG A3dH A3dI A3dJ A3dK A3dL A3dM A3dN A3dO A3dP A3dT A3dU A3\ -dV A3dW A3dX A3dY A3dZ A3db A3dc A3dm A3dn A3do A3dp A3dq A3dr A3ds A3dt A3du\ - A3dv A3dx A3dy A3dz A3d$ A3d& A3d: A3d; A3d< A3d= A3d> A3d? A3d@ A3d[ A3d] A\ -3d_ A3d` A3d{ A3d| A3d~ A3e0 A3e2 A3e3 A3e4 A3e5 A3e6 A3e8 A3e9 A3eA A3eB A3e\ -C A3eD A3eE A3eF A3eG A3eH A3eI A3eJ A3eU A3eV A3eW A3eX A3eY A3ea A3eb A3ec \ -A3ed A3ee A3ef A3eg A3eh A3ei A3ej A3ek A3el A3em A3en A3eo A3ep A3er A3es A3\ -et A3ew A3ex A3ey A3ez A3e$ A3e% A3e& A3e' A3e( A3e) A3e* A3e+ A3e, A3e- A3e.\ - A3e/ A3e: A3e; A3e< A3e= A3e? A3e@ A3e[ A3e^ A3e` A3e{ A3e| A3e} A3e~ A3f1 A\ -3f2 A3f3 A3f4 A3f5 A3f6 A3f7 A3f8 A3f9 A3fA A3fB A3fC A3fD A3fF A3fG A3fH A3f\ -I A3fK A3fL A3fM A3fN A3fO A3fQ A3fS A3fT A3fU A3fV A3fW A3fX A3fY A3fZ A3fa \ -A3fb A3fc A3fd A3ff A3fh A3fi A3fj A3fk A3fl A3fn A3fo A3fp A3fs A3ft A3fu A3\ -fv A3fw A3fx A3fy A3fz A3f# A3f$ A3f% A3f& A3f' A3f( A3f) A3f+ A3f, A3f- A3f/\ - A3f: A3f; A3f< A3f= A3f? A3f@ A3f[ A3f] A3f^ A3f_ A3f` A3f{ A3f| A3f} A3f~ A\ -3g0 A3g1 A3g2 A3g3 A3g5 A3g6 A3g7 A3g8 A3gC A3gF A3gG A3gH A3gI A3gJ A3gL A3g\ -M A3gN A3gO A3gP A3gQ A3gR A3gS A3gT A3gU A3gV A3gW A3gX A3gY A3ga A3gb A3gc \ -A3gg A3gh A3gi A3gl A3gm A3gn A3go A3gp A3gq A3gr A3gs A3gt A3gu A3gv A3gw A3\ -gx A3gz A3g# A3g% A3g& A3g* A3g+ A3g, A3g/ A3g: A3g; A3g< A3g= A3g> A3g? A3g@\ - A3g[ A3g] A3g^ A3g_ A3g` A3g{ A3g} A3h0 A3h1 A3h2 A3h4 A3h5 A3h6 A3h7 A3hB A\ -3hC A3hD A3hE A3hF A3hG A3hH A3hI A3hJ A3hK A3hL A3hM A3hN A3hR A3hU A3hW A3h\ -X A3hY A3hZ A3ha A3hc A3hd A3he A3hf A3hg A3hh A3hi A3hj A3hk A3hl A3hm A3hn \ -A3ho A3hp A3hr A3hs A3ht A3hv A3hw A3hx A3hy A3hz A3h$ A3h% A3h& A3h' A3h( A3\ -h) A3h* A3h+ A3h, A3h- A3h. A3h/ A3h: A3h; A3h@ A3h[ A3h` A3h{ A3h| A3h} A3h~\ - A3i0 A3i1 A3i2 A3i3 A3i5 A3i6 A3i7 A3i8 A3i9 A3iB A3iC A3iE A3iI A3iK A3iL A\ -3iM A3iN A3iO A3iP A3iQ A3iR A3iS A3iT A3iU A3iV A3iX A3iY A3iZ A3ia A3ib A3i\ -e A3if A3ii A3il A3im A3in A3io A3ip A3iq A3ir A3is A3it A3iu A3iv A3iw A3ix \ -A3iz A3i# A3i$ A3i% A3i( A3i, A3i- A3i: A3i; A3i= A3i> A3i? A3i@ A3i[ A3i] A3\ -i^ A3i_ A3i` A3i} A3i~ A3j0 A3j1 A3j2 A3j3 A3j4 A3j5 A3j6 A3j7 A3jA A3jB A3jF\ - A3jG A3jH A3jI A3jJ A3jK A3jL A3jN A3jO A3jP A3jR A3jS A3jT A3jU A3jV A3jW A\ -3jX A3jZ A3je A3jf A3jg A3jh A3ji A3jj A3jk A3jl A3jn A3jo A3jp A3jr A3js A3j\ -t A3ju A3jv A3jw A3jx A3jy A3jz A3j# A3j$ A3j% A3j* A3j+ A3j, A3j- A3j. A3j; \ -A3j< A3j= A3j@ A3j[ A3j] A3j^ A3j_ A3j` A3j{ A3j| A3j} A3j~ A3k1 A3k3 A3k4 A3\ -k5 A3k6 A3k7 A3k8 A3kA A3kB A3kC A3kF A3kG A3kH A3kI A3kJ A3kK A3kL A3kM A3kN\ - A3kO A3kP A3kR A3kS A3kT A3kV A3kW A3kX A3kY A3ka A3kb A3kc A3ke A3ki A3kj A\ -3kk A3kl A3km A3kn A3ko A3kp A3kq A3kr A3kt A3ku A3kw A3kx A3ky A3k# A3k$ A3k\ -% A3k& A3k( A3k) A3k* A3k- A3k. A3k/ A3k: A3k; A3k< A3k= A3k> A3k@ A3k^ A3k_ \ -A3k` A3k| A3k} A3k~ A3l0 A3l2 A3l3 A3l5 A3l6 A3l7 A3l8 A3lA A3lB A3lC A3lD A3\ -lE A3lF A3lH A3lI A3lJ A3lK A3lN A3lO A3lP A3lQ A3lR A3lS A3lT A3lV A3lY A3la\ - A3lb A3lc A3ld A3ln A3lo A3lp A3lq A3lr A3ls A3lt A3lu A3lv A3l) A3l* A3l- A\ -3l: A3l; A3l< A3l= A3l> A3l? A3l@ A3l[ A3l] A3l^ A3l` A3l{ A3l| A3l} A3m0 A3m\ -1 A3m3 A3m4 A3m5 A3m7 A3m8 A3m9 A3mA A3mB A3mC A3mD A3mE A3mF A3mG A3mH A3mI \ -A3mJ A3mK A3mL A3mM A3mO A3mP A3mS A3mT A3mV A3mW A3mX A3mY A3mZ A3ma A3mc A3\ -md A3me A3mf A3mg A3mh A3mi A3mj A3mk A3ml A3mm A3mn A3mo A3mp A3mq A3ms A3mt\ - A3mu A3mx A3my A3mz A3m# A3m% A3m& A3m' A3m( A3m) A3m* A3m+ A3m, A3m- A3m. A\ -3m/ A3m: A3m; A3m< A3m= A3m> A3m@ A3m[ A3m] A3m_ A3m{ A3m| A3m} A3n0 A3n1 A3n\ -2 A3n3 A3n4 A3n5 A3n6 A3n7 A3n8 A3n9 A3nA A3nB A3nC A3nD A3nF A3nG A3nH A3nI \ -A3nJ A3nL A3nM A3nN A3nO A3nP A3nS A3nT A3nU A3nV A3nW A3nX A3nY A3nZ A3na A3\ -nb A3nc A3nd A3ne A3nf A3ni A3nj A3nk A3nl A3nm A3nn A3no A3np A3nq A3ns A3nt\ - A3nu A3nv A3nw A3nx A3ny A3nz A3n# A3n$ A3n% A3n& A3n' A3n( A3n* A3n+ A3n, A\ -3n- A3n. A3n/ A3n; A3n< A3n= A3n> A3n@ A3n] A3n^ A3n_ A3n` A3n{ A3n| A3n} A3n\ -~ A3o0 A3o1 A3o2 A3o3 A3o4 A3o5 A3o7 A3o8 A3o9 A3oD A3oE A3oG A3oH A3oI A3oK \ -A3oM A3oN A3oO A3oP A3oQ A3oR A3oS A3oT A3oU A3oV A3oW A3oX A3oZ A3oa A3oc A3\ -od A3oh A3oi A3oj A3ok A3om A3on A3oo A3op A3oq A3or A3os A3ot A3ou A3ov A3ow\ - A3ox A3oy A3oz A3o# A3o% A3o& A3o' A3o) A3o* A3o+ A3o, A3o- A3o/ A3o; A3o< A\ -3o= A3o> A3o? A3o@ A3o[ A3o] A3o^ A3o_ A3o` A3o{ A3o| A3o} A3p1 A3p2 A3p4 A3p\ -5 A3p6 A3p7 A3p8 A3pA A3pB A3pC A3pD A3pE A3pF A3pG A3pH A3pI A3pJ A3pK A3pL \ -A3pM A3pN A3pQ A3pR A3pS A3pT A3pV A3pW A3pX A3pY A3pZ A3pa A3pc A3pd A3pe A3\ -pf A3pg A3ph A3pi A3pj A3pk A3pl A3pm A3pn A3po A3pu A3pw A3px A3py A3pz A3p#\ - A3p' A3p( A3p) A3p* A3p+ A3p, A3p- A3p. A3p/ A3p: A3p; A3p< A3p= A3p> A3p[ A\ -3p] A3p_ A3p` A3p{ A3p| A3p} A3p~ A3q0 A3q1 A3q2 A3q3 A3q4 A3q6 A3q7 A3q8 A3q\ -9 A3qA A3qB A3qD A3qE A3qF A3qJ A3qN A3qO A3qP A3qQ A3qR A3qS A3qT A3qU A3qV \ -A3qW A3qX A3qY A3qZ A3qa A3qb A3qd A3qe A3qf A3qj A3qm A3qn A3qo A3qp A3qq A3\ -qr A3qs A3qt A3qu A3qv A3qw A3qy A3q# A3q$ A3q% A3q& A3q' A3q* A3q- A3q. A3q:\ - A3q= A3q> A3q? A3q@ A3q[ A3q] A3q^ A3q_ A3q{ A3q| A3q} A3r1 A3r2 A3r3 A3r4 A\ -3r5 A3r6 A3r7 A3r8 A3rA A3rG A3rH A3rI A3rJ A3rK A3rL A3rN A3rO A3rR A3rS A3r\ -T A3rU A3rV A3rW A3rX A3rY A3ra A3re A3rf A3rh A3ri A3rj A3rk A3rl A3rm A3rn \ -A3ro A3rr A3rt A3ru A3rv A3rw A3rx A3ry A3rz A3r# A3r$ A3r% A3r( A3r) A3r* A3\ -r+ A3r, A3r- A3r/ A3r: A3r< A3r= A3r? A3r[ A3r] A3r^ A3r_ A3r` A3r{ A3r| A3r}\ - A3r~ A3s2 A3s4 A3s5 A3s6 A3s7 A3s8 A3s9 A3sA A3sC A3sI A3sJ A3sK A3sL A3sM A\ -3sN A3sO A3sP A3sQ A3sS A3sU A3sV A3sW A3sX A3sY A3sZ A3sa A3sc A3sf A3sg A3s\ -j A3sk A3sl A3sm A3sn A3so A3sp A3sq A3sr A3sv A3sz A3s$ A3s% A3s& A3s( A3s) \ -A3s* A3s, A3s/ A3s: A3s; A3s< A3s= A3s> A3s? A3s@ A3s[ A3s] A3s` A3s{ A3s| A3\ -s} A3s~ A3t0 A3t1 A3t2 A3t3 A3t5 A3t6 A3t9 A3tB A3tC A3tD A3tE A3tF A3tG A3tI\ - A3tJ A3tL A3tP A3tQ A3tR A3tS A3tT A3tV A3tX A3tY A3tZ A3tc A3td A3te A3to A\ -3tp A3tq A3tr A3ts A3tt A3tu A3tv A3tw A3tx A3tz A3t# A3t$ A3t& A3t( A3t) A3t\ -* A3t, A3t- A3t: A3t; A3t< A3t= A3t> A3t? A3t@ A3t[ A3t] A3t^ A3t_ A3uD A3uE \ -A3uF A3uG A3uH A3uI A3uJ A3uK A3uL A3uM A3uN A3uP A3uQ A3uT A3uU A3uW A3uX A3\ -uY A3uZ A3ua A3ub A3uc A3ud A3ue A3uf A3ug A3uh A3ui A3uj A3uk A3ul A3um A3un\ - A3uo A3up A3uq A3ur A3us A3ut A3uu A3uv A3uy A3uz A3u# A3u$ A3u& A3u' A3u( A\ -3u) A3u* A3u+ A3u, A3u- A3u. A3u/ A3u: A3u; A3u< A3u= A3u> A3u@ A3u[ A3u] A3u\ -^ A3u` A3u| A3u} A3u~ A3v1 A3v2 A3v3 A3v4 A3v5 A3v6 A3v7 A3v8 A3v9 A3vA A3vB \ -A3vC A3vD A3vE A3vF A3vG A3vI A3vJ A3vK A3vM A3vN A3vO A3vP A3vQ A3vS A3vT A3\ -vU A3vV A3vW A3vX A3vY A3vZ A3va A3vb A3vc A3vd A3ve A3vf A3vg A3vh A3vj A3vk\ - A3vl A3vn A3vo A3vp A3vq A3vr A3vt A3vv A3vw A3vx A3vy A3vz A3v# A3v$ A3v% A\ -3v& A3v' A3v( A3v) A3v* A3v- A3v. A3v/ A3v: A3v< A3v= A3v> A3v? A3v] A3v^ A3v\ -_ A3v` A3v{ A3v| A3v} A3v~ A3w0 A3w1 A3w2 A3w3 A3w4 A3w6 A3w7 A3w8 A3w9 A3wA \ -A3wG A3wH A3wI A3wJ A3wK A3wN A3wO A3wP A3wQ A3wR A3wS A3wT A3wU A3wV A3wW A3\ -wX A3wY A3wZ A3wa A3wb A3wc A3wd A3we A3wi A3wj A3wk A3wl A3wo A3wp A3wq A3wr\ - A3ws A3wt A3wu A3wv A3ww A3wx A3wy A3wz A3w# A3w$ A3w& A3w' A3w( A3w+ A3w, A\ -3w- A3w. A3w: A3w; A3w< A3w= A3w> A3w? A3w@ A3w[ A3w] A3w^ A3w_ A3w` A3w{ A3w\ -| A3w} A3w~ A3x2 A3x3 A3x4 A3x5 A3x7 A3x8 A3x9 A3xA A3xB A3xD A3xE A3xF A3xG \ -A3xH A3xI A3xJ A3xK A3xL A3xM A3xN A3xO A3xP A3xQ A3xT A3xW A3xX A3xY A3xZ A3\ -xa A3xe A3xf A3xg A3xh A3xi A3xj A3xk A3xl A3xm A3xn A3xo A3xp A3xq A3xr A3xv\ - A3xy A3xz A3x# A3x$ A3x% A3x' A3x( A3x) A3x* A3x+ A3x, A3x- A3x. A3x/ A3x: A\ -3x; A3x< A3x= A3x> A3x] A3x^ A3x` A3x{ A3x| A3x} A3x~ A3y0 A3y1 A3y2 A3y3 A3y\ -4 A3y5 A3y9 A3yA A3yB A3yD A3yF A3yK A3yM A3yN A3yO A3yP A3yQ A3yR A3yS A3yT \ -A3yU A3yV A3yW A3yX A3yY A3yZ A3ya A3yb A3yc A3yd A3yf A3yh A3yk A3yp A3yq A3\ -yr A3ys A3yt A3yu A3yv A3yw A3yx A3yy A3yz A3y# A3y$ A3y% A3y& A3y( A3y* A3y+\ - A3y. A3y/ A3y; A3y= A3y> A3y@ A3y[ A3y] A3y^ A3y_ A3y` A3y| A3y} A3y~ A3z2 A\ -3z3 A3z4 A3z5 A3z6 A3z7 A3z8 A3z9 A3zC A3zH A3zI A3zJ A3zK A3zL A3zM A3zN A3z\ -O A3zP A3zS A3zT A3zU A3zV A3zW A3zX A3zY A3zZ A3zb A3zf A3zh A3zi A3zj A3zk \ -A3zl A3zm A3zn A3zo A3zp A3zs A3zu A3zv A3zw A3zx A3zy A3zz A3z# A3z$ A3z% A3\ -z' A3z) A3z* A3z+ A3z, A3z- A3z. A3z/ A3z; A3z> A3z? A3z[ A3z] A3z^ A3z_ A3z`\ - A3z{ A3z| A3z} A3z~ A3#0 A3#1 A3#5 A3#6 A3#7 A3#8 A3#9 A3#B A3#C A3#D A3#E A\ -3#G A3#J A3#K A3#L A3#M A3#N A3#O A3#P A3#Q A3#R A3#U A3#X A3#Y A3#Z A3#a A3#\ -b A3#c A3#e A3#i A3#j A3#k A3#l A3#m A3#n A3#o A3#p A3#q A3#r A3#s A3#t A3#v \ -A3#y A3#z A3## A3#$ A3#% A3#& A3#' A3#( A3#) A3#/ A3#; A3#< A3#= A3#> A3#? A3\ -#@ A3#[ A3#] A3#^ A3#` A3#~ A3$0 A3$1 A3$2 A3$3 A3$5 A3$6 A3$8 A3$9 A3$C A3$D\ - A3$E A3$F A3$G A3$H A3$J A3$L A3$P A3$R A3$S A3$T A3$V A3$W A3$X A3$Y A3$c A\ -3$d A3$e A3$f A3$p A3$q A3$r A3$s A3$t A3$u A3$v A3$w A3$x A3$y A3$z A3$% A3$\ -& A3$' A3$( A3$= A3$> A3$? A3$@ A3$[ A3$] A3$^ A3$_ A3$` A3${ A3$} A3%0 A3%1 \ -A3%3 A3%4 A3%5 A3%7 A3%9 A3%C A3%D A3%E A3%F A3%G A3%H A3%I A3%J A3%K A3%L A3\ -%M A3%W A3%X A3%Y A3%Z A3%b A3%c A3%d A3%e A3%f A3%g A3%h A3%k A3%l A3%m A3%n\ - A3%o A3%p A3%q A3%r A3%s A3%t A3%u A3%v A3%w A3%x A3%y A3%z A3%# A3%& A3%' A\ -3%( A3%) A3%* A3%+ A3%. A3%/ A3%: A3%; A3%< A3%= A3%> A3%? A3%@ A3%[ A3%] A3%\ -^ A3%_ A3%` A3%{ A3%| A3&0 A3&1 A3&2 A3&3 A3&4 A3&5 A3&6 A3&A A3&B A3&C A3&D \ -A3&E A3&F A3&G A3&H A3&I A3&J A3&K A3&L A3&M A3&N A3&O A3&P A3&Q A3&R A3&S A3\ -&T A3&U A3&V A3&W A3&X A3&Z A3&b A3&c A3&d A3&e A3&f A3&g A3&k A3&l A3&m A3&n\ - A3&o A3&p A3&q A3&r A3&s A3&t A3&u A3&v A3&w A3&x A3&y A3&z A3&# A3&% A3&& A\ -3&' A3&( A3&) A3&* A3&+ A3&. A3&/ A3&: A3&; A3&< A3&= A3&> A3&? A3&@ A3&[ A3&\ -] A3&^ A3&_ A3&` A3&{ A3&| A3'0 A3'1 A3'2 A3'3 A3'4 A3'5 A3'6 A3'9 A3'A A3'B \ -A3'F A3'I A3'J A3'K A3'L A3'M A3'N A3'O A3'P A3'Q A3'S A3'T A3'U A3'V A3'W A3\ -'Y A3'a A3'b A3'c A3'd A3'f A3'j A3'k A3'l A3'm A3'n A3'o A3'p A3'q A3'r A3's\ - A3'u A3'v A3'w A3'x A3'y A3'$ A3'% A3'& A3'' A3'( A3'- A3'. A3'/ A3': A3'; A\ -3'< A3'= A3'> A3'? A3'@ A3'[ A3'^ A3'_ A3'` A3'{ A3'| A3'~ A3(0 A3(1 A3(2 A3(\ -3 A3(4 A3(6 A3(7 A3(8 A3(B A3(C A3(D A3(H A3(I A3(J A3(K A3(L A3(N A3(O A3(P \ -A3(Q A3(R A3(S A3(T A3(U A3(V A3(X A3(a A3(b A3(c A3(d A3(e A3(g A3(i A3(j A3\ -(k A3(m A3(n A3(o A3(p A3(q A3(r A3(s A3(t A3(u A3(v A3(w A3(z A3(# A3(% A3(&\ - A3(' A3(( A3(, A3(- A3(. A3(< A3(= A3(> A3(? A3(@ A3([ A3(_ A3(` A3({ A3(| A\ -3(} A3(~ A3)0 A3)1 A3)2 A3)3 A3)4 A3)6 A3)7 A3)A A3)B A3)C A3)G A3)H A3)I A3)\ -J A3)K A3)M A3)N A3)O A3)P A3)Q A3)R A3)S A3)T A3)U A3)Y A3)b A3)c A3)d A3)h \ -A3)i A3)j A3)l A3)m A3)n A3)o A3)p A3)q A3)r A3)s A3)t A3)u A3)v A3)w A3)y A3\ -)# A3)$ A3)% A3)& A3)' A3)* A3)+ A3), A3)- A3). A3)/ A3): A3)> A3)@ A3)[ A3)]\ - A3)_ A3)` A3){ A3)| A3)} A3)~ A3*0 A3*1 A3*2 A3*5 A3*6 A3*7 A3*8 A3*9 A3*A A\ -3*B A3*E A3*I A3*K A3*L A3*M A3*N A3*O A3*P A3*Q A3*R A3*S A3*T A3*U A3*X A3*\ -Y A3*Z A3*a A3*b A3*c A3*g A3*h A3*k A3*l A3*m A3*n A3*o A3*p A3*q A3*r A3*s \ -A3*t A3*u A3*v A3*x A3*y A3*z A3*# A3*% A3*& A3** A3*+ A3*, A3*- A3*. A3*/ A3\ -*= A3*> A3*? A3*@ A3*[ A3*] A3*^ A3*_ A3*` A3*{ A3*| A3*~ A3+2 A3+3 A3+5 A3+6\ - A3+7 A3+8 A3+9 A3+A A3+E A3+F A3+G A3+H A3+I A3+J A3+K A3+L A3+M A3+N A3+P A\ -3+Q A3+T A3+U A3+W A3+X A3+Y A3+Z A3+a A3+b A3+c A3+f A3+g A3+h A3+i A3+j A3+\ -k A3+l A3+m A3+n A3+p A3+r A3+s A3+t A3+u A3+v A3+w A3+y A3+z A3+% A3+' A3+) \ -A3+* A3++ A3+, A3+- A3+. A3+: A3+< A3+= A3+> A3+? A3+@ A3+[ A3+] A3+^ A3+_ A3\ -+~ A3,0 A3,2 A3,3 A3,4 A3,5 A3,6 A3,7 A3,8 A3,9 A3,D A3,E A3,F A3,G A3,H A3,I\ - A3,J A3,K A3,L A3,M A3,O A3,P A3,Q A3,U A3,V A3,W A3,X A3,Y A3,Z A3,a A3,e A\ -3,f A3,g A3,q A3,r A3,s A3,t A3,u A3,v A3,w A3,x A3,y A3,+ A3,: A3,= A3,> A3,\ -? A3,@ A3,[ A3,] A3,^ A3,_ A3,` A3,{ A3,| A3,} A3-0 A3-2 A3-3 A3-5 A3-6 A3-8 \ -A3-B A3-C A3-D A3-F A3-G A3-H A3-I A3-J A3-K A3-L A3-M A3-N A3-O A3-Q A3-R A3\ --T A3-U A3-V A3-X A3-Y A3-Z A3-a A3-d A3-e A3-f A3-g A3-h A3-i A3-j A3-m A3-n\ - A3-o A3-p A3-q A3-r A3-s A3-t A3-u A3-v A3-w A3-x A3-y A3-z A3-# A3-$ A3-% A\ -3-' A3-( A3-) A3-* A3-+ A3-, A3-: A3-; A3-< A3-= A3-> A3-? A3-@ A3-[ A3-] A3-\ -^ A3-_ A3-` A3-{ A3-| A3-} A3.0 A3.2 A3.3 A3.4 A3.5 A3.6 A3.7 A3.8 A3.B A3.C \ -A3.D A3.E A3.F A3.G A3.H A3.I A3.J A3.K A3.L A3.M A3.N A3.O A3.P A3.Q A3.R A3\ -.S A3.T A3.U A3.V A3.W A3.X A3.Y A3.a A3.c A3.d A3.e A3.f A3.g A3.h A3.j A3.l\ - A3.m A3.n A3.o A3.p A3.q A3.r A3.s A3.t A3.u A3.v A3.w A3.x A3.y A3.z A3.% A\ -3.& A3.' A3.( A3.) A3.* A3.+ A3.- A3./ A3.: A3.; A3.< A3.= A3.> A3.? A3.@ A3.\ -[ A3.] A3.^ A3._ A3.` A3.{ A3.| A3.~ A3/0 A3/1 A3/2 A3/3 A3/4 A3/5 A3/6 A3/A \ -A3/B A3/C A3/H A3/J A3/K A3/L A3/M A3/N A3/O A3/P A3/Q A3/R A3/T A3/V A3/W A3\ -/X A3/Z A3/a A3/b A3/c A3/d A3/e A3/f A3/g A3/k A3/l A3/m A3/n A3/o A3/p A3/q\ - A3/r A3/s A3/t A3/v A3/w A3/x A3/y A3/$ A3/% A3/& A3/' A3/( A3/) A3/* A3/, A\ -3/. A3// A3/: A3/; A3/< A3/= A3/> A3/? A3/@ A3/] A3/_ A3/` A3/{ A3/} A3:0 A3:\ -1 A3:2 A3:3 A3:4 A3:5 A3:6 A3:9 A3:B A3:C A3:D A3:E A3:H A3:I A3:J A3:K A3:M \ -A3:N A3:O A3:P A3:Q A3:R A3:S A3:T A3:U A3:V A3:W A3:X A3:Z A3:b A3:c A3:d A3\ -:e A3:f A3:i A3:j A3:k A3:l A3:p A3:q A3:r A3:s A3:t A3:u A3:v A3:w A3:x A3:#\ - A3:$ A3:% A3:' A3:( A3:) A3:- A3:. A3:/ A3:: A3:; A3:= A3:> A3:? 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A4L/ A\ -4L: A4L; A4L< A4L= A4L> A4L] A4L^ A4L_ A4L` A4L{ A4L| A4L} A4L~ A4M0 A4M1 A4M\ -2 A4M3 A4M4 A4M5 A4M6 A4M7 A4MA A4MB A4MC A4MD A4ME A4MF A4MJ A4MK A4ML A4MM \ -A4MN A4MO A4MP A4MQ A4MR A4MS A4MT A4MU A4MV A4MW A4MX A4MY A4MZ A4Ma A4Mb A4\ -Mc A4Md A4Me A4Mf A4Mg A4Mi A4Mk A4Ml A4Mm A4Mn A4Mo A4Mp A4Mq A4Mt A4Mu A4Mv\ - A4Mw A4Mx A4My A4Mz A4M# A4M$ A4M% A4M& A4M' A4M( A4M) A4M* A4M+ A4M. A4M/ A\ -4M: A4M; A4M< A4M= A4M> A4M[ A4M] A4M^ A4M_ A4M` A4M{ A4M| A4M} A4M~ A4N0 A4N\ -1 A4N2 A4N3 A4N4 A4N5 A4N6 A4N7 A4N9 A4NA A4NB A4NC A4ND A4NE A4NI A4NJ A4NK \ -A4NL A4NN A4NO A4NT A4NU A4NV A4NW A4NX A4NY A4NZ A4Na A4Nb A4Nc A4Nd A4Ne A4\ -Nf A4Ng A4Nj A4Nk A4Nl A4Nm A4Nn A4Ns A4Nt A4Nv A4Nw A4Nx A4Ny A4Nz A4N# A4N$\ - A4N% A4N& A4N' A4N( A4N) A4N* A4N+ A4N- A4N. A4N/ A4N= A4N[ A4N] A4N^ A4N_ A\ -4N` A4N{ A4N| A4N} A4N~ A4O0 A4O1 A4O2 A4O3 A4O4 A4O6 A4O9 A4OA A4OB A4OC A4O\ -D A4OH A4OI A4OJ A4OK A4OL A4OM A4OO A4OQ A4OR A4OS A4OU A4OV A4OW A4OX A4OY \ -A4OZ A4Oc A4Od A4Oe A4Og A4Oh A4Oi A4Oj A4Ok A4Ol A4Om A4On A4Or A4Os A4Ot A4\ -Ow A4Ox A4Oy A4Oz A4O# A4O& A4O' A4O( A4O* A4O+ A4O, A4O- A4O. A4O/ A4O: A4O;\ - A4O? A4O@ A4O[ A4O] A4O^ A4O` A4O{ A4O| A4O} A4O~ A4P0 A4P1 A4P2 A4P4 A4P5 A\ -4P6 A4P7 A4PA A4PB A4PC A4PF A4PG A4PH A4PI A4PJ A4PK A4PL A4PP A4PQ A4PR A4P\ -T A4PU A4PV A4PW A4PX A4PZ A4Pa A4Pb A4Pc A4Pd A4Pe A4Ph A4Pi A4Pj A4Pk A4Pl \ -A4Pm A4Pq A4Pr A4Ps A4Pw A4Px A4Py A4Pz A4P% A4P& A4P' A4P( A4P* A4P+ A4P, A4\ -P- A4P. A4P/ A4P: A4P= A4P[ A4P] A4P^ A4P| A4P} A4P~ A4Q0 A4Q2 A4Q3 A4Q4 A4Q5\ - A4Q6 A4Q7 A4Q8 A4Q9 A4QA A4QB A4QC A4QF A4QG A4QI A4QJ A4QK A4QN A4QO A4QP A\ -4QQ A4QS A4QT A4QU A4QV A4QW A4QX A4QY A4QZ A4Qa A4Qb A4Qc A4Qd A4Qf A4Qg A4Q\ -i A4Qj A4Qk A4Ql A4Qp A4Qq A4Qr A4Qs A4Qv A4Qw A4Qx A4Qy A4Qz A4Q# A4Q$ A4Q% \ -A4Q& A4Q) A4Q* A4Q+ A4Q, A4Q- A4Q: A4Q; A4Q= A4Q> A4Q? A4Q@ A4Q[ A4Q] A4Q{ A4\ -Q} A4Q~ A4R0 A4R1 A4R2 A4R3 A4R4 A4R5 A4R6 A4R7 A4R8 A4RC A4RE A4RF A4RG A4RH\ - A4RI A4RJ A4RK A4RQ A4RR A4RS A4RT A4RU A4RV A4RW A4RX A4RY A4Ra A4Rb A4Rc A\ -4Rf A4Rg A4Rh A4Ri A4Rj A4Rk A4Rl A4Ro A4Rp A4Rr A4Rs A4Rt A4Ru A4Rv A4Rw A4R\ -x A4R# A4R$ A4R% A4R& A4R' A4R( A4R) A4R* A4R+ A4R. A4R: A4R; A4R< A4R= A4R> \ -A4R? A4R@ A4R[ A4R` A4R| A4R} A4R~ A4S0 A4S1 A4S2 A4S3 A4S4 A4S5 A4S6 A4S7 A4\ -S8 A4SB A4SC A4SD A4SE A4SF A4SG A4SH A4SI A4SN A4SO A4SP A4SQ A4SR A4SS A4ST\ - A4SU A4SV A4SW A4SX A4Sa A4Se A4Sf A4Sg A4Sh A4Si A4Sj A4Sl A4Sw A4Sx A4Sy A\ -4Sz A4S# A4S$ A4S% A4S& A4S' A4S; A4S? A4S@ A4S^ A4S_ A4S` A4S{ A4S| A4S} A4S\ -~ A4T0 A4T1 A4T2 A4T3 A4T4 A4T6 A4T8 A4T9 A4TB A4TD A4TG A4TK A4TL A4TM A4TN \ -A4TO A4TP A4TQ A4TR A4TS A4TT A4TV A4TW A4TY A4TZ A4Ta A4Tc A4Td A4Te A4Tf A4\ -Tg A4Th A4Ti A4Tj A4Tm A4Tn A4To A4Tp A4Tq A4Tr A4Tv A4Tw A4Tx A4Ty A4Tz A4T#\ - A4T$ A4T% A4T& A4T' A4T( A4T) A4T* A4T+ A4T, A4T. A4T: A4T; A4T< A4T= A4T> A\ -4T? A4T^ A4T_ A4T` A4T{ A4T| A4T} A4T~ A4U0 A4U1 A4U2 A4U3 A4U4 A4U5 A4U6 A4U\ -7 A4U8 A4U9 A4UB A4UC A4UD A4UE A4UF A4UG A4UH A4UK A4UL A4UM A4UN A4UO A4UP \ -A4UQ A4UR A4US A4UT A4UU A4UV A4UW A4UX A4UY A4UZ A4Ua A4Ub A4Uc A4Ud A4Ue A4\ -Uf A4Ug A4Uh A4Uj A4Ul A4Um A4Un A4Uo A4Up A4Uq A4Uu A4Uv A4Uw A4Ux A4Uy A4Uz\ - A4U# A4U$ A4U% A4U& A4U' A4U( A4U) A4U* A4U+ A4U- A4U. A4U/ A4U: A4U; A4U< A\ -4U= A4U> A4U@ A4U] A4U^ A4U_ A4U` A4U{ A4U| A4U} A4U~ A4V0 A4V1 A4V2 A4V3 A4V\ -4 A4V5 A4V6 A4V9 A4VA A4VB A4VC A4VD A4VE A4VF A4VJ A4VK A4VL A4VN A4VO A4VQ \ -A4VS A4VU A4VV A4VW A4VX A4VY A4VZ A4Va A4Vb A4Vc A4Vd A4Ve A4Vf A4Vg A4Vi A4\ -Vj A4Vk A4Vl A4Vm A4Vn A4Vp A4Vv A4Vw A4Vx A4Vy A4Vz A4V# A4V$ A4V% A4V& A4V'\ - A4V( A4V) A4V* A4V- A4V. A4V/ A4V: A4V? A4V[ A4V] A4V_ A4V` A4V{ A4V| A4V} A\ -4V~ A4W0 A4W1 A4W2 A4W3 A4W4 A4W5 A4W7 A4WA A4WB A4WC A4WD A4WE A4WF A4WH A4W\ -I A4WJ A4WK A4WL A4WM A4WN A4WQ A4WR A4WS A4WT A4WX A4WY A4WZ A4Wa A4Wd A4We \ -A4Wf A4Wg A4Wi A4Wj A4Wk A4Wl A4Wm A4Wn A4Wo A4Wr A4Ws A4Wt A4Wu A4Wv A4Ww A4\ -Wx A4Wy A4Wz A4W# A4W$ A4W' A4W( A4W) A4W- A4W. A4W/ A4W: A4W; A4W< A4W@ A4W[\ - A4W] A4W^ A4W_ A4W{ A4W| A4W} A4W~ A4X0 A4X1 A4X5 A4X6 A4X7 A4X9 A4XA A4XB A\ -4XC A4XD A4XF A4XH A4XI A4XJ A4XK A4XL A4XM A4XQ A4XR A4XS A4XT A4XV A4XW A4X\ -X A4XY A4XZ A4Xc A4Xd A4Xe A4Xf A4Xg A4Xi A4Xj A4Xk A4Xl A4Xm A4Xn A4Xo A4Xr \ -A4Xs A4Xt A4Xu A4Xv A4Xx A4Xy A4Xz A4X# A4X$ A4X& A4X' A4X( A4X) A4X, A4X- A4\ -X. A4X/ A4X: A4X; A4X] A4X^ A4X_ A4X` A4X} A4X~ A4Y0 A4Y3 A4Y4 A4Y5 A4Y6 A4Y7\ - A4Y8 A4Y9 A4YA A4YB A4YC A4YD A4YE A4YG A4YH A4YJ A4YK A4YL A4YP A4YQ A4YR A\ -4YU A4YV A4YW A4YX A4YY A4YZ A4Ya A4Yb A4Yc A4Yd A4Ye A4Yh A4Yi A4Yj A4Yk A4Y\ -l A4Ym A4Yq A4Yr A4Ys A4Yt A4Yu A4Yw A4Yx A4Yy A4Yz A4Y# A4Y$ A4Y% A4Y& A4Y' \ -A4Y) A4Y+ A4Y, A4Y- A4Y. A4Y: A4Y= A4Y> A4Y? A4Y@ A4Y[ A4Y] A4Y^ A4Y| A4Y} A4\ -Z0 A4Z1 A4Z2 A4Z3 A4Z4 A4Z5 A4Z6 A4Z7 A4Z8 A4Z9 A4ZA A4ZD A4ZF A4ZG A4ZH A4ZI\ - A4ZJ A4ZK A4ZO A4ZQ A4ZR A4ZS A4ZT A4ZU A4ZV A4ZW A4ZX A4ZY A4ZZ A4Zc A4Ze A\ -4Zf A4Zg A4Zh A4Zi A4Zj A4Zk A4Zl A4Zn A4Zs A4Zt A4Zu A4Zv A4Zw A4Zx A4Zy A4Z\ -# A4Z$ A4Z% A4Z& A4Z' A4Z( A4Z) A4Z* A4Z+ A4Z, A4Z. A4Z: A4Z< A4Z= A4Z> A4Z? \ -A4Z@ A4Z[ A4Z] A4Z` A4Z| A4Z} A4Z~ A4a0 A4a1 A4a2 A4a3 A4a4 A4a5 A4a6 A4a7 A4\ -a8 A4aA A4aE A4aF A4aG A4aH A4aI A4aJ A4aM A4aQ A4aR A4aS A4aT A4aU A4aV A4aW\ - A4aX A4aY A4aa A4ac A4ae A4af A4ag A4ah A4ai A4aj A4ak A4an A4ax A4ay A4az A\ -4a# A4a$ A4a% A4a& A4a' A4a( A4a) A4a* A4a- A4a. A4a/ A4a: A4a` A4a{ A4a| A4a\ -} A4a~ A4b0 A4b1 A4b2 A4b3 A4b5 A4b6 A4b7 A4b8 A4bA A4bB A4bD A4bE A4bI A4bJ \ -A4bM A4bN A4bO A4bP A4bQ A4bR A4bS A4bT A4bU A4be A4bf A4bg A4bh A4bi A4bj A4\ -bm A4bn A4bo A4bp A4bq A4br A4bs A4bu A4bw A4bx A4by A4bz A4b# A4b$ A4b% A4b&\ - A4b' A4b( A4b) A4b* A4b+ A4b, A4b- A4b/ A4b: A4b; A4b< A4b= A4b> A4b? A4b@ A\ -4b_ A4b` A4b{ A4b| A4b} A4b~ A4c0 A4c1 A4c2 A4c3 A4c4 A4c5 A4c6 A4c7 A4c8 A4c\ -A A4cC A4cD A4cE A4cF A4cG A4cH A4cJ A4cL A4cM A4cN A4cO A4cP A4cQ A4cR A4cS \ -A4cT A4cU A4cV A4cW A4cX A4cY A4cZ A4ca A4cb A4cc A4cd A4ce A4cf A4cg A4ch A4\ -ci A4cj A4cl A4cm A4cn A4co A4cp A4cq A4cr A4cu A4cv A4cw A4cx A4cy A4cz A4c#\ - A4c$ A4c% A4c& A4c' A4c( A4c) A4c* A4c+ A4c, A4c- A4c: A4c; A4c< A4c= A4c> A\ -4c? A4c^ A4c_ A4c` A4c{ A4c| A4c} A4c~ A4d0 A4d1 A4d2 A4d3 A4d4 A4d5 A4d6 A4d\ -7 A4dA A4dB A4dC A4dD A4dE A4dF A4dG A4dK A4dL A4dM A4dN A4dO A4dP A4dT A4dU \ -A4dW A4dX A4dY A4dZ A4da A4db A4dc A4dd A4de A4df A4dg A4dh A4di A4dl A4dm A4\ -dn A4dp A4dq A4dw A4dx A4dy A4dz A4d# A4d$ A4d% A4d& A4d' A4d( A4d) A4d* A4d+\ - A4d. A4d/ A4d: A4d; A4d[ A4d_ A4d` A4d{ A4d| A4d} A4d~ A4e0 A4e1 A4e2 A4e3 A\ -4e4 A4e5 A4e6 A4e7 A4e9 A4eB A4eC A4eD A4eE A4eF A4eG A4eH A4eJ A4eK A4eL A4e\ -M A4eN A4eO A4eP A4eS A4eT A4eU A4eW A4eX A4eY A4eZ A4ea A4eb A4ee A4ef A4eg \ -A4ek A4el A4em A4en A4eo A4ep A4eq A4et A4eu A4ev A4ew A4ey A4ez A4e# A4e$ A4\ -e% A4e( A4e) A4e* A4e+ A4e, A4e. A4e/ A4e: A4e; A4e< A4e= A4e> A4e[ A4e] A4e^\ - A4e| A4e} A4e~ A4f0 A4f1 A4f2 A4f3 A4f5 A4f6 A4f7 A4f8 A4f9 A4fA A4fC A4fD A\ -4fE A4fG A4fH A4fI A4fJ A4fK A4fL A4fM A4fN A4fR A4fS A4fT A4fX A4fY A4fZ A4f\ -a A4fd A4fe A4ff A4fh A4fj A4fk A4fl A4fm A4fn A4fo A4fq A4fs A4ft A4fu A4fw \ -A4fx A4fy A4fz A4f# A4f% A4f& A4f' A4f( A4f) A4f, A4f- A4f. A4f/ A4f: A4f; A4\ -f< A4f> A4f^ A4f_ A4f` A4f| A4f~ A4g0 A4g1 A4g2 A4g4 A4g5 A4g6 A4g7 A4g8 A4g9\ - A4gA A4gB A4gC A4gD A4gF A4gH A4gI A4gK A4gL A4gM A4gO A4gQ A4gR A4gS A4gU A\ -4gV A4gW A4gX A4gY A4gZ A4ga A4gb A4gc A4gd A4ge A4gh A4gi A4gk A4gl A4gm A4g\ -n A4gr A4gs A4gt A4gv A4gw A4gx A4gy A4gz A4g# A4g$ A4g% A4g& A4g' A4g( A4g* \ -A4g+ A4g, A4g- A4g. A4g/ A4g; A4g> A4g? A4g@ A4g[ A4g] A4g^ A4g_ A4h1 A4h2 A4\ -h3 A4h4 A4h5 A4h6 A4h7 A4h8 A4h9 A4hB A4hC A4hD A4hF A4hG A4hH A4hI A4hJ A4hK\ - A4hL A4hO A4hP A4hQ A4hS A4hT A4hU A4hV A4hW A4hX A4hY A4hZ A4ha A4hc A4he A\ -4hh A4hi A4hj A4hk A4hl A4hm A4hq A4hs A4ht A4hu A4hv A4hw A4hx A4hy A4hz A4h\ -# A4h$ A4h% A4h& A4h' A4h( A4h) A4h* A4h+ A4h, A4h- A4h. A4h> A4h? A4h@ A4h[ \ -A4h] A4h^ A4h_ A4i0 A4i1 A4i2 A4i3 A4i4 A4i5 A4i6 A4i7 A4i8 A4iA A4iB A4iC A4\ -iD A4iF A4iG A4iH A4iI A4iJ A4iK A4iO A4iQ A4iR A4iS A4iT A4iU A4iV A4iW A4iX\ - A4iY A4iZ A4ia A4id A4ie A4ig A4ih A4ii A4ij A4ik A4il A4iy A4iz A4i# A4i$ A\ -4i% A4i& A4i' A4i( A4i) A4i+ A4i, A4i- A4i/ A4i; A4i< A4i= A4i> A4i[ A4i_ A4i\ -{ A4i| A4i} A4i~ A4j0 A4j1 A4j2 A4j3 A4j4 A4jN A4jO A4jP A4jQ A4jR A4jS A4jT \ -A4jU A4jV A4jW A4jX A4jZ A4ja A4jd A4je A4jf A4jg A4jh A4ji A4jj A4jk A4jl A4\ -jm A4jn A4jo A4jp A4jq A4jr A4js A4jt A4ju A4jv A4jx A4jz A4j# A4j$ A4j& A4j'\ - A4j( A4j) A4j* A4j+ A4j, A4j- A4j. A4j/ A4j: A4j; A4j< A4j= A4j> A4j? A4j@ A\ -4j[ A4j] A4j_ A4j| A4j} A4k1 A4k2 A4k3 A4k4 A4k5 A4k6 A4k7 A4k8 A4k9 A4kA A4k\ -B A4kC A4kD A4kE A4kF A4kG A4kH A4kI A4kK A4kM A4kP A4kQ A4kS A4kT A4kU A4kV \ -A4kW A4kX A4kY A4kZ A4ka A4kb A4kf A4kh A4kj A4kk A4kl A4km A4kn A4ko A4kp A4\ -kq A4kr A4ks A4kt A4ku A4kv A4kw A4kx A4ky A4kz A4k# A4k$ A4k' A4k) A4k* A4k+\ - A4k. A4k/ A4k: A4k; A4k< A4k= A4k> A4k? A4k@ A4k[ A4k] A4k^ A4k_ A4k` A4k{ A\ -4k| A4k} A4k~ A4l0 A4l2 A4l5 A4l8 A4l9 A4lA A4lB A4lC A4lD A4lE A4lF A4lG A4l\ -H A4lI A4lJ A4lK A4lL A4lM A4lN A4lO A4lQ A4lR A4lU A4lV A4lW A4lX A4lY A4la \ -A4lb A4lc A4ld A4le A4lg A4lh A4li A4lj A4lk A4ll A4lm A4ln A4lo A4lp A4lr A4\ -lv A4lw A4lx A4l# A4l$ A4l% A4l& A4l( A4l* A4l+ A4l, A4l- A4l. A4l/ A4l: A4l;\ - A4l< A4l@ A4l^ A4l_ A4l` A4l} A4l~ A4m0 A4m1 A4m2 A4m5 A4m6 A4m7 A4m8 A4m9 A\ -4mA A4mD A4mE A4mF A4mG A4mH A4mI A4mJ A4mK A4mN A4mO A4mP A4mQ A4mT A4mU A4m\ -V A4mY A4mZ A4mb A4mc A4md A4mf A4mg A4mh A4mi A4mj A4mk A4ml A4mn A4mo A4mp \ -A4mq A4mr A4mu A4mv A4mw A4my A4m' A4m( A4m) A4m* A4m+ A4m, A4m- A4m. A4m; A4\ -m< A4m= A4m> A4m@ A4m[ A4m] A4m^ A4m_ A4m{ A4m| A4m} A4n0 A4n2 A4n3 A4n4 A4n5\ - A4n6 A4n7 A4n8 A4n9 A4nA A4nB A4nC A4nD A4nH A4nI A4nJ A4nK A4nL A4nN A4nO A\ -4nP A4nQ A4nR A4nV A4nW A4nX A4nY A4nZ A4na A4nb A4nc A4nd A4ne A4nf A4ng A4n\ -j A4nk A4nl A4nm A4nq A4nr A4ns A4nw A4nx A4ny A4nz A4n# A4n$ A4n% A4n& A4n' \ -A4n( A4n) A4n, A4n. A4n/ A4n: A4n; A4n< A4n> A4n? A4n@ A4n` A4n{ A4n~ A4o0 A4\ -o1 A4o3 A4o4 A4o5 A4o6 A4o7 A4o8 A4o9 A4oA A4oB A4oD A4oE A4oF A4oG A4oH A4oI\ - A4oK A4oL A4oM A4oQ A4oR A4oT A4oU A4oV A4oW A4oX A4oY A4oZ A4oa A4ob A4oc A\ -4od A4oe A4og A4oh A4oi A4oj A4ok A4om A4oo A4ot A4ou A4ov A4ow A4ox A4oy A4o\ -z A4o# A4o$ A4o% A4o& A4o' A4o) A4o* A4o+ A4o, A4o. A4o/ A4o: A4o< A4o= A4o> \ -A4o? A4o@ A4o[ A4o] A4o{ A4o| A4p0 A4p1 A4p2 A4p3 A4p4 A4p6 A4p7 A4p8 A4p9 A4\ -pC A4pD A4pE A4pF A4pG A4pH A4pI A4pJ A4pL A4pM A4pN A4pP A4pQ A4pR A4pT A4pU\ - A4pV A4pZ A4pb A4pc A4pd A4pf A4pg A4ph A4pi A4pj A4pk A4pl A4pn A4pp A4pq A\ -4pr A4pt A4pu A4pv A4pw A4px A4py A4p# A4p$ A4p% A4p) A4p* A4p+ A4p, A4p- A4p\ -/ A4p: A4p; A4p= A4p> A4p? A4p[ A4p] A4p^ A4p_ A4p{ A4p| A4p} A4p~ A4q0 A4q1 \ -A4q4 A4q5 A4q6 A4q8 A4q9 A4qA A4qB A4qC A4qD A4qE A4qH A4qI A4qJ A4qK A4qL A4\ -qM A4qN A4qP A4qQ A4qR A4qT A4qU A4qV A4qW A4qX A4qb A4qc A4qd A4qe A4qg A4qh\ - A4qi A4qk A4ql A4qm A4qn A4qp A4qz A4q# A4q$ A4q% A4q& A4q' A4q( A4q) A4q* A\ -4q> A4q@ A4q[ A4q] A4q_ A4q{ A4q| A4q} A4q~ A4r0 A4r1 A4r2 A4r3 A4r4 A4r5 A4r\ -7 A4r8 A4r9 A4rA A4rC A4rD A4rF A4rH A4rJ A4rN A4rO A4rP A4rQ A4rR A4rS A4rT \ -A4rU A4rV A4rW A4rX A4rZ A4ra A4rc A4rd A4re A4rg A4rh A4ri A4rj A4rk A4rl A4\ -rm A4rn A4ro A4rp A4rq A4rr A4rs A4rt A4ru A4rx A4r# A4r$ A4r& A4r' A4r( A4r)\ - A4r* A4r+ A4r, A4r- A4r. A4r/ A4r: A4r; A4r< A4r= A4r> A4r? A4r@ A4r[ A4r] A\ -4r^ A4r| A4r} A4s1 A4s2 A4s3 A4s4 A4s5 A4s6 A4s7 A4s8 A4s9 A4sA A4sB A4sC A4s\ -D A4sE A4sF A4sG A4sH A4sI A4sJ A4sK A4sM A4sO A4sQ A4sT A4sU A4sV A4sW A4sX \ -A4sY A4sZ A4sa A4sb A4sd A4sg A4sj A4sk A4sl A4sm A4sn A4so A4sp A4sq A4sr A4\ -ss A4st A4su A4sv A4sw A4sx A4sy A4sz A4s# A4s$ A4s% A4s' A4s( A4s) A4s. A4s/\ - A4s: A4s; A4s< A4s= A4s> A4s? A4s@ A4s[ A4s] A4s^ A4s_ A4s` A4s{ A4s| A4s} A\ -4s~ A4t0 A4t3 A4t4 A4t5 A4t8 A4tA A4tB A4tC A4tD A4tE A4tF A4tG A4tH A4tI A4t\ -J A4tK A4tL A4tM A4tN A4tO A4tQ A4tR A4tV A4tW A4tX A4ta A4tb A4tc A4td A4tg \ -A4th A4ti A4tj A4tk A4tl A4tm A4tn A4to A4tp A4tr A4ts A4tw A4tx A4ty A4t$ A4\ -t% A4t& A4t' A4t( A4t* A4t+ A4t, A4t- A4t. A4t/ A4t: A4t; A4t< A4t= A4t_ A4t`\ - A4t{ A4t| A4t} A4u0 A4u1 A4u2 A4u3 A4u5 A4u6 A4u7 A4u8 A4u9 A4uA A4uB A4uD A\ -4uE A4uF A4uG A4uH A4uI A4uJ A4uK A4uM A4uO A4uP A4uQ A4uS A4uT A4uU A4uV A4u\ -W A4uY A4ud A4uf A4ug A4uh A4ui A4uj A4uk A4ul A4uo A4up A4uq A4ur A4us A4uv \ -A4uw A4ux A4uy A4u% A4u& A4u* A4u+ A4u, A4u- A4u. A4u/ A4u; A4u< A4u= A4u> A4\ -u? A4u@ A4u^ A4u_ A4u` A4u{ A4u| A4v0 A4v1 A4v3 A4v5 A4v6 A4v7 A4v8 A4v9 A4vA\ - A4vB A4vC A4vD A4vG A4vI A4vK A4vL A4vM A4vO A4vP A4vQ A4vR A4vS A4vT A4vU A\ -4vW A4vX A4vY A4vZ A4va A4vb A4vc A4vd A4ve A4vf A4vi A4vl A4vm A4vn A4vo A4v\ -q A4vr A4vs A4vt A4vu A4vx A4vy A4vz A4v# A4v$ A4v% A4v& A4v' A4v( A4v) A4v+ \ -A4v, A4v- A4v/ A4v: A4v; A4v? A4v@ A4v[ A4v` A4v{ A4v} A4w2 A4w4 A4w5 A4w6 A4\ -w7 A4w8 A4w9 A4wA A4wB A4wC A4wF A4wG A4wH A4wI A4wJ A4wL A4wM A4wO A4wS A4wV\ - A4wW A4wX A4wY A4wZ A4wa A4wb A4wc A4wd A4wf A4wh A4wi A4wj A4wk A4wl A4wo A\ -4wp A4wv A4ww A4wx A4wy A4wz A4w# A4w$ A4w% A4w& A4w' A4w( A4w+ A4w, A4w- A4w\ -/ A4w: A4w< A4w> A4w? A4w@ A4w[ A4w] A4w^ A4w_ A4w` A4w~ A4x0 A4x3 A4x4 A4x5 \ -A4x6 A4x7 A4x9 A4xA A4xC A4xF A4xG A4xH A4xI A4xJ A4xK A4xP A4xT A4xU A4xV A4\ -xW A4xY A4xZ A4xa A4xc A4xf A4xg A4xh A4xi A4xj A4xk A4xl A4xm A4xo A4xp A4xt\ - A4xv A4xw A4xx A4x# A4x$ A4x% A4x& A4x' A4x* A4x+ A4x, A4x- A4x/ A4x: A4x; A\ -4x< A4x> A4x] A4x^ A4x_ A4x` A4x{ A4x} A4x~ A4y0 A4y1 A4y4 A4y5 A4y6 A4y7 A4y\ -B A4yC A4yD A4yE A4yI A4yK A4yL A4yM A4yO A4yP A4yQ A4yR A4yS A4yW A4yX A4yY \ -A4ya A4yb A4yc A4yd A4ye A4yh A4yi A4yl A4ym A4yn A4yo A4yp A4y# A4y$ A4y% A4\ -y& A4y' A4y( A4y) A4y* A4y+ A4y, A4y. A4y/ A4y: A4y< A4y> A4y} A4y~ A4z0 A4z1\ - A4z2 A4z3 A4z4 A4z5 A4z6 A4z7 A4z8 A4zA A4zC A4zD A4zF A4zI A4zL A4zM A4zP A\ -4zQ A4zR A4zS A4zT A4zU A4zV A4zW A4zX A4zh A4zi A4zj A4zk A4zl A4zm A4zn A4z\ -o A4zp A4zq A4zr A4zs A4zt A4zu A4zv A4zy A4zz A4z& A4z' A4z( A4z) A4z* A4z+ \ -A4z, A4z- A4z. A4z/ A4z: A4z; A4z< A4z= A4z> A4z? A4z@ A4z[ A4z] A4z^ A4z` A4\ -z{ A4z} A4#1 A4#3 A4#4 A4#5 A4#6 A4#7 A4#8 A4#9 A4#A A4#B A4#C A4#D A4#E A4#F\ - A4#G A4#H A4#I A4#J A4#K A4#M A4#O A4#P A4#T A4#U A4#V A4#W A4#X A4#Y A4#Z A\ -4#a A4#b A4#c A4#d A4#e A4#g A4#i A4#j A4#k A4#m A4#n A4#o A4#p A4#q A4#r A4#\ -s A4#t A4#u A4#v A4#w A4#x A4#y A4#z A4## A4#$ A4#% A4#& A4#( A4#* A4#+ A4#. \ -A4#: A4#; A4#< A4#= A4#> A4#? A4#@ A4#[ A4#] A4#^ A4#_ A4#` A4#{ A4#| A4#} A4\ -#~ A4$0 A4$1 A4$2 A4$3 A4$7 A4$8 A4$B A4$C A4$D A4$E A4$F A4$G A4$H A4$I A4$J\ - A4$K A4$L A4$M A4$N A4$O A4$P A4$Q A4$R A4$V A4$W A4$X A4$Y A4$b A4$c A4$d A\ -4$e A4$h A4$i A4$j A4$k A4$l A4$m A4$n A4$o A4$p A4$q A4$r A4$s A4$x A4$y A4$\ -z A4$# A4$$ A4$& A4$' A4$( A4$* A4$, A4$- A4$. A4$/ A4$: A4$; A4$< A4$= A4$> \ -A4$_ A4$` A4${ A4$| A4%0 A4%1 A4%2 A4%3 A4%5 A4%6 A4%7 A4%8 A4%9 A4%A A4%B A4\ -%C A4%D A4%E A4%G A4%H A4%I A4%J A4%K A4%L A4%M A4%N A4%P A4%Q A4%R A4%S A4%V\ - A4%W A4%X A4%Y A4%b A4%c A4%h A4%i A4%j A4%k A4%l A4%m A4%n A4%q A4%r A4%s A\ -4%u A4%v A4%w A4%x A4%y A4%$ A4%% A4%& A4%( A4%* A4%+ A4%, A4%- A4%. A4%/ A4%\ -: A4%< A4%> A4%? A4%@ A4%[ A4%_ A4%` A4%{ A4%| A4%~ A4&5 A4&6 A4&7 A4&8 A4&9 \ -A4&A A4&B A4&C A4&D A4&E A4&G A4&K A4&L A4&M A4&N A4&R A4&S A4&T A4&X A4&Y A4\ -&Z A4&a A4&b A4&c A4&d A4&e A4&f A4&i A4&j A4&l A4&m A4&n A4&o A4&p A4&r A4&s\ - A4&t A4&u A4&v A4&y A4&z A4&# A4&$ A4&% A4&& A4&' A4&( A4&) A4&+ A4&, A4&- A\ -4&: A4&; A4&< A4&= A4&> A4&@ A4&[ A4&] A4&{ A4&} A4'2 A4'5 A4'6 A4'7 A4'8 A4'\ -9 A4'A A4'B A4'C A4'D A4'F A4'H A4'I A4'J A4'K A4'M A4'O A4'P A4'R A4'V A4'W \ -A4'X A4'Y A4'Z A4'a A4'b A4'c A4'd A4'e A4'f A4'i A4'j A4'k A4'l A4'm A4'o A4\ -'p A4'v A4'x A4'y A4'z A4'# A4'$ A4'% A4'& A4'' A4'( A4'+ A4', A4'- A4'. A4':\ - A4'; A4'= A4'> A4'? A4'@ A4'[ A4'] A4'^ A4'_ A4'` A4'{ A4(0 A4(1 A4(4 A4(5 A\ -4(6 A4(A A4(B A4(D A4(G A4(H A4(I A4(J A4(K A4(L A4(N A4(O A4(Q A4(U A4(V A4(\ -W A4(X A4(Y A4(Z A4(b A4(d A4(g A4(h A4(i A4(j A4(k A4(l A4(m A4(p A4(q A4(u \ -A4(w A4(x A4(y A4(# A4($ A4(% A4(& A4(' A4() A4(+ A4(, A4(- A4(; A4(< A4(= A4\ -(@ A4([ A4(_ A4(` A4({ A4(| A4(} A4)0 A4)1 A4)2 A4)6 A4)7 A4)8 A4)9 A4)B A4)C\ - A4)D A4)E A4)G A4)K A4)L A4)M A4)N A4)O A4)Q A4)R A4)S A4)T A4)X A4)Y A4)Z A\ -4)a A4)b A4)d A4)e A4)f A4)g A4)k A4)m A4)n A4)o A4)q A4)r B B2% B2& B2' B2( \ -B2) B2* B2. B2/ B2: B2; B2< B2= B30 B31 B32 B36 B3R B3S B3T B3U B3V B3W B3a B\ -3b B3c B3d B3e B3f B3= B3@ B3[ B3] B3{ B84 B85 B86 B8J B8W B8Z B8f B8i B8k B8\ -m B8p B8q B8_ B8` B8{ B90 B9: B9; B9< B9@ BA& BA' BA( BA) BA* BA+ BA/ BA: BA;\ - BA< BA= BA> BA] BA^ BA_ BA` BA{ BA| BA} BB1 BB2 BB3 BBG BBS BBT BBU BBV BBW \ -BBX BBb BBc BBd BBe BBf BBg BBk BBl BBm BBn BBo BBp BB[ BB] BB^ BB| BC6 BC* B\ -C- BC. BC/ BC= BO7 BOC BOG BOM BOO BOQ BO| BP3 BP5 BP7 BPB BPF BP] BP{ BQ1 BQ\ -5 BQ& BQ' BQ( BQ) BQ* BQ+ BQ, BQ- BQ. BQ/ BQ: BQ; BQ< BQ= BQ> BQ[ BQ] BQ^ BQ`\ - BQ| BQ} BQ~ BR0 BR1 BR2 BR3 BR4 BR5 BR7 BR9 BRC BRD BRE BRF BRG BRH BRI BRJ \ -BRK BRM BRN BRO BRP BRQ BRT BRU BRV BRX BRa BRb BRc BRd BRe BRf BRg BRh BRi B\ -Rj BRk BRl BRm BRn BRo BRp BRq BRr BRu BRv BRw BRx BRy BRz BR# BR$ BR% BR& BR\ -' BR( BR) BR* BR+ BR- BR. BR/ BR: BR= BR> BR? BR@ BR[ BR] BR^ BR_ BR` BR| BS0\ - BS1 BS2 BS3 BS4 BS5 BS6 BS7 BS8 BS9 BSA BSB BSE BSF BSG BSI BSJ BSK BSO BSQ \ -BSR BSS BST BSU BSV BSW BSX BSY BSZ BSa BSb BSc BSd BSe BSf BSg BSh BSj BSl B\ -Sm BSn BSo BSp BSq BSr BSs BSt BSu BSv BSw BSy BS# BS$ BS% BS& BS' BS) BS* BS\ -+ BS, BS- BS. BS/ BS: BS; BS< BS> BS? BS] BS^ BS_ BS` BS{ BS| BS} BS~ BT0 BT1\ - BT4 BT5 BT6 BT8 BTB BTD BTE BTG BTH BTI BTJ BTK BTL BTM BTN BTO BTP BTQ BTR \ -BTS BTT BTU BTV BTW BTX BW9 BWD BWI BWM BWR BWW BWX BWZ BWa BWc BWd BWe BWf B\ -Wh BWi BWk BWl BWn BWp BWq BWs BWt BWv BW~ BX3 BX8 BXC BXH BXM BXN BXP BXQ BX\ -S BXT BXU BXV BXX BXY BXa BXb BXd BXf BXg BXi BXj BXl BX; BX= BX_ BX{ BX| BY3\ - BY5 BY6 BYC BYD BYF BYG BYI BYJ BYK BYL BYN BYO BYQ BYR BYT BYV BYW BYY BYZ \ -BYb BY' BY( BY) BY* BY+ BY, BY- BY. BY/ BY: BY; BY< BY= BY> BY[ BY] BY^ BY_ B\ -Y| BY} BY~ BZ0 BZ1 BZ2 BZ3 BZ4 BZ5 BZ6 BZ8 BZ9 BZA BZD BZE BZF BZG BZH BZI BZ\ -J BZK BZL BZN BZP BZQ BZR BZT BZU BZW BZY BZb BZc BZd BZe BZf BZg BZh BZi BZj\ - BZk BZl BZm BZn BZo BZp BZq BZr BZs BZv BZw BZx BZy BZz BZ# BZ$ BZ% BZ& BZ' \ -BZ( BZ) BZ* BZ+ BZ- BZ. BZ/ BZ: BZ< BZ> BZ? BZ@ BZ[ BZ] BZ^ BZ_ BZ` BZ{ BZ| B\ -a0 Ba3 Ba4 Ba5 Ba6 Ba7 Ba8 Ba9 BaA BaB BaC BaE BaF BaG BaH BaJ BaN BaO BaQ Ba\ -R BaS BaT BaU BaV BaW BaX BaY BaZ Baa Bab Bac Bad Bae Baf Bag Bah Bai Bak Bam\ - Ban Bao Bap Baq Bar Bas Bat Bau Bav Baw Bax Bay Ba$ Ba% Ba& Ba( Ba) Ba* Ba+ \ -Ba, Ba- Ba. Ba/ Ba: Ba; Ba< Ba= Ba[ Ba] Ba^ Ba_ Ba` Ba{ Ba| Ba} Ba~ Bb0 Bb1 B\ -b3 Bb5 Bb6 Bb7 BbA BbC BbD BbG BbH BbI BbJ BbK BbL BbM BbN BbO BbP BbQ BbR Bb\ -S BbT BbU BbV BbW BbX BbY Be8 BeF BeI BeJ BeN BeQ BeX BeY Bea Beb Bed Bee Bef\ - Beh Bei Bek Bel Ben Beo Bep Ber Bes Beu Bev Be} Bf4 Bf7 BfE BfH BfI BfN BfO \ -BfQ BfR BfT BfU BfV BfX BfY Bfa Bfb Bfd Bfe Bff Bfh Bfi Bfk Bfl Bf< Bf? Bf_ B\ -f| Bg3 Bg6 BgD BgE BgG BgH BgJ BgK BgL BgN BgO BgQ BgR BgT BgU BgV BgX BgY Bg\ -a Bgb Bg( Bg) Bg* Bg+ Bg, Bg- Bg. Bg/ Bg: Bg; Bg< Bg= Bg> Bg? Bg[ Bg^ Bg_ Bg`\ - Bg{ Bg~ Bh0 Bh1 Bh2 Bh3 Bh4 Bh5 Bh6 Bh7 BhA BhC BhD BhE BhF BhG BhH BhI BhJ \ -BhK BhL BhM BhP BhQ BhR BhS BhU BhW Bha Bhb Bhc Bhd Bhe Bhf Bhg Bhh Bhi Bhj B\ -hk Bhl Bhm Bhn Bho Bhp Bhq Bhr Bhs Bht Bhw Bhx Bhy Bhz Bh# Bh$ Bh% Bh& Bh' Bh\ -( Bh) Bh* Bh+ Bh- Bh. Bh/ Bh: Bh; Bh> Bh? Bh@ Bh[ Bh] Bh^ Bh_ Bh` Bh{ Bh| Bh}\ - Bh~ Bi1 Bi4 Bi5 Bi6 Bi7 Bi8 Bi9 BiA BiB BiC BiF BiG BiH BiI BiL BiM BiO BiQ \ -BiS BiT BiU BiV BiW BiX BiY BiZ Bia Bib Bic Bid Bie Bif Big Bih Bii Bij Bil B\ -in Bio Bip Biq Bir Bis Bit Biu Biv Biw Bix Biy Bi$ Bi% Bi& Bi' Bi( Bi* Bi+ Bi\ -, Bi- Bi. Bi/ Bi: Bi; Bi< Bi= Bi@ Bi[ Bi_ Bi` Bi{ Bi| Bi} Bi~ Bj0 Bj1 Bj2 Bj3\ - Bj4 Bj6 Bj7 Bj8 BjA BjB BjE BjH BjI BjJ BjK BjL BjM BjN BjO BjP BjQ BjR BjS \ -BjT BjU BjV BjW BjX BjY BjZ B1T* B1T+ B1T, B1T- B1T. B1T/ B1T: B1T; B1T< B1T@\ - B1Ux B1Uy B1Uz B1U# B1U& B1U' B1U( B1U, B1U? B1U@ B1U[ B1V> B1V? B1V@ B1V[ B\ -1V] B1V^ B1V| B1WC B1WD B1WE B1WI B1WJ B1WK B1WL B1WM B1WN B1WR B1WS B1WT B1W\ -d B1We B1Wf B1Wm B1Wn B1Wo B1Ws B1Wt B1Wu B1W* B1W- B1W. B1W/ B1W= B1W{ B1W| \ -B1W} B1Yq B1Yr B1Ys B1Yt B1Yu B1Yv B1Yz B1Y# B1Y$ B1Y. B1Y/ B1Y: B1Y; B1Y< B1\ -Y= B1Y_ B1Z9 B1ZA B1ZB B1ZF B1ZG B1ZH B1ZI B1ZJ B1ZK B1ZO B1ZP B1ZQ B1Z$ B1Z%\ - B1Z& B1Z' B1Z: B1Z^ B1Z_ B1Z` B1b+ B1b, B1b- B1b. B1b; B1b< B1b= B1b[ B1b] B\ -1b^ B1c0 B1cy B1cz B1c# B1c$ B1c% B1c& B1c' B1c( B1c) B1c- B1c@ B1do B1dp B1d\ -q B1dr B1du B1dv B1dw B1d# B1d, B1d- B1d. B1d? B1d] B1d^ B1d_ B1d} B1d~ B1e0 \ -B1e7 B1eD B1eE B1eF B1eJ B1eK B1eL B1eM B1eN B1eO B1eS B1eT B1eU B1eV B1eW B1\ -eX B1eb B1ec B1ed B1ee B1ef B1eg B1ek B1el B1em B1en B1eo B1ep B1ew B1ex B1ey\ - B1e% B1e& B1e' B1e+ B1e, B1e- B1e. B1e/ B1e: B1e> B1e| B1fy B1f$ B1f% B1f& B\ -1f* B1f= B1f> B1f? B1gr B1gs B1gt B1gu B1gv B1gw B1g# B1g$ B1g% B1g& B1g' B1g\ -( B1g, B1g- B1g. B1g/ B1g: B1g; B1g< B1g` B1g{ B1g| B1h4 B1hA B1hB B1hC B1hG \ -B1hH B1hI B1hJ B1hK B1hL B1hP B1hQ B1hR B1hS B1hT B1hU B1hY B1hZ B1ha B1h% B1\ -h& B1h' B1h( B1h) B1h* B1h; B1h_ B1is B1it B1iu B1iv B1i' B1i: B1i; B1i< B2YU\ - B2YV B2YW B2Ya B2Yd B2Ye B2Yf B2Yk B2Yn B2Yo B2Yt B2Yu B2Yw B2Yx B2Yz B2Y# B\ -2Y% B2Y' B2Y( B2Y) B2Y* B2Y+ B2Y, B2Y/ B2Y: B2Y; B2Y< B2Y= B2Y> B2Y? B2ZK B2Z\ -L B2ZM B2ZR B2ZT B2ZU B2ZV B2Za B2Zd B2Ze B2Zj B2Zk B2Zm B2Zn B2Zp B2Zq B2Zu \ -B2Zv B2Zw B2Zx B2Zy B2Zz B2Z# B2Z$ B2Z& B2Z' B2Z( B2Z) B2Z* B2Z+ B2a8 B2aA B2\ -aB B2aC B2aG B2aJ B2aK B2aL B2aQ B2aT B2aU B2aZ B2aa B2ac B2ad B2af B2ag B2aj\ - B2ak B2al B2am B2an B2ao B2ap B2as B2at B2au B2av B2aw B2ax B2ay B2gV B2gW B\ -2gX B2gc B2ge B2gf B2gg B2gk B2gn B2gu B2gx B2g# B2g' B2g( B2g) B2g* B2g+ B2g\ -, B2g- B2g/ B2g: B2g; B2g< B2g= B2g> B2g? B2g@ B2hL B2hM B2hN B2hR B2hU B2hV \ -B2hW B2ha B2hd B2hk B2hn B2hq B2hu B2hv B2hw B2hx B2hy B2hz B2h# B2h$ B2h' B2\ -h( B2h) B2h* B2h+ B2h, B2iB B2iC B2iD B2iH B2iK B2iL B2iM B2iQ B2iT B2ia B2id\ - B2ig B2il B2im B2in B2io B2ip B2iq B2ir B2iu B2iv B2iw B2ix B2iy B2iz B2oW B\ -2oX B2oY B2oc B2of B2og B2oh B2ol B2oo B2ow B2oz B2o% B2o) B2o* B2o+ B2o, B2o\ -- B2o. B2o: B2o< B2o= B2o> B2o? B2o@ B2o[ B2pM B2pN B2pO B2pS B2pV B2pW B2pX \ -B2pb B2pe B2pm B2pp B2ps B2pt B2pw B2px B2py B2pz B2p# B2p$ B2p& B2p( B2p) B2\ -p* B2p+ B2p, B2p- B2qC B2qD B2qE B2qJ B2qL B2qM B2qN B2qR B2qU B2qc B2qf B2qi\ - B2qm B2qn B2qo B2qp B2qq B2qr B2qs B2qu B2qv B2qw B2qx B2qy B2qz B2q# B2wX B\ -2wY B2wZ B2wd B2wg B2wh B2wi B2wn B2wq B2wr B2ww B2wx B2wz B2w# B2w% B2w& B2w\ -' B2w( B2w) B2w- B2w. B2w/ B2w: B2w; B2w< B2w> B2w@ B2w[ B2w] B2xN B2xO B2xP \ -B2xT B2xW B2xX B2xY B2xd B2xg B2xh B2xm B2xn B2xp B2xq B2xs B2xt B2xu B2xv B2\ -xw B2x# B2x$ B2x% B2x& B2x' B2x( B2x* B2x, B2x- B2x. B2yD B2yE B2yF B2yK B2yM\ - B2yN B2yO B2yT B2yW B2yX B2yc B2yd B2yf B2yg B2yi B2yj B2yk B2yl B2ym B2yp B\ -2yq B2yr B2ys B2yt B2yu B2yv B2yw B2yy B2yz B2y# B2y$ B2z1 B2z2 B2z3 B2z5 B2z\ -6 B2z7 B2z8 B2z9 B2zA B2zB B2zF B2zH B2zI B2zJ B2zK B2zL B2zM B2zO B2zP B2zQ \ -B2zR B2zS B2zT B2zU B2zY B2zZ B2za B2zd B2ze B2zf B2zg B2zh B2zj B2zk B2zl B2\ -zm B2zn B2zo B2zt B2zu B2zv B2zy B2zz B2z# B2z$ B2z% B2z' B2z( B2z) B2z* B2z+\ - B2z, B2z: B2z; B2z< B2z> B2z[ B2z^ B2z_ B2z{ B2z| B2z} B2z~ B2#0 B2#1 B2#2 B\ -2#3 B2#6 B2#8 B2#9 B2#A B2#E B2#F B2#G B2#H B2#I B2#J B2#L B2#Q B2#T B2#U B2#\ -V B2#W B2#X B2#Z B2#a B2#b B2#c B2#d B2#e B2#f B2#g B2#m B2#n B2#o B2#p B2#q \ -B2#r B2#t B2#u B2#v B2#w B2#x B2#y B2#z B2## B2#% B2#& B2#' B2#( B2#) B2#* B2\ -#. B2#< B2#= B2#> B2#? B2#@ B2#[ B2#] B2#^ B2#{ B2#} B2#~ B2$0 B2$2 B2$3 B2$4\ - B2$5 B2$6 B2$7 B2$8 B2$9 B2$A B2$B B2$D B2$E B2$H B2$I B2$J B2$K B2$L B2$P B\ -2$Q B2$R B2$S B2$T B2$U B2$V B2$X B2$Z B2$a B2$b B2$e B2$f B2$g B2$k B2$l B2$\ -m B2$n B2$o B2$p B2$q B2$r B2$t B2$u B2$v B2$w B2'Y B2'Z B2'a B2'f B2'h B2'i \ -B2'j B2'n B2'q B2'x B2'# B2'& B2'( B2') B2'* B2'. B2'/ B2': B2'; B2'< B2'= B2\ -'> B2'? B2'[ B2'] B2'^ B2(M B2(O B2(P B2(Q B2(U B2(X B2(Y B2(Z B2(d B2(g B2(n\ - B2(q B2(t B2(v B2(w B2(x B2($ B2(% B2(& B2(' B2(( B2() B2(, B2(- B2(. B2(/ B\ -2)E B2)F B2)G B2)K B2)N B2)O B2)P B2)T B2)W B2)d B2)g B2)j B2)l B2)m B2)n B2)\ -r B2)s B2)t B2)u B2)v B2)w B2)z B2)# B2)$ B2)% B2*2 B2*3 B2*5 B2*6 B2*7 B2*8 \ -B2*9 B2*A B2*B B2*C B2*E B2*F B2*G B2*J B2*K B2*L B2*P B2*Q B2*R B2*S B2*T B2\ -*U B2*W B2*c B2*d B2*e B2*f B2*g B2*h B2*j B2*k B2*l B2*m B2*n B2*o B2*p B2*q\ - B2*s B2*x B2*z B2*# B2*$ B2*% B2*' B2*( B2*) B2** B2*+ B2*, B2*- B2*. B2*: B\ -2*; B2*< B2*= B2*> B2*] B2*| B2*} B2*~ B2+0 B2+1 B2+2 B2+4 B2+5 B2+7 B2+8 B2+\ -9 B2+A B2+B B2+C B2+E B2+F B2+G B2+H B2+I B2+J B2+K B2+N B2+O B2+Q B2+R B2+U \ -B2+V B2+W B2+a B2+b B2+c B2+d B2+e B2+f B2+h B2+i B2+k B2+l B2+n B2+p B2+q B2\ -+r B2+v B2+w B2+x B2+y B2+z B2+# B2+$ B2+% B2+' B2+( B2+) B2+* B2+, B2+/ B2+:\ - B2+; B2+= B2+> B2+? B2+@ B2+[ B2+] B2+{ B2+~ B2,0 B2,1 B2,3 B2,4 B2,5 B2,6 B\ -2,7 B2,8 B2,9 B2,A B2,C B2,D B2,E B2,F B2,H B2,K B2,L B2,M B2,N B2,P B2,Q B2,\ -R B2,S B2,T B2,U B2,V B2,a B2,b B2,c B2,e B2,f B2,g B2,h B2,i B2,j B2,l B2,m \ -B2,n B2,o B2,p B2,q B2,u B2,v B2,w B2,z B2/Z B2/a B2/b B2/f B2/i B2/j B2/k B2\ -/o B2/r B2/z B2/% B2/( B2/) B2/* B2/+ B2// B2/: B2/; B2/< B2/= B2/> B2/? B2/]\ - B2/^ B2/_ B2:P B2:Q B2:R B2:W B2:Y B2:Z B2:a B2:e B2:h B2:p B2:s B2:v B2:w B\ -2:x B2:y B2:% B2:& B2:' B2:( B2:) B2:* B2:, B2:- B2:. B2:/ B2:: B2;F B2;G B2;\ -H B2;L B2;O B2;P B2;Q B2;U B2;X B2;f B2;i B2;l B2;m B2;n B2;o B2;s B2;t B2;u \ -B2;v B2;w B2;x B2;y B2;$ B2;% B2;& B2<3 B2<4 B2<8 B2<9 B2 B2<[ B2<^ B2<{ B2<| B2<} B2<~ B2=0 B2=1 B2=2 B2=3 B2=9 B2=A B2=B B2=C B2=D \ -B2=F B2=G B2=H B2=I B2=J B2=K B2=L B2=M B2=P B2=R B2=T B2=U B2=V B2=W B2=X B2\ -=Z B2=a B2=b B2=c B2=d B2=e B2=f B2=g B2=l B2=m B2=p B2=q B2=r B2=s B2=t B2=u\ - B2=w B2=x B2=y B2=z B2=# B2=$ B2=( B2=) B2=* B2=, B2=- B2=: B2=; B2== B2=> B\ -2=? B2=@ B2=[ B2=] B2=^ B2=_ B2={ B2=| B2=} B2>0 B2>1 B2>2 B2>6 B2>7 B2>8 B2>\ -9 B2>A B2>B B2>C B2>E B2>I B2>L B2>M B2>N B2>P B2>Q B2>R B2>S B2>T B2>U B2>V \ -B2>W B2>Y B2>Z B2>f B2>g B2>h B2>i B2>j B2>l B2>m B2>n B2>o B2>p B2>q B2>r B2\ ->s B2>u B2>v B2>w B2>x B2>z B2[a B2[b B2[c B2[g B2[h B2[j B2[k B2[l B2[t B2[u\ - B2[z B2[# B2[% B2[& B2[( B2[* B2[+ B2[, B2[- B2[. B2[/ B2[= B2[> B2[? B2[@ B\ -2[[ B2[] B2[^ B2[_ B2[` B2]Q B2]R B2]S B2]W B2]X B2]Z B2]a B2]b B2]j B2]k B2]\ -p B2]q B2]s B2]t B2]w B2]x B2]y B2]z B2]# B2]$ B2]% B2]) B2]* B2]+ B2], B2]- \ -B2]. B2]/ B2]: B2]; B2^G B2^H B2^I B2^M B2^N B2^P B2^Q B2^R B2^Z B2^a B2^f B2\ -^g B2^i B2^j B2^n B2^o B2^p B2^q B2^r B2^s B2^w B2^x B2^y B2^z B2^# B2^$ B2^%\ - B2^& B2^' B2_6 B2_7 B2_8 B2_9 B2_A B2_B B2_C B2_D B2_E B2_F B2_G B2_H B2_J B\ -2_L B2_M B2_N B2_O B2_R B2_S B2_T B2_U B2_V B2_W B2_X B2_Y B2_Z B2_d B2_e B2_\ -f B2_g B2_h B2_j B2_k B2_l B2_n B2_o B2_p B2_q B2_r B2_s B2_t B2_u B2_w B2_y \ -B2_z B2_# B2_$ B2_% B2_& B2_' B2_( B2_) B2_* B2_+ B2_, B2_. B2_: B2_; B2_< B2\ -_@ B2_[ B2_] B2_{ B2_| B2_} B2_~ B2`0 B2`1 B2`2 B2`3 B2`4 B2`5 B2`6 B2`7 B2`8\ - B2`9 B2`B B2`C B2`D B2`F B2`G B2`H B2`I B2`J B2`K B2`L B2`M B2`N B2`O B2`P B\ -2`T B2`U B2`V B2`W B2`Z B2`a B2`b B2`c B2`f B2`g B2`h B2`i B2`j B2`k B2`n B2`\ -o B2`p B2`q B2`r B2`s B2`t B2`u B2`v B2`w B2`x B2`y B2`z B2`$ B2`& B2`' B2`( \ -B2`, B2`- B2`. 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B30/ B30: B30; B30< B31H B31I B31J B31N B31O B31Q B\ -31R B31S B31W B31Z B31g B31j B31o B31p B31q B31r B31s B31t B31x B31y B31z B31\ -# B31$ B31% B31& B31' B31( B327 B328 B329 B32A B32B B32C B32D B32E B32F B32G \ -B32H B32I B32K B32L B32M B32N B32O B32R B32S B32T B32U B32V B32W B32X B32Y B3\ -2Z B32a B32e B32f B32g B32j B32k B32l B32m B32n B32q B32r B32s B32t B32u B32v\ - B32y B32z B32# B32$ B32% B32& B32' B32( B32) B32* B32+ B32, B32- B32. B32/ B\ -32; B32< B32= B32[ B32] B32^ B32| B32} B32~ B330 B331 B332 B333 B334 B335 B33\ -6 B337 B338 B33A B33C B33D B33E B33H B33I B33J B33K B33L B33M B33N B33O B33P \ -B33Q B33U B33V B33W B33X B33a B33b B33c B33e B33f B33g B33h B33i B33j B33k B3\ -3l B33n B33o B33p B33q B33r B33s B33t B33u B33v B33w B33x B33y B33z B33# B33&\ - B33' B33( B33) B33- B33. B33/ B33= B33> B33? B33@ B33[ B33] B33^ B33_ B33` B\ -33{ B33| B33} B341 B342 B343 B344 B345 B346 B348 B349 B34A B34B B34C B34D B34\ -E B34F B34G B34K B34L B34M B34N B34P B34Q B34R B34S B34T B34W B34X B34Y B34Z \ -B34a B34b B34d B34f B34g B34h B34i B34j B34k B34l B34m B34n B34o B34p B34q B3\ -4t B34u B34v B34w B34# B34$ B34% B37c B37d B37e B37i B37j B37l B37m B37n B37r\ - B37u B37% B37( B37, B37- B37. B37/ B37: B37; B37? B37@ B37[ B37] B37^ B37_ B\ -37` B37{ B37| B38S B38T B38U B38Y B38Z B38b B38c B38d B38h B38k B38s B38v B38\ -z B38# B38$ B38% B38& B38' B38+ B38, B38- B38. B38/ B38: B38; B38< B38= B39I \ -B39J B39K B39O B39P B39R B39S B39T B39a B39i B39l B39o B39p B39q B39r B39s B3\ -9t B39u B39y B39z B39# B39$ B39% B39& B39' B39( B39) B3A8 B3A9 B3AA B3AB B3AC\ - B3AD B3AE B3AF B3AG B3AH B3AI B3AJ B3AM B3AN B3AO B3AP B3AQ B3AS B3AT B3AU B\ -3AV B3AW B3AX B3AY B3AZ B3Aa B3Ab B3Af B3Ag B3Ah B3Ak B3Al B3Am B3An B3Ao B3A\ -r B3As B3At B3Au B3Av B3Aw B3Ay B3Az B3A# B3A$ B3A% B3A& B3A' B3A( B3A) B3A* \ -B3A+ B3A, B3A- B3A. B3A/ B3A< B3A= B3A> B3A] B3A^ B3A_ B3A} B3A~ B3B0 B3B1 B3\ -B2 B3B3 B3B4 B3B5 B3B6 B3B7 B3B8 B3B9 B3BA B3BD B3BE B3BF B3BH B3BJ B3BK B3BL\ - B3BM B3BN B3BO B3BP B3BQ B3BR B3BV B3BW B3BX B3BZ B3Ba B3Bb B3Bc B3Bd B3Be B\ -3Bh B3Bi B3Bj B3Bk B3Bl B3Bm B3Bo B3Bq B3Br B3Bs B3Bt B3Bu B3Bv B3Bw B3Bx B3B\ -y B3Bz B3B# B3B$ B3B& B3B' B3B( B3B) B3B* B3B. B3B/ B3B: B3B> B3B? 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CS@ CS] CS{ CS} CS~ CT1 CT5 CT7 CT8 CT9 CTA CTB CTC CTD CTE CTF\ - CTG CTH CTI CTJ CTK CTL CTM CTN CTO CTP CTQ CTR CTS CTT CTU CTV CTW CTX CTc \ -CTd CTf CTg CTh CTi CTj CTk CTl CTm CTn CTo CTp CTq CTr CTs CTt CTu CTv CTw C\ -Tx CTy CUO CUP CUQ CUR CUS CUT CUU CUV CUW CUX CUY CUZ CUa CUb CUc CUd CUe CU\ -f CUg CUi CUm CUo CVE CVF CVG CVH CVI CVJ CVK CVL CVM CVN CVP CVT CVV CVW CVX\ - CVY CVZ CVa CVb CVc CVd CVe CWD CWH CWJ CWK CWN CWR CWT CWU CWY CWZ CWa CWb \ -CWc CWd CWe CWf CWg CWh CWi CWj CWn CWo CWp CWt CWu CWv CWz CW# CW$ CW% CW& C\ -W' CW( CW) CW* CW. CW/ CW: CW; CW< CW= CW> CW? CW@ CX5 CX7 CX8 CXA CXC CXF CX\ -H CXK CXO CXP CXQ CXR CXS CXT CXU CXV CXW CXX CXY CXZ CXd CXe CXf CXj CXk CXl\ - CXp CXq CXr CXs CXt CXu CXv CXw CXx CX$ CX% CX& CX' CX( CX) CX* CX+ CX, CX^ \ -CX` CX} CX~ CY2 CY3 CY5 CY9 CYE CYF CYG CYH CYI CYJ CYK CYL CYM CYN CYO CYP C\ -YT CYU CYV CYZ CYa CYb CYf CYg CYh CYi CYj CYk CYl CYm CYn CYr CYs CYt CYu CY\ -v CYw CYx CYy CYz CY) CY* CY, CY. CY/ CY; CY? CY@ CY{ CY| CY} CY~ CZ1 CZ2 CZ3\ - CZ4 CZ5 CZ6 CZ7 CZ8 CZ9 CZA CZB CZC CZD CZE CZF CZG CZH CZI CZJ CZK CZL CZM \ -CZN CZO CZP CZQ CZR CZa CZb CZc CZd CZe CZf CZg CZh CZi CZj CZk CZl CZm CZn C\ -Zo CZp CZq CZr CZs CZt CZu CZv CZw CZx CZy CZz CZ# CZ$ CZ% CZ& CZ' CZ( CZ) CZ\ -* CZ+ CZ, CZ- CZ. CZ/ CZ: CZ; CZ< CZ= CZ> CZ? CZ@ CZ[ CZ] CZ^ CZ_ CZ` CZ{ CZ|\ - CZ} CZ~ Ca0 Ca1 Ca2 Ca3 Ca4 Ca5 Ca6 Ca7 Ca8 Ca9 CaA CaB CaC CaD CaE CaF CaG \ -CaH CaI CaJ CaK CaL CaM CaN CaO CaP CaQ CaR CaS CaT CaW CaY CaZ Caa Cab Cac C\ -ad Cae Caf Cag Cah Cai Caj Cak Cal Cam Can Cao Cap Caq Car Cas Cat Cau Cav Ca\ -w Cax Cay Caz Ca# Ca$ Ca% Ca& Ca' Ca( Ca) Ca* Ca+ Ca, Ca. Ca/ Ca; Ca? Ca[ Ca]\ - Ca_ Ca} Ca~ Cb2 Cb4 Cb7 Cb8 Cb9 CbA CbB CbC CbD CbE CbF CbG CbH CbI CbJ CbK \ -CbL CbM CbN CbO CbP CbQ CbR CbS CbT CbU CbV CbW CbX CbY Cbd Cbe Cbg Cbh Cbi C\ -bj Cbk Cbl Cbm Cbn Cbo Cbp Cbq Cbr Cbs Cbt Cbu Cbv Cbw Cbx Cby Cbz CcP CcQ Cc\ -R CcS CcT CcU CcV CcW CcX CcY CcZ Cca Ccb Ccc Ccd Cce Ccf Ccg Ccl Ccm Cco Ccp\ - CdF CdG CdH CdI CdJ CdK CdL CdM CdN CdO CdP CdR CdS CdX CdY CdZ Cda Cdb Cdc \ -Cdd Cde Cdf CeE CeG CeJ CeK CeO CeP CeR CeV CeZ Cea Ceb Cec Ced Cee Cef Ceg C\ -eh Cel Cem Cen Ceo Cep Ceq Cer Ces Cet Ce# Ce$ Ce% Ce& Ce' Ce( Ce) Ce* Ce+ Ce\ -, Ce- Ce. Ce< Ce= Ce> Ce] Ce^ Ce_ Cf5 Cf6 Cf8 CfC CfD CfE CfG CfK CfP CfQ CfR\ - CfS CfT CfU CfV CfW CfX Cfb Cfc Cfd Cfe Cff Cfg Cfh Cfi Cfj Cfq Cfr Cfs Cft \ -Cfu Cfv Cfw Cfx Cfy Cfz Cf# Cf$ Cf( Cf) Cf* Cf. Cf/ Cf: Cf_ Cf` Cf| Cg1 Cg3 C\ -g5 Cg8 Cg9 CgF CgG CgH CgI CgJ CgK CgL CgM CgN CgR CgS CgT CgU CgV CgW CgX Cg\ -Y CgZ Cgg Cgh Cgi Cgj Cgk Cgl Cgm Cgn Cgo Cgp Cgq Cgr Cgv Cgw Cgx Cg$ Cg% Cg&\ - Cg* Cg+ Cg- Cg/ Cg= Cg? Cg[ Cg] Cg_ Cg` Cg~ Ch1 Ch2 Ch3 Ch4 Ch5 Ch6 Ch7 Ch8 \ -Ch9 ChA ChB ChC ChD ChE ChF ChG ChH ChI ChJ ChK ChL ChM ChN ChO ChP ChQ ChR C\ -hS Chb Chc Chd Che Chf Chg Chh Chi Chj Chk Chl Chm Chn Cho Chp Chq Chr Chs Ch\ -t Chu Chv Chw Chx Chy Chz Ch# Ch$ Ch% Ch& Ch' Ch( Ch) Ch* Ch+ Ch, Ch- Ch. Ch/\ - Ch: Ch; Ch< Ch= Ch> Ch? Ch@ Ch[ Ch] Ch^ Ch_ Ch` Ch{ Ch| Ch} Ch~ Ci0 Ci1 Ci2 \ -Ci3 Ci4 Ci5 Ci6 Ci7 Ci8 Ci9 CiA CiB CiC CiD CiE CiF CiG CiH CiI CiJ CiK CiL C\ -iM CiN CiO CiP CiQ CiR CiS CiU CiW CiX CiY Cib Cic Cid Cie Cif Cig Cih Cii Ci\ -j Cik Cil Cim Cin Cio Cip Ciq Cir Cis Cit Ciu Civ Ciw Cix Ciy Ciz Ci# Ci$ Ci%\ - Ci& Ci' Ci( Ci) Ci* Ci+ Ci, Ci- Ci/ Ci= Ci? Ci@ Ci[ Ci^ Ci{ Ci| Cj1 Cj5 Cj7 \ -Cj8 Cj9 CjA CjB CjC CjD CjE CjF CjG CjH CjI CjJ CjK CjL CjM CjN CjO CjP CjQ C\ -jR CjS CjT CjU CjV CjW CjX CjY CjZ Cje Cjf Cjh Cji Cjj Cjk Cjl Cjm Cjn Cjo Cj\ -p Cjq Cjr Cjs Cjt Cju Cjv Cjw Cjx Cjy Cjz Cj# CkQ CkR CkS CkT CkU CkV CkW CkX\ - CkY CkZ Cka Ckb Ckc Ckd Cke Ckf Ckg Ckh Cki Ckj Ckl Ckm ClG ClH ClI ClJ ClK \ -ClL ClM ClN ClO ClT ClU ClW ClX ClY ClZ Cla Clb Clc Cld Cle Clf Clg CL C>M C>O C>S C>T C>U C>V C>W C>X C>Y C>Z C>a C>b C>c C>d C>e \ -C>f C>g C>h C>i C>j C>k C_k C_m C_n C_o C_p C_q C_r C_s C_t C_u C_v C_w C_x C\ -_y C_z C_# C_$ C_% C_& C_' C_( C`V C`W C`Y C`c C`e C`f C`g C`h C`i C`j C`k C`\ -l C`m C`n C`o C`p C`q C`r C`s C`t C`u C`v C{M C{N C{P C{T C{U C{V C{W C{X C{Y\ - C{Z C{a C{b C{c C{d C{e C{f C{g C{h C{i C{j C{k C{l C12j C12k C12m C12p C12q\ - C12r C12s C12t C12u C12v C12w C12x C12y C12z C12# C12$ C12% C12& C12' C12( C\ -12) C13Y C13a C13b C13f C13g C13h C13i C13j C13k C13l C13m C13n C13o C13p C13\ -q C13r C13s C13t C13u C13v C13w C14N C14O C14Q C14U C14V C14W C14X C14Y C14Z \ -C14a C14b C14c C14d C14e C14f C14g C14h C14i C14j C14k C14l C14m C17; C17< C1\ -7> C17@ C17[ C17] C17^ C17_ C17` C17{ C17| C17} C17~ C180 C181 C182 C183 C184\ - C185 C186 C187 C188 C18$ C18% C18& C18' C18( C18) C18* C18+ C18, C18. C18/ C\ -18: C18; C18@ C18[ C18] C18^ C18_ C18` C18{ C18| C18} C19r C19s C19t C19u C19\ -v C19w C19x C19y C19z C19# C19$ C19% C19& C19' C19( C19) C19* C19+ C19, C19- \ -C19/ C19; C1F< C1F= C1F? C1F[ C1F] C1F^ C1F_ C1F` C1F{ C1F| C1F} C1F~ C1G0 C1\ -G1 C1G2 C1G3 C1G4 C1G5 C1G6 C1G7 C1G8 C1G9 C1G% C1G& C1G' C1G( C1G) C1G* C1G+\ - C1G, C1G- C1G; C1G= C1G? C1G@ C1G[ C1G] C1G^ C1G_ C1G` C1G{ C1G| C1G} C1G~ C\ -1Hs C1Ht C1Hu C1Hv C1Hw C1Hx C1Hy C1Hz C1H# C1H$ C1H% C1H& C1H' C1H( C1H) C1H\ -* C1H+ C1H, C1H. C1H/ C1H= C1H? C1N= C1N> C1N@ C1N] C1N^ C1N_ C1N` C1N{ C1N| \ -C1N} C1N~ C1O0 C1O1 C1O2 C1O3 C1O4 C1O5 C1O6 C1O7 C1O8 C1O9 C1OA C1O& C1O' C1\ -O( C1O) C1O* C1O+ C1O, C1O- C1O. C1O/ C1O; C1O? C1O@ C1O] C1O^ C1O_ C1O` C1O{\ - C1O| C1O} C1O~ C1P0 C1Pt C1Pu C1Pv C1Pw C1Px C1Py C1Pz C1P# C1P$ C1P% C1P& C\ -1P' C1P( C1P) C1P* C1P+ C1P, C1P- C1P< C1P= C1P> C1P? C1T* C1T+ C1T, C1T- C1T\ -. C1T/ C1T: C1T; C1T< C1Ux C1Uy C1Uz C1U$ C1U( C1U) C1U* C1U+ C1U- C1U; C1U< \ -C1U= C1U> C1U@ C1U_ C1Vn C1Vo C1Vp C1Vq C1Vr C1Vs C1Vt C1Vu C1Vv C1bJ C1bM C1\ -b+ C1b, C1b- C1b. C1b/ C1b: C1b; C1b< C1b= C1c9 C1cC C1cy C1cz C1c& C1c* C1c+\ - C1c/ C1c= C1c> C1c] C1d5 C1d9 C1dE C1dM C1do C1dp C1dq C1dr C1ds C1dt C1du C\ -1dv C1dw C1jj C1jk C1jr C1jt C1jv C1jz C1j# C1j$ C1j' C1j+ C1j, C1j- C1j. C1j\ -/ C1j: C1j; C1j< C1j= C1j> C1kZ C1ka C1kb C1kd C1ke C1kf C1kz C1k$ C1k& C1k+ \ -C1k- C1k/ C1k> C1k@ C1k] C1lP C1lQ C1lR C1lT C1lU C1lV C1lp C1lq C1lr C1ls C1\ -lt C1lu C1lv C1lw C1lx C2Ya C2Yb C2Yc C2Yd C2Ye C2Yf C2Yg C2Yh C2Yi C2Ym C2Yn\ - C2Yo C2Yp C2Yq C2Yr C2Yv C2Yw C2Yx C2Yy C2Yz C2Y# C2Y- C2Y. C2Y/ C2Y: C2Y; C\ -2Y< C2Y= C2Y> C2Y? C2Y^ C2Y_ C2Y` C2Y{ C2Y| C2Y} C2Z8 C2Z9 C2ZA C2ZB C2ZC C2Z\ -D C2ZE C2ZF C2ZG C2ZH C2ZI C2ZJ C2ZK C2ZL C2ZM C2ZN C2ZO C2ZP C2ZQ C2ZS C2ZV \ -C2ZW C2Zc C2Zd C2Ze C2Zf C2Zg C2Zh C2Zl C2Zm C2Zn C2Zo C2Zp C2Zq C2Zr C2Zs C2\ -Zt C2Zu C2Zv C2Zw C2Zx C2Zy C2Zz C2Z$ C2Z( C2Z* C2Z+ C2Z/ C2Z: C2Z; C2Z< C2Z=\ - C2Z> C2Z? C2Z@ C2Z[ C2Z] C2Z^ C2Z_ C2Z` C2Z{ C2Z| C2Z} C2a1 C2a3 C2a6 C2a8 C\ -2a9 C2aB C2aF C2aG C2aH C2aI C2aJ C2aK C2aL C2aM C2aN C2aO C2aS C2aT C2aU C2a\ -V C2aW C2aX C2ab C2ac C2ad C2ae C2af C2ag C2ah C2ak C2am C2ap C2aq C2ar C2as \ -C2at C2au C2av C2aw C2ax C2ay C2a% C2a& C2a' C2a( C2a) C2a* C2a- C2a. C2a; C2\ -a= C2a> C2a? C2a@ C2a[ C2a] C2a^ C2a_ C2a` C2a{ C2b1 C2b5 C2b6 C2b7 C2b8 C2b9\ - C2bA C2bB C2bC C2bD C2bE C2bF C2bG C2bH C2bI C2bJ C2bK C2bL C2bM C2bN C2bX C\ -2bY C2bZ C2ba C2bb C2bc C2bd C2be C2bf C2bh C2bi C2bk C2bl C2bn C2bo C2bt C2b\ -u C2bw C2by C2bz C2b# C2b$ C2b% C2b& C2b' C2b( C2b) C2b* C2b+ C2b, C2b- C2b. \ -C2b/ C2b: C2b; C2b< C2b{ C2b| C2b} C2b~ C2c0 C2c1 C2c2 C2c3 C2c4 C2c6 C2c7 C2\ -c9 C2cA C2cC C2cD C2cE C2cF C2cG C2cH C2cI C2cJ C2cK C2cL C2cM C2cP C2cR C2cS\ - C2cW C2cX C2cY C2cZ C2ca C2cb C2cc C2cd C2ce C2cf C2cg C2ch C2ci C2cj C2ck C\ -2cl C2cm C2cn C2co C2cp C2cq C2cr C2cs C2ct C2cu C2cv C2cw C2cz C2c$ C2c% C2c\ -) C2c* C2c+ C2c, C2c- C2c. C2c/ C2c: C2c; C2c= C2c[ C2c` C2c{ C2c| C2c} C2c~ \ -C2d0 C2d1 C2d2 C2d3 C2d5 C2d6 C2d8 C2dD C2dE C2dF C2dG C2dH C2dI C2dJ C2dK C2\ -dL C2dM C2dN C2dO C2dP C2dQ C2dR C2dS C2dT C2dU C2dV C2dW C2dX C2dY C2dZ C2da\ - C2db C2dc C2dd C2df C2dg C2di C2dj C2dl C2dm C2d# C2d$ C2d& C2d' C2d( C2d) C\ -2d+ C2d- C2d/ C2d: C2d; C2d< C2d= C2d> C2d? C2d@ C2d[ C2d] C2d^ C2d| C2d} C2e\ -0 C2e1 C2e3 C2e4 C2e5 C2e6 C2e7 C2e8 C2e9 C2eA C2eB C2eC C2eD C2eF C2eH C2eJ \ -C2eK C2eU C2eV C2eW C2eX C2eY C2eZ C2ea C2eb C2ec C2ed C2ee C2eg C2ei C2ek C2\ -el C2ev C2ew C2ex C2ey C2ez C2e# C2e$ C2e% C2e& C2e( C2e) C2e* C2e+ C2e- C2e/\ - C2e; C2e< C2e= C2e> C2e@ C2e] C2e^ C2e_ C2e` C2e{ C2e| C2e} C2e~ C2f0 C2f1 C\ -2f2 C2f3 C2f8 C2f9 C2fC C2fD C2fE C2fF C2fH C2fJ C2fL C2fM C2fR C2fS C2fT C2f\ -U C2fV C2fW C2fX C2fY C2fZ C2fa C2fb C2fc C2fe C2fg C2fh C2fi C2fj C2fl C2fm \ -C2fr C2fs C2fu C2fv C2fw C2fx C2fy C2fz C2f# C2f$ C2f% C2f& C2f' C2f( C2f) C2\ -f* C2f+ C2f, C2f- C2f. C2f/ C2f; C2f= C2f> C2f? C2f@ C2g1 C2g2 C2g7 C2g8 C2gA\ - C2gC C2gE C2gF C2gG C2gH C2gJ C2gK C2gL C2gM C2gN C2gO C2gP C2gQ C2gR C2gb C\ -2gc C2gd C2ge C2gf C2gg C2gh C2gi C2gj C2gk C2gl C2gm C2gw C2gx C2gy C2g. C2g\ -/ C2g: C2g; C2g< C2g= C2g> C2g? C2g@ C2g| C2g} C2g~ C2h9 C2hA C2hB C2hC C2hD \ -C2hE C2hF C2hG C2hH C2hL C2hM C2hN C2hO C2hP C2hQ C2hS C2hT C2hV C2hZ C2ha C2\ -hb C2hc C2hm C2hn C2ho C2hs C2ht C2hu C2hv C2hw C2hx C2hy C2hz C2h# C2h% C2h&\ - C2h( C2h, C2h= C2h> C2h? C2h@ C2h[ C2h] C2h^ C2h_ C2h` C2h{ C2h| C2h} C2h~ C\ -2i0 C2i2 C2i6 C2iC C2iG C2iH C2iI C2iJ C2iK C2iL C2iM C2iN C2iO C2iQ C2iR C2i\ -S C2ic C2id C2ie C2ii C2im C2io C2ip C2ir C2is C2it C2iu C2iw C2ix C2iy C2iz \ -C2i) C2i* C2i+ C2i. C2i: C2i; C2i? C2i@ C2i] C2i^ C2i_ C2i` C2i{ C2i| C2j1 C2\ -j4 C2j8 C2j9 C2jB C2jC C2jE C2jF C2jG C2jH C2jI C2jJ C2jK C2jL C2jM C2jN C2jO\ - C2jY C2jZ C2ja C2jb C2jc C2jd C2je C2jf C2jg C2ji C2jl C2jo C2jy C2jz C2j# C\ -2j$ C2j% C2j& C2j' C2j( C2j) C2j* C2j+ C2j, C2j- C2j. C2j/ C2j: C2j; C2j< C2j\ -= C2j| C2j} C2j~ C2k0 C2k1 C2k2 C2k3 C2k4 C2k5 C2k6 C2k9 C2kC C2kF C2kG C2kH \ -C2kI C2kJ C2kK C2kL C2kM C2kN C2kV C2kX C2kY C2kZ C2ka C2kb C2kc C2kd C2kf C2\ -kh C2kj C2kk C2kl C2km C2kn C2kp C2kq C2kr C2ks C2kt C2ku C2kv C2kw C2kx C2k)\ - C2k* C2k+ C2k, C2k- C2k. C2k/ C2k: C2k; C2k< C2k@ C2k^ C2k| C2k} C2l0 C2l3 C\ -2l4 C2lC C2lE C2lF C2lG C2lH C2lI C2lJ C2lK C2lM C2lN C2lO C2lP C2lQ C2lR C2l\ -S C2lT C2lU C2lV C2lW C2lX C2lY C2lZ C2la C2lb C2lc C2ld C2le C2lh C2lk C2ln \ -C2l$ C2l% C2l' C2l( C2l+ C2l- C2l/ C2l< C2l= C2l> C2l? C2l@ C2l[ C2l] C2l^ C2\ -l_ C2m0 C2m1 C2m4 C2m5 C2m7 C2m8 C2m9 C2mA C2mB C2mC C2mE C2mG C2mL C2mV C2mW\ - C2mX C2mY C2mZ C2ma C2mb C2mc C2md C2me C2mj C2ml C2mw C2mx C2my C2mz C2m# C\ -2m$ C2m% C2m& C2m' C2m( C2m- C2m/ C2m= C2m? C2m[ C2m_ C2m` C2m| C2m~ C2n1 C2n\ -2 C2n4 C2n5 C2n7 C2n8 C2nD C2nF C2nK C2nM C2nN C2nP C2nQ C2nU C2nV C2nW C2nX \ -C2nY C2nZ C2na C2nc C2ne C2ng C2nl C2nq C2nr C2nt C2nu C2nv C2nx C2ny C2nz C2\ -n# C2n$ C2n% C2n& C2n' C2n( C2n) C2n* C2n+ C2n, C2n- C2n. C2n/ C2n: C2n? C2n[\ - C2o5 C2o7 C2o8 C2oA C2oD C2oF C2oK C2oL C2oM C2oN C2oO C2oP C2oQ C2oR C2oS C\ -2oc C2od C2oe C2of C2og C2oh C2oi C2oj C2ok C2ol C2om C2on C2o# C2o$ C2o% C2o\ -/ C2o: C2o; C2o< C2o= C2o> C2o? C2o@ C2o[ C2o` C2o{ C2o| C2pA C2pB C2pC C2pD \ -C2pE C2pF C2pG C2pH C2pI C2pM C2pN C2pO C2pP C2pQ C2pR C2pS C2pT C2pV C2pZ C2\ -pb C2pc C2pd C2pq C2pr C2ps C2pt C2pu C2pv C2pw C2px C2py C2pz C2p# C2p$ C2p'\ - C2p) C2p* C2p, C2p; C2p< C2p[ C2p] C2p^ C2p| C2p} C2p~ C2q1 C2q5 C2q7 C2q8 C\ -2qD C2qH C2qI C2qJ C2qK C2qL C2qM C2qN C2qP C2qQ C2qR C2qS C2qT C2qg C2qh C2q\ -i C2qk C2ql C2qn C2qs C2qt C2qu C2qv C2qw C2qx C2qz C2q# C2q' C2q( C2q) C2q- \ -C2q. C2q: C2q> C2q@ C2q[ C2q] C2q^ C2q_ C2q` C2q{ C2q| C2r2 C2r5 C2r9 C2rA C2\ -rC C2rF C2rG C2rH C2rI C2rJ C2rK C2rL C2rM C2rN C2rO C2rP C2rZ C2ra C2rb C2rc\ - C2rd C2re C2rf C2rg C2rh C2rk C2rn C2rq C2ry C2r# C2r% C2r& C2r( C2r) C2r+ C\ -2r, C2r- C2r. C2r/ C2r: C2r; C2r< C2r= C2r> C2r} C2r~ C2s0 C2s1 C2s2 C2s3 C2s\ -4 C2s5 C2s6 C2s7 C2sA C2sD C2sG C2sH C2sI C2sJ C2sK C2sL C2sM C2sN C2sO C2sU \ -C2sY C2sZ C2sb C2sc C2sd C2sf C2sg C2sh C2si C2sj C2sk C2sl C2sn C2sp C2sq C2\ -sr C2ss C2st C2su C2sv C2sw C2sx C2sy C2s& C2s+ C2s, C2s- C2s. C2s/ C2s: C2s;\ - C2s< C2s= C2s> C2s_ C2s} C2t1 C2t2 C2t5 C2t8 C2tF C2tG C2tI C2tL C2tM C2tO C\ -2tP C2tQ C2tR C2tS C2tT C2tU C2tV C2tW C2tX C2tY C2tZ C2ta C2tb C2tc C2td C2t\ -e C2tf C2th C2tk C2tn C2t% C2t& C2t( C2t) C2t, C2t. C2t= C2t> C2t@ C2t] C2t_ \ -C2t` C2u0 C2u4 C2u5 C2u6 C2u7 C2u8 C2uA C2uB C2uC C2uE C2uJ C2uL C2uW C2uX C2\ -uY C2uZ C2ua C2ub C2uc C2ud C2ue C2ug C2ui C2un C2ux C2uy C2uz C2u# C2u$ C2u%\ - C2u& C2u' C2u( C2u) C2u. C2u: C2u= C2u? C2u_ C2u` C2u| C2u~ C2v0 C2v1 C2v2 C\ -2v7 C2v9 C2vA C2vC C2vF C2vH C2vJ C2vR C2vT C2vU C2vV C2vW C2vX C2vY C2va C2v\ -b C2vc C2vf C2vh C2vm C2vn C2vp C2vs C2vw C2vx C2v# C2v$ C2v% C2v& C2v' C2v( \ -C2v) C2v* C2v+ C2v, C2v- C2v. C2v/ C2v: C2v= C2v? C2v[ C2w4 C2w5 C2w7 C2w8 C2\ -wC C2wH C2wM C2wN C2wO C2wP C2wR C2wT C2z4 C2z5 C2z7 C2z8 C2z9 C2zB C2zC C2zD\ - C2zI C2zJ C2zK C2zL C2zM C2zN C2zO C2zP C2zQ C2zS C2zT C2zV C2zW C2za C2zb C\ -2ze C2zf C2zj C2zk C2zl C2zm C2zn C2zo C2zp C2zq C2zr C2zw C2zx C2zy C2z# C2z\ -$ C2z% C2z& C2z' C2z( C2z) C2z* C2z+ C2z, C2z. C2z/ C2z; C2z< C2z@ C2z[ C2z] \ -C2z^ C2z_ C2z` C2z{ C2z| C2z} C2z~ C2#0 C2#1 C2#2 C2#3 C2#4 C2#5 C2#6 C2#7 C2\ -#9 C2#C C2#D C2#G C2#H C2#I C2#J C2#K C2#L C2#M C2#N C2#O C2#P C2#Q C2#R C2#S\ - C2#T C2#U C2#V C2#W C2#X C2#Y C2#a C2#b C2#e C2#g C2#i C2#j C2#k C2#l C2#m C\ -2#n C2#o C2#p C2#q C2#s C2#t C2#w C2#y C2## C2#$ C2#% C2#& C2#' C2#( C2#) C2#\ -* C2#+ C2#- C2#. C2#/ C2#< C2#[ C2#^ C2#_ C2#{ C2#} C2#~ C2$0 C2$1 C2$2 C2$3 \ -C2$4 C2$5 C2$6 C2$9 C2$A C2$B C2$H C2$I C2$K C2$O C2$P C2$Q C2$R C2$S C2$T C2\ -$U C2$V C2$W C2$X C2$Z C2$a C2$c C2$g C2$h C2$i C2$j C2$k C2$l C2$m C2$n C2$o\ - C2$p C2$q C2$s C2$u C2$x C2$& C2$( C2$+ C2$, C2$- C2$. C2$/ C2$: C2$; C2$< C\ -2$= C2$> C2$? C2$@ C2$[ C2$] C2$^ C2$_ C2$` C2${ C2%6 C2%7 C2%8 C2%9 C2%A C2%\ -B C2%C C2%D C2%E C2%F C2%G C2%H C2%I C2%J C2%K C2%L C2%M C2%N C2%O C2%P C2%Q \ -C2%R C2%S C2%T C2%U C2%V C2%W C2%X C2%Y C2%Z C2%a C2%b C2%c C2%d C2%e C2%f C2\ -%h C2%i C2%j C2%m C2%p C2%q C2%r C2%s C2%t C2%u C2%v C2%w C2%x C2%' C2%( C2%*\ - C2%+ C2%, C2%- C2%. C2%/ C2%: C2%; C2%< C2%= C2%> C2%? C2%@ C2%[ C2%] C2%^ C\ -2%_ C2%` C2%{ C2%} C2&0 C2&3 C2&5 C2&6 C2&7 C2&8 C2&9 C2&A C2&B C2&C C2&D C2&\ -G C2&L C2&N C2&O C2&P C2&Q C2&R C2&S C2&T C2&U C2&V C2&W C2&X C2&Y C2&Z C2&a \ -C2&b C2&c C2&d C2&e C2&f C2&g C2&h C2&j C2&k C2&l C2&m C2&n C2&o C2&p C2&q C2\ -&r C2&s C2&t C2&u C2&v C2&w C2&x C2&# C2&' C2&( C2&) C2&* C2&+ C2&, C2&- C2&.\ - C2&/ C2&: C2&; C2&< C2&= C2&> C2&? C2&@ C2&[ C2&] C2&^ C2&_ C2&` C2&{ C2'4 C\ -2'5 C2'6 C2'7 C2'8 C2'9 C2'A C2'B C2'C C2'D C2'E C2'M C2'N C2'O C2'P C2'Q C2'\ -R C2'S C2'T C2'U C2*5 C2*6 C2*8 C2*9 C2*D C2*F C2*G C2*H C2*J C2*K C2*L C2*M \ -C2*N C2*O C2*P C2*Q C2*R C2*V C2*X C2*Y C2*a C2*b C2*d C2*i C2*j C2*k C2*l C2\ -*m C2*n C2*o C2*p C2*q C2*r C2*s C2*w C2*x C2*# C2*$ C2*% C2*& C2*' C2*( C2*)\ - C2** C2*+ C2*, C2*- C2*. C2*/ C2*> C2*? C2*[ C2*] C2*^ C2*_ C2*` C2*{ C2*| C\ -2*} C2*~ C2+0 C2+1 C2+2 C2+3 C2+4 C2+5 C2+6 C2+7 C2+8 C2+B C2+D C2+G C2+H C2+\ -I C2+J C2+K C2+L C2+M C2+N C2+O C2+P C2+Q C2+R C2+S C2+T C2+U C2+V C2+W C2+X \ -C2+Y C2+Z C2+a C2+f C2+g C2+i C2+j C2+k C2+l C2+m C2+n C2+o C2+p C2+q C2+r C2\ -+s C2+t C2+w C2+y C2+$ C2+% C2+& C2+' C2+( C2+) C2+* C2++ C2+, C2+- C2+; C2+<\ - C2+= C2+[ C2+] C2+_ C2+} C2+~ C2,0 C2,1 C2,2 C2,3 C2,4 C2,5 C2,6 C2,7 C2,9 C\ -2,A C2,B C2,E C2,H C2,J C2,M C2,N C2,Q C2,R C2,S C2,T C2,U C2,V C2,W C2,X C2,\ -Y C2,a C2,c C2,d C2,f C2,i C2,j C2,k C2,l C2,m C2,n C2,o C2,p C2,q C2,s C2,t \ -C2,u C2,x C2,' C2,+ C2,, C2,- C2,. C2,/ C2,: C2,; C2,< C2,= C2,> C2,? C2,@ C2\ -,[ C2,] C2,^ C2,_ C2,` C2,{ C2,| C2-3 C2-6 C2-7 C2-8 C2-9 C2-A C2-B C2-C C2-D\ - C2-E C2-F C2-G C2-H C2-I C2-J C2-K C2-L C2-M C2-N C2-O C2-R C2-S C2-T C2-U C\ -2-V C2-W C2-X C2-Y C2-Z C2-a C2-b C2-c C2-d C2-e C2-f C2-g C2-h C2-l C2-m C2-\ -n C2-q C2-r C2-s C2-t C2-u C2-v C2-w C2-x C2-y C2-' C2-( C2-+ C2-, C2-- C2-. \ -C2-/ C2-: C2-; C2-< C2-= C2-> C2-? C2-@ C2-[ C2-] C2-^ C2-_ C2-` C2-{ C2-} C2\ --~ C2.0 C2.3 C2.6 C2.7 C2.8 C2.9 C2.A C2.B C2.C C2.D C2.E C2.K C2.M C2.O C2.P\ - C2.Q C2.R C2.S C2.T C2.U C2.V C2.W C2.X C2.Y C2.Z C2.a C2.b C2.c C2.d C2.e C\ -2.f C2.g C2.h C2.i C2.k C2.l C2.n C2.o C2.p C2.q C2.r C2.s C2.t C2.u C2.v C2.\ -w C2.x C2.z C2.$ C2.& C2.( C2.* C2.+ C2., C2.- C2.. C2./ C2.: C2.; C2.< C2.= \ -C2.> C2.? C2.@ C2.[ C2.] C2.^ C2._ C2.` C2.{ C2.} C2/5 C2/6 C2/7 C2/8 C2/9 C2\ -/A C2/B C2/C C2/D C2/G C2/I C2/N C2/O C2/P C2/Q C2/R C2/S C2/T C2/U C2/V C2<6\ - C2<7 C2<9 C2 C20 \ -C2>1 C2>2 C2>3 C2>4 C2>5 C2>6 C2>7 C2>8 C2>A C2>F C2>H C2>I C2>J C2>L C2>P C2\ ->R C2>S C2>T C2>U C2>V C2>W C2>X C2>Y C2>Z C2>c C2>d C2>g C2>i C2>j C2>k C2>l\ - C2>m C2>n C2>o C2>p C2>q C2>r C2>s C2>t C2>x C2># C2>' C2>* C2>- C2>. C2>/ C\ -2>: C2>; C2>< C2>= C2>> C2>? C2>@ C2>[ C2>] C2>^ C2>_ C2>` C2>{ C2>| C2>} C2?\ -3 C2?6 C2?8 C2?9 C2?A C2?B C2?C C2?D C2?E C2?F C2?G C2?H C2?I C2?J C2?K C2?L \ -C2?M C2?N C2?O C2?P C2?Q C2?T C2?U C2?V C2?X C2?Y C2?Z C2?a C2?b C2?c C2?d C2\ -?e C2?f C2?g C2?h C2?i C2?l C2?p C2?q C2?r C2?s C2?t C2?u C2?v C2?w C2?x C2?y\ - C2?z C2?% C2?' C2?, C2?- C2?. C2?/ C2?: C2?; C2?< C2?= C2?> C2?? C2?@ C2?[ C\ -2?] C2?^ C2?_ C2?` C2?{ C2?| C2?} C2?~ C2@3 C2@6 C2@7 C2@9 C2@A C2@B C2@C C2@\ -D C2@E C2@H C2@K C2@P C2@Q C2@R C2@S C2@T C2@U C2@V C2@W C2@X C2@Y C2@Z C2@a \ -C2@b C2@c C2@d C2@e C2@f C2@g C2@h C2@i C2@l C2@m C2@o C2@p C2@q C2@r C2@s C2\ -@t C2@u C2@v C2@w C2@x C2@y C2@z C2@# C2@' C2@* C2@+ C2@, C2@- C2@. C2@/ C2@:\ - C2@; C2@< C2@= C2@> C2@? C2@@ C2@[ C2@] C2@^ C2@_ C2@` C2@{ C2[6 C2[7 C2[8 C\ -2[9 C2[A C2[B C2[C C2[D C2[E C2[K C2[L C2[O C2[P C2[Q C2[R C2[S C2[T C2[U C2[\ -V C2[W C2_6 C2_8 C2_9 C2_A C2_C C2_D C2_E C2_F C2_G C2_H C2_I C2_J C2_K C2_M \ -C2_N C2_P C2_T C2_V C2_W C2_Z C2_b C2_d C2_e C2_f C2_g C2_h C2_i C2_j C2_k C2\ -_l C2_m C2_n C2_o C2_p C2_r C2_t C2_u C2_z C2_# C2_% C2_& C2_' C2_( C2_) C2_*\ - C2_+ C2_, C2_- C2_. C2_/ C2_: C2_; C2_? C2_] C2__ C2_` C2_{ C2_~ C2`3 C2`4 C\ -2`6 C2`7 C2`B C2`C C2`D C2`E C2`F C2`G C2`H C2`I C2`J C2`L C2`M C2`N C2`P C2`\ -T C2`U C2`V C2`W C2`X C2`Y C2`Z C2`a C2`b C2`d C2`e C2`g C2`k C2`l C2`m C2`n \ -C2`o C2`p C2`q C2`r C2`s C2`t C2`u C2`v C2`w C2`y C2`z C2`# C2`$ C2`' C2`* C2\ -`+ C2`. C2`: C2`; C2`> C2`@ C2`] C2`^ C2`_ C2`` C2`{ C2`| C2`} C2`~ C2{0 C2{1\ - C2{3 C2{4 C2{5 C2{6 C2{7 C2{8 C2{B C2{D C2{F C2{H C2{K C2{L C2{N C2{O C2{S C\ -2{T C2{U C2{V C2{W C2{X C2{Y C2{Z C2{a C2{b C2{c C2{d C2{e C2{f C2{g C2{h C2{\ -i C2{j C2{m C2{o C2{p C2{r C2{t C2{u C2{x C2{y C327 C329 C32A C32B C32D C32E \ -C32F C32G C32H C32I C32J C32K C32L C32N C32R C32T C32U C32X C32Y C32a C32b C3\ -2e C32f C32g C32h C32i C32j C32k C32l C32m C32n C32o C32q C32s C32t C32u C32v\ - C32z C32# C32% C32& C32( C32) C32* C32+ C32, C32- C32. C32/ C32: C32< C32? C\ -32[ C32^ C32` C32{ C32| C330 C337 C338 C33A C33B C33C C33D C33E C33F C33G C33\ -H C33I C33J C33K C33O C33Q C33R C33S C33U C33V C33W C33X C33Y C33Z C33a C33b \ -C33c C33d C33f C33i C33j C33m C33n C33o C33p C33q C33r C33s C33t C33u C33v C3\ -3w C33x C33y C33z C33$ C33& C33' C33( C33+ C33- C33; C33< C33? C33[ C33^ C33_\ - C33` C33{ C33| C33} C33~ C340 C341 C342 C343 C345 C347 C348 C349 C34A C34D C\ -34G C34H C34I C34K C34M C34Q C34S C34T C34U C34V C34W C34X C34Y C34Z C34a C34\ -b C34c C34d C34e C34f C34g C34h C34i C34j C34k C34l C34p C34r C34s C34u C34v \ -C34# C34% C3A8 C3AA C3AB C3AC C3AE C3AF C3AG C3AH C3AI C3AJ C3AK C3AL C3AM C3\ -AP C3AR C3AS C3AU C3AX C3AZ C3Ac C3Ad C3Af C3Ag C3Ah C3Ai C3Aj C3Ak C3Al C3Am\ - C3An C3Ao C3Ap C3Ar C3As C3At C3Av C3Aw C3A# C3A% C3A& C3A( C3A) C3A* C3A+ C\ -3A, C3A- C3A. C3A/ C3A: C3A; C3A< C3A@ C3A[ C3A] C3A{ C3A| C3A} C3B1 C3B5 C3B\ -6 C3BB C3BC C3BD C3BE C3BF C3BG C3BH C3BI C3BJ C3BK C3BL C3BN C3BO C3BS C3BT \ -C3BV C3BW C3BX C3BY C3BZ C3Ba C3Bb C3Bc C3Bd C3Be C3Bf C3Bh C3Bl C3Bn C3Bo C3\ -Bp C3Bq C3Br C3Bs C3Bt C3Bu C3Bv C3Bw C3Bx C3By C3Bz C3B$ C3B& C3B' C3B( C3B.\ - C3B: C3B< C3B= C3B@ C3B] C3B_ C3B` C3B{ C3B| C3B} C3B~ C3C0 C3C1 C3C2 C3C3 C\ -3C4 C3C5 C3C6 C3C7 C3C9 C3CB C3CD C3CE C3CF C3CI C3CO C3CP C3CR C3CS C3CU C3C\ -V C3CW C3CX C3CY C3CZ C3Ca C3Cb C3Cc C3Cd C3Ce C3Cf C3Cg C3Ch C3Ci C3Cj C3Ck \ -C3Cl C3Cm C3Co C3Cr C3Cs C3Cz C3C# C3C$ C3C& C3K( C3K+ C3K, C3K- C3K. C3K/ C3\ -K: C3K; C3K< C3K= C3K> C3K? C3K@ C3K[ C3K] C3K^ C3K_ C3K` C3L2 C3L3 C3L4 C3L5\ - C3L6 C3L7 C3L8 C3L9 C3LA C3LB C3LC C3LD C3LM C3LN C3LP C3LQ C3LR C3LS C3LT C\ -3LU C3LV C3LW C3LX C3LY C3LZ C3La C3Lb C3Lc C3Ld C3Le C3Lf C3Lg C3Lh C3Li C3L\ -j C3Lk C3Ll C3Lm C3Lp C3Lt C3Lu C3Lw C3L' C3L( C3L) C3L* C3L+ C3L- C3L. C3L: \ -C3L; C3L< C3L= C3L> C3L? C3L@ C3L[ C3L] C3L^ C3L_ C3L` C3L{ C3L| C3L} C3L~ C3\ -M0 C3M1 C3M2 C3M3 C3M4 C3M5 C3M6 C3M7 C3M8 C3M9 C3MA C3MC C3MD C3ME C3MH C3MQ\ - C3MS C3MT C3MU C3MV C3MX C3MZ C3Ma C3Mb C3Mc C3Md C3Me C3Mf C3Mg C3Mh C3Mi C\ -3Mj C3Mk C3Ml C3Mm C3Mn C3Mo C3Mp C3Mq C3Mr C3Ms C3Mt C3Mu C3Mw C3My C3M$ C3M\ -& C3M' C3M( C3M) C3M* C3M+ C3M, C3M- C3M. C3M@ C3M] C3M^ C3M_ C3M` C3M} C3M~ \ -C3N0 C3N1 C3N2 C3N3 C3N4 C3N5 C3N6 C3N7 C3N8 C3N9 C3NA C3NB C3NC C3ND C3NE C3\ -NF C3NG C3NH C3NI C3NQ C3NS C3NT C3NU C3NV C3NW C3NY C3NZ C3S) C3S, C3S- C3S.\ - C3S/ C3S: C3S; C3S< C3S= C3S> C3S? C3S@ C3S[ C3S] C3S^ C3S_ C3S} C3T4 C3T5 C\ -3T6 C3T7 C3T8 C3T9 C3TA C3TB C3TC C3TF C3TN C3TO C3TP C3TQ C3TR C3TT C3TU C3T\ -V C3TW C3TX C3TY C3TZ C3Ta C3Tb C3Tc C3Td C3Te C3Tf C3Tg C3Th C3Ti C3Tj C3Tk \ -C3Tl C3Tm C3To C3Tp C3Tq C3Tt C3Tx C3T# C3T' C3T( C3T* C3T+ C3T, C3T- C3T. C3\ -T: C3T; C3T< C3T= C3T> C3T? C3T@ C3T[ C3T] C3T^ C3T_ C3T` C3T{ C3T| C3T} C3T~\ - C3U0 C3U1 C3U2 C3U3 C3U4 C3U5 C3U6 C3U7 C3U8 C3U9 C3UA C3UB C3UC C3UD C3UH C\ -3UK C3UP C3UU C3UX C3UY C3UZ C3Ua C3Ub C3Uc C3Ud C3Ue C3Uf C3Ug C3Uh C3Ui C3U\ -j C3Uk C3Ul C3Um C3Un C3Uo C3Up C3Uq C3Ur C3Us C3Ut C3Uu C3Ux C3U# C3U$ C3U% \ -C3U' C3U( C3U) C3U* C3U+ C3U, C3U- C3U. C3U/ C3U= C3U@ C3U^ C3U_ C3U` C3U{ C3\ -U| C3U} C3V0 C3V2 C3V3 C3V4 C3V5 C3V6 C3V7 C3V8 C3V9 C3VA C3VB C3VC C3VD C3VE\ - C3VF C3VG C3VH C3VI C3VJ C3VP C3VS C3VT C3VU C3VV C3VX C3VY C3Va C3Vb C3a* C\ -3a- C3a. C3a/ C3a: C3a; C3a< C3a= C3a> C3a? C3a@ C3a[ C3a] C3a^ C3a_ C3a` C3a\ -~ C3b1 C3b5 C3b6 C3b7 C3b8 C3b9 C3bA C3bB C3bC C3bD C3bG C3bN C3bO C3bP C3bR \ -C3bS C3bU C3bV C3bW C3bX C3bY C3bZ C3ba C3bb C3bc C3bd C3be C3bf C3bg C3bh C3\ -bi C3bj C3bk C3bl C3bm C3bn C3bo C3bs C3bt C3bu C3bz C3b( C3b* C3b+ C3b- C3b.\ - C3b/ C3b: C3b; C3b< C3b= C3b> C3b? C3b@ C3b[ C3b] C3b^ C3b_ C3b` C3b{ C3b| C\ -3b} C3b~ C3c0 C3c1 C3c2 C3c3 C3c4 C3c5 C3c6 C3c7 C3c8 C3c9 C3cA C3cB C3cC C3c\ -D C3cF C3cH C3cK C3cP C3cR C3cT C3cV C3cW C3cX C3cY C3cZ C3ca C3cd C3ce C3cf \ -C3cg C3ch C3ci C3cj C3ck C3cl C3cm C3cn C3co C3cp C3cq C3cr C3cs C3ct C3cu C3\ -cv C3cw C3c# C3c$ C3c% C3c( C3c) C3c* C3c+ C3c, C3c- C3c. C3c/ C3c: C3c@ C3c{\ - C3c| C3c} C3c~ C3d0 C3d1 C3d2 C3d3 C3d4 C3d5 C3d6 C3d7 C3d8 C3d9 C3dA C3dB C\ -3dC C3dD C3dE C3dF C3dG C3dH C3dI C3dJ C3dK C3dN C3dP C3dT C3dU C3dV C3dW C3d\ -X C3dZ C3da C3dc C3gC C3gE C3gF C3gG C3gJ C3gK C3gM C3gN C3gR C3gS C3gT C3gU \ -C3gV C3gW C3gX C3gY C3gZ C3ga C3gb C3gc C3gd C3ge C3gf C3gg C3gh C3gi C3gl C3\ -gn C3go C3gq C3gs C3gt C3gx C3g# C3g% C3g& C3g) C3g+ C3g- C3g. C3g/ C3g: C3g;\ - C3g< C3g= C3g> C3g? C3g@ C3g[ C3g] C3g^ C3g_ C3g` C3g{ C3g| C3g} C3h0 C3h1 C\ -3h4 C3h6 C3h8 C3h9 C3hA C3hB C3hC C3hD C3hE C3hF C3hG C3hH C3hI C3hJ C3hK C3h\ -L C3hM C3hN C3hO C3hP C3hU C3hV C3hX C3hY C3hZ C3ha C3hb C3hc C3hd C3he C3hf \ -C3hg C3hh C3hi C3hj C3hm C3hn C3hs C3hu C3hw C3hy C3h# C3h$ C3h% C3h& C3h' C3\ -h( C3h) C3h* C3h+ C3h- C3h. C3h: C3h> C3h@ C3h[ C3h] C3h` C3h} C3h~ C3i0 C3i1\ - C3i2 C3i3 C3i4 C3i5 C3i6 C3i9 C3iB C3iF C3iG C3iH C3iI C3iJ C3iK C3iL C3iM C\ -3iN C3iO C3iP C3iQ C3iR C3iS C3iT C3iU C3iV C3iW C3iX C3iZ C3ic C3id C3ig C3i\ -i C3ik C3im C3ir C3is C3iu C3iv C3iz C3i# C3i$ C3i% C3i& C3i' C3i( C3i) C3i* \ -C3oD C3oF C3oG C3oH C3oK C3oL C3oQ C3oR C3oS C3oT C3oU C3oV C3oW C3oX C3oY C3\ -oZ C3oa C3ob C3oc C3od C3oe C3of C3og C3oh C3oi C3oj C3ok C3om C3op C3ot C3ox\ - C3oy C3oz C3o& C3o( C3o+ C3o, C3o. C3o/ C3o: C3o; C3o< C3o= C3o> C3o? C3o@ C\ -3o[ C3o] C3o^ C3o_ C3o` C3o{ C3o| C3o} C3o~ C3p1 C3p2 C3p5 C3p7 C3p9 C3pA C3p\ -B C3pC C3pD C3pE C3pF C3pG C3pH C3pI C3pJ C3pK C3pL C3pM C3pN C3pO C3pP C3pQ \ -C3pU C3pW C3pX C3pZ C3pa C3pb C3pc C3pd C3pe C3pf C3pg C3ph C3pi C3pn C3pp C3\ -pr C3pt C3pu C3pv C3py C3p$ C3p% C3p& C3p' C3p( C3p) C3p* C3p+ C3p, C3p- C3p.\ - C3p: C3p> C3p[ C3p] C3p^ C3p{ C3p~ C3q0 C3q1 C3q2 C3q3 C3q4 C3q5 C3q6 C3q7 C\ -3qA C3qC C3qH C3qI C3qJ C3qK C3qL C3qM C3qN C3qO C3qP C3qQ C3qR C3qS C3qT C3q\ -U C3qV C3qW C3qX C3qY C3qZ C3qe C3qf C3qh C3qo C3qp C3qu C3qv C3qx C3qy C3q# \ -C3q$ C3q% C3q& C3q' C3q( C3q) C3q* C3q+ C3wE C3wH C3wI C3wO C3wP C3wR C3wS C3\ -wT C3wU C3wV C3wW C3wX C3wY C3wZ C3wa C3wb C3wc C3wd C3we C3wf C3wg C3wh C3wi\ - C3wj C3wk C3wl C3wp C3wr C3wv C3wy C3w# C3w% C3w( C3w) C3w+ C3w, C3w/ C3w: C\ -3w; C3w< C3w= C3w> C3w? C3w@ C3w[ C3w] C3w^ C3w_ C3w` C3w{ C3w| C3w} C3w~ C3x\ -0 C3x2 C3x3 C3x6 C3x8 C3xA C3xB C3xC C3xD C3xE C3xF C3xG C3xH C3xI C3xJ C3xK \ -C3xL C3xM C3xN C3xO C3xP C3xQ C3xR C3xV C3xW C3xY C3xZ C3xb C3xc C3xd C3xe C3\ -xf C3xg C3xh C3xi C3xj C3xl C3xq C3xs C3xv C3xy C3xz C3x# C3x% C3x& C3x' C3x(\ - C3x) C3x* C3x+ C3x, C3x- C3x. C3x= C3x> C3x] C3x^ C3x_ C3x| C3y0 C3y1 C3y2 C\ -3y3 C3y4 C3y5 C3y6 C3y7 C3y8 C3yA C3yE C3yG C3yH C3yI C3yJ C3yK C3yL C3yM C3y\ -N C3yO C3yP C3yQ C3yR C3yS C3yT C3yU C3yV C3yW C3yX C3yY C3yZ C3ya C3yb C3ye \ -C3yg C3ym C3yo C3yp C3yq C3ys C3yu C3yy C3y# C3y$ C3y% C3y& C3y' C3y( C3y) C3\ -y* C3y+ C3y, C3$j C3$k C3$m C3$o C3$p C3$r C3$s C3$x C3$y C3$z C3$# C3$$ C3$%\ - C3$& C3$' C3$( C3$) C3$- C3$/ C3$; C3$< C3$? C3$@ C3$] C3$^ C3${ C3$| C3$} C\ -3$~ C3%0 C3%1 C3%2 C3%3 C3%4 C3%7 C3%9 C3%C C3%D C3%E C3%F C3%G C3%H C3%I C3%\ -J C3%K C3%L C3%M C3%Q C3%R C3%T C3%V C3%b C3%c C3%d C3%f C3%g C3%h C3%i C3%j \ -C3%k C3%l C3%m C3%n C3%o C3%p C3%q C3%r C3%s C3%u C3%w C3%$ C3%% C3%& C3%( C3\ -%) C3%* C3%+ C3%, C3%- C3%. C3%/ C3%: C3%; C3%< C3%> C3%? C3%@ C3%[ C3%] C3%^\ - C3%` C3%{ C3%| C3%} C3%~ C3&0 C3&1 C3&2 C3&3 C3&4 C3&6 C3&8 C3&9 C3&A C3&B C\ -3&C C3&G C3&I C3&J C3&P C3&R C3&S C3&U C3&V C3&W C3&X C3&Y C3&Z C3&a C3&b C3&\ -c C3&d C3&e C3&f C3&j C3&m C3&r C3&s C3&u C3&v C3&w C3&x C3&y C3&z C3&# C3&$ \ -C3&% C3&& C3&' C3&( C3&+ C3&/ C3&: C3&; C3&< C3&= C3&> C3&? 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C3>/ C3>: C3>? C3>@ C3>^ C3>` C3>} C3>~ C3?0 C3?1 C3?2 C3?3 C3?\ -4 C3?5 C3?6 C3?8 C3?9 C3?C C3?E C3?G C3?H C3?I C3?J C3?K C3?L C3?M C3?N C3?O \ -C3?P C3?Q C3?W C3?X C3?c C3?d C3?g C3?h C3?i C3?j C3?k C3?l C3?m C3?n C3?o C3\ -?p C3?q C3?r C3?s C3?u C3?v C3?w C3?x C3?z C3?$ C3?% C3?& C3?+ C3?, C3?- C3?.\ - C3?/ C3?: C3?; C3?< C3?= C3?> C3?? C3?@ C3?[ C3?] C3?_ C3?{ C3?| C3?} C3?~ C\ -3@0 C3@1 C3@2 C3@3 C3@4 C3@5 C3@6 C3@7 C3@8 C3@A C3@B C3@C C3@D C3@F C3@G C3@\ -L C3@N C3@R C3@S C3@U C3@V C3@X C3@Y C3@Z C3@a C3@b C3@c C3@d C3@e C3@f C3@g \ -C3@i C3@k C3@n C3@q C3@r C3@t C3@u C3@y C3@z C3@# C3@$ C3@% C3@& C3@' C3@( C3\ -@) C3@+ C3@- C3@/ C3@; C3@= C3@> C3@? C3@@ C3@[ C3@] C3@^ C3@_ C3@` C3@{ C3@~\ - C3[3 C3[4 C3[6 C3[7 C3[C C3[D D D2& D2' D2) D2* D2+ D2, D2< D2= D2> D2? D2] \ -D2^ D39 D3A D3B D3C D3D D3E D3P D3Q D3V D3W D3Y D3Z D3a D3b D3j D3k D3n D3o D\ -3s D3u D3v D3w D3y D3z D3' D3( D3* D3+ D3- D3/ D3= D3> D3? D3@ D3[ D3] D4) D4\ -* D4+ D4, D4- D4. D8Z D8a D8u D8x D8$ D9k D9u D9$ DA' DA( DA* DA+ DA, DA. DA<\ - DA= DA@ DA[ DA] DA_ DBT DBU DBW DBX DBZ DBa DBe DBg DBh DBj DBk DBl DBt DBv \ -DBw DBx DBz DB$ DB( DB* DB, DB- DB. DB/ DDa DDb DDd DDe DDf DDg DDl DDn DDp D\ -Dq DDr DDs DDy DDz DD' DD( DD) DD* DD- DD. DD? DD@ DD] DD_ DEn DEo DEt DEu DE\ -w DEy DEz DE# DE+ DE- DE/ DE: DOC DP2 DQ& DQ' DQ* DQ, DQ. DQ; DQ< DQ? DQ] DQ_\ - DQ| DQ} DR1 DR2 DR3 DR4 DR5 DR7 DR8 DR9 DRA DRC DRD DRF DRG DRH DRI DRJ DRK \ -DRL DRM DRO DRP DRY DRa DRb DRc DRd DRe DRf DRg DRh DRi DR@ DR[ DR] DR^ DR_ D\ -R` DR{ DR| DR} DR~ DS0 DS1 DS2 DS3 DS4 DS5 DS6 DS7 DS8 DS9 DSA DSB DSC DSD DS\ -E DSF DSG DSH DSI DSJ DSK DSL DSM DSN DSO DSP DSQ DSR DSS DST DT7 DT8 DT9 DTA\ - DTB DTC DTD DTE DTF DTP DTQ DTR DTS DTT DTU DTZ DTa DTc DTg DTh DTi DTk DTl \ -DTm DTn DTp DTq DTr DTs DTt DTu DTv DTw DTx DTy DT# DT$ DT' DT) DT+ DT- DT. D\ -T/ DT: DT; DT< DT> DT? DT@ DT[ DT] DT^ DT_ DT` DT{ DT| DT} DT~ DU1 DU2 DU4 DU\ -5 DU6 DU7 DU8 DU9 DUA DUB DUC DUD DUE DUF DUI DUM DUN DWF DWG DWH DWL DWW DWX\ - DWZ DWa DWc DWd DWe DWf DWh DWi DWk DWl DWn DWp DWq DWs DWt DWv DWx DWy DW# \ -DW$ DW& DW' DW( DW* DW+ DW- DW. DW: DW; DW< DW> DW? DW[ DW] DX4 DX6 DX8 DXA D\ -Xn DXo DXq DXr DXt DXu DXv DXx DXy DX# DX$ DX& DX' DX( DX* DX+ DX- DX. DX^ DX\ -| DX} DX~ DY' DY( DY+ DY- DY; DY< DY> DY? DY_ DY{ DY~ DZ0 DZ2 DZ3 DZ5 DZ6 DZ7\ - DZ8 DZ9 DZA DZB DZC DZE DZF DZH DZI DZJ DZL DZM DZN DZO DZP DZR DZX DZb DZc \ -DZd DZe DZf DZg DZh DZi DZj DZ[ DZ] DZ^ DZ_ DZ` DZ{ DZ| DZ} DZ~ Da0 Da1 Da2 D\ -a3 Da4 Da5 Da6 Da7 Da8 Da9 DaA DaB DaC DaD DaE DaF DaG DaH DaI DaJ DaK DaL Da\ -M DaN DaO DaP DaQ DaT DaX DaY Db8 Db9 DbA DbB DbC DbD DbE DbF DbG DbQ DbR DbS\ - DbT DbU DbV Dba Dbb Dbd Dbh Dbj Dbk Dbl Dbm Dbn Dbo Dbp Dbr Dbs Dbt Dbu Dbv \ -Dbw Dbx Dby Dbz Db% Db' Db* Db+ Db, Db- Db. Db: Db; Db< Db= Db? Db@ Db[ Db] D\ -b^ Db_ Db` Db{ Db| Db~ Dc0 Dc1 Dc2 Dc3 Dc5 Dc6 Dc7 Dc8 Dc9 DcA DcB DcC DcD Dc\ -E DcF DcG DcH DcL DcO DeE DeH DeL DeM DeX DeY Dea Deb Ded Dee Def Deh Dei Dek\ - Del Den Deo Dep Der Des Deu Dev Dey Dez De$ De% De' De( De) De* De, De- De/ \ -De: De< De> De? De[ De] De_ Df4 Df7 DfB DfC Dfo Dfp Dfr Dfs Dfu Dfv Dfw Dfx D\ -fz Df# Df% Df& Df( Df* Df+ Df- Df. Df: Df_ Df| Dg1 Dg2 Dg( Dg) Dg, Dg. Dg; Dg\ -> Dg? Dg] Dg^ Dg} Dg~ Dh1 Dh2 Dh3 Dh4 Dh6 Dh7 Dh9 DhA DhB DhD DhE DhF DhG DhH\ - DhJ DhL DhM DhO DhP DhQ DhR DhS DhV Dhc Dhd Dhe Dhf Dhg Dhh Dhi Dhj Dhk Dh] \ -Dh^ Dh_ Dh` Dh{ Dh| Dh} Dh~ Di0 Di1 Di2 Di3 Di4 Di5 Di6 Di7 Di8 Di9 DiA DiB D\ -iC DiD DiE DiF DiG DiH DiI DiJ DiK DiL DiM DiN DiO DiP DiQ DiR DiT DiW DiX Dj\ -9 DjA DjB DjC DjD DjE DjF DjG DjH DjR DjS DjT DjX DjY DjZ Djb Djc Dje Dji Djj\ - Djl Djm Djn Djo Djq Djr Djs Djt Dju Djv Djw Djx Djy Djz Dj# Dj% Dj( Dj) Dj, \ -Dj- Dj/ Dj; Dj< Dj= Dj> Dj? Dj@ Dj[ Dj] Dj^ Dj_ Dj` Dj{ Dj| Dj} Dk0 Dk1 Dk3 D\ -k4 Dk5 Dk6 Dk7 Dk8 Dk9 DkA DkB DkC DkD DkE DkF DkG DkI DkK DkM DkO D\ - D<@ D=3 D=4 D=5 D=6 D=7 D=8 D=9 D=A D=B D=E D=F D=H D_g D_k D_o D_p D_q D_r \ -D_s D_t D_u D_v D_w D_) D_* D_+ D_, D_- D_. D_/ D_: D_; D_= D_> D`4 D`5 D`6 D\ -`7 D`8 D`9 D`A D`B D`C D`E D`J D`K D12i D12k D12p D12q D12r D12s D12t D12u D1\ -2v D12w D12x D12* D12+ D12, D12- D12. D12/ D12: D12; D12< D12= D12_ D135 D136\ - D137 D138 D139 D13A D13B D13C D13D D13F D13G D1TJ D1Tb D1T* D1T+ D1T, D1T- D\ -1T. D1T/ D1T: D1T; D1T< D1UA D1UC D1Ux D1U# D1U$ D1U& D1U) D1U, D1U- D1U/ D1U\ -< D1U? D1U@ D1U] D1b+ D1b, D1b- D1b. D1b/ D1b: D1b; D1b< D1b= D1cy D1cz D1c# \ -D1c* D1c+ D1c, D1c= D1c> D1c? D1do D1dp D1dq D1dr D1ds D1dt D1du D1dv D1dw D2\ -Ya D2Yb D2Yc D2Yd D2Ye D2Yf D2Yg D2Yh D2Yi D2Yk D2Yl D2Yn D2Yo D2Yq D2Yr D2Yt\ - D2Yu D2Yw D2Yx D2Yz D2Y# D2Y- D2Y. D2Y/ D2Y: D2Y; D2Y< D2Y= D2Y> D2Y? D2Y[ D\ -2Y] D2Y_ D2Y` D2Y| D2Y} D2Z8 D2Z9 D2ZA D2ZB D2ZC D2ZD D2ZE D2ZF D2ZG D2ZH D2Z\ -I D2ZJ D2ZK D2ZL D2ZM D2ZN D2ZO D2ZP D2ZQ D2ZU D2ZV D2ZW D2Zd D2Ze D2Zg D2Zh \ -D2Zk D2Zm D2Zn D2Zp D2Zq D2Zr D2Zs D2Zt D2Zu D2Zv D2Zw D2Zx D2Zy D2Zz D2Z% D2\ -Z& D2Z' D2Z+ D2Z- D2Z. D2Z: D2Z; D2Z= D2Z? D2Z@ D2Z[ D2Z] D2Z^ D2Z_ D2Z` D2Z{\ - D2Z| D2Z} D2a0 D2a2 D2a5 D2a8 D2a9 D2aG D2aH D2aI D2aJ D2aK D2aL D2aQ D2aR D\ -2aT D2aU D2aW D2aX D2aZ D2aa D2ac D2ad D2af D2ag D2ah D2aj D2al D2ao D2aq D2a\ -r D2as D2at D2au D2av D2a# D2a$ D2a& D2a' D2a) D2a* D2a- D2a: D2a; D2a< D2a> \ -D2a? D2a@ D2a_ D2a` D2a{ D2a} D2b2 D2b4 D2b6 D2b7 D2b8 D2b9 D2bA D2bB D2bD D2\ -bF D2bG D2bH D2bI D2bJ D2bK D2bL D2bM D2bN D2bX D2bY D2ba D2bc D2bd D2be D2bh\ - D2bj D2bm D2bt D2bu D2bz D2b% D2b& D2b' D2b( D2b) D2b* D2b+ D2b, D2b- D2b. D\ -2b/ D2b: D2b; D2b< D2b{ D2b| D2b~ D2c1 D2c2 D2c3 D2c6 D2c8 D2cB D2cE D2cF D2c\ -G D2cH D2cI D2cJ D2cK D2cL D2cM D2cN D2cR D2cT D2cW D2cX D2cY D2cZ D2ca D2cb \ -D2dV D2dW D2dY D2da D2db D2dc D2df D2dh D2dk D2gb D2gc D2gd D2ge D2gf D2gg D2\ -gh D2gi D2gj D2gk D2gn D2gq D2gu D2gx D2g# D2g. D2g/ D2g: D2g; D2g< D2g= D2g>\ - D2g? D2g@ D2g^ D2g{ D2g~ D2h9 D2hA D2hB D2hC D2hD D2hE D2hF D2hG D2hH D2hJ D\ -2hK D2hM D2hN D2hP D2hQ D2hS D2hT D2hU D2hX D2ha D2hg D2hk D2hq D2hs D2hu D2h\ -v D2hx D2hy D2h# D2h% D2h& D2h' D2h* D2h< D2h? D2h@ D2h[ D2h^ D2h_ D2h{ D2h| \ -D2h~ D2i2 D2i6 D2i7 D2i9 D2iA D2iK D2iL D2iM D2iN D2iO D2iP D2iQ D2iT D2iW D2\ -ia D2id D2ig D2ii D2in D2iq D2iu D2iv D2iw D2ix D2iy D2iz D2i% D2i( D2i+ D2i-\ - D2i: D2i< D2i? D2i@ D2i[ D2i] D2i^ D2i_ D2j0 D2jA D2jC D2jE D2jF D2jG D2jH D\ -2jI D2jJ D2jK D2jL D2jM D2jN D2jO D2jY D2jZ D2ja D2jb D2jc D2jd D2je D2jf D2j\ -g D2ji D2jk D2jp D2jv D2jx D2j# D2j$ D2j( D2j* D2j+ D2j, D2j- D2j. D2j/ D2j: \ -D2j; D2j< D2j= D2j| D2j} D2j~ D2k0 D2k1 D2k2 D2k3 D2k4 D2k5 D2k6 D2kB D2kD D2\ -kF D2kG D2kH D2kI D2kJ D2kK D2kL D2kM D2kN D2kU D2ka D2kc D2ke D2kf D2kk D2kl\ - D2km D2kn D2kp D2kq D2kr D2ks D2kt D2ku D2kv D2kw D2kx D2k$ D2k) D2k* D2k+ D\ -2k, D2k- D2k. D2k/ D2k: D2k; D2k< D2k> D2k{ D2k} D2l2 D2l3 D2lC D2lF D2lG D2l\ -H D2lI D2lN D2lO D2lP D2lQ D2lR D2lS D2lT D2lU D2lV D2lW D2lX D2lY D2lZ D2la \ -D2lb D2lc D2ld D2le D2lh D2lj D2ll D2ly D2lz D2l$ D2l( D2l, D2l: D2l< D2l= D2\ -l@ D2l[ D2l] D2l_ D2l| D2l~ D2m2 D2m4 D2m5 D2m6 D2m7 D2m8 D2m9 D2mE D2mI D2mJ\ - D2mV D2mW D2mX D2mY D2mZ D2ma D2mb D2mc D2md D2me D2mi D2mm D2mw D2mx D2my D\ -2mz D2m# D2m$ D2m% D2m& D2m' D2m( D2m, D2m: D2m= D2m] D2m_ D2m` D2m} D2m~ D2n\ -0 D2n2 D2n4 D2n6 D2n7 D2n9 D2nD D2nH D2nI D2nO D2nP D2nU D2nV D2nW D2nX D2nY \ -D2nZ D2ne D2ni D2nj D2no D2nq D2nu D2nv D2nw D2nx D2n$ D2n% D2n& D2n' D2n( D2\ -n) D2n* D2n+ D2n, D2n- D2n. D2n/ D2n: D2n> D2n] D2o4 D2o6 D2o7 D2o9 D2oD D2oI\ - D2oK D2oL D2oO D2oP D2oQ D2oS D2z1 D2z2 D2z4 D2z9 D2zA D2zC D2zD D2zI D2zJ D\ -2zK D2zL D2zM D2zN D2zO D2zP D2zQ D2zV D2zX D2zY D2za D2zb D2zg D2zh D2zj D2z\ -k D2zl D2zm D2zn D2zo D2zp D2zq D2zr D2zt D2zu D2zw D2zx D2z$ D2z% D2z& D2z' \ -D2z( D2z) D2z* D2z+ D2z, D2z- D2z. D2z: D2z> D2z@ D2z[ D2z] D2z^ D2z_ D2z` D2\ -z{ D2z| D2z} D2z~ D2#0 D2#1 D2#2 D2#3 D2#4 D2#5 D2#6 D2#7 D2#C D2#D D2#E D2#F\ - D2#H D2#I D2#J D2#K D2#L D2#M D2#N D2#O D2#P D2#Q D2#R D2#S D2#T D2#U D2#V D\ -2#W D2#X D2#Y D2#Z D2#a D2#c D2#e D2#i D2#j D2#k D2#l D2#m D2#n D2#o D2#p D2#\ -q D2#u D2#v D2#x D2#z D2## D2#$ D2#% D2#& D2#' D2#( D2#) D2#* D2#+ D2#, D2#- \ -D2#< D2#@ D2#] D2#_ D2#{ D2#} D2#~ D2$0 D2$1 D2$2 D2$3 D2$4 D2$5 D2$6 D2$A D2\ -$B D2$E D2$F D2$H D2$I D2$J D2$M D2$P D2$Q D2$R D2$S D2$T D2$U D2$V D2$W D2$X\ - D2$Y D2$c D2$d D2$e D2$h D2$i D2$j D2$k D2$l D2$m D2$n D2$o D2$p D2$q D2$y D\ -2$$ D2$) D2$+ D2$, D2$- D2$. D2$/ D2$: D2$; D2$< D2$= D2$> D2$? D2$@ D2$[ D2$\ -] D2$^ D2$_ D2$` D2${ D2%4 D2%5 D2%6 D2%7 D2%8 D2%9 D2%A D2%B D2%C D2%D D2%E \ -D2%F D2%G D2%H D2%I D2%J D2%K D2%L D2%M D2%N D2%Q D2%R D2%S D2%V D2%X D2%Z D2\ -%a D2%b D2%d D2%e D2%g D2%m D2%= D2%? D2%@ D2%[ D2%^ D2%_ D2%{ D2&2 D2&7 D2&8\ - D2&9 D2&B D2&G D2&J D2&N D2&O D2&P D2&Q D2&R D2&S D2&T D2&U D2&V D2&W D2&X D\ -2&Y D2&Z D2&a D2&b D2&c D2&d D2&e D2&f D2&h D2&i D2&l D2&o D2&q D2&r D2&s D2&\ -u D2&v D2&$ D2&& D2*3 D2*5 D2*9 D2*B D2*C D2*H D2*I D2*J D2*K D2*L D2*M D2*N \ -D2*O D2*P D2*Q D2*R D2*T D2*X D2*Z D2*a D2*e D2*g D2*h D2*j D2*k D2*l D2*m D2\ -*n D2*o D2*p D2*q D2*r D2*s D2*u D2*v D2*# D2*$ D2*% D2*& D2*' D2*( D2*) D2**\ - D2*+ D2*, D2*- D2*: D2*= D2*[ D2*] D2*^ D2*_ D2*` D2*{ D2*| D2*} D2*~ D2+0 D\ -2+1 D2+2 D2+3 D2+4 D2+5 D2+6 D2+7 D2+8 D2+9 D2+B D2+D D2+E D2+I D2+J D2+K D2+\ -L D2+M D2+N D2+O D2+P D2+Q D2+R D2+S D2+T D2+U D2+V D2+W D2+X D2+Y D2+Z D2+b \ -D2+c D2+g D2+i D2+j D2+k D2+l D2+m D2+n D2+o D2+p D2+q D2+r D2+s D2+t D2+v D2\ -+x D2+$ D2+% D2+& D2+' D2+( D2+) D2+* D2++ D2+, D2+: D2+> D2+@ D2+^ D2+| D2+}\ - D2+~ D2,0 D2,1 D2,2 D2,3 D2,4 D2,5 D2,6 D2,7 D2,8 D2,C D2,H D2,L D2,M D2,N D\ -2,Q D2,R D2,S D2,T D2,U D2,V D2,W D2,X D2,Y D2,a D2,d D2,f D2,h D2,i D2,j D2,\ -k D2,l D2,m D2,n D2,o D2,p D2,q D2,u D2,w D2,x D2,y D2,( D2,* D2,, D2,- D2,. \ -D2,/ D2,: D2,; D2,< D2,= D2,> D2,? D2,@ D2,[ D2,] D2,^ D2,_ D2,` D2,{ D2,| D2\ -,~ D2-3 D2-7 D2-8 D2-9 D2-A D2-B D2-C D2-D D2-E D2-F D2-G D2-H D2-I D2-J D2-K\ - D2-L D2-M D2-N D2-O D2-Q D2-R D2-T D2-X D2-Y D2-Z D2-a D2-b D2-c D2-d D2-e D\ -2-f D2-g D2-k D2-l D2-o D2-p D2-q D2-r D2-s D2-t D2-u D2-v D2-w D2-x D2-y D2-\ -) D2-* D2-+ D2-, D2-- D2-. D2-/ D2-: D2-; D2-< D2-= D2-> D2-? D2-@ D2-[ D2-] \ -D2-^ D2-_ D2-` D2-{ D2.0 D2.2 D2.3 D2.4 D2.8 D2.A D2.B D2.C D2.D D2.O D2.P D2\ -.Q D2.R D2.S D2.T D2.U D2.V D2.W D2.X D2.Y D2.Z D2.a D2.b D2.c D2.d D2.e D2.f\ - D2.g D2.h D2.j D2.k D2.m D2.p D2.q D2.r D2.s D2.t D2.u D2.v D2.w D2.x D2.y D\ -2.z D2.% D2.& D2.* D2.+ D2., D2.- D2.. D2./ D2.: D2.; D2.< D2.= D2.> D2.? D2.\ -@ D2.[ D2.] D2.^ D2._ D2.` D2.{ D2/3 D2/5 D2/6 D2/7 D2/8 D2/9 D2/A D2/B D2/C \ -D2/D D2/F D2/H D2/N D2/O D2/P D2/Q D2/R D2/S D2/T D2/U D2/V D2<3 D2<4 D2<6 D2\ - D3B? D3B^ D3B_ D3B` D3B{ D3B| D3B} D3B~ D3C0 D3C1 D3C2 D3C\ -3 D3C5 D3C6 D3C7 D3CA D3CB D3CC D3CE D3CF D3CG D3CM D3CN D3CP D3CT D3CU D3CV \ -D3CW D3CX D3CY D3CZ D3Ca D3Cb D3Cc D3Cd D3Ce D3Cf D3Cg D3Ch D3Ci D3Cj D3Ck D3\ -Cl D3Cn D3Co D3Cp D3Cs D3Cz D3C# D3C% D3C& D3K) D3K* D3K, D3K- D3K/ D3K: D3K;\ - D3K< D3K= D3K> D3K? D3K@ D3K[ D3K] D3K^ D3K~ D3L0 D3L2 D3L3 D3L4 D3L5 D3L6 D\ -3L7 D3L8 D3L9 D3LA D3LB D3LE D3LI D3LM D3LN D3LO D3LP D3LR D3LT D3LU D3LV D3L\ -X D3LZ D3La D3Lb D3Ld D3Le D3Lg D3Li D3Lj D3Lk D3Lm D3Lt D3L^ D3L_ D3L{ D3L} \ -D3L~ D3M0 D3M2 D3M3 D3M5 D3M7 D3M8 D3M9 D3MB D3ME D3MP D3MT D3MV D3MW D3MY D3\ -MZ D3Mb D3Mc D3Md D3Me D3Mf D3Mg D3Mh D3Mi D3Mj D3Mk D3Ml D3Mm D3Mo D3Mq D3Mr\ - D3Ms D3Mu D3Mx D3M& D3M' D3M) D3M+ D3M, D3M- D3S* D3S+ D3S- D3S. D3S: D3S; D\ -3S< D3S= D3S> D3S? D3S@ D3S[ D3S] D3S^ D3S_ D3S{ D3S~ D3T4 D3T5 D3T6 D3T7 D3T\ -8 D3T9 D3TA D3TB D3TC D3TH D3TN D3TO D3TP D3TQ D3TS D3TU D3TV D3TW D3TX D3TY \ -D3TZ D3Ta D3Tb D3Tc D3Td D3Te D3Tf D3Tg D3Th D3Ti D3Tj D3Tk D3Tl D3Tm D3Tq D3\ -Ts D3Tt D3Tu D3T% D3T) D3T* D3T+ D3T, D3T. D3T: D3T; D3T< D3T= D3T> D3T? D3T@\ - D3T[ D3T] D3T^ D3T_ D3T` D3T{ D3T| D3T} D3T~ D3U0 D3U1 D3U2 D3U3 D3U4 D3U5 D\ -3U6 D3U7 D3U8 D3U9 D3UA D3UB D3UC D3UD D3UI D3UK D3US D3UV D3UW D3UY D3UZ D3U\ -b D3Uc D3Ud D3Ue D3Uf D3Ug D3Uh D3Ui D3Uj D3Uk D3Ul D3Um D3Un D3Uo D3Up D3Uq \ -D3Ur D3Us D3Ut D3Uu D3Uv D3Ux D3U% D3U& D3U' D3U( D3U) D3U* D3U+ D3U, D3U- D3\ -U. D3U/ D3U; D3U< D3U? D3U^ D3U_ D3U{ D3U| D3U~ D3V0 D3V2 D3V3 D3V4 D3V5 D3V6\ - D3V7 D3V8 D3V9 D3VA D3VB D3VC D3VD D3VE D3VF D3VG D3VH D3VI D3VJ D3VL D3VO D\ -3VT D3VV D3VX D3VY D3VZ D3Va E E8b E8e E8f E8g E8h E8l E8n E8o E8p E8r E8& E8\ -) E8+ E8, E8- E8: E8= E8> E8? E8@ E8_ E8` E8{ E8| E8} E8~ E93 E94 E95 E96 E97\ - E98 E9C E9D E9E E9F E9G E9H E9L E9N E9Q E9V E9X E9d E9e E9j E9l E9p E9q E9w \ -E9y E9# E9) E9+ E9, E9: E9; E9< E9= E9> E9? E9^ E9_ E9` E9{ E9| E9} EA2 EA3 E\ -A4 EA5 EA6 EA7 EAC EAD EAG EAK EAM EAN EAT EAU EAX EAf EAo EAp EAz EB1 EB2 EB\ -3 EB5 EBJ EBK EBL EBM EBU EBV EBW EBX EBb EBe EBf EBt EBu EBv EBw EBx EBy EB%\ - EB& EB' EB( EB) EB* EB. EB/ EB: EB; EB< EB= EB? EB^ EB` EC1 EC2 EC9 ECA ECC \ -ECK ECM ECN ECU ECV ECY ECb ECf ECj ECk ECl ECm ECn ECo ECs ECt ECu ECv ECw E\ -Cx EC$ EC% EC& EC' EC( EC) EC- EC/ EC@ EC[ ED0 ED1 EDA EDB EDD EDG EDH EDK ED\ -L EDR EDU EDV ED# ED$ ED% ED& ED- ED. ED: ED~ EE2 EE3 EEF EEG EEJ EEK EEL EEP\ - EEQ EER EES EET EEU EEY EEZ EEa EEb EEc EEd EEh EEi EEj EEk EEl EEm EEq EEs \ -EE# EE$ EE& EE* EE+ EE, EE: EE< EE? EE^ EE~ EF1 EF2 EF5 EF9 EFA EFF EFG EFH E\ -FI EFJ EFK EFO EFP EFQ EFR EFS EFT EFX EFY EFZ EFa EFb EFc EFd EFg EFh EFj EF\ -n EFq EFr EFt EFy EF# EF& EF' EF( EF+ EF- EF/ EF< EF? 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E|@ E|[ E|] E|^ E|_ E|` E|{\ - E|| E|} E}3 E}4 E}5 E}6 E}A E}B E}C E}G E}H E}I E}L E}M E}N E}O E}P E}R E}T \ -E}U E}V E}W E}X E}b E}c E}d E}h E}i E}j E}l E}n E}o E}p E}q E}r E}s E}v E}y E\ -}# E}& E}' E}+ E}- E}; E}= E}_ E}` E}{ E}| E~0 E~1 E~2 E~3 E~4 E~5 E~9 E~A E~\ -B E~G E~H E~L E~M E~N E~O E~P E~Q E~R E~S E~T E~U E~V E~W E~X E~b E~c E~g E~h\ - E~i E~k E~m E~n E~o E~p E~q E~r E~u E~v E~w E~x E~$ E~% E~& E~* E~+ E~, E~= \ -E~? E~[ E~_ E~{ E~| E108 E10A E10F E10H E10L E10M E10N E10P E10R E10S E10T E1\ -0V E10Z E10a E10b E10l E10m E10n E10o E10p E10q E10r E10s E10t E10u E10v E10w\ - E10x E10$ E10& E10' E10( E10) E10, E10- E10. E10< E10= E10> E10] E10^ E10_ E\ -10` E10{ E10} E110 E111 E112 E113 E116 E117 E118 E119 E11D E11E E11F E11H E11\ -J E11K E11L E11M E11N E11O E11P E11R E11T E11U E11Z E11a E11e E11g E11h E11k \ -E11m E11o E11p E11t E11u E11v E11w E11x E11z E11# E11$ E11% E11& E11' E11+ E1\ -1, E11- E11[ E11] E11^ E11_ E11` E11{ E11| E11} E11~ E120 E121 E122 E127 E128\ - E12C E12D E12E E12G E12I E12J E12K E12L E12M E12N E12P E12W E12X E12Y E12Z E\ -12d E12e E12f E12m E12n E12# E12$ E12& E12* E12, E12= E12[ E12] E12^ E12` E12\ -| E12} E12~ E133 E135 E136 E137 E13B E13C E13D E13H E13I E13J E13K E13L E13M \ -E13N E13O E13P E13Q E13R E13S E13X E13Y E13Z E13a E13b E13f E13g E13h E13l E1\ -3m E13n E13r E13s E13t E13v E13w E13x E13y E13# E13$ E13% E13) E13* E13+ E13/\ - E13: E13; E13? E13@ E13[ E13] E13^ E13_ E13` E13| E13~ E140 E145 E146 E14A E\ -14C E14D E14G E14I E14L E14T E14V E14W E14X E14Y E14Z E14a E14e E14f E14g E14\ -l E14m E14q E14r E14s E14t E14u E14v E14w E14x E14y E14z E14# E14$ E14. E14/ \ -E14: E14> E14? E14@ E14[ E14] E14^ E14` E14{ E14| E14} E14~ E153 E154 E155 E1\ -59 E15A E15B E15' E15( E15) E15, E15- E15. E15/ E15: E15; E15< E15= E15> E15?\ - E15@ E15[ E15] E15_ E15` E15{ E15| E15} E16U E16W E16X E16Y E16d E16f E16g E\ -16i E16j E16k E16l E16m E16n E16o E16p E16q E16r E16t E16u E16v E16w E16x E16\ -y E16z E16& E16' E16( E16* E16+ E16, E16- E16. E16/ E16< E16= E16> E16@ E16[ \ -E16_ E16` E16{ E16| E16} E16~ E170 E171 E172 E173 E174 E175 E176 E17A E17B E1\ -7C E17D E17F E17G E17H E17I E17J E17L E17M E17N E17O E17Q E17R E17T E17U E17V\ - E17W E17X E17b E17c E17d E17e E17f E17h E17i E17j E17? E17@ E17] E17^ E17` E\ -17{ E17} E17~ E181 E182 E184 E18a E18b E18c E18f E18j E18k E18l E18m E18n E18\ -o E18p E18q E18r E18s E18u E18v E18w E18x E18~ E190 E192 E193 E194 E19C E19D \ -E19E E19F E19G E19I E19J E19K E19L E19M E19N E19P E19Q E19R E19S E19T E19U E1\ -9V E19Z E19a E19b E19c E19e E19f E19g E19h E19l E19m E19n E19s E19u E19v E19w\ - E19# E19$ E19% E19& E19' E19( E19, E19- E19. E19< E19= E19> E19? E19[ E19] E\ -19^ E19_ E19{ E19| E19} E1A0 E1A1 E1A2 E1A3 E1A7 E1A8 E1A9 E1AD E1AE E1AF E1A\ -m E1Ao E1Ap E1Ar E1As E1Au E1Av E1Ax E1Ay E1A# E1A$ E1A& E1B6 E1B7 E1B8 E1BC \ -E1BD E1BE E1BF E1BH E1BI E1BJ E1BK E1BL E1BM E1BN E1BO E1BP E1BR E1BS E1BT E1\ -B$ E1B% E1B& E1B, E1B- E1B/ E1B: E1B; E1B< E1B= E1B> E1B? E1B@ E1B[ E1B] E1B^\ - E1B` E1B{ E1B| E1B} E1B~ E1C0 E1C1 E1C5 E1C6 E1C7 E1C8 E1C9 E1CB E1CC E1CD E\ -1CF E1CQ E1CR E1CS E1CT E1CU E1CV E1CW E1CX E1CY E1CZ E1Ca E1Cb E1Cf E1Cg E1C\ -h E1Cl E1Cm E1Cn E1Co E1Cq E1Cr E1Cs E1Ct E1Cx E1Cy E1C# E1C$ E1C% E1C) E1C* \ -E1C+ E1C/ E1C: E1C; E1DO E1DP E1DQ E1DT E1DW E1Da E1Df E1Dg E1Di E1Dj E1Dl E1\ -Dp E1Ds E1Dw E1Dx E1D# E1D( E1D) E1D* E1D. E1D/ E1D: E1D; E1D< E1D> E1D? E1D@\ - E1D[ E1D] E1D^ E1D` E1D{ E1D| E1D} E1D~ E1E6 E1E7 E1E8 E1EC E1ED E1EE E1EI E\ -1EK E1EL E1EM E1EO E1EP E1EQ E1EU E1EW E1EX E1EY E1EZ E1Ed E1Ee E1Eh E1Ei E1E\ -j E1Ek E1El E1Em E1Eo E1Ep E1Eq E1Er E1Et E1Eu E1Ev E1Ew E1Ex E1Ey E1Ez E1E# \ -E1E' E1E( E1E) E1E* E1E, E1E- E1E. E1E/ E1E< E1E= E1E> E1E? E1E[ E1E] E1E` E1\ -E{ E1E| E1E} E1F2 E1F3 E1F4 E1F5 E1F6 E1F7 E1FB E1FC E1FD E1FH E1FI E1FJ E1FK\ - E1FL E1FN E1FO E1FP E1FU E1FV E1FW E1FX E1FY E1Fc E1Fd E1Fe E1Fi E1Fj E1Fk E\ -1Fl E1Fp E1Fs E1Fy E1F& E1F' E1F- E1F. E1F? E1F@ E1G1 E1G2 E1GA E1GC E1GI E1G\ -K E1GN E1GQ E1GT E1GU E1GW E1GX E1Gb E1Gc E1Gd E1Gf E1Gl E1Gn E1Go E1Gp E1Gq \ -E1Gr E1Gs E1Gt E1Gv E1Gw E1Gx E1Gy E1G( E1G) E1G* E1G. E1G/ E1G: E1G] E1G_ E1\ -G` E1G{ E1H3 E1H4 E1H5 E1HA E1HB E1HC E1HE E1HF E1HG E1HH E1HI E1HK E1HL E1HM\ - E1HN E1HP E1HQ E1HR E1HS E1HT E1HU E1HV E1HW E1Ha E1Hb E1Hc E1Hd E1He E1Hg E\ -1Hh E1Hi E1Hk E1Hq E1Hr E1Ht E1Hv E1Hw E1Hx E1Hy E1Hz E1H# E1H$ E1H% E1H& E1H\ -' E1H( E1H) E1H- E1H. E1H/ E1H; E1H< E1H= E1H> E1H? E1H[ E1H^ E1H_ E1H` E1H| \ -E1H} E1H~ E1I1 E1I2 E1I3 E1I4 E1I8 E1I9 E1IA E1IB E1ID E1IE E1IF E1IG E1IH E1\ -IK E1IM E1IP E1IS E1IU E1IV E1Ia E1Ib E1Ic E1Id E1If E1Ih E1In E1Io E1Ip E1Ir\ - E1Iu E1Iv E1Iy E1Iz E1I, E1I- E1I: E1I[ E1I^ E1I_ E1I| E1I} E1J0 E1J1 E1J3 E\ -1J7 E1J8 E1J9 E1JD E1JE E1JF E1JG E1JH E1JJ E1JK E1JL E1JM E1JN E1JO E1JP E1J\ -Q E1JS E1JT E1JU E1Jh E1Ji E1Jj E1Jo E1Jp E1Jq E1Jr E1Jt E1Ju E1Jv E1Jz E1J$ \ -E1J% E1J& E1J' E1J. E1J/ E1J; E1J< E1J= E1J> E1J[ E1J] E1J^ E1J` E1J{ E1J| E1\ -J} E1J~ E1K0 E1K1 E1K2 E1K6 E1K7 E1K8 E1KA E1KB E1KC E1KD E1KE E1KH E1KI E1KJ\ - E1KK E1KQ E1KR E1KS E1KT E1KU E1KV E1KW E1KX E1KY E1KZ E1Ka E1Kb E1Kc E1Kg E\ -1Kh E1Ki E1Kj E1Kl E1Km E1Kn E1Ko E1Kq E1Ks E1Kt E1Ku E1Kw E1Kx E1Ky E1Kz E1K\ -$ E1K% E1K& E1K* E1K+ E1K, E1K- E1K. E1K: E1K; E1K< E1K@ E1K[ E1K^ E1K| E1K~ \ -E1L1 E1L5 E1L7 E1L9 E1LA E1LB E1LC E1LS E1LU E1LW E1LY E1Lb E1Lf E1Lg E1Li E1\ -Lk E1Ln E1Ls E1Lu E1Lz E1L$ E1L) E1L* E1L+ E1L- E1L/ E1L: E1L; E1L> E1L? E1L@\ - E1L[ E1L] E1L^ E1L_ E1L{ E1L| E1L} E1L~ E1M0 E1MD E1ME E1MF E1MO E1MP E1MQ E\ -1MR E1MY E1MZ E1Ma E1Mh E1Mj E1Mk E1Ml E1Mm E1Mo E1Mq E1Mr E1Ms E1Mt E1Mu E1M\ -w E1Mx E1My E1Mz E1M# E1M$ E1M( E1M) E1M* E1M+ E1M, E1M. E1M/ E1M: E1M; E1M| \ -E1M} E1M~ E1N0 E1N1 E1N2 E1N3 E1N4 E1N5 E1N6 E1N7 E1N8 E1NC E1ND E1NE E1NG E1\ -NH E1NI E1NJ E1NK E1NN E1NO E1NP E1NQ E1NS E1NT E1NV E1NW E1NX E1NY E1NZ E1Nd\ - E1Ne E1Nf E1Ng E1Ni E1Nj E1Nk E1Nl E1Nq E1Nr E1Nt E1Nv E1Ny E1N# E1N( E1N* E\ -1N+ E1N- E1N= E1N@ E1N] E1N_ E1N{ E1N} E1O1 E1OC E1OD E1OH E1OP E1OR E1OV E1O\ -X E1OY E1Oc E1Od E1Oe E1Og E1Oh E1On E1Oo E1Op E1Oq E1Or E1Os E1Ot E1Ou E1Ow \ -E1Ox E1Oy E1Oz E1O) E1O* E1O+ E1O/ E1O: E1O; E1O? E1O_ E1O` E1O{ E1O| E1P2 E1\ -P4 E1P5 E1P6 E1PB E1PC E1PD E1PE E1PG E1PH E1PI E1PK E1PM E1PN E1PO E1PP E1PQ\ - E1PS E1PT E1PU E1PV E1PW E1PX E1Pb E1Pc E1Pd E1Pf E1Pg E1Ph E1Pi E1Pj E1Pn E\ -1Po E1Pp E1Pr E1Ps E1Pw E1Px E1Py E1Pz E1P# E1P$ E1P% E1P& E1P' E1P( E1P) E1P\ -* E1P. E1P/ E1P: E1P> E1P? E1P@ E1P_ E1P` E1P{ E1Q0 E1Q2 E1Q3 E1Q4 E1Q5 E1Q9 \ -E1QA E1QB E1QC E1QD E1QF E1QG E1QH E1QL E1QN E1QQ E1QU E1QV E1Qb E1Qf E1Qh E1\ -Qi E1Qm E1Qn E1Qp E1Qr E1Q$ E1Q& E1Q( E1Q) E1Q- E1Q/ E1Q< E1Q_ E1Q} E1Q~ E1R0\ - E1R2 E1R4 E1R8 E1R9 E1RA E1RE E1RF E1RG E1RK E1RL E1RM E1RN E1RO E1RP E1RQ E\ -1RR E1RT E1RU E1RV E1Rc E1Rd E1Re E1Ri E1Rj E1Rk E1Ro E1Rp E1Ru E1Rv E1Rw E1R\ -$ E1R% E1R& E1R' E1R( E1R. E1R: E1R; E1R< E1R= E1R> E1R] E1R^ E1R_ E1R` E1R{ \ -E1R} E1R~ E1S0 E1S1 E1S2 E1S3 E1S7 E1S8 E1S9 E1SA E1SC E1SD E1SE E1SF E1SJ E1\ -SK E1SL E1SO E1SS E1ST E1SU E1SY E1SZ E1Sa E1Sb E1Sc E1Sd E1Sh E1Si E1Sj E1Sk\ - E1Sl E1Sn E1So E1Sp E1St E1Su E1Sv E1Sx E1Sy E1Sz E1S# E1S% E1S& E1S' E1S+ E\ -1S, E1S- E1S; E1S< E1S= E1S[ E1T1 E1T2 E1T6 E1T8 E1T9 E1TB E1TC E1T* E1T+ E1T\ -, E1T- E1T[ E1T^ E1T` E1T{ E1T| E1T} E1U1 E1UI E1UL E1US E1UU E1UV E1Ux E1Uy \ -E1Uz E1U# E1U) E1U* E1U+ E1U/ E1U; E1U[ E1U} E1V1 E1VI E1VK E1Vu E1Vv E1Vw E1\ -Vx E1Vy E1V# E1V( E1V) E1V* E1V- E1V. E1V/ E1V] E1V^ E1V| E1W0 E1W2 E1W7 E1Wd\ - E1We E1Wf E1Wi E1Wp E1Wt E1Wu E1Wv E1Ww E1Wx E1W, E1W] E1W| E1X0 E1XT E1XU E\ -1XV E1Xc E1Xd E1Xe E1Xj E1Xk E1X$ E1X% E1X) E1X= E1X@ E1YO E1YP E1YQ E1YS E1Y\ -T E1YU E1Yb E1Yc E1Yd E1Yh E1Yj E1Yo E1Yq E1Yr E1Yy E1Y# E1Y$ E1Y( E1Z9 E1ZA \ -E1ZB E1ZO E1ZP E1ZR E1ZS E1ZT E1Ze E1Zo E1Zq E1Zr E1Z# E1Z~ E1a0 E1a1 E1a8 E1\ -a9 E1aA E1aD E1aE E1aF E1aK E1aU E1aW E1ae E1ao E1aq E1a^ E1a` E1a| E1a} E1a~\ - E1b0 E1b3 E1b7 E1b8 E1b9 E1bE E1bF E1bU E1bX E1bh E1bj E1bl E1bp E1b$ E1b% E\ -1b+ E1b, E1b- E1b` E1b{ E1b| E1b} E1b~ E1cA E1cK E1cU E1cV E1cZ E1cb E1ch E1c\ -l E1cm E1cs E1cw E1cy E1cz E1c# E1c* E1c+ E1c, E1c; E1c< E1d0 E1d4 E1dA E1du \ -E1dv E1dx E1dy E1dz E1d) E1d* E1d+ E1d/ E1d; E1d^ E1e9 E1eE E1eF E1eK E1eQ E1\ -eV E1eW E1ee E1ef E1eg E1et E1eu E1ew E1ex E1ey E1e+ E1e] E1e^ E1f0 E1f4 E1f5\ - E1fC E1fE E1fG E1fK E1fU E1fV E1fW E1fd E1fe E1ff E1fj E1fk E1fy E1f$ E1f+ E\ -1f] E1f{ E1g0 E1g2 E1g4 E1gB E1gC E1gH E1gQ E1gS E1gT E1gU E1gV E1gc E1gd E1g\ -e E1gj E1gk E1gq E1gr E1gt E1gx E1g$ E1g/ E1g: E1g~ E1h1 E1h3 E1h5 E1hA E1hB \ -E1hC E1hP E1hR E1hS E1hT E1hU E1hr E1h% E1h& E1h* E1h/ E1h: E1h` E1h~ E1i0 E1\ -i1 E1i2 E1i9 E1iA E1iB E1iF E1iH E1iX E1ir E1ix E1i% E1i& E1i' E1i- E1i/ E1i?\ - E1i| E1i} E1i~ E1j0 E1j1 E1j8 E1j9 E1jA E1jE E1jF E1jX E1jj E1jk E1jn E1jp E\ -1jq E1j$ E1j, E1j- E1j. E1j] E1j` E1j{ E1j} E1j~ E1k0 E1k2 E1kz E1k# E1k$ E1k\ -+ E1k, E1k- E1k; E1k< E1lT E1lW E1lX E1lZ E1lg E1lm E1ln E1lu E1lv E1lx E1ly \ -E1lz E1l# E1l$ E1l* E1l+ E1l, E1l; E1l< E1l` E1m3 E1mE E1mF E1mL E1mU E1mV E1\ -mW E1mY E1mf E1mg E1mh E1mj E1mu E1mw E1mx E1my E1mz E1m# E1m^ E1n3 E1n4 E1n5\ - E1nE E1nF E1nK E1nL E1nP E1nS E1nV E1nW E1nX E1nZ E1ne E1nf E1ng E1nk E1nm E\ -1nq E1n] E1n^ E1o0 E1o4 E1o5 E1oC E1oE E1oI E1oS E1oT E1oU E1oV E1oW E1oZ E1o\ -d E1oe E1of E1oj E1ok E1ou E1o: E1o< E1o| E1p3 E1p4 E1p7 E1pB E1pC E1pD E1pO \ -E1pR E1pS E1pT E1pU E1pV E1pt E1p# E1p& E1p( E1p) E1p/ E1p: E1p@ E1p~ E1q0 E1\ -q1 E1q2 E1q3 E1qA E1qB E1qC E1qH E1qI E1qO E1qZ E1qa E1q% E1q& E1q/ E1q: E1q|\ - E1q} E1r0 E1r1 E1r2 E1r9 E1rA E1rB E1rF E1rH E2Yc E2Yd E2Ye E2Yf E2Y. E2Y/ E\ -2Y= E2Y> E2Y? E2Z9 E2ZA E2ZE E2ZF E2ZI E2ZJ E2ZN E2ZO E2ZP E2ZT E2ZU E2ZV E2Z\ -W E2ZX E2ZY E2ZZ E2Zc E2Zd E2Ze E2Zi E2Zj E2Zo E2Zq E2Zu E2Zv E2Zw E2Zx E2Zz \ -E2Z' E2Z( E2Z- E2Z= E2Z> E2Z^ E2Z_ E2Z` E2Z{ E2Z| E2a1 E2a2 E2a3 E2aA E2aB E2\ -aI E2aN E2aO E2aT E2aU E2aW E2aX E2aZ E2ab E2ac E2ad E2ai E2aj E2an E2ao E2ap\ - E2at E2au E2av E2aw E2ax E2ay E2a# E2a% E2a& E2a' E2a, E2a- E2a; E2a< E2a= E\ -2a[ E2a] E2a^ E2a_ E2a` E2a{ E2b0 E2b1 E2b2 E2b3 E2b4 E2b5 E2b7 E2b9 E2bA E2b\ -B E2bF E2bG E2bH E2bL E2bM E2bN E2bS E2bT E2bV E2bW E2bb E2bi E2bm E2bn E2bo \ -E2bs E2bt E2bv E2bw E2bx E2b$ E2b% E2b* E2b; E2b< E2b^ E2b_ E2b` E2b~ E2c0 E2\ -c1 E2c2 E2c3 E2c4 E2c8 E2c9 E2cA E2cG E2cK E2cQ E2cR E2cS E2cT E2cU E2cZ E2cb\ - E2cm E2cn E2cs E2ct E2cu E2cv E2cw E2c# E2c$ E2c% E2c- E2c. E2c_ E2c~ E2d0 E\ -2d1 E2d3 E2d4 E2d7 E2d8 E2d9 E2dJ E2dK E2dL E2dP E2dQ E2dR E2dS E2dT E2dU E2d\ -V E2dY E2dZ E2da E2dk E2dl E2dm E2dq E2dr E2ds E2dt E2du E2dv E2dz E2d# E2d$ \ -E2d% E2d& E2d' E2d( E2d+ E2d, E2d- E2d; E2d= E2d[ E2d^ E2d| E2d} E2d~ E2e2 E2\ -e7 E2e8 E2eD E2eE E2eI E2eJ E2eK E2eP E2eS E2eT E2eY E2eZ E2ee E2ej E2el E2es\ - E2et E2eu E2ey E2ez E2e# E2e$ E2e% E2e& E2e( E2e* E2e+ E2e, E2e] E2e{ E2e| E\ -2e} E2f0 E2f1 E2f6 E2fI E2fJ E2fO E2fP E2fQ E2fR E2fS E2fW E2fX E2fY E2ff E2f\ -s E2fy E2fz E2f# E2f$ E2f) E2f* E2f+ E2f? E2f@ E2f[ E2f` E2f{ E2f| E2f} E2f~ \ -E2g0 E2g3 E2g4 E2g5 E2g6 E2gG E2gH E2gI E2gM E2gN E2gO E2gP E2gQ E2gR E2gb E2\ -ge E2gf E2gg E2gk E2gl E2gq E2gr E2gs E2g) E2g> E2g? E2g@ E2h3 E2h4 E2hA E2hG\ - E2hH E2hJ E2hK E2hO E2hP E2hQ E2hU E2hV E2hW E2hX E2hY E2hZ E2hb E2hd E2he E\ -2hf E2hp E2hv E2hw E2hx E2hz E2h# E2h) E2h- E2h/ E2h= E2h> E2h^ E2h_ E2h{ E2h\ -| E2h} E2i2 E2i3 E2i4 E2iD E2iJ E2iU E2iV E2iX E2iY E2ib E2ic E2id E2ie E2io \ -E2ip E2iq E2iu E2iv E2iw E2ix E2iy E2iz E2i& E2i' E2i( E2i< E2i= E2i> E2i] E2\ -i^ E2i_ E2i` E2i{ E2i| E2j1 E2j2 E2j3 E2j4 E2j5 E2j6 E2jA E2jB E2jC E2jc E2jn\ - E2jo E2jp E2jw E2jx E2jy E2j- E2j; E2j= E2j@ E2j_ E2j` E2j{ E2k0 E2k1 E2k2 E\ -2k3 E2k4 E2k5 E2k9 E2kA E2kB E2kM E2kR E2kS E2kT E2kU E2kW E2ka E2kg E2km E2k\ -n E2ks E2kt E2kv E2kw E2kx E2k$ E2k% E2k& E2k- E2k_ E2l0 E2l1 E2l2 E2l4 E2l6 \ -E2l8 E2l9 E2lA E2lG E2lK E2lL E2lM E2lQ E2lR E2lS E2lT E2lU E2lV E2lX E2lZ E2\ -la E2lb E2lg E2ll E2lm E2ln E2lr E2ls E2lt E2lu E2lv E2lw E2l# E2l$ E2l% E2l&\ - E2l' E2l( E2l, E2l- E2l. E2l} E2l~ E2m0 E2mJ E2mK E2mL E2mY E2ma E2mk E2ml E\ -2mt E2mu E2mv E2mz E2m# E2m$ E2m% E2m& E2m' E2m+ E2m, E2m- E2m< E2m| E2m} E2m\ -~ E2n0 E2n1 E2n7 E2nI E2nJ E2nO E2nP E2nR E2nS E2nT E2nX E2nY E2nZ E2nh E2nu \ -E2nz E2n# E2n$ E2n% E2n* E2n+ E2n, E2n@ E2n[ E2n] E2n{ E2n| E2n} E2n~ E2o0 E2\ -o1 E2o2 E2o5 E2o6 E2o7 E2oC E2oH E2oI E2oJ E2oN E2oO E2oP E2oQ E2oR E2oS E2od\ - E2of E2og E2oh E2on E2os E2ot E2o+ E2o? E2o@ E2o[ E2p5 E2p6 E2pG E2pI E2pP E\ -2pQ E2pR E2pV E2pW E2pX E2pY E2pZ E2pa E2pd E2pe E2pf E2pg E2pw E2px E2py E2p\ -z E2p# E2p) E2p> E2p@ E2p_ E2p{ E2p| E2p} E2p~ E2q3 E2q4 E2q5 E2qE E2qJ E2qV \ -E2qW E2qY E2qZ E2qd E2qe E2qf E2qp E2qq E2qr E2qv E2qw E2qx E2qy E2qz E2q# E2\ -q' E2q( E2q) E2q/ E2q= E2q> E2q? 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E30~ E311 E312 E313 E315 E316 E317 E319 E31N E31O E31P E3\ -1Z E31a E31b E31c E31d E31f E31g E31h E31i E31j E31k E31o E31q E31# E31$ E31%\ - E31) E31* E31+ E31< E31= E322 E323 E327 E328 E329 E32B E32C E32D E32E E32F E\ -32G E32H E32I E32e E32f E32g E32i E32j E32n E32o E32p E32$ E32% E32' E32; E32\ -< E32= E338 E33E E33L E33M E33N E33X E33Y E33Z E33b E33c E33d E33e E33f E33g \ -E33h E33m E33n E33o E33z E33# E33% E33' E33( E33) E33+ E33= E33> E33? E33^ E3\ -3_ E33` E345 E346 E347 E349 E34B E34C E34D E34E E34F E34G E34K E34M E34W E34X\ - E34Y E34c E34d E34e E34h E34m E34n E34y E34$ E34% E34) E34* E34+ E34. E34/ E\ -34: E34; E34< E34= E34> E354 E355 E357 E358 E35J E35K E35L E35b E35c E35d E35\ -k E35l E35m E35/ E35< E35= E35[ E35] E35^ E363 E364 E365 E369 E36A E36B E36I \ -E36J E36K E36U E36V E36X E36Y E36a E36b E36c E36d E36f E36m E36n E36o E36s E3\ -6t E36u E36' E36( E36) E36+ E36- E36. 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F1E_ F1E{ F1E| F1E} F\ -1E~ F1F0 F1F1 F1F2 F1F3 F1F4 F1F5 F1F6 F1F7 F1FB F1FC F1FD F1FE F1FG F1FH F1F\ -I F1FJ F1FL F1FN F1FO F1FP F1FR F1FS F1FT F1FU F1FW F1FX F1FY F1Fc F1Fd F1Fe \ -F1Ff F1Fh F1Fi F1Fj F1Fk F1F? F1F] F1F{ F1GB F1GK F1GL F1GN F1GO F1GQ F1GR F1\ -GU F1GX F1Gb F1Gc F1Gd F1Gf F1Gk F1Gl F1Gn F1Go F1Gp F1Gq F1Gr F1Gs F1Gu F1Gv\ - F1Gw F1Gx F1Gy F1G( F1G) F1G* F1G. F1G/ F1G: F1G[ F1G] F1G_ F1G` F1G{ F1H3 F\ -1H4 F1H5 F1H9 F1HC F1HE F1HF F1HG F1HH F1HI F1HL F1HM F1HN F1HP F1HQ F1HR F1H\ -S F1HT F1HU F1HV F1HW F1Ha F1Hb F1Hc F1Hd F1Hf F1Hg F1Hh F1Hi F1Hq F1Hr F1Hu \ -F1Hv F1Hw F1Hx F1H$ F1H% F1H& F1H' F1H( F1H) F1H- F1H. F1H/ F1H= F1H> F1H? F1\ -H@ F1H[ F1H^ F1H_ F1H` F1H| F1H} F1H~ F1I1 F1I2 F1I3 F1I4 F1I8 F1I9 F1IA F1IE\ - F1IF F1IG F1IK F1IL F1IP F1IT F1IV F1Ib F1Id F1Ie F1If F1Ip F1I# F1I. F1I{ F\ -1I~ F1J0 F1J2 F1J3 F1J7 F1J8 F1J9 F1JD F1JE F1JF F1JH F1JJ F1JK F1JL F1JM F1J\ -N F1JO F1JP F1JQ F1JS F1JT F1JU F1Jh F1Ji F1Jj F1Jn F1Jr F1Jt F1Ju F1Jv F1J$ \ -F1J% F1J& F1J' F1J/ F1J: F1J; F1J< F1J= F1J> F1J@ F1J[ F1J] F1J^ F1J` F1J{ F1\ -J| F1J} F1J~ F1K0 F1K1 F1K2 F1K6 F1K7 F1K8 F1KA F1KB F1KC F1KD F1KE F1KH F1KI\ - F1KJ F1KK F1KR F1KS F1KT F1KU F1KV F1KW F1KX F1KY F1KZ F1Ka F1Kb F1Kc F1Kg F\ -1Kh F1Ki F1Km F1Kn F1Ko F1Kq F1Ks F1Kt F1Ku F1Kz F1K# F1K$ F1K% F1K& F1K* F1K\ -+ F1K, F1K: F1K; F1K< F1K@ F1K_ F1L0 F1L1 F1L6 F1L7 F1L8 F1L9 F1LB F1Lf F1Lg \ -F1Lk F1L) F1L* F1L+ F1L/ F1L: F1L; F1L> F1L? F1L@ F1L[ F1L] F1L^ F1L_ F1L` F1\ -L| F1L} F1L~ F1M0 F1M7 F1M8 F1M9 F1MD F1ME F1MF F1MJ F1MO F1MP F1MQ F1MR F1MW\ - F1MX F1MY F1MZ F1Ma F1Mg F1Mi F1Mj F1Mk F1Ml F1Mm F1Mo F1Mq F1Mr F1Ms F1Mt F\ -1Mu F1Mw F1Mx F1My F1Mz F1M# F1M$ F1M( F1M) F1M* F1M, F1M- F1M. F1M/ F1M: F1M\ -> F1M? F1M@ F1M] F1M| F1M} F1M~ F1N0 F1N1 F1N2 F1N3 F1N4 F1N5 F1N6 F1N7 F1N8 \ -F1NC F1ND F1NE F1NG F1NI F1NJ F1NK F1NN F1NO F1NP F1NQ F1NS F1NU F1NV F1NX F1\ -NY F1NZ F1Nd F1Ne F1Nf F1Ng F1Nj F1Nk F1Nl F1Nr F1Nt F1N# F1N( F1N- F1N@ F1O4\ - F1OD F1OH F1OO F1OQ F1OT F1OU F1OW F1OY F1Oc F1Od F1Oe F1Og F1Oh F1On F1Oo F\ -1Op F1Oq F1Or F1Os F1Ot F1Ov F1Ow F1Ox F1Oy F1Oz F1O/ F1O: F1O; F1O? F1O_ F1O\ -` F1O{ F1O| F1P2 F1P4 F1P5 F1P6 F1PD F1PE F1PG F1PH F1PI F1PK F1PM F1PN F1PO \ -F1PP F1PQ F1PS F1PT F1PU F1PV F1PW F1PX F1Pb F1Pc F1Pd F1Pe F1Pf F1Ph F1Pi F1\ -Pj F1Pn F1Po F1Pp F1Pw F1Px F1Py F1Pz F1P# F1P$ F1P% F1P& F1P' F1P( F1P) F1P*\ - F1P. F1P/ F1P: F1P> F1P? F1P@ F1P_ F1P` F1P{ F1Q0 F1Q2 F1Q3 F1Q4 F1Q5 F1Q9 F\ -1QA F1QB F1QC F1QF F1QG F1QH F1QL F1QP F1QV F1Qa F1Qc F1Qf F1Qg F1Qm F1Qr F1Q\ -v F1Q# F1Q/ F1Q@ F1Q` F1Q} F1R1 F1R3 F1R8 F1R9 F1RA F1RE F1RF F1RG F1RK F1RL \ -F1RM F1RN F1RO F1RP F1RQ F1RR F1RT F1RU F1RV F1Rc F1Rd F1Re F1Ri F1Rj F1Rk F1\ -Ru F1Rv F1Rw F1R& F1R' F1R( F1R. F1R/ F1R; F1R< F1R= F1R> F1R] F1R^ F1R_ F1R`\ - F1R{ F1R} F1R~ F1S0 F1S1 F1S2 F1S3 F1S7 F1S8 F1S9 F1SA F1SC F1SD F1SE F1SF F\ -1SO F1SS F1ST F1SU F1SY F1SZ F1Sa F1Sb F1Sc F1Sd F1Sh F1Si F1Sj F1Sl F1Sm F1S\ -n F1So F1Sp F1St F1Su F1Sv F1Sx F1Sy F1S# F1S$ F1S% F1S& F1S' F1S+ F1S, F1S- \ -F1S; F1S< F1S= F1S[ F1S_ F1S{ F1T1 F1T7 F1TB F1TE F1T* F1T+ F1T, F1T- F1T^ F1\ -T_ F1T{ F1T| F1T} F1U1 F1U9 F1UJ F1UL F1UU F1UV F1Ux F1Uy F1Uz F1U) F1U* F1U+\ - F1U/ F1U: F1V1 F1V9 F1VK F1Vt F1Vv F1Vw F1Vx F1Vy F1V( F1V) F1V* F1V/ F1V: F\ -1V[ F1V] F1W1 F1W2 F1Wd F1We F1Wf F1Wt F1Wu F1Wv F1Ww F1Wx F1W, F1W[ F1W] F1W\ -| F1X1 F1XT F1XU F1XV F1Xc F1Xd F1Xe F1Xj F1Xk F1Xz F1X# F1X= F1X? F1X[ F1YN \ -F1YP F1YQ F1YS F1YT F1YU F1Yb F1Yc F1Yd F1Yh F1Yj F1Yn F1Yr F1Ys F1Yx F1Yz F1\ -Y$ F1Z9 F1ZA F1ZB F1ZO F1ZQ F1ZR F1ZS F1ZT F1Zr F1Zz F1Z~ F1a0 F1a1 F1a8 F1a9\ - F1aA F1aE F1aG F1aX F1aY F1ap F1a{ F1a| F1a} F1a~ F1b0 F1b7 F1b8 F1b9 F1bD F\ -1bE F1bh F1bj F1bo F1b+ F1b, F1b- F1b^ F1b_ F1b{ F1b| F1b} F1b~ F1cV F1cZ F1c\ -h F1co F1cw F1cy F1cz F1c# F1c* F1c+ F1c, F1c: F1c< F1ds F1dv F1dw F1dx F1dy \ -F1dz F1d% F1d) F1d* F1d+ F1d/ F1d: F1e2 F1eE F1eS F1eX F1ee F1ef F1eg F1ej F1\ -et F1eu F1ew F1ex F1ey F1f4 F1fJ F1fU F1fV F1fW F1fd F1fe F1ff F1fj F1fk F1fq\ - F1f] F1g3 F1g4 F1gB F1gP F1gQ F1gS F1gT F1gU F1gV F1gc F1gd F1ge F1gj F1gk F\ -1gs F1g: F1h1 F1h2 F1hA F1hB F1hC F1hQ F1hR F1hS F1hT F1hU F1hX F1h: F1h~ F1i\ -0 F1i1 F1i2 F1i9 F1iA F1iB F1iD F1iG F1iH F1i$ F1i& F1i- F1i. F1i? F1i{ F1i| \ -F1i~ F1j0 F1j1 F1j3 F1j8 F1j9 F1jA F1jE F1jG F1jj F1jk F1jp F1j, F1j- F1j. F1\ -j{ F1j| F1j} F1j~ F1k0 F1kz F1k# F1k$ F1k+ F1k, F1k- F1k< F1k= F1lS F1lg F1lv\ - F1lw F1ly F1lz F1l# F1l* F1l+ F1l, F1l: F1l< F1mG F1mX F1mY F1ma F1mf F1mg F\ -1mh F1mu F1mw F1mx F1my F1mz F1n4 F1n6 F1n9 F1nD F1nG F1nV F1nW F1nX F1ne F1n\ -f F1ng F1nk F1nm F1o4 F1oJ F1oS F1oT F1oU F1oV F1oW F1od F1oe F1of F1oj F1ok \ -F1o; F1o| F1p4 F1p7 F1pB F1pC F1pD F1pQ F1pR F1pT F1pU F1pV F1p' F1p: F1p; F1\ -p@ F1p| F1q1 F1q2 F1q3 F1qA F1qB F1qC F1qG F1qH F1q& F1q. F1q| F1q~ F1r0 F1r1\ - F1r2 F1r9 F1rA F1rB F1rG F1rH F2Yc F2Yd F2Ye F2Yf F2Y. F2Y/ F2Y= F2Y> F2Y? F\ -2Z8 F2ZA F2ZF F2ZG F2ZI F2ZN F2ZO F2ZP F2ZT F2ZU F2ZV F2ZW F2ZX F2ZY F2ZZ F2Z\ -c F2Zd F2Ze F2Zo F2Zu F2Zv F2Zw F2Zx F2Zy F2Z& F2Z( F2Z= F2Z> F2Z^ F2Z_ F2Z` \ -F2Z{ F2Z| F2a1 F2a2 F2a3 F2aB F2aC F2aI F2aO F2aT F2aU F2aV F2aX F2aa F2ab F2\ -ac F2ad F2an F2ao F2ap F2at F2au F2av F2aw F2ax F2ay F2az F2a% F2a& F2a' F2a;\ - F2a< F2a= F2a[ F2a] F2a^ F2a_ F2a` F2a{ F2b0 F2b1 F2b2 F2b3 F2b4 F2b5 F2b6 F\ -2b9 F2bA F2bB F2bG F2bH F2bL F2bN F2bS F2bW F2bb F2bi F2bm F2bn F2bo F2bw F2b\ -x F2b$ F2b& F2b+ F2b: F2b; F2b^ F2b_ F2b` F2b~ F2c0 F2c1 F2c2 F2c3 F2c4 F2c6 \ -F2c8 F2c9 F2cA F2cK F2cQ F2cR F2cS F2cT F2cV F2ca F2cg F2cm F2cn F2cs F2ct F2\ -cu F2cv F2cw F2c# F2c$ F2c% F2c, F2c_ F2c~ F2d0 F2d2 F2d3 F2d4 F2d7 F2d8 F2d9\ - F2dJ F2dK F2dL F2dP F2dQ F2dR F2dS F2dT F2dU F2dW F2dY F2dZ F2da F2dg F2dk F\ -2dl F2dm F2dq F2dr F2ds F2dt F2du F2dv F2dz F2d# F2d$ F2d% F2d& F2d' F2d+ F2d\ -, F2d- F2d= F2d] F2d} F2d~ F2eD F2eI F2eJ F2eK F2eR F2eY F2eZ F2ee F2ej F2el \ -F2es F2et F2eu F2ey F2ez F2e# F2e$ F2e% F2e& F2e* F2e+ F2e, F2e{ F2e| F2e} F2\ -f0 F2f1 F2fI F2fJ F2fO F2fP F2fQ F2fR F2fS F2fW F2fX F2fY F2fy F2fz F2f# F2f$\ - F2f' F2f) F2f* F2f+ F2f? F2f@ F2f[ F2f` F2f{ F2f| F2f} F2f~ F2g0 F2g3 F2g4 F\ -2g5 F2g6 F2gG F2gH F2gI F2gM F2gN F2gO F2gP F2gQ F2gR F2gb F2ge F2gf F2gg F2g\ -l F2gr F2g> F2g? F2g@ F2h4 F2h5 F2hB F2hF F2hH F2hJ F2hK F2hO F2hP F2hQ F2hU \ -F2hV F2hW F2hX F2hY F2hZ F2hb F2hd F2he F2hf F2hk F2hv F2hw F2hx F2hy F2h# F2\ -h/ F2h= F2h> F2h^ F2h_ F2h{ F2h| F2h} F2i2 F2i3 F2i4 F2iO F2iU F2iV F2iW F2iY\ - F2ic F2id F2ie F2ij F2io F2ip F2iq F2iu F2iv F2iw F2ix F2iy F2iz F2i$ F2i& F\ -2i' F2i( F2i< F2i= F2i> F2i] F2i^ F2i_ F2i` F2i{ F2i| F2j1 F2j2 F2j3 F2j4 F2j\ -5 F2j6 F2j8 F2jA F2jB F2jC F2jS F2jn F2jo F2jp F2j% F2j& F2j< F2j= F2j_ F2j` \ -F2j{ F2k0 F2k1 F2k2 F2k3 F2k4 F2k5 F2k9 F2kA F2kB F2kL F2kR F2kS F2kT F2kV F2\ -kW F2ki F2km F2kn F2ks F2kt F2kv F2kw F2kx F2k$ F2k% F2k& F2k/ F2l0 F2l1 F2l3\ - F2l4 F2l6 F2l8 F2l9 F2lA F2lG F2lK F2lL F2lM F2lQ F2lR F2lS F2lT F2lU F2lV F\ -2lZ F2la F2lb F2ll F2lm F2ln F2lr F2ls F2lt F2lu F2lv F2lw F2l# F2l$ F2l% F2l\ -& F2l' F2l( F2l, F2l- F2l. F2m8 F2mJ F2mK F2mL F2mU F2mk F2ml F2mt F2mu F2mv \ -F2mz F2m# F2m$ F2m% F2m& F2m' F2m+ F2m, F2m- F2m| F2m} F2m~ F2n0 F2n1 F2n7 F2\ -nI F2nJ F2nO F2nP F2nR F2nS F2nT F2nX F2nY F2nZ F2nz F2n# F2n$ F2n% F2n* F2n+\ - F2n, F2n@ F2n[ F2n] F2n{ F2n| F2n} F2n~ F2o0 F2o1 F2o2 F2o5 F2o6 F2o7 F2oC F\ -2oH F2oI F2oJ F2oN F2oO F2oP F2oQ F2oR F2oS F2od F2of F2og F2oh F2on F2os F2o\ -t F2o+ F2o? F2o@ F2o[ F2p4 F2p6 F2pG F2pH F2pP F2pQ F2pR F2pV F2pW F2pX F2pY \ -F2pZ F2pa F2pd F2pe F2pf F2pg F2pq F2pw F2px F2py F2p# F2p$ F2p* F2p> F2p@ F2\ -p_ F2p{ F2p| F2p} F2p~ F2q3 F2q4 F2q5 F2qJ F2qP F2qV F2qW F2qX F2qZ F2qd F2qe\ - F2qf F2qp F2qq F2qr F2qv F2qw F2qx F2qy F2qz F2q# F2q' F2q( F2q) F2q= F2q> F\ -2q? 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G-/ G-:\ - G-; G-< G-= G-> G-? G-~ G.0 G.1 G.5 G.6 G.7 G.C G.H G.I G.J G.K G.L G.M G.N \ -G.O G.P G.Q G.R G.S G.T G.U G.V G.W G.X G.Y G.i G.j G.k G.l G.m G.n G.o G.p G\ -.q G/G G/H G/I G/J G/K G/L G/M G/N G/O G/P G/Q G/S G/U G/W G/X G/h G/i G/j G/\ -k G/l G/m G/n G/o G/p G/z G/# G/$ G/% G/& G/' G/( G/) G/* G// G/: G/; G/< G/]\ - G/^ G/_ G/` G:1 G:2 G:3 G:4 G:a G:b G:c G:d G:e G:f G:h G:i G:k G:l G:n G:o \ -G:* G:+ G:, G:- G:. G:/ G:: G:; G:< G:> G:? G:@ G:[ G:^ G:` G:~ G;5 G;6 G;7 G\ -;8 G;9 G;A G;B G;C G;D G;< G;= G;> G;? G;@ G;[ G;] G;^ G;_ G;` G;{ G;| G;} G;\ -~ G<0 G<1 G<2 G<3 G G=? G=[ G=] G>q G>& G>' G>( G>) G>* G>+ G>, G>- G>. G>/ G>:\ - G>; G>< G>= G>> G>? G>@ G>[ G?0 G?n G?p G?# G?$ G?& G?' G?. G?/ G?: G?; G?< \ -G?= G?> G?? 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G11@ G11[ G11] G11\ -^ G11_ G11` G11{ G11| G11} G11~ G120 G121 G122 G123 G124 G125 G12E G12F G12G \ -G12H G12I G12J G12K G12L G12M G12N G12O G12P G12Q G12R G12S G12T G12U G12V G1\ -2W G12^ G12` G13B G13E G13F G13G G13H G13I G13J G13K G13L G13M G13N G13O G13P\ - G13Q G13R G13S G13T G13U G13V G13W G13X G13Y G13Z G13a G13b G13c G13d G13e G\ -13f G13g G13h G13i G13j G13k G13l G13m G13n G13x G13y G13z G13# G13$ G13% G13\ -& G13' G13( G13. G13= G13> G13@ G13[ G13^ G13_ G147 G14C G14P G14Q G14S G14U \ -G14e G14f G14g G14h G14i G14j G14k G14l G14m G14r G14( G14) G14* G14+ G14, G1\ -4- G14. G14/ G14: G14; G14< G14= G14> G14? G14@ G14[ G14] G14^ G14` G15P G15Q\ - G15S G15T G15Y G15b G15) G15: G15; G15< G15= G15> G15? G15@ G15[ G15] G16T G\ -16U G16V G16W G16X G16Y G16Z G16a G16b G16d G16e G16f G16g G16i G16k G16l G16\ -n G16o G16q G16r G16t G16u G16v G16w G16x G16y G16z G16# G16$ G16% G16& G16' \ -G16( G16) G16* G16+ G16, G16- G16. G16] G16^ G16_ G16} G16~ G170 G17F G17J G1\ -7K G17L G17M G17N G17O G17P G17Q G17R G17b G17c G17d G17e G17f G17g G17h G17i\ - G17j G17` G17{ G17} G17~ G184 G185 G187 G188 G18d G18e G18f G18g G18h G18i G\ -18~ G190 G191 G192 G193 G194 G195 G196 G197 G19H G19I G19J G19K G19L G19M G19\ -N G19O G19P G19i G19j G19k G19l G19m G19n G19o G19p G19q G19# G19$ G19& G19' \ -G19) G19* G19, G19- G19. G19/ G19: G19; G19< G19= G19> G19} G19~ G1A0 G1A1 G1\ -A2 G1A3 G1A4 G1A5 G1A6 G1A7 G1A8 G1A9 G1AA G1AB G1AC G1AD G1AE G1AF G1Au G1Av\ - G1Ax G1Ay G1A& G1A' G1A) G1A* G1BG G1BH G1BJ G1BK G1BM G1BN G1BO G1BP G1BQ G\ -1BR G1BS G1BT G1BU G1BV G1BW G1B* G1B+ G1B, G1B- G1B. G1B/ G1B: G1B; G1B< G1B\ -= G1B> G1B? G1B@ G1B[ G1B] G1B^ G1B_ G1B` G1C5 G1C6 G1C8 G1CA G1CC G1CD G1CL \ -G1CW G1CX G1CY G1CZ G1Ca G1Cb G1Cc G1Cd G1Ce G1Co G1Cp G1Cq G1Cr G1Cs G1Ct G1\ -Cu G1Cv G1Cw G1Cx G1Cz G1C$ G1C% G1C& G1C' G1Dr G1Ds G1D& G1D' G1D) G1D; G1D<\ - G1D= G1D> G1D? G1D@ G1D[ G1D] G1D^ G1EC G1ED G1EE G1EF G1EG G1EH G1EI G1EJ G\ -1EK G1EM G1EN G1EP G1EQ G1ES G1ET G1EU G1EV G1EW G1EX G1EY G1EZ G1Ea G1Eb G1E\ -c G1Ed G1Ef G1Eh G1Ei G1Ej G1Ek G1Eo G1Er G1Eu G1Ev G1Ew G1Ex G1Ey G1Ez G1E# \ -G1E$ G1E% G1E& G1E( G1E) G1E+ G1E, G1E. G1E/ G1E^ G1E_ G1E` G1E{ G1E| G1E} G1\ -FH G1FK G1FL G1FM G1FN G1FO G1FP G1FQ G1FR G1FS G1Fc G1Fd G1Fe G1Ff G1Fg G1Fh\ - G1Fi G1Fj G1Fk G1Fx G1F# G1F+ G1F. G1GB G1GC G1GN G1Ge G1Gf G1Gg G1Gh G1Gi G\ -1Gj G1G% G1G& G1G' G1G( G1G) G1G* G1G+ G1G, G1G- G1H0 G1H1 G1H2 G1H3 G1H4 G1H\ -5 G1H6 G1H7 G1H8 G1HI G1HJ G1HK G1HL G1HM G1HN G1HO G1HP G1HQ G1Hj G1Hk G1Hl \ -G1Hm G1Hn G1Ho G1Hp G1Hq G1Hr G1H% G1H( G1H+ G1H- G1H. G1H/ G1H: G1H; G1H< G1\ -H= G1H> G1H? G1H~ G1I0 G1I1 G1I2 G1I3 G1I4 G1I5 G1I6 G1I7 G1I8 G1I9 G1IA G1IB\ - G1IC G1ID G1IE G1IF G1IG G1IV G1I- G1I. G1J5 G1J6 G1JI G1JL G1JO G1JP G1JQ G\ -1JR G1JS G1JT G1JU G1JV G1JW G1JX G1J+ G1J, G1J- G1J. G1J/ G1J: G1J; G1J< G1J\ -= G1J> G1J? 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G3k/ G3k: G3k; G3l` G3l{ G3l} \ -G3l~ G3m1 G3m2 G3m4 G3m5 G3np G3pR G3pS G3pT G3pU G3pV G3pW G3pX G3pY G3pZ G3\ -p$ G3p' G3p* G3qi G3qj G3qk G3ql G3qm G3qn G3qo G3qp G3qq G3r8 G3r9 G3s# G3s&\ - G3s) G3s* G3s+ G3s, G3s- G3s. G3s/ G3s: G3s; G3s< G3t{ G3t~ G3u2 G3u6 G3vu G\ -3xS G3xT G3xU G3xV G3xW G3xX G3xY G3xZ G3xa G3yj G3yk G3yl G3ym G3yn G3yo G3y\ -p G3yq G3yr G3z9 G3zA G3#T G3## G3#& G3#) G3#+ G3#, G3#- G3#. G3#/ G3#: G3#; \ -G3#< G3#= G3$p G3$q G3$r G3$s G3$t G3$u G3$v G3$w G3$x G3%< G3%? G3%] G3&_ G3\ -&` G3&{ G3&| G3&} G3&~ G3'0 G3'1 G3'2 G3(& G3(' G3(( G3(, G3(- G3(. G3)1 G3)2\ - G3)3 G3)4 G3)5 G3)6 G3)7 G3)8 G3)9 G3*j G3*k G3*l G3*m G3*n G3*o G3*p G3*q G\ -3*r G3,q G3,r G3,s G3,t G3,u G3,v G3,w G3,x G3,y G3-? G3-] G3-` G3.` G3.{ G3.\ -| G3.} G3.~ G3/0 G3/1 G3/2 G3/3 G3:* G3:+ G3:, G3:- G3:. G3:/ G3;2 G3;3 G3;4 \ -G3;5 G3;6 G3;7 G3;8 G3;9 G3;A G3 G3>r G3>s G3>t G3>u G3>v G3>w G3>x G3>y G3>z G3?? 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KW= KW@ KXL KXM KXN KXO KXP KXQ KXR KXS KXT KXV KXW KXY KXZ KXb KXc \ -KXe KXf KXg KXh KXi KXj KXk KXl KXm KXn KXo KXp KXq KXr KXs KXt KXu KXv KXx K\ -Xz KX# KX$ KX% KX( KX) KX* KX+ KX, KX- KX. KX/ KX: KX; KX< KX= KX> KX? KX@ KX\ -[ KX] KY2 KY3 KY4 KY5 KY6 KY7 KY8 KY9 KYA KYB KYE KYK KYL KYM KYN KYO KYP KYQ\ - KYR KYS KYa KYd KYk KYl KYm KYn KYo KYp KYq KYr KYs KYt KYz KY/ KY: KY; KY< \ -KY= KY> KY? KY@ KY[ KY] KY^ KY` KY| KY~ KZ0 KZ4 KZ9 KZA KZL KZP KZV KZd KZj K\ -Zl KZo KZ_ KZ| Ka1 Ka2 Ka9 KaA KaB KaC KaD KaE KaF KaG KaH KaI KaJ KaK KaL Ka\ -M KaN KaO KaP KaQ KaU KaV KaW KaX KaY KaZ Kaa Kab Kac Kad Kae Kaf Kag Kah Kai\ - Kak Kal Kan Kao Kaq Kar Kas Kat Kau Kav Kaw Kax Kay Kaz Ka# Ka$ Ka% Ka& Ka' \ -Ka( Ka) Ka* Ka+ Ka, Ka- Ka. Ka/ Ka: Ka; Ka< Ka= Ka> Ka? Ka` Ka} Ka~ Kb0 Kb1 K\ -b2 Kb3 Kb4 Kb5 Kb6 Kb7 KbD KbF KbH KbI KbK KbM KbO KbP KbX KbY Kbi Kbj Kbk Kb\ -l Kbm Kbn Kbo Kbp Kbq Kbs Kbt Kbv Kbw Kby Kbz Kb( Kb. Kb: Kb@ Kb| Kc3 Kc6 Kc8\ - KcE KcG KcJ Kcq Kcr Kcs Kct Kcu Kcv Kcw Kcx Kcy Kc% Kc& Kc' Kc( Kc) Kc* Kc+ \ -Kc, Kc- Kc. Kc/ Kc: Kc; Kc< Kc= Kc^ Kc` Kc| Kc} Kd6 Kd7 Kd8 Kd9 KdA KdB KdC K\ -dD KdE KdG KdH KdI KdJ KdL KdN KdO KdP KdQ KdR KdS KdT KdU KdV KdW KdX KdY Kd\ -Z Kda Kdb Kdc Kdd Kde Kdf Kdj Kdm Kdq Kdr Kdt Kdu Kdw Kdx Kd$ Kd& Kd* Kd+ Kd,\ - Kd- Kd. Kd/ Kd: Kd; Kd< Kd] Kd_ Kd{ Kd| Kd} Kd~ Ke0 Ke1 Ke2 Ke3 Ke4 KeE KeF \ -KeG KeH KeI KeJ KeK KeL KeM KeN KeO KeP KeQ KeR KeS KeT KeU KeV Keg Ken Keq K\ -es Ke) Ke, Ke= Ke^ KfM KfN KfO KfP KfQ KfR KfS KfT KfU KfW KfX KfZ Kfa Kfc Kf\ -d Kfe Kff Kfg Kfh Kfi Kfj Kfk Kfl Kfm Kfn Kfo Kfp Kfq Kfr Kfs Kft Kfu Kfv Kfw\ - Kfy Kf# Kf$ Kf% Kf& Kf( Kf) Kf* Kf+ Kf, Kf- Kf. Kf/ Kf: Kf; Kf< Kf= Kf> Kf? \ -Kf@ Kf[ Kf] Kf^ Kg3 Kg4 Kg5 Kg6 Kg7 Kg8 Kg9 KgA KgB KgK KgL KgM KgN KgO KgP K\ -gQ KgR KgS KgT Kgi Kgm Kgn Kgo Kgp Kgq Kgr Kgs Kgt Kgu Kg: Kg; Kg< Kg= Kg> Kg\ -? Kg@ Kg[ Kg] Kg_ Kg` Kg{ Kg| Kg~ Kh1 Kh7 Kh9 KhC KhJ KhM KhO Khd Khg Khn Kht\ - Kh` Ki6 KiA KiB KiC KiD KiE KiF KiG KiH KiI KiJ KiK KiL KiM KiN KiO KiP KiQ \ -KiR KiS KiT KiU KiV KiW KiX Kib Kic Kid Kie Kif Kig Kih Kii Kij Kil Kim Kio K\ -ip Kir Kis Kit Kiu Kiv Kiw Kix Kiy Kiz Ki# Ki$ Ki% Ki& Ki' Ki( Ki) Ki* Ki+ Ki\ -, Ki- Ki. Ki/ Ki: Ki; Ki< Ki= Ki> Ki? Ki@ Kj0 Kj1 Kj2 Kj3 Kj4 Kj5 Kj6 Kj7 Kj8\ - KjI KjK KjM KjN KjO KjP KjT Kjj Kjk Kjl Kjm Kjn Kjo Kjp Kjq Kjr Kjs Kju Kjv \ -Kjx Kjy Kj# Kj. Kj? Kj] Kj_ Kk3 Kk6 KkA KkH KkN Kkr Kks Kkt Kku Kkv Kkw Kkx K\ -ky Kkz Kk# Kk$ Kk% Kk) Kk* Kk+ Kk, Kk- Kk. Kk/ Kk: Kk; Kk< Kk= Kk> Kk{ Kl6 Kl\ -7 Kl8 Kl9 KlA KlB KlC KlD KlE KlF KlH KlI KlJ KlK KlM KlO KlP KlQ KlR KlS KlT\ - KlU KlV KlW KlX KlY KlZ Kla Klb Klc Kld Kle Klf Klg Klq Klr Klt Klu Klw Klx \ -Kl# Kl+ Kl, Kl- Kl. Kl/ Kl: Kl; Kl< Kl= Kl| Kl} Kl~ Km0 Km1 Km2 Km3 Km4 Km5 K\ --M K-O K-Q K-U K-V K-X K-Z K-- K-. K-/ K-: K-; K-< K-= K-> K-? K-@ K-[ K-] K-\ -^ K-_ K-` K-{ K-| K-} K-~ K.0 K.1 K.2 K.3 K.4 K.5 K.6 K.7 K.8 K.9 K.A K.B K.C\ - K.D K.E K.F K.G K.I K.J K.K K.L K.N K.P K.h K.i K.j K.k K.l K.m K.n K.o K.p \ -K.q K/G K/H K/I K/J K/K K/L K/M K/N K/O K/Y K/Z K/a K/b K/c K/d K/e K/f K/g K\ -/i K/j K/k K/l K/m K/n K/p K/q K/r K/s K/u K/w K/x K/y K/$ K/% K/' K/* K/] K/\ -^ K/_ K/` K:1 K:2 K:3 K:g K:h K:i K:j K:k K:m K:n K:o K:p K:q K:r K:s K:t K:u\ - K:v K:w K:x K:y K:z K:# K:' K:( K:) K:* K:+ K:, K:- K:. K:/ K:; K:< K:= K:> \ -K:@ K:[ K:] K:^ K:_ K:` K:{ K:| K:} K:~ K;2 K;3 K;4 K;6 K;8 K;9 K;A K;B K;C K\ -;D K;F K;G K;I K;J K;L K;M K;[ K;` K;{ K;} K<0 K<2 K<3 K K`\ -? K`@ K`[ K`] K`^ K`_ K`~ K{4 K{6 K{L K{M K{N K{O K{Q K{R K{S K{T K{d K{e K{f\ - K{g K{h K{i K{j K{k K{l K{r K{t K{v K{w K{x K{y K{z K{# K{$ K{% K{& K{) K{+ \ -K{: K{; K{< K{= K{> K{? K{@ K{[ K{] K{^ K{_ K{` K{~ K|0 K|1 K|2 K|3 K|4 K|5 K\ -|6 K|7 K|8 K|9 K|A K|c K|e K|r K|s K|z K|/ K|: K|; K|< K|= K|> K|? K|@ K|[ K|\ -] K|^ K|_ K|` K|{ K|| K|} K|~ K}0 K}1 K}2 K}3 K}4 K}5 K}6 K}7 K}8 K}9 K}A K}B\ - K}C K}D K}E K}F K}G K}H K}I K}J K}K K}M K}O K}Q K}R K}Y K}g K}k K}l K}m K}n \ -K}o K}p K}q K}r K}s K}w K}$ K}* K}, K}< K~0 K~1 K~2 K~3 K~4 K~5 K~6 K~7 K~8 K\ -~D K~I K~J K~L K~M K~N K~O K~P K~Q K~b K~d K~e K~f K~g K~h K~i K~j K~l K~m K~\ -n K~o K~p K~q K~r K~s K~t K~u K~v K~w K~x K~y K~z K~# K~% K~& K~( K~) K~+ K~,\ - K10O K10P K10T K10V K10i K10j K10k K10l K10m K10n K10o K10p K10q K10r K10s K\ -10t K10u K10v K10w K10x K10y K10z K10# K10$ K10% K10& K10' K10( K10, K10- K10\ -. K10/ K10: K10; K10< K10= K10> K10? K10@ K10[ K10] K10^ K10_ K10` K10{ K10| \ -K10} K10~ K110 K111 K112 K113 K114 K115 K116 K117 K118 K119 K11A K11B K11C K1\ -1D K11E K11F K11H K11I K11K K11L K11N K11O K11W K11c K11e K11p K11r K11z K11#\ - K11$ K11% K11& K11' K11( K11) K11* K11] K11} K11~ K120 K121 K123 K125 K12F K\ -12G K12H K12I K12J K12K K12L K12M K12N K12X K12Y K12Z K12a K12b K12c K12d K12\ -e K12f K12^ K12` K12~ K130 K13F K13G K13I K13J K13L K13M K13N K13O K13P K13Q \ -K13R K13S K13T K13U K13V K13e K13n K13o K13p K13q K13r K13s K13t K13u K13v K1\ -3w K13x K13y K13# K13% K13' K13( K13) K13* K13+ K13, K13- K13. K13/ K13: K13;\ - K13< K13= K13> K13? K13@ K13[ K13] K13^ K13_ K13~ K141 K147 K14C K14I K14M K\ -14N K14O K14P K14Q K14R K14S K14T K14U K14g K14h K14i K14j K14k K14l K14m K14\ -w K14x K14y K14z K14# K14$ K14% K14& K14' K14: K14; K14< K14= K14> K14? K14@ \ -K14[ K14] K14^ K14| K14} K14~ K150 K151 K152 K153 K154 K156 K157 K158 K15A K1\ -5B K15P K15Q K15S K15T K15Z K15b K15c K15: K15; K15< K15= K15> K15? K15@ K15[\ - K15] K15^ K15_ K15` K15{ K15| K15} K15~ K160 K161 K16T K16U K16V K16W K16X K\ -16Y K16Z K16a K16b K16c K16d K16e K16f K16g K16h K16i K16j K16k K16u K16v K16\ -x K16y K16z K16# K16$ K16& K16' K16) K16+ K16- K16. K16/ K16: K16; K16< K16? \ -K16@ K16[ K16] K16^ K16_ K16` K16{ K16| K16} K16~ K170 K171 K172 K174 K175 K1\ -77 K178 K17B K17C K17D K17E K17F K17G K17H K17I K17O K17S K17U K17V K17W K17X\ - K17Y K17Z K17a K17i K17@ K17` K17{ K17} K184 K185 K187 K188 K18j K18k K18l K\ -18m K18n K18o K18q K18r K18s K18t K18u K18v K18x K18y K18z K18# K193 K19H K19\ -J K19K K19M K19N K19P K19Q K19T K19U K19V K19W K19X K19Y K19b K19c K19d K19e \ -K19f K19g K19h K19p K19r K19s K19t K19x K19y K19z K19# K19% K19& K19' K19( K1\ -9) K19* K19+ K19, K19- K19. K19/ K19: K19; K19< K19> K19? K19@ K19[ K19^ K19`\ - K19{ K19| K19} K1A0 K1A3 K1A4 K1A5 K1A8 K1AB K1AC K1AD K1AE K1AF K1Al K1Am K\ -1Ao K1Ap K1Au K1Av K1Ax K1Ay K1A& K1A) K1BF K1BG K1BH K1BI K1BJ K1BK K1BL K1B\ -M K1BN K1BO K1BP K1BR K1BT K1BV K1BW K1B= K1B> K1B? K1B@ K1B[ K1B] K1B^ K1B_ \ -K1B` K1B{ K1B| K1B} K1B~ K1C0 K1C2 K1C3 K1C4 K1C6 K1C7 K1C9 K1CA K1CB K1CC K1\ -CD K1CE K1CF K1CG K1CH K1CI K1CJ K1CR K1CW K1CX K1CY K1CZ K1Ca K1Cb K1Cc K1Cd\ - K1Ce K1Ck K1Co K1Cr K1Ct K1Cu K1Cw K1Cx K1Cy K1Cz K1C# K1C$ K1C% K1C' K1C( K\ -1C) K1C* K1C+ K1C, K1C- K1C. K1C/ K1C; K1Df K1Dg K1Dr K1D& K1D' K1D; K1D< K1D\ -= K1D> K1D? K1D@ K1D[ K1D] K1D^ K1D_ K1D` K1D{ K1D| K1D} K1D~ K1E0 K1E1 K1E2 \ -K1EF K1EL K1EM K1EN K1EO K1EP K1EQ K1ER K1ES K1ET K1EU K1EX K1EY K1EZ K1Ea K1\ -Eb K1Ec K1Ee K1Eg K1Eh K1Ei K1Ej K1Ek K1El K1Ew K1Ex K1Ez K1E# K1E$ K1E% K1E&\ - K1E( K1E) K1E+ K1E- K1E/ K1E: K1E; K1E< K1E= K1E> K1E? K1E@ K1E[ K1E] K1E^ K\ -1E_ K1E` K1E{ K1E| K1E} K1E~ K1F0 K1F1 K1F3 K1F4 K1F6 K1F7 K1F9 K1FA K1FB K1F\ -C K1FD K1FE K1FF K1FG K1FH K1FI K1FJ K1FR K1FT K1FU K1FV K1FW K1FX K1FY K1FZ \ -K1Fa K1Fb K1Fh K1Fp K1Fs K1F+ K1F. K1GN K1GO K1GZ K1Ga K1Gk K1Gl K1Gm K1Gn K1\ -Go K1Gp K1Gq K1Gr K1Gs K1Gt K1Gu K1Gv K1Gw K1Gx K1Gy K1Gz K1G# K1G$ K1G& K1G[\ - K1G] K1G^ K1G_ K1G` K1G{ K1G| K1G} K1G~ K1H5 K1HJ K1HK K1HM K1HN K1HP K1HQ K\ -1HR K1HS K1HT K1HU K1HV K1HW K1HX K1HY K1HZ K1Ha K1Hb K1Hc K1Hd K1He K1Hf K1H\ -g K1Hh K1Hi K1Hs K1Ht K1Hu K1Hv K1Hw K1Hx K1H$ K1H% K1H& K1H' K1H( K1H) K1H* \ -K1H+ K1H, K1H- K1H. K1H/ K1H: K1H; K1H< K1H= K1H> K1H? K1H@ K1H[ K1H] K1H^ K1\ -H_ K1H` K1H{ K1H| K1H} K1H~ K1I1 K1I3 K1I4 K1I5 K1I6 K1I8 K1I9 K1IA K1IB K1IC\ - K1ID K1IE K1IF K1IG K1IK K1IY K1Id K1Ig K1I^ K1I_ K1J5 K1J6 K1JG K1JH K1JI K\ -1JJ K1JK K1JL K1JM K1JN K1JO K1JP K1JQ K1JS K1JU K1JW K1JX K1JY K1JZ K1Ja K1J\ -b K1Jc K1Jd K1Je K1Jf K1Jg K1Jj K1Jk K1Jl K1Jm K1Jn K1Jo K1Jp K1J; K1J> K1J? \ -K1J@ K1J[ K1J] K1J^ K1J_ K1J` K1J{ K1J| K1J} K1J~ K1K0 K1K1 K1K2 K1K3 K1K4 K1\ -K5 K1K7 K1K8 K1K9 K1KA K1KB K1KD K1KE K1KI K1KJ K1KK K1KL K1KM K1KN K1KW K1KX\ - K1KY K1KZ K1Ka K1Kb K1Kc K1Kd K1Ke K1Kf K1Km K1Kp K1Kq K1Ks K1Kt K1Kv K1Kw K\ -1Ky K1Kz K1K# K1K$ K1K% K1K& K1K' K1K( K1K) K1K* K1K+ K1K, K1K- K1K. K1K/ K1K\ -: K1K; K1K< K1K] K1K` K1L8 K1LB K1Lf K1Lg K1Lv K1L# K1L$ K1L: K1L< K1L= K1L> \ -K1L? K1L@ K1L[ K1L] K1L^ K1L_ K1L` K1L{ K1L| K1L} K1L~ K1M0 K1M1 K1M2 K1M3 K1\ -MD K1MJ K1MM K1MN K1MO K1MP K1MQ K1MR K1MS K1MT K1MU K1MV K1MW K1MX K1MY K1MZ\ - K1Ma K1Mb K1Mc K1Md K1Me K1Mf K1Mg K1Mi K1Mj K1Mk K1Ml K1Mm K1Mr K1Mu K1Mw K\ -1Mx K1My K1Mz K1M# K1M$ K1M% K1M& K1M' K1M( K1M* K1M, K1M- K1M. K1M/ K1M; K1M\ -< K1M= K1M> K1M? K1M@ K1M[ K1M] K1M^ K1M_ K1M` K1M{ K1M| K1M} K1M~ K1N0 K1N1 \ -K1N2 K1N3 K1N5 K1N6 K1N8 K1N9 K1NB K1ND K1NE K1NF K1NG K1NH K1NI K1NJ K1NK K1\ -NQ K1NS K1NU K1NV K1NW K1NX K1NY K1NZ K1Na K1Nb K1Nc K1Ng K1Nj K1Nu K1N( K1N.\ - K1OQ K1OS K1OW K1OY K1Od K1Oe K1Ol K1Om K1On K1Oo K1Op K1Oq K1Or K1Os K1Ot K\ -1Ou K1Ov K1Ow K1Oy K1Oz K1O$ K1O% K1O- K1O. K1O] K1O^ K1O_ K1O` K1O{ K1O| K1O\ -} K1O~ K1P0 K1P2 K1P9 K1PF K1PI K1PJ K1PK K1PM K1PN K1PP K1PQ K1PS K1PT K1PU \ -K1PV K1PW K1PX K1PY K1PZ K1Pa K1Pb K1Pc K1Pd K1Pe K1Pf K1Pg K1Ph K1Pi K1Pj K1\ -Pw K1Px K1Py K1Pz K1P# K1P$ K1P& K1P' K1P( K1P) K1P* K1P+ K1P, K1P- K1P/ K1P:\ - K1P; K1P< K1P= K1P> K1P? K1P@ K1P[ K1P^ K1P_ K1P` K1P{ K1P| K1P} K1P~ K1Q0 K\ -1Q2 K1Q4 K1Q5 K1Q6 K1Q7 K1QA K1QB K1QC K1QD K1QE K1QF K1QG K1QH K1QO K1QV K1Q\ -Y K1Qf K1Qi K1Q| K1Q} K1R3 K1R4 K1RH K1RI K1RJ K1RK K1RL K1RM K1RN K1RO K1RP \ -K1RQ K1RR K1RT K1RV K1RX K1RY K1RZ K1Ra K1Rb K1Rc K1Rd K1Rf K1Rg K1Rh K1Ri K1\ -Rj K1Rk K1Rl K1Rm K1Rn K1Ro K1Rq K1R& K1R) K1R; K1R? K1R@ K1R[ K1R] K1R^ K1R_\ - K1R` K1R{ K1R| K1R} K1R~ K1S0 K1S1 K1S2 K1S3 K1S4 K1S5 K1S6 K1S7 K1S8 K1S9 K\ -1SA K1SB K1SC K1SD K1SE K1SF K1SG K1SH K1SI K1SM K1SN K1SO K1SQ K1SR K1SY K1S\ -Z K1Sa K1Sb K1Sc K1Sd K1Se K1Sf K1Sg K1Sl K1So K1Sr K1Ss K1Su K1Sv K1Sx K1Sy \ -K1S# K1S$ K1S% K1S& K1S' K1S( K1S) K1S* K1S+ K1S, K1S- K1S. K1S/ K1S: K1S; K1\ -S< K1S= K1S? K1S] K1T9 K1TR K1UA K1UL K1UR K1VH K1Wd K1We K1Wf K1Wg K1Wh K1Wi\ - K1Wj K1Wk K1Wl K1Wq K1Wu K1Wz K1W& K1Yx K1Y$ K1Y* K1Y+ K1Zt K1Zx K1a2 K1a5 K\ -1aB K1aG K1aZ K1ah K1a_ K1a{ K1bC K1bF K1bu K1bv K1b( K1b) K1cb K1co K1cu K1c\ -w K1c% K1c) K1c+ K1c: K1db K1de K1ds K1dw K1d+ K1d, K1ec K1ee K1ef K1eg K1eh \ -K1ei K1ej K1ek K1el K1em K1fB K1fH K1fN K1g1 K1gO K1gS K1gX K1gb K1gg K1gk K1\ -i3 K1iD K1i| K1jE K1jy K1jz K1j' K1j( K1ku K1kw K1lb K1le K1mf K1mi K1mj K1mk\ - K1ml K1mm K1mn K1nZ K1nd K1ni K1nr K1p1 K1p7 K1p- K1p[ K1p} K1q7 K1qH K1qw K\ -1q{ K1rD K2Ya K2Yb K2Yc K2Yd K2Ye K2Yf K2Yg K2Yh K2Yi K2Yn K2Yr K2Y- K2Y. K2Y\ -/ K2Y: K2Y; K2Y< K2Y= K2Y> K2Y? K2Z8 K2Z9 K2ZA K2ZB K2ZC K2ZD K2ZE K2ZF K2ZG \ -K2ZI K2ZQ K2ZR K2ZU K2ZV K2ZW K2ZY K2ZZ K2Za K2Zb K2Zc K2Zd K2Ze K2Zf K2Zg K2\ -Zh K2Zi K2Zj K2Zl K2Zn K2Zp K2Zq K2Zw K2Z( K2Z- K2Z. K2Z: K2Z; K2Z= K2Z> K2Z|\ - K2a5 K2a6 K2aI K2aQ K2aR K2aS K2aU K2aV K2aW K2aZ K2aa K2ab K2ad K2ae K2af K\ -2ah K2ai K2aj K2ak K2al K2am K2an K2ao K2ap K2ax K2az K2a# K2a& K2a' K2a( K2a\ -* K2a+ K2a, K2a- K2a. K2a/ K2a: K2a; K2a< K2a= K2a^ K2b3 K2b7 K2bA K2bB K2bC \ -K2bE K2bJ K2bM K2ba K2bb K2bc K2bd K2be K2bi K2bn K2b& K2b* K2b, K2b. K2b/ K2\ -b: K2b; K2b= K2b> K2b? K2b@ K2b[ K2b] K2b^ K2b_ K2b` K2b~ K2c6 K2c8 K2cA K2cB\ - K2cC K2cP K2cQ K2cR K2cV K2cW K2cX K2cY K2cZ K2ca K2cb K2cc K2cd K2ce K2cf K\ -2ch K2ci K2cj K2ck K2cl K2cm K2cn K2cs K2cw K2c[ K2c_ K2d3 K2d4 K2d5 K2d7 K2d\ -8 K2d9 K2dA K2dB K2dC K2dI K2dM K2dN K2dQ K2dR K2dS K2dU K2dV K2dW K2dZ K2da \ -K2db K2dd K2de K2df K2dg K2dh K2di K2dj K2dk K2dm K2ds K2d$ K2d( K2d, K2d- K2\ -d. K2d: K2d@ K2d] K2eB K2eD K2eE K2eG K2eH K2eJ K2eK K2eX K2eZ K2ea K2eb K2ec\ - K2ee K2ei K2em K2en K2eo K2ep K2eq K2er K2es K2et K2eu K2e% K2e( K2e) K2e* K\ -2e, K2e- K2e. K2e: K2e< K2e= K2e> K2e? K2e@ K2e[ K2e] K2e} K2e~ K2fI K2fL K2f\ -M K2fP K2fR K2fT K2fU K2fV K2fW K2fX K2fY K2fZ K2fa K2fb K2fq K2fs K2fy K2f% \ -K2f' K2f( K2f) K2f+ K2f, K2f- K2f/ K2f: K2f; K2f= K2f> K2f? K2f@ K2f[ K2f~ K2\ -g1 K2g2 K2g4 K2g5 K2g6 K2g7 K2g8 K2g9 K2gI K2gJ K2gL K2gM K2gN K2gQ K2gR K2gb\ - K2gc K2gd K2ge K2gf K2gg K2gh K2gi K2gj K2gl K2g. K2g/ K2g: K2g; K2g< K2g= K\ -2g> K2g? K2g@ K2h9 K2hA K2hB K2hC K2hD K2hE K2hF K2hG K2hH K2hK K2hS K2hT K2h\ -U K2hW K2hX K2hY K2ha K2hb K2hc K2hd K2he K2hf K2hg K2hh K2hi K2hj K2hn K2ho \ -K2hp K2hq K2hz K2h% K2h- K2h: K2h; K2h= K2h> K2h` K2iL K2iQ K2iS K2iT K2iU K2\ -iX K2iY K2iZ K2ib K2ic K2id K2ig K2ih K2ii K2ij K2ik K2il K2im K2in K2io K2ip\ - K2iq K2iv K2iz K2i$ K2i% K2i& K2i( K2i) K2i* K2i, K2i- K2i. K2i/ K2i: K2i; K\ -2i< K2i= K2i> K2i] K2i{ K2j1 K2j8 K2j9 K2jA K2jC K2jD K2jE K2jI K2jY K2ja K2j\ -e K2jf K2jg K2jl K2j+ K2j, K2j. K2j: K2j< K2j= K2j> K2j? K2j@ K2j[ K2j] K2j^ \ -K2j_ K2j` K2j{ K2k1 K2k5 K2k8 K2kA K2kD K2kE K2kO K2kP K2kT K2kW K2kX K2kY K2\ -kZ K2ka K2kb K2kc K2kd K2ke K2kf K2kg K2kh K2ki K2kj K2kk K2kl K2km K2kn K2ko\ - K2ku K2k[ K2l5 K2l6 K2l7 K2l8 K2l9 K2lA K2lB K2lC K2lD K2lG K2lL K2lO K2lP K\ -2lQ K2lS K2lT K2lU K2lX K2lY K2lZ K2lb K2lc K2ld K2lf K2lg K2li K2lj K2lk K2l\ -l K2lm K2ln K2lv K2l' K2l* K2l+ K2l, K2l. K2l/ K2l: K2l= K2m0 K2mD K2mF K2mG \ -K2mI K2mJ K2mL K2mV K2mX K2mY K2mZ K2ma K2ml K2mn K2mo K2mp K2mq K2mr K2ms K2\ -mt K2mu K2mv K2m# K2m' K2m( K2m+ K2m, K2m/ K2m: K2m; K2m< K2m= K2m> K2m? K2m@\ - K2m[ K2m] K2m^ K2n1 K2nL K2nO K2nP K2nS K2nU K2nV K2nW K2nX K2nY K2nZ K2na K\ -2nb K2nc K2ns K2n# K2n' K2n) K2n* K2n+ K2n. K2n/ K2n: K2n; K2n= K2n> K2n? K2n\ -@ K2n[ K2n] K2o2 K2o3 K2o4 K2o5 K2o6 K2o7 K2o8 K2o9 K2oA K2oG K2oK K2oL K2oO \ -K2oP K2oQ K2oS K2oc K2od K2oe K2of K2og K2oh K2oi K2oj K2ok K2on K2o/ K2o: K2\ -o; K2o< K2o= K2o> K2o? K2o@ K2o[ K2pA K2pB K2pC K2pD K2pE K2pF K2pG K2pH K2pI\ - K2pN K2pR K2pS K2pU K2pW K2pb K2pc K2pd K2pe K2pf K2pg K2ph K2pi K2pj K2pl K\ -2pm K2pn K2po K2pq K2ps K2px K2p$ K2p, K2p. K2p: K2p; K2p= K2p> K2p@ K2p_ K2p\ -} K2qR K2qS K2qV K2qW K2qX K2qZ K2qa K2qb K2qe K2qf K2qg K2qi K2ql K2qm K2qn \ -K2qo K2qp K2qq K2qr K2qx K2q$ K2q& K2q' K2q( K2q+ K2q, K2q/ K2q: K2q; K2q< K2\ -q= K2q> K2q? K2q} K2r3 K2r7 K2r8 K2rA K2rB K2rC K2rF K2rG K2rH K2ra K2rb K2rc\ - K2rd K2re K2rn K2r- K2r. K2r/ K2r: K2r< K2r> K2r? K2r@ K2r[ K2r] K2r^ K2r_ K\ -2r` K2r{ K2r| K2s4 K2s7 K2s8 K2sB K2sC K2sD K2sF K2sR K2sU K2sV K2sW K2sY K2s\ -Z K2sa K2sb K2sc K2sd K2se K2sf K2sg K2sh K2si K2sk K2sl K2sm K2sn K2so K2sp \ -K2sx K2s_ K2t0 K2t6 K2t8 K2t9 K2tA K2tB K2tC K2tD K2tE K2tJ K2tO K2tQ K2tR K2\ -tS K2tV K2tW K2tX K2tZ K2ta K2tb K2te K2tf K2tg K2th K2ti K2tj K2tk K2tl K2tm\ - K2tn K2to K2tt K2tx K2t% K2t) K2t* K2t, K2t. K2t; K2t< K2t? K2u3 K2uA K2uE K\ -2uF K2uH K2uI K2uK K2uL K2uX K2uY K2uc K2ud K2ue K2un K2uo K2up K2uq K2ur K2u\ -s K2ut K2uu K2uv K2uw K2u% K2u) K2u* K2u- K2u. K2u/ K2u; K2u< K2u= K2u? K2u@ \ -K2u[ K2u] K2u^ K2u_ K2u~ K2vM K2vR K2vS K2vU K2vV K2vW K2vX K2vY K2vZ K2va K2\ -vb K2vc K2vd K2vq K2v& K2v( K2v) K2v, K2v- K2v. K2v: K2v; K2v< K2v= K2v> K2v?\ - K2v@ K2v[ K2v] K2v^ K2v~ K2w0 K2w3 K2w5 K2w6 K2w7 K2w8 K2w9 K2wA K2wB K2wJ K\ -2wM K2wN K2wO K2wQ K2wR K2wS K2wq K2wu K2w* K2w+ K2w, K2w- K2w. K2w/ K2w; K2w\ -= K2w> K2w@ K2w[ K2x5 K2x6 K2x7 K2x8 K2x9 K2xA K2xC K2xD K2xE K2xH K2xJ K2xK \ -K2xL K2xM K2xN K2xO K2xP K2xQ K2xR K2xS K2xV K2xd K2xe K2xf K2xh K2xi K2xj K2\ -xu K2xw K2xx K2xy K2xz K2x# K2x$ K2x% K2x^ K2x_ K2x` K2x{ K2x| K2x} K2x~ K2y0\ - K2yB K2yJ K2yK K2yN K2yP K2yS K2yT K2yU K2yV K2yW K2yX K2yY K2yZ K2ya K2yb K\ -2yd K2ye K2yf K2yg K2yh K2yi K2yj K2yo K2y% K2y' K2y( K2y) K2y* K2y+ K2y, K2y\ -- K2y@ K2z9 K2zA K2zB K2zC K2zD K2zE K2zF K2zG K2zH K2zU K2zY K2zj K2zk K2zl \ -K2zm K2zn K2zo K2zp K2zq K2zr K2z' K2z( K2z) K2z* K2z+ K2z, K2z- K2z/ K2z: K2\ -z; K2z= K2z> K2z? K2z] K2z^ K2z_ K2z{ K2z} K2#5 K2#8 K2#9 K2#A K2#B K2#C K2#D\ - K2#E K2#F K2#G K2#H K2#I K2#L K2#M K2#N K2#P K2#s K2#t K2#u K2#v K2#w K2#x K\ -2#y K2#z K2#* K2#: K2#? K2#@ K2#[ K2#] K2#^ K2#_ K2#` K2#{ K2#| K2#~ K2$0 K2$\ -1 K2$2 K2$3 K2$5 K2$6 K2$O K2$P K2$R K2$S K2$T K2$W K2$X K2$Y K2$b K2$c K2$e \ -K2$f K2$+ K2$, K2$- K2$. K2$/ K2$: K2$; K2$< K2$= K2%9 K2%A K2%B K2%C K2%D K2\ -%E K2%F K2%G K2%I K2%J K2%K K2%L K2%N K2%S K2%W K2%g K2%h K2%i K2%j K2%k K2%l\ - K2%m K2%n K2%o K2%q K2%r K2%u K2%w K2%x K2%$ K2%* K2%+ K2%, K2%- K2%. K2%/ K\ -2%: K2%; K2%< K2%{ K2%} K2%~ K2&0 K2&1 K2&3 K2&4 K2&9 K2&F K2&H K2&J K2&K K2&\ -L K2&l K2&o K2&p K2&q K2&r K2&s K2&t K2&u K2&v K2&w K2&x K2&y K2&$ K2&% K2&& \ -K2&' K2&( K2&) K2&+ K2&- K2&. K2&/ K2&: K2'I K2'M K2'N K2'Q K2'R K2'S K2'U K2\ -'p K2'( K2') K2'* K2'. K2'/ K2': K2'< K2'= K2'? K2'@ K2'^ K2(3 K2(4 K2(5 K2(6\ - K2(7 K2(8 K2(C K2(E K2(G K2(H K2(I K2(L K2(M K2(N K2(O K2(P K2(Q K2(R K2(S K\ -2(T K2(V K2(d K2(e K2(h K2(i K2(j K2(l K2(p K2(v K2(w K2(x K2(y K2(z K2($ K2(\ -% K2(& K2(, K2(/ K2([ K2(^ K2(_ K2(` K2({ K2(| K2(} K2)0 K2)1 K2)6 K2)8 K2)K \ -K2)M K2)O K2)R K2)S K2)T K2)U K2)V K2)W K2)X K2)Y K2)Z K2)a K2)b K2)c K2)d K2\ -)e K2)f K2)g K2)h K2)i K2)j K2)k K2)t K2)w K2)y K2)& K2)' K2)( K2)) K2)* K2)+\ - K2), K2)- K2). K2)= K2)] K2)} K2*A K2*B K2*C K2*E K2*F K2*G K2*I K2*X K2*k K\ -2*l K2*m K2*n K2*o K2*p K2*q K2*r K2*s K2*% K2*& K2*' K2*( K2*) K2** K2*. K2*\ -/ K2*: K2*; K2*< K2*= K2*> K2*? K2*@ K2*] K2*_ K2*` K2*| K2*~ K2+6 K2+9 K2+A \ -K2+B K2+C K2+D K2+E K2+F K2+G K2+H K2+I K2+L K2+M K2+P K2+Q K2+T K2+W K2+i K2\ -+o K2+q K2+t K2+v K2+w K2+y K2+z K2+# K2+% K2+& K2+> K2+? K2+@ K2+[ K2+] K2+^\ - K2+_ K2+` K2+{ K2+| K2+} K2,0 K2,1 K2,3 K2,4 K2,5 K2,6 K2,7 K2,D K2,F K2,K K\ -2,O K2,R K2,S K2,T K2,V K2,X K2,Z K2,c K2,h K2,i K2,o K2,y K2,, K2,- K2,. K2,\ -/ K2,; K2,< K2,= K2-7 K2-8 K2-9 K2-D K2-E K2-F K2-G K2-H K2-I K2-J K2-K K2-L \ -K2-M K2-N K2-O K2-W K2-h K2-i K2-j K2-k K2-l K2-m K2-n K2-o K2-p K2-s K2-u K2\ --v K2-x K2-% K2-+ K2-, K2-- K2-. K2-/ K2-: K2-; K2-< K2-= K2-^ K2-{ K2-} K2-~\ - K2.0 K2.2 K2.4 K2.5 K2.6 K2.F K2.J K2.K K2.L K2.N K2.P K2.W K2.c K2.k K2.l K\ -2.p K2.q K2.r K2.s K2.t K2.u K2.v K2.w K2.x K2.y K2.# K2.$ K2.% K2.& K2.( K2.\ -) K2.+ K2.. K2.: K2.< K2.> K2.@ K2/0 K2/8 K2/B K2/I K2/M K2/N K2/P K2/Q K2/U \ -K2/V K2/k K2/p K2/) K2/* K2/+ K2/, K2/- K2/. K2/< K2/> K2/? K2/[ K2/] K2/_ K2\ -:4 K2:5 K2:6 K2:A K2:B K2:C K2:D K2:E K2:G K2:I K2:K K2:L K2:M K2:N K2:O K2:P\ - K2:Q K2:R K2:S K2:T K2:U K2:Z K2:d K2:e K2:g K2:h K2:i K2:l K2:m K2:t K2:w K\ -2:y K2:z K2:$ K2:% K2:& K2:' K2:, K2:/ K2:@ K2:` K2:{ K2:| K2:} K2:~ K2;0 K2;\ -1 K2;6 K2;B K2;M K2;N K2;O K2;Q K2;R K2;S K2;U K2;V K2;W K2;X K2;Y K2;Z K2;a \ -K2;b K2;c K2;e K2;g K2;h K2;j K2;l K2;r K2;t K2;z K2;$ K2;' K2;( K2;+ K2;, K2\ -;- K2;. K2;= K2;@ K2;{ K2;~ K2 K20 K2>1 K2>2 K2>3 K2>4 K2>5 K2>6 K2>7 K2>8 K2>E K2>G\ - K2>N K2>R K2>V K2>W K2>X K2>Z K2>b K2>c K2>f K2>m K2>x K2>( K2>- K2>. K2>: K\ -2>; K2>< K2>= K2>? K2?8 K2?9 K2?A K2?B K2?C K2?D K2?I K2?J K2?K K2?L K2?M K2?\ -N K2?O K2?V K2?i K2?j K2?k K2?l K2?m K2?n K2?o K2?p K2?q K2?t K2?v K2?y K2?z \ -K2?$ K2?+ K2?, K2?- K2?. K2?/ K2?: K2?; K2?< K2?= K2?> K2?@ K2?{ K2?} K2?~ K2\ -@0 K2@1 K2@2 K2@3 K2@4 K2@5 K2@6 K2@G K2@I K2@J K2@K K2@P K2@U K2@g K2@h K2@q\ - K2@r K2@s K2@t K2@u K2@v K2@w K2@x K2@y K2@z K2@# K2@$ K2@% K2@& K2@' K2@( K\ -2@) K2@* K2@+ K2@< K2@= K2@? K2@{ K2[4 K2[9 K2[C K2[M K2[R K2[T K2[U K2[V K2[\ -g K2[h K2[i K2[j K2[k K2[l K2[m K2[n K2[o K2[w K2[= K2[> K2[? K2[@ K2[[ K2[] \ -K2[^ K2[` K2]E K2]F K2]G K2]I K2]J K2]K K2]L K2]M K2]O K2]P K2]Q K2]S K2]T K2\ -]U K2]h K2]t K2]x K2]y K2]z K2]# K2]$ K2]% K2]& K2]' K2]( K2]) K2]* K2]: K2];\ - K2]] K2]` K2]{ K2]| K2]} K2]~ K2^0 K2^1 K2^2 K2^3 K2^4 K2^5 K2^7 K2^9 K2^E K\ -2^F K2^G K2^I K2^J K2^K K2^M K2^N K2^O K2^P K2^Q K2^R K2^S K2^T K2^U K2^X K2^\ -w K2^y K2^z K2^# K2^$ K2^% K2^& K2^' K2^` K2^{ K2^| K2^} K2^~ K2_0 K2_1 K2_2 \ -K2_9 K2_C K2_D K2_E K2_F K2_G K2_H K2_I K2_J K2_K K2_R K2_g K2_h K2_j K2_l K2\ -_: K2_; K2_< K2_= K2_> K2_? K2_@ K2_[ K2_] K2`K K2`L K2`M K2`N K2`O K2`P K2`Q\ - K2`R K2`S K2`T K2`U K2`V K2`W K2`X K2`a K2`b K2`g K2`t K2`u K2`w K2`x K2`y K\ -2`$ K2`% K2`' K2`( K2`* K2`+ K2`- K2`. K2`? K2`^ K2`_ K2`` K2`{ K2`| K2`~ K2{\ -0 K2{1 K2{2 K2{4 K2{5 K2{6 K2{7 K2{8 K2{9 K2{A K2{B K2{C K2{D K2{E K2{F K2{G \ -K2{H K2{I K2{J K2{L K2{M K2{N K2{O K2{P K2{Q K2{R K2{f K2{t K2{u K2{v K2{w K2\ -{x K2{y K2{z K2{# K2{* K2{. K2{/ K2{: K2{; K2{< K2{= K2{> K2{? K2{@ K2{` K2{|\ - K2|I K2|J K2|K K2|L K2|M K2|N K2|O K2|P K2|Q K2|d K2|e K2|g K2|h K2|_ K2|~ K\ -2}1 K2}2 K2}3 K2}6 K2}7 K2}8 K2}9 K2}B K2}D K2}F K2}G K2}H K2}I K2}J K2}K K2}\ -L K2}M K2}N K2}O K2}P K2}Q K2}R K2}S K2}T K2}U K2}X K2}Y K2}h K2}n K2}r K2}t \ -K2}v K2}w K2}x K2}y K2}z K2}# K2}$ K2}& K2}' K2}( K2}) K2}* K2}+ K2}} K2}~ K2\ -~0 K2~1 K2~2 K2~4 K2~5 K2~6 K2~7 K2~8 K2~9 K2~A K2~B K2~C K2~D K2~E K2~F K2~G\ - K2~I K2~J K2~K K2~L K2~M K2~N K2~O K2~h K2~i K2~j K2~k K2~l K2~m K2~n K2~o K\ -2~p K2~< K2~> K2~? K2~@ K2~[ K2~] K2~^ K2~_ K2~` K2~{ K30A K30F K30G K30H K30\ -I K30J K30K K30L K30M K30N K30P K30Q K30R K30U K30c K30i K30u K30w K30y K30z \ -K30# K30$ K30% K30& K30' K30( K30) K30- K30. K30/ K30; K30< K30@ K30^ K30{ K3\ -0| K30} K30~ K310 K311 K312 K313 K314 K318 K31A K31B K31D K31F K31G K31H K31J\ - K31K K31L K31N K31O K31P K31Q K31R K31S K31T K31U K31V K31Z K31d K31i K31l K\ -31w K31y K31# K31$ K31% K31& K31( K31. K31: K31@ K31` K31{ K31~ K320 K321 K32\ -2 K323 K329 K32B K32D K32E K32F K32G K32H K32I K32J K32K K32L K32M K32e K32g \ -K32l K32m K32o K32v K32; K32< K32> K32? K32@ K32[ K32] K32^ K32{ K32~ K337 K3\ -3K K33L K33M K33N K33O K33P K33Q K33R K33S K33T K33U K33V K33W K33X K33Y K33Z\ - K33a K33b K33c K33e K33q K33v K33x K33y K33z K33% K33& K33( K33) K33+ K33, K\ -33. K33/ K33= K33^ K33_ K33` K33{ K33| K33} K33~ K340 K341 K342 K343 K344 K34\ -5 K346 K347 K348 K349 K34A K34B K34C K34D K34E K34F K34G K34H K34I K34J K34K \ -K34L K34M K34N K34O K34R K34S K34g K34k K34o K34u K34v K34w K34y K34z K34# K3\ -4$ K34% K34) K34, K34/ K34: K34; K34< K34= K34> K34? K34@ K34[ K355 K35K K35L\ - K35M K35N K35O K35P K35Q K35R K35b K35d K35e K35f K35l K35o K35v K35z K35- K\ -35= K35@ K35~ K360 K362 K363 K364 K367 K368 K369 K36A K36C K36E K36G K36H K36\ -I K36J K36K K36L K36M K36N K36O K36P K36Q K36R K36S K36T K36U K36V K36W K36X \ -K36Y K36Z K36b K36q K36s K36t K36u K36v K36w K36x K36y K36z K36# K36$ K36% K3\ -6& K36' K36( K36) K36* K36+ K36, K36; K36? K36@ K36~ K370 K371 K372 K373 K374\ - K375 K376 K378 K379 K37A K37B K37C K37D K37E K37F K37G K37H K37I K37J K37K K\ -37L K37N K37O K37i K37j K37k K37l K37m K37n K37o K37p K37q K37t K37- K37? K37\ -@ K37[ K37] K37^ K37_ K37` K37| K389 K38G K38H K38I K38K K38L K38M K38N K38O \ -K38Q K38S K38U K38W K38k K38o K38z K38# K38$ K38% K38& K38' K38( K38) K38* K3\ -8, K38- K38/ K38: K38[ K38| K38} K38~ K390 K391 K392 K393 K394 K395 K396 K397\ - K39D K39E K39G K39H K39I K39K K39L K39M K39O K39P K39Q K39R K39S K39T K39U K\ -39V K39W K39Z K39j K39m K39t K39y K39z K39$ K39% K39& K39' K39) K39/ K39; K39\ -` K39{ K39| K3A0 K3A1 K3A2 K3A3 K3A4 K3A8 K3AE K3AF K3AG K3AH K3AI K3AJ K3AK \ -K3AL K3AM K3AN K3Af K3Ah K3Aj K3Ak K3As K3Au K3A< K3A= K3A> K3A? K3A[ K3A] K3\ -A^ K3A_ K3A{ K3B2 K3BC K3BI K3BM K3BN K3BO K3BP K3BQ K3BR K3BS K3BT K3BU K3BV\ - K3BX K3BY K3BZ K3Bb K3Bc K3Bd K3Bk K3Bm K3Br K3Bv K3Bw K3By K3Bz K3B# K3B& K\ -3B' K3B) K3B* K3B, K3B- K3B/ K3B: K3B` K3B{ K3B} K3B~ K3C0 K3C1 K3C2 K3C3 K3C\ -4 K3C6 K3C7 K3C8 K3C9 K3CA K3CB K3CC K3CD K3CE K3CF K3CG K3CH K3CI K3CJ K3CK \ -K3CL K3CN K3CO K3CP K3CQ K3CR K3CS K3CT K3Cl K3Cp K3Cu K3Cw K3Cy K3Cz K3C# K3\ -C$ K3C% K3C& K3C. K3C: K3C; K3C< K3C= K3C> K3C? K3C@ K3C[ K3C] K3C` K3DK K3DL\ - K3DM K3DN K3DO K3DP K3DR K3DS K3De K3Dj K3Dk K3Dq K3Dt K3Dv K3Dx K3D= K3E0 K\ -3E1 K3E3 K3E4 K3E5 K3E8 K3E9 K3EA K3EB K3ED K3EF K3EH K3EI K3EJ K3EK K3EL K3E\ -M K3EN K3EO K3EP K3EQ K3ER K3ES K3EU K3EV K3EW K3EX K3EZ K3Ea K3Ef K3Eg K3Et \ -K3Ew K3Ex K3Ey K3E# K3E% K3E& K3E( K3E) K3E* K3E+ K3E, K3E- K3E< K3F2 K3F3 K3\ -F4 K3F5 K3F6 K3F7 K3F8 K3F9 K3FA K3FB K3FC K3FD K3FE K3FF K3FG K3FH K3FJ K3FK\ - K3FL K3FM K3FN K3FO K3FP K3FQ K3Fj K3Fk K3Fl K3Fm K3Fn K3Fo K3Fp K3Fq K3Fr K\ -3Fs K3Ft K3Fw K3Fx K3Fy K3F@ K3F[ K3F] K3F^ K3F_ K3F` K3F{ K3F| K3F} K3G8 K3G\ -9 K3GA K3GB K3GD K3GE K3GG K3GY K3Gb K3Gh K3Gq K3Gr K3Gs K3Gv K3Gx K3Gy K3Gz \ -K3G: K3G? K3G@ K3G[ K3G] K3G^ K3G_ K3G` K3G{ K3G| K3H3 K3H7 K3H8 K3HB K3HC K3\ -HD K3HF K3HG K3HH K3HI K3HJ K3HK K3HL K3HM K3HN K3HO K3Hm K3Ho K3Hx K3Hz K3H#\ - K3H% K3H& K3H' K3H( K3H) K3H* K3H/ K3H@ K3H] K3H` K3H{ K3H| K3H} K3I0 K3I4 K\ -3IF K3IG K3IJ K3IK K3IL K3IN K3IO K3IP K3IQ K3IR K3IS K3IT K3IU K3IV K3IW K3I\ -g K3Ih K3Ii K3Ij K3Ik K3Il K3Im K3In K3Io K3Iq K3Ir K3Is K3It K3Iu K3Iv K3Iw \ -K3Ix K3J5 K3J6 K3J8 K3J9 K3JB K3JC K3JM K3JX K3JY K3JZ K3Ja K3Jb K3Jd K3Je K3\ -Jo K3Jq K3Jr K3Js K3Ju K3Jv K3Jw K3J( K3J) K3J* K3J+ K3J- K3J. K3J: K3J; K3J<\ - K3J= K3J> K3J? K3J@ K3J[ K3J] K3J^ K3J_ K3J} K3KF K3KH K3KI K3KK K3KL K3KQ K\ -3Kc K3Kd K3Kh K3Kn K3Kp K3Kr K3Ks K3Kt K3Ku K3Kx K3Ky K3Kz K3K# K3K$ K3K% K3K\ -& K3K' K3K_ K3K` K3K{ K3K| K3K} K3K~ K3L0 K3L1 K3L2 K3LD K3LE K3LF K3LH K3LI \ -K3LJ K3LM K3LN K3LP K3LQ K3LS K3LT K3Le K3Lf K3Lh K3Li K3Lk K3Ll K3Lv K3Lw K3\ -Lx K3Ly K3Lz K3L# K3L$ K3L% K3L& K3L, K3L. K3L< K3M2 K3M3 K3M4 K3M5 K3M6 K3M7\ - K3M8 K3M9 K3MA K3MG K3MK K3MN K3MO K3MP K3MQ K3MS K3MY K3Mc K3Md K3Mf K3Mh K\ -3Mj K3Mk K3Mv K3M' K3M( K3M) K3M* K3M, K3M- K3M. K3M/ K3M; K3M< K3M= K3M> K3M\ -? K3M@ K3M[ K3M{ K3N0 K3NI K3NJ K3NK K3NL K3NM K3NN K3NO K3NP K3NQ K3NR K3NS \ -K3NT K3NU K3NV K3NW K3NZ K3Na K3Nk K3Nl K3Nm K3Nn K3No K3Np K3Nq K3Nr K3Ns K3\ -Nt K3Nu K3Nw K3Nx K3Ny K3Nz K3N# K3N$ K3N% K3N& K3N? K3N[ K3N^ K3N_ K3N` K3N{\ - K3N| K3N} K3N~ K3OA K3OB K3OC K3OD K3OE K3OG K3OH K3ON K3Ob K3Oc K3Oe K3Of K\ -3Oh K3On K3Oq K3Ou K3Ov K3Ow K3Ox K3Oy K3Oz K3O# K3O) K3O+ K3O? K3O@ K3O[ K3O\ -] K3O^ K3O_ K3O` K3O{ K3O| K3O} K3P3 K3P8 K3PA K3PB K3PC K3PF K3PG K3PH K3PI \ -K3PJ K3PK K3PL K3PM K3PN K3PP K3PV K3PX K3Pd K3Pp K3Pu K3P# K3P$ K3P% K3P& K3\ -P( K3P) K3P+ K3P. K3P= K3P@ K3P[ K3P_ K3P{ K3P~ K3Q3 K3Q5 K3Q6 K3QF K3QG K3QI\ - K3QJ K3QK K3QN K3QO K3QQ K3QR K3QS K3QT K3QU K3QW K3QX K3Qh K3Qi K3Qj K3Qk K\ -3Ql K3Qm K3Qn K3Qo K3Qp K3Qq K3Qr K3Qt K3Qu K3Qv K3Qw K3Qy K3Q$ K3Q] K3R6 K3R\ -8 K3R9 K3RB K3RC K3RE K3RI K3RV K3RX K3RZ K3Rb K3Rc K3Re K3Rf K3Rh K3Ro K3Rp \ -K3Rq K3Rr K3Rs K3Rt K3Ru K3Rv K3Rw K3Rx K3R% K3R+ K3R- K3R/ K3R; K3R< K3R= K3\ -R> K3R? K3R@ K3R[ K3R] K3R^ K3R_ K3R` K3S6 K3SE K3SG K3SH K3SJ K3SK K3SM K3SV\ - K3Sa K3Si K3Sl K3So K3Sp K3Sr K3St K3Sv K3Sw K3Sx K3Sy K3S# K3S$ K3S% K3S& K\ -3S' K3S( K3S: K3S; K3S[ K3S{ K3S| K3S} K3S~ K3T0 K3T1 K3T2 K3T3 K3TD K3TE K3T\ -H K3TI K3TJ K3TL K3TN K3TQ K3TT K3TU K3Te K3Ti K3Tk K3Tl K3Tw K3Tx K3Ty K3Tz \ -K3T# K3T$ K3T% K3T& K3T' K3T+ K3T= K3T} K3U3 K3U4 K3U5 K3U6 K3U7 K3U8 K3U9 K3\ -UA K3UB K3UG K3UK K3UL K3UM K3UO K3UP K3UR K3US K3UT K3Ue K3Uf K3Ug K3Uh K3Uj\ - K3Ul K3Uo K3Uq K3U# K3U& K3U' K3U( K3U) K3U* K3U+ K3U, K3U. K3U/ K3U: K3U; K\ -3U= K3U> K3U? K3U@ K3U[ K3U] K3V0 K3VB K3VE K3VK K3VL K3VM K3VN K3VO K3VP K3V\ -Q K3VR K3VS K3VU K3VV K3VW K3VY K3VZ K3Va K3Vb K3Vl K3Vm K3Vn K3Vo K3Vp K3Vq \ -K3Vr K3Vs K3Vt K3Vv K3Vw K3Vx K3Vy K3Vz K3V# K3V$ K3V& K3V( K3V> K3V^ K3V_ K3\ -V` K3V{ K3V| K3V} K3V~ K3W0 K3WA K3WB K3WD K3WE K3WG K3WH K3WI K3WV K3Wc K3Wf\ - K3Wi K3Wn K3Wt K3Wu K3Wv K3Ww K3Wx K3Wy K3Wz K3W- K3W= K3W? K3W[ K3W] K3W^ K\ -3W_ K3W` K3W{ K3W| K3W} K3W~ K3X2 K3X7 K3XA K3XB K3XC K3XE K3XF K3XG K3XI K3X\ -J K3XK K3XL K3XM K3XN K3XP K3XQ K3XV K3XX K3Xh K3Xo K3X% K3X& K3X( K3X) K3X* \ -K3X+ K3X, K3X< K3X[ K3X_ K3X` K3X} K3X~ K3Y1 K3Y2 K3Y4 K3Y5 K3Y7 K3YI K3YJ K3\ -YK K3YM K3YN K3YO K3YR K3YS K3YU K3YV K3YW K3YX K3YY K3Yi K3Yj K3Yk K3Yl K3Ym\ - K3Yn K3Yo K3Yp K3Yq K3Yr K3Ys K3Yu K3Yv K3Yw K3Yx K3Yy K3Yz K3Y$ K3Y| K3Z8 K\ -3Z9 K3ZB K3ZC K3ZE K3ZF K3ZM K3ZU K3ZZ K3Za K3Zc K3Zd K3Ze K3Zf K3Zj K3Zq K3Z\ -r K3Zt K3Zu K3Zv K3Zw K3Zy K3Z' K3Z+ K3Z, K3Z- K3Z/ K3Z: K3Z< K3Z= K3Z? K3Z@ \ -K3Z[ K3Z] K3Z_ K3Z` K3Z{ K3a1 K3a5 K3aD K3aF K3aG K3aI K3aJ K3aL K3aM K3aP K3\ -aQ K3aZ K3am K3aq K3ar K3as K3at K3au K3av K3aw K3ax K3ay K3az K3a# K3a$ K3a%\ - K3a& K3a( K3a) K3a- K3a/ K3a` K3a{ K3a| K3b0 K3b1 K3b2 K3b3 K3b4 K3bE K3bG K\ -3bH K3bI K3bL K3bM K3bO K3bP K3bR K3bS K3bU K3bV K3bh K3bi K3bl K3bn K3bu K3b\ -x K3by K3bz K3b# K3b$ K3b% K3b& K3b' K3b( K3b@ K3c0 K3c4 K3c5 K3c6 K3c7 K3c8 \ -K3c9 K3cA K3cB K3cC K3cN K3cO K3cQ K3cR K3cS K3cT K3cc K3cd K3ce K3cg K3ci K3\ -cj K3ck K3cl K3co K3cv K3cw K3c* K3c+ K3c, K3c- K3c. K3c/ K3c; K3c< K3c= K3c>\ - K3c? K3c@ K3c[ K3c^ K3c~ K3dJ K3dL K3dM K3dN K3dO K3dP K3dQ K3dR K3dS K3dT K\ -3dU K3dV K3dW K3dX K3dY K3dZ K3da K3db K3dc K3dv K3dx K3dz K3d# K3d$ K3d% K3d\ -: K3d; K3d= K3d> K3d? K3d@ K3d[ K3e6 K3eD K3eF K3eI K3eJ K3eU K3ec K3ed K3ee \ -K3ef K3eg K3eh K3ei K3ej K3ek K3el K3em K3ep K3er K3et K3eu K3ev K3ew K3ex K3\ -ey K3ez K3e# K3e$ K3e% K3e( K3e* K3e+ K3e- K3e= K3e{ K3f0 K3fb K3fc K3fd K3fe\ - K3ff K3fg K3fh K3fj K3fk K3fl K3fn K3fp K3fr K3fs K3ft K3fv K3fw K3fx K3f# K\ -3f$ K3f- K3f@ K3f^ K3f_ K3f` K3f~ K3g0 K3g1 K3g2 K3g3 K3g4 K3g5 K3g6 K3g7 K3g\ -8 K3gI K3gL K3gR K3gS K3gW K3gZ K3gs K3gt K3gu K3gv K3gw K3gx K3gy K3gz K3g# \ -K3g- K3g. K3g/ K3g: K3g; K3g= K3g> K3g? K3h5 K3h8 K3h9 K3hB K3hD K3hF K3hG K3\ -hH K3hI K3hL K3hM K3hO K3hP K3hY K3hZ K3hb K3hc K3hd K3hg K3hh K3hi K3hj K3hk\ - K3hl K3hm K3hn K3ho K3hp K3hq K3hr K3ht K3hu K3hv K3hw K3hx K3hy K3i7 K3i8 K\ -3iA K3iB K3iC K3iD K3iE K3iF K3iK K3iO K3iZ K3ia K3ib K3ic K3id K3ih K3ii K3i\ -j K3il K3im K3io K3ip K3iq K3is K3it K3iu K3iv K3iw K3ix K3iy K3i> K3i? 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K4C= K4C] K4C_ K4C` K4C{ K4D5\ - K4D6 K4DJ K4DL K4DN K4DQ K4DT K4Da K4De K4Dh K4Dk K4Dl K4Dm K4Dn K4Do K4Dp K\ -4Dq K4Dr K4Ds K4Dt K4Du K4Dx K4Dz K4D# K4D$ K4D- K4D^ K4D` K4E0 K4E1 K4E2 K4E\ -3 K4E4 K4E5 K4E6 K4E7 K4E8 K4EB K4ED K4EG K4EH K4EJ K4ET K4Ef K4Eh K4Ek K4En \ -K4Eo K4Ep K4Eq K4Er K4Ew K4E& K4E( K4E+ K4E, K4E- K4E. K4E/ K4E: K4E; K4E< K4\ -E= K4E> K4E? K4E@ K4E] K4E^ K4E` K4E{ K4E} K4E~ K4F0 K4F1 K4F2 K4F3 K4F4 K4F6\ - K4F7 K4FQ K4FR K4FS K4FT K4FU K4FV K4FW K4FX K4FY K4Fc K4Fk K4Fs K4Fu K4Fw K\ -4Fy K4Fz K4F& K4F( K4F| K4F} K4F~ K4G2 K4G3 K4G5 K4G6 K4G8 K4G9 K4GA K4GC K4G\ -G K4GH K4GI K4GK K4GL K4GN K4GO K4GR K4GW K4Gf K4Gl K4Gy K4G% K4G( K4G+ K4G- \ -K4G. K4G: K4G; K4G= K4G> K4G? 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K4L[ K4L] K4L^ K4L_ K4L` K4L{ K4L| K4L} K4L~ K4M0 K4MA K4MB K4\ -MC K4MD K4ME K4MF K4MG K4MH K4MI K4MJ K4MK K4MO K4MP K4MR K4MT K4MU K4MV K4MW\ - K4MY K4Ma K4Md K4Me K4Mg K4Mh K4Mn K4M] K4M_ K4M| K4N7 K4N9 K4NA K4NB K4NF K\ -4NG K4NH K4NS K4NU K4NW K4NX K4NY K4NZ K4Nl K4Ns K4Nt K4Nu K4Nv K4Nx K4Ny K4N\ -z K4N# K4N~ K4O0 K4O4 K4O5 K4O7 K4OH K4OI K4OJ K4OK K4OL K4OM K4ON K4OO K4OP \ -K4OQ K4OS K4OT K4OZ K4Ob K4Oc K4Od K4Of K4Og K4Oh K4Os K4Ot K4Ou K4Ow K4Oy K4\ -Oz K4O# K4O% K4O( K4O) K4O* K4O} K4O~ K4P2 K4P3 K4P4 K4P6 K4PD K4PG K4PH K4PI\ - K4PJ K4PK K4PL K4PM K4PN K4PO K4Pq K4Pr K4Ps K4Pt K4Pu K4Pv K4Pw K4Px K4Py K\ -4Pz K4P$ K4P% K4P& K4P' K4P/ K4Q6 K4Q7 K4Q8 K4Q9 K4QA K4QD K4QO K4QP K4QQ K4Q\ -R K4QS K4QT K4QU K4QW K4Qy K4Qz K4Q$ K4Q' K4Q* K4Q+ K4Q. K4Q/ K4Q: K4Q< K4R8 \ -K4RE K4RF K4RG K4RJ K4RK K4RL K4RM K4RO K4RP K4RQ K4RS K4RT K4RU K4RX K4RY K4\ -RZ K4Rb K4Rc K4Rm K4Ry K4Rz K4R$ K4R% K4R' K4R( K4R* K4R+ K4R/ K4R> K4SC K4SD\ - K4SG K4SH K4SJ K4SK K4SM K4SN K4SO K4SP K4SQ K4SR K4SS K4ST K4SU K4SV K4SW K\ -4SX K4SY K4SZ K4Sc K4Sd K4Si K4S$ K4S& K4S) K4S, K4S. K4S: K4S@ K4S` K4S{ K4S\ -| K4S} K4T0 K4T2 K4T9 K4TA K4TL K4TM K4TP K4TQ K4TR K4TT K4TX K4Tg K4Ti K4Tj \ -K4Tk K4Tq K4T# K4T' K4T( K4T+ K4T, K4T- K4T. K4T/ K4T; K4T< K4T^ K4T_ K4T` K4\ -T{ K4T| K4T} K4T~ K4U0 K4U1 K4UB K4UC K4UD K4UE K4UF K4UG K4UH K4UI K4UJ K4UK\ - K4UN K4UP K4UQ K4UR K4US K4UU K4UV K4UW K4UX K4UZ K4Ub K4Uc K4Ud K4Uf K4Ug K\ -4Uj K4Uk K4Ur K4U# K4U+ K4U; K4U] K4U_ K4U{ K4U~ K4V5 K4V6 K4VA K4VB K4VC K4V\ -D K4VE K4VF K4VS K4VU K4VW K4VY K4VZ K4Vc K4Vj K4Vl K4Vt K4Vu K4Vw K4Vx K4Vz \ -K4V# K4V, K4V[ K4V_ K4W1 K4W2 K4W5 K4W7 K4WI K4WJ K4WK K4WL K4WM K4WN K4WO K4\ -WP K4WQ K4WV K4WW K4WZ K4Wa K4Wb K4We K4Wf K4Wg K4Wi K4Ws K4Ww K4Wx K4Wz K4W$\ - K4W% K4W& K4W' K4W( K4W+ K4W, K4W. K4W? K4W| K4X0 K4X1 K4X2 K4X4 K4X5 K4X6 K\ -4X8 K4XB K4XH K4XI K4XJ K4XK K4XL K4XM K4XN K4XO K4XP K4Xe K4Xh K4Xl K4Xq K4X\ -r K4Xs K4Xt K4Xu K4Xv K4Xw K4Xx K4Xy K4Xz K4X# K4X$ K4X% K4X) K4X+ K4X= K4Y6 \ -K4Y8 K4YB K4YC K4YF K4YH K4YQ K4YR K4YS K4YU K4YV K4YW K4Yf K4Yg K4Yv K4Y$ K4\ -Y% K4Y( K4Y* K4Y, K4Y- K4Y. K4Y/ K4Y: K4Y; K4Y< K4Y= K4Y> K4Z1 K4Z4 K4ZI K4ZJ\ - K4ZK K4ZL K4ZM K4ZN K4ZO K4ZP K4ZQ K4ZR K4ZS K4ZT K4ZV K4ZW K4ZX K4Za K4Zb K\ -4Zd K4Ze K4Zf K4Zl K4Zt K4Zv K4Zz K4Z# K4Z% K4Z& K4Z( K4Z) K4Z* K4Z, K4Z. K4Z\ -[ K4Z^ K4aA K4aC K4aG K4aH K4aK K4aM K4aN K4aO K4aP K4aQ K4aR K4aS K4aT K4aU \ -K4aV K4aW K4aX K4aa K4ab K4ac K4ae K4ak K4am K4az K4a& K4a* K4a, K4a. K4a/ K4\ -a: K4a; K4a[ K4a^ K4a| K4a~ K4b0 K4b2 K4b8 K4b9 K4bM K4bN K4bO K4bP K4bR K4bS\ - K4bT K4bV K4bY K4be K4bg K4bh K4bi K4bs K4bv K4b& K4b( K4b) K4b* K4b+ K4b- K\ -4b. K4b/ K4b? 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K4g/ K4g: K4g\ -= K4g> K4g_ K4h0 K4h6 K4hA K4hD K4hG K4hH K4hI K4hJ K4hK K4hL K4hM K4hP K4hQ \ -K4hT K4hU K4hV K4hX K4hY K4hZ K4hd K4he K4hg K4hs K4hu K4h# K4h$ K4h& K4h' K4\ -h) K4h* K4h: K4h< K4h= K4i4 K4iA K4iG K4iK K4iM K4iN K4iO K4iP K4iQ K4iR K4iS\ - K4iT K4iU K4iV K4iW K4iY K4iZ K4ia K4ib K4ic K4id K4ie K4io K4iy K4iz K4i# K\ -4i$ K4i% K4i& K4i' K4i( K4i) K4i* K4i, K4i- K4i< K4i{ K4i| K4i} K4i~ K4j1 K4j\ -3 K4j4 K4jW K4jX K4jY K4jZ K4ja K4jd K4je K4jj K4jk K4jq K4jt K4ju K4jv K4j# \ -K4j) K4j* K4j+ K4j, K4j- K4j. K4j/ K4j: K4j; K4j_ K4j` K4j| K4j} K4j~ K4k2 K4\ -k3 K4k4 K4k5 K4k7 K4k8 K4kA K4kT K4kV K4kW K4kY K4kZ K4ka K4kb K4kd K4k* K4k-\ - K4k. K4k/ K4k< K4k@ K4k] K4k^ K4l0 K4lD K4lE K4lF K4lG K4lH K4lI K4lK K4ld K\ -4le K4lf K4lh K4li K4lj K4ll K4lx K4ly K4l$ K4l& K4l^ K4l` K4l{ K4l| K4m0 K4m\ -1 K4m2 K4m3 K4m7 K4m9 K4mB K4mC K4mD K4mE K4mF K4mG K4mH K4mI K4mJ K4mS K4mT \ -K4md K4me K4mf K4mh K4mi K4ms K4mu K4mw K4mx K4mz K4m# K4m% K4m/ K4m: K4m; K4\ -m< K4m= K4m> K4m? 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M{@ M{[ M{] M{^ M\ -{_ M{` M{{ M{| M{} M|2 M|3 M|6 M|8 M|9 M|A M|c M|e M|g M|/ M|: M|; M|> M|@ M|\ -[ M|] M|^ M|_ M|` M|| M|} M|~ M}0 M}1 M}2 M}3 M}9 M}A M}B M}L M}M M}O M}P M}Q\ - M}R M}h M}j M}k M}l M}o M}p M}q M}s M}} M}~ M~0 M~1 M~2 M~3 M~4 M~5 M~A M~F \ -M~G M~I M~J M~K M~M M~U M~W M~X M~Y M~Z M~a M~c M~i M~k M~m M~n M~o M~p M~q M\ -~r M~s M~t M~u M~y M~z M~# M~% M~& M~' M~( M~) M~+ M~, M10I M10J M10K M10M M1\ -0N M10O M10i M10k M10m M10n M10o M10p M10q M10r M10s M10u M10v M10w M10x M10y\ - M10z M10# M10$ M10% M10) M10* M10+ M10, M10- M10. M10= M10> M10[ M10] M10^ M\ -10_ M10{ M10~ M110 M113 M117 M118 M119 M11A M11B M11C M11F M11H M11I M11K M11\ -M M11N M11O M11Q M11Y M11f M11j M11u M11v M11z M11# M11$ M11( M11) M11* M11| \ -M11} M120 M121 M122 M12C M12D M12F M12G M12H M12J M12K M12L M12N M12U M12V M1\ -2W M12X M12Y M12Z M12a M12c M12e M12f M12{ M12| M130 M13F M13G M13H M13I M13J\ - M13K M13N M13O M13P M13Q M13R M13S M13U M13V M13Z M13a M13b M13c M13d M13e M\ -13h M13i M13k M13l M13m M13n M13o M13p M13q M13t M13u M13w M13x M13y M13( M13\ -) M13* M13+ M13: M13; M13= M13> M13? M13@ M13[ M13^ M13_ M13{ M149 M14B M14J \ -M14N M14Y M14Z M14a M14b M14c M14d M14e M14f M14q M14r M14s M14w M14x M14y M1\ -4& M14' M14; M14< M14= M14> M14[ M14] M14^ M14| M14} M14~ M153 M154 M157 M158\ - M159 M15A M15B M15: M15; M15< M15> M15? M15@ M15[ M15] M15^ M15_ M15` M15{ M\ -160 M161 M16T M16U M16V M16X M16c M16d M16j M16o M16q M16r M16s M16t M16] M16\ -^ M16_ M16` M16{ M16| M171 M172 M175 M176 M177 M178 M179 M17B M17C M17D M17E \ -M17I M17< M17= M17] M17^ M17` M17{ M17} M17~ M182 M184 M187 M18k M18m M18n M1\ -8o M18p M18q M18r M18u M18v M18x M18y M18z M18# M195 M196 M19H M19J M19K M19L\ - M19M M19v M19x M19y M19z M19# M19& M19' M19( M19* M19, M19- M19. M19= M19> M\ -1Am M1Ap M1Ar M1As M1Au M1Av M1Ay M1A# M1A& M1A' M1A* M1BF M1BG M1BH M1BI M1B\ -J M1BK M1BM M1BN M1BO M1BP M1BR M1BS M1BT M1BU M1B- M1B= M1B> M1B? M1B^ M1B` \ -M1CQ M1CR M1CS M1CT M1CU M1CV M1CW M1CX M1CY M1CZ M1Cc M1Cd M1Ck M1Df M1Dg M1\ -Dl M1D; M1D< M1D= M1D? M1D@ M1D[ M1D] M1D^ M1D_ M1D` M1D{ M1D} M1E1 M1E2 M1EA\ - M1EB M1EC M1EI M1EJ M1EL M1EM M1EN M1EO M1EP M1EQ M1EU M1EV M1EW M1EZ M1Ed M\ -1Ef M1Eq M1Er M1Es M1Et M1Eu M1Ew M1Ex M1Ey M1Ez M1E# M1E$ M1E% M1E& M1E* M1E\ -+ M1E, M1E. M1E/ M1E: M1E; M1E< M1E@ M1E[ M1E] M1E^ M1E_ M1E` M1F1 M1F3 M1F5 \ -M1F7 M1F8 M1F9 M1FA M1FC M1FD M1FP M1FT M1FU M1FX M1FY M1Fa M1Fb M1Fi M1GT M1\ -GU M1GW M1GX M1GZ M1Ga M1Gl M1Gm M1Gn M1Go M1Gp M1Gq M1Gr M1Gs M1Gt M1Gw M1Gy\ - M1Gz M1G# M1G$ M1G( M1G* M1G[ M1G] M1G^ M1G| M1G} M1G~ M1HF M1HH M1HJ M1HK M\ -1HL M1HM M1HN M1HR M1HS M1HT M1HU M1HV M1HY M1HZ M1Ha M1Hb M1Hc M1He M1Hf M1H\ -g M1Hp M1Hq M1Hr M1Hs M1Ht M1Hu M1Hy M1Hz M1H# M1H% M1H' M1H( M1H) M1H+ M1H, \ -M1H. M1H/ M1H> M1H? M1H@ M1H[ M1H^ M1H_ M1H~ M1I1 M1I3 M1I5 M1I6 M1I7 M1I8 M1\ -I9 M1IA M1IB M1IC M1ID M1IG M1IH M1IM M1IO M1IS M1Ia M1Ih M1I@ M1I_ M1I{ M1JG\ - M1JH M1JI M1JJ M1JK M1JL M1JN M1JO M1JP M1JQ M1JS M1JT M1JU M1JW M1JZ M1Jf M\ -1Jh M1Jj M1Jt M1Ju M1Jv M1Jw M1Jx M1Jy M1J% M1J& M1J' M1J> M1J? M1J@ M1J` M1J\ -{ M1J| M1J} M1J~ M1K1 M1K2 M1K3 M1K4 M1K5 M1K7 M1K8 M1KC M1KD M1KE M1KI M1KJ \ -M1KK M1KR M1KS M1KT M1KU M1KV M1KW M1KX M1KY M1KZ M1Kc M1Ke M1Kf M1Kg M1Kl M1\ -Km M1Kn M1Ko M1Kp M1Kq M1Kt M1Kw M1Kz M1K# M1K$ M1K% M1K& M1K' M1K( M1K* M1K+\ - M1K, M1K; M1K< M1K? M1K^ M1L4 M1L5 M1LA M1LC M1Lf M1Lg M1Li M1L- M1L. M1L< M\ -1L= M1L> M1L@ M1L[ M1L] M1L^ M1L_ M1L` M1L{ M1L| M1M0 M1M2 M1M3 M1M8 M1M9 M1M\ -A M1MB M1MM M1MN M1MO M1MP M1MQ M1MR M1Mq M1Mr M1Mt M1Mu M1Mv M1Mw M1My M1Mz \ -M1M% M1M& M1M' M1M) M1M, M1M/ M1M: M1M; M1M_ M1M` M1M{ M1M| M1M} M1M~ M1N3 M1\ -N6 M1N7 M1N9 M1NA M1NB M1ND M1NE M1NF M1NG M1NH M1NJ M1NN M1NO M1NP M1NS M1NT\ - M1NU M1NV M1NW M1NY M1NZ M1Nb M1Nc M1Nd M1Ng M1Nh M1Ni M1Nj M1Nk M1Nl M1N( M\ -1OK M1OM M1OO M1OP M1OR M1Om M1On M1Oo M1Op M1Oq M1Or M1Os M1Ot M1Ov M1Ox M1O\ -z M1O# M1O$ M1O% M1O* M1O+ M1O< M1O= M1O? M1O] M1O^ M1O_ M1O} M1O~ M1P0 M1P2 \ -M1P4 M1P7 M1P8 M1P9 M1PC M1PH M1PI M1PJ M1PK M1PM M1PN M1PO M1PS M1PT M1PU M1\ -PV M1PW M1PX M1PY M1Pa M1Pb M1Pc M1Pd M1Pf M1Pg M1Pj M1Pn M1Po M1Pp M1Pq M1Pr\ - M1Ps M1Pt M1Pu M1Pv M1Pz M1P# M1P$ M1P& M1P' M1P( M1P) M1P* M1P- M1P? M1P@ M\ -1P] M1P^ M1Q2 M1Q4 M1Q5 M1Q6 M1Q7 M1Q8 M1Q9 M1QA M1QB M1QC M1QD M1QE M1QF M1Q\ -c M1Qh M1R0 M1R1 M1R2 M1R3 M1R5 M1R7 M1RH M1RI M1RJ M1RK M1RL M1RM M1RO M1RP \ -M1RQ M1RR M1RT M1RU M1RV M1RX M1RY M1RZ M1Rb M1Rj M1Rk M1Rl M1Ru M1Rv M1Rw M1\ -Rx M1Ry M1Rz M1R# M1R& M1R' M1R( M1R+ M1R. M1R: M1R; M1R> M1R? M1R@ M1R[ M1R^\ - M1R` M1R{ M1R} M1R~ M1S0 M1S1 M1S3 M1S4 M1S5 M1S6 M1S8 M1S9 M1SA M1SD M1SE M\ -1SF M1SG M1SH M1SI M1SJ M1SK M1SL M1SQ M1SR M1SS M1ST M1SU M1SY M1SZ M1Sa M1S\ -b M1Sd M1Se M1Sg M1Si M1Sl M1Sm M1Sn M1So M1Sp M1Sr M1Ss M1Su M1Sw M1Sy M1S# \ -M1S$ M1S% M1S& M1S' M1S( M1S) M1S+ M1S, M1S- M1S? M1S_ M1T4 M1TE M1T- M1T. M1\ -T/ M1UV M1U& M1U/ M1VB M1VE M1Vv M1V: M1V| M1W7 M1W9 M1Wd M1We M1Wf M1Wo M1Wz\ - M1W. M1W] M1W| M1X. M1Yn M1Yv M1Y% M1ZK M1ZY M1Z~ M1aA M1ab M1a@ M1b9 M1bo M\ -1b. M1b/ M1b: M1co M1c' M1c; M1eb M1ec M1ee M1ef M1eg M1fS M1gA M1gG M1gM M1g\ -V M1ge M1g{ M1g| M1h{ M1i) M1i[ M1j6 M1j8 M1jF M1jn M1j/ M1j: M1j; M1k$ M1lr \ -M1lx M1l+ M1l; M1mP M1mU M1mV M1mg M1n5 M1nF M1nL M1nS M1nX M1nc M1ng M1nm M1\ -np M1oA M1oS M1p6 M1p7 M1p+ M1p{ M1q1 M1qB M1qE M1q) M1rE M2Ya M2Yb M2Yc M2Ye\ - M2Yf M2Yi M2Y- M2Y. M2Y/ M2Y> M2Y? M2Z8 M2Z9 M2ZA M2ZB M2ZC M2ZI M2ZK M2ZL M\ -2ZM M2ZN M2ZO M2ZP M2ZQ M2ZR M2ZT M2ZX M2ZZ M2Za M2Zb M2Zf M2Zj M2Zk M2Zo M2Z\ -q M2Zu M2Z& M2Z' M2Z( M2Z- M2Z. M2Z/ M2Z; M2Z^ M2Z{ M2a4 M2a5 M2a6 M2aL M2aO \ -M2aQ M2aR M2aT M2aX M2aZ M2aa M2ab M2ac M2ae M2af M2ah M2ai M2aj M2am M2an M2\ -ap M2au M2av M2az M2a# M2a& M2a' M2a( M2a* M2a+ M2a, M2a- M2a. M2a: M2a= M2a^\ - M2a` M2a{ M2b2 M2b7 M2bB M2bC M2bD M2bE M2bG M2bJ M2bN M2bS M2bW M2bY M2bb M\ -2bi M2bk M2bl M2bm M2bn M2bo M2b# M2b$ M2b% M2b+ M2b, M2b/ M2b: M2b; M2b< M2b\ -= M2b> M2b? M2b@ M2b[ M2b] M2c6 M2cB M2cC M2cD M2cH M2cI M2cK M2cN M2cS M2cW \ -M2cX M2cY M2cc M2ce M2cf M2ch M2ct M2cw M2c# M2c$ M2c% M2c> M2c~ M2d1 M2d2 M2\ -d4 M2d5 M2d7 M2d9 M2dA M2dB M2dG M2dH M2dK M2dM M2dN M2dV M2dW M2dY M2db M2dd\ - M2de M2dg M2dq M2dr M2d% M2d( M2d) M2d+ M2d, M2d- M2d: M2d= M2d? M2d] M2e5 M\ -2eA M2eD M2eE M2eF M2eG M2eH M2eJ M2eV M2eW M2ee M2eg M2eh M2ei M2ej M2el M2e\ -m M2en M2eo M2es M2et M2eu M2e) M2e* M2e+ M2e, M2e; M2e< M2e} M2f0 M2f1 M2f8 \ -M2f9 M2fA M2fH M2fJ M2fL M2fM M2fT M2fU M2fV M2fX M2fm M2fx M2fz M2f' M2f( M2\ -f) M2f+ M2f, M2f: M2f; M2f} M2g0 M2g2 M2g3 M2g5 M2g6 M2g7 M2g9 M2gE M2gG M2gI\ - M2gJ M2gL M2gb M2gc M2gd M2gg M2gi M2gl M2gp M2gr M2g( M2g* M2g. M2g/ M2g: M\ -2g< M2g> M2g@ M2h3 M2h7 M2h8 M2h9 M2hA M2hB M2hD M2hE M2hG M2hK M2hL M2hM M2h\ -N M2hO M2hP M2hQ M2hS M2hT M2hV M2hZ M2ha M2hb M2hc M2he M2hh M2hj M2hk M2hq \ -M2hw M2hx M2hz M2h' M2h( M2h) M2h- M2h. M2h; M2h? M2h` M2h| M2i5 M2i6 M2i7 M2\ -iQ M2iS M2iZ M2ib M2id M2ie M2ig M2ih M2io M2iu M2iw M2i$ M2i% M2i& M2i( M2i)\ - M2i* M2i/ M2i` M2i| M2j8 M2jA M2jD M2jE M2jF M2jY M2ja M2jk M2jm M2jn M2jo M\ -2jp M2j+ M2j- M2j; M2j< M2j= M2j> M2j? M2j@ M2j[ M2j] M2j^ M2k1 M2k8 M2kC M2k\ -D M2kE M2kI M2kK M2kO M2kV M2kX M2kY M2kZ M2kh M2ki M2km M2kn M2ks M2kt M2k$ \ -M2k% M2k& M2k) M2k> M2k` M2l1 M2l3 M2l4 M2l6 M2l7 M2l8 M2l9 M2lC M2lD M2lG M2\ -lI M2lJ M2lK M2lL M2lM M2lO M2lP M2lR M2lV M2lX M2lY M2la M2lc M2ld M2lf M2lg\ - M2ll M2lm M2ln M2ls M2lt M2lv M2l, M2l- M2l. M2mD M2mF M2mG M2mH M2mI M2mV M\ -2mW M2mh M2mi M2mj M2mk M2ml M2mn M2mo M2mp M2mt M2mu M2mv M2m' M2m( M2m+ M2m\ -, M2m- M2m/ M2m: M2m; M2m< M2m> M2m@ M2n0 M2n9 M2nA M2nB M2nJ M2nK M2nL M2nQ \ -M2nU M2nV M2nW M2nm M2ny M2nz M2n$ M2n' M2n) M2n* M2n+ M2n. M2n: M2n< M2n= M2\ -n> M2n? M2n[ M2n| M2n~ M2o0 M2o2 M2o4 M2o5 M2o7 M2o8 M2o9 M2oC M2oE M2oF M2oG\ - M2oH M2oI M2oK M2oL M2oN M2oR M2oc M2od M2oe M2og M2oj M2ok M2on M2oo M2ot M\ -2o* M2o+ M2o/ M2o: M2o; M2o> M2o? M2o@ M2p5 M2p7 M2p8 M2pA M2pB M2pC M2pD M2p\ -F M2pI M2pM M2pN M2pO M2pP M2pQ M2pR M2pb M2pc M2pd M2pg M2ph M2pq M2pw M2p( \ -M2p) M2p* M2p; M2p| M2p~ M2q1 M2q6 M2q7 M2q8 M2qJ M2qL M2qO M2qR M2qS M2qY M2\ -qa M2qb M2qd M2qf M2qg M2qi M2qj M2qk M2ql M2qn M2qq M2qr M2qv M2qw M2qy M2q$\ - M2q& M2q' M2q( M2q+ M2q, M2q- M2q. M2q/ M2q; M2q< M2q_ M2q{ M2q| M2r3 M2rA M\ -2rB M2rE M2rF M2rG M2rl M2rm M2ro M2rp M2rq M2r' M2r( M2r, M2r- M2r< M2r= M2r\ -> M2r? M2r@ M2r[ M2r] M2r^ M2r_ M2r| M2s3 M2s5 M2s6 M2sD M2sE M2sF M2sK M2sL \ -M2sM M2sN M2sQ M2sR M2sT M2sX M2sY M2sZ M2sa M2sh M2si M2sn M2sp M2sv M2sx M2\ -s% M2s& M2s' M2t3 M2t5 M2t6 M2t8 M2tA M2tB M2tC M2tE M2tK M2tO M2tQ M2tX M2tZ\ - M2ta M2tc M2te M2tf M2th M2ti M2tm M2tn M2to M2ts M2tu M2t) M2t- M2t. M2t/ M\ -2t; M2t< M2uC M2uD M2uE M2uF M2uH M2uI M2uJ M2uS M2ui M2uj M2uk M2um M2un M2u\ -o M2up M2uq M2us M2uu M2uv M2uw M2u# M2u$ M2u& M2u, M2u- M2u. M2u; M2u< M2u> \ -M2u@ M2u[ M2u~ M2v1 M2vA M2vB M2vC M2vE M2vG M2vI M2vJ M2vK M2vM M2vP M2vT M2\ -vV M2vW M2vX M2v# M2v$ M2v( M2v) M2v, M2v- M2v. M2v: M2v; M2v< M2v> M2v? M2v@\ - M2w1 M2w2 M2w3 M2w4 M2w6 M2w7 M2wA M2wB M2wJ M2wM M2wN M2wT M2wg M2wh M2wj M\ -2wk M2w: M2w= M2w> M2w? M2w@ M2xB M2xC M2xF M2xH M2xI M2xJ M2xK M2xL M2xM M2x\ -V M2xW M2xZ M2xd M2xe M2xf M2xg M2xh M2xi M2xj M2xk M2xo M2xp M2xw M2x% M2x[ \ -M2x_ M2x| M2yB M2yK M2yM M2yN M2yO M2yP M2yQ M2yR M2yS M2yT M2yU M2yW M2yX M2\ -yZ M2yb M2yl M2yw M2yy M2y' M2y: M2y| M2y} M2z9 M2zB M2zC M2zE M2zQ M2zd M2ze\ - M2zf M2zg M2zh M2zi M2zj M2zk M2zl M2zn M2zo M2zx M2z$ M2z% M2z& M2z* M2z+ M\ -2z, M2z- M2z/ M2z: M2z; M2z< M2z? M2z` M2z{ M2z| M2z} M2#8 M2#9 M2#A M2#B M2#\ -C M2#D M2#E M2#F M2#H M2#T M2#W M2#X M2#y M2#z M2#' M2#- M2#? M2#@ M2#[ M2#] \ -M2#^ M2#_ M2#` M2$2 M2$4 M2$5 M2$6 M2$A M2$C M2$I M2$Y M2$Z M2$t M2$v M2$, M2\ -$- M2$< M2$= M2$] M2%3 M2%6 M2%7 M2%8 M2%9 M2%A M2%B M2%F M2%G M2%I M2%J M2%L\ - M2%M M2%N M2%W M2%a M2%b M2%c M2%d M2%e M2%f M2%g M2%h M2%i M2%l M2%n M2%o M\ -2%s M2%t M2%u M2%* M2%+ M2%, M2%- M2%/ M2%: M2%; M2%< M2&1 M2&D M2&G M2&R M2&\ -U M2&d M2&f M2&o M2&p M2&q M2&s M2&u M2&v M2&w M2&x M2&# M2&$ M2&% M2&( M2&. \ -M2'1 M2'2 M2'F M2'h M2'j M2'k M2'm M2'p M2'( M2') M2'* M2'. M2'/ M2': M2'< M2\ -'= M2'> M2'? M2'@ M2'] M2'^ M2(3 M2(4 M2(5 M2(6 M2(7 M2(8 M2(E M2(F M2(H M2(I\ - M2(J M2(K M2(L M2(M M2(N M2(P M2(T M2(V M2(X M2(a M2(d M2(e M2(g M2(h M2(i M\ -2(j M2(k M2(l M2(m M2(p M2(r M2(u M2(# M2(% M2() M2(; M2(> M2([ M2(_ M2(| M2(\ -} M2)1 M2)2 M2)F M2)G M2)I M2)J M2)M M2)N M2)O M2)P M2)Q M2)R M2)S M2)T M2)U \ -M2)V M2)X M2)Z M2)a M2)c M2)e M2)g M2)' M2), M2*B M2*C M2*e M2*f M2*g M2*h M2\ -*i M2*j M2*k M2*l M2*m M2*o M2*r M2*x M2*/ M2*; M2*< M2*= M2*] M2*` M2*| M2*}\ - M2*~ M2+9 M2+A M2+B M2+C M2+D M2+E M2+F M2+H M2+T M2+W M2+X M2+c M2+l M2+s M\ -2+z M2+% M2++ M2+? M2+@ M2+[ M2+] M2+^ M2+_ M2+` M2+| M2,1 M2,4 M2,5 M2,6 M2,\ -7 M2,A M2,C M2,I M2,K M2,R M2,U M2,X M2,h M2,i M2,n M2,v M2,x M2,, M2,- M2-6 \ -M2-I M2-L M2-M M2-N M2-O M2-b M2-c M2-d M2-e M2-f M2-g M2-h M2-i M2-j M2-k M2\ --l M2-o M2-t M2-u M2-v M2-+ M2-, M2-- M2-/ M2-: M2-; M2-< M2-= M2-@ M2-_ M2-}\ - M2-~ M2.1 M2.2 M2.B M2.P M2.U M2.Z M2.k M2.p M2.q M2.r M2.v M2.w M2.x M2.# M\ -2.$ M2.% M2.& M2.( M2.) M2.. M2.] M2.^ M2/1 M2/2 M2/5 M2/A M2/D M2/F M2/N M2/\ -Q M2/U M2/j M2/k M2/m M2/n M2/p M2/) M2/* M2/+ M2// M2/: M2/; M2/< M2/? M2/@ \ -M2/[ M2/] M2/^ M2:4 M2:5 M2:6 M2:7 M2:8 M2:9 M2:F M2:H M2:I M2:J M2:K M2:L M2\ -:M M2:N M2:O M2:Q M2:T M2:e M2:g M2:h M2:i M2:j M2:k M2:l M2:m M2:y M2:% M2:)\ - M2:` M2:} M2;5 M2;8 M2;E M2;O M2;P M2;Q M2;R M2;S M2;T M2;U M2;V M2;W M2;Z M\ -2;a M2;e M2;f M2;h M2;o M2;u M2;v M2;z M2;% M2;' M2;- M2;= M2;^ M2;} M2<0 M2<\ -C M2 M21 M2>2 M2>5 M2>6 M2>7 M2>8 M2>B M2>D M2>F M\ -2>T M2>Y M2>h M2>j M2>n M2>p M2>- M2>? M2?8 M2?9 M2?A M2?B M2?C M2?D M2?I M2?\ -J M2?M M2?N M2?O M2?P M2?i M2?j M2?k M2?q M2?t M2?u M2?v M2?w M2?z M2?% M2?' \ -M2?) M2?, M2?- M2?. M2?/ M2?: M2?< M2?= M2?> M2?@ M2?] M2?~ M2@2 M2@5 M2@B M2\ -@D M2@O M2@P M2@U M2@X M2@Z M2@p M2@q M2@r M2@s M2@t M2@w M2@x M2@y M2@z M2@%\ - M2@& M2@' M2@. M2@? M2@{ M2[6 M2[9 M2[A M2[D M2[O M2[Q M2[R M2[g M2[h M2[i M\ -2[j M2[k M2[l M2[m M2[n M2[o M2[> M2[? M2[_ M2[` M2]E M2]G M2]H M2]J M2]O M2]\ -h M2]r M2]s M2]t M2]x M2]y M2]z M2]$ M2]% M2]& M2]( M2]/ M2]; M2]< M2]] M2]^ \ -M2]_ M2]` M2]{ M2]| M2]} M2^0 M2^1 M2^2 M2^8 M2^9 M2^E M2^F M2^M M2^N M2^O M2\ -^R M2^T M2^X M2^Z M2^a M2^b M2^d M2^h M2^i M2^j M2^r M2^s M2^y M2^% M2^& M2^'\ - M2^. M2^/ M2^: M2^[ M2^] M2^{ M2^| M2^} M2^~ M2_8 M2_C M2_D M2_E M2_F M2_G M\ -2_H M2_I M2_J M2_K M2_L M2_b M2_e M2_q M2_r M2_t M2_* M2_: M2_; M2_[ M2_] M2_\ -~ M2`K M2`L M2`M M2`U M2`X M2`Y M2`Z M2`a M2`b M2`f M2`g M2`o M2`p M2`q M2`v \ -M2`w M2`x M2`z M2`# M2`$ M2`% M2`' M2`( M2`- M2`> M2`? M2`@ M2`| M2`} M2`~ M2\ -{0 M2{2 M2{5 M2{6 M2{A M2{B M2{C M2{J M2{K M2{Y M2{e M2{f M2{g M2{v M2{$ M2{+\ - M2{. M2{/ M2{: M2{; M2{< M2{= M2{> M2{? M2{@ M2{] M2{_ M2{| M2|F M2|H M2|J M\ -2|K M2|L M2|N M2|n M2|q M2|r M2|v M2|{ M2|| M2|} M2|~ M2}0 M2}2 M2}3 M2}4 M2}\ -5 M2}7 M2}9 M2}A M2}H M2}I M2}J M2}S M2}T M2}U M2}V M2}W M2}X M2}b M2}g M2}h \ -M2}l M2}n M2}o M2}r M2}u M2}v M2}w M2}$ M2}) M2}+ M2}< M2}= M2}> M2}} M2~1 M2\ -~3 M2~7 M2~8 M2~9 M2~E M2~H M2~I M2~S M2~T M2~h M2~i M2~j M2~k M2~l M2~m M2~n\ - M2~o M2~p M2~s M2~y M2~, M2~: M2~? M2~@ M2~^ M2~` M2~{ M307 M30C M30F M30H M\ -30I M30K M30M M30T M30U M30b M30i M30l M30o M30r M30s M30t M30u M30y M30z M30\ -# M30% M30& M30' M30) M30, M30: M30< M30^ M30_ M30` M30{ M30| M30} M30~ M311 \ -M312 M313 M319 M31A M31F M31G M31N M31O M31P M31R M31a M31b M31c M31e M31f M3\ -1i M31j M31k M31* M31/ M31: M31; M327 M32D M32E M32F M32G M32H M32I M32J M32K\ - M32L M32m M32r M32u M32; M32< M32? M32] M32^ M32{ M33L M33M M33N M33U M33V M\ -33Y M33Z M33a M33b M33c M33g M33h M33k M33p M33q M33r M33w M33x M33$ M33% M33\ -& M33( M33) M33+ M33@ M33[ M33_ M33~ M340 M341 M343 M346 M347 M349 M34B M34C \ -M34D M34K M34L M34X M34Y M34a M34e M34f M34g M34h M34k M34q M34s M34u M34v M3\ -4w M34y M34$ M34% M34- M34/ M34: M34; M34< M34= M34> M34? M34@ M34[ M35K M35L\ - M35M M35O M35Q M35f M35o M35r M35v M35` M35| M35} M35~ M360 M361 M363 M364 M\ -365 M36A M36B M36G M36I M36J M36K M36S M36T M36U M36V M36W M36X M36Y M36d M36\ -h M36i M36m M36o M36t M36v M36w M36x M36z M36% M36' M36* M36, M36. M36: M36= \ -M36> M36? M36@ M36` M36{ M36~ M370 M371 M374 M378 M379 M37A M37F M37I M37J M3\ -7S M37T M37X M37Y M37i M37j M37k M37l M37m M37n M37o M37p M37q M37z M37. M37:\ - M37; M37@ M37[ M37] M37{ M37| M389 M38E M38G M38I M38J M38L M38O M38t M38u M\ -38v M38z M38# M38$ M38& M38' M38( M38* M38. M38; M38= M38_ M38` M38{ M38| M38\ -} M38~ M390 M392 M393 M394 M39A M39B M39D M39G M39H M39O M39P M39Q M39S M39T \ -M39V M39Z M39b M39c M39d M39f M39g M39j M39k M39l M39q M39u M39( M39) M39+ M3\ -9: M39; M39< M39? M39] M39^ M39} M39~ M3A1 M3AE M3AF M3AG M3AH M3AI M3AJ M3AK\ - M3AL M3AM M3Ab M3Ap M3As M3At M3Au M3Av M3A; M3A< M3A^ M3A_ M3A{ M3A} M3BB M\ -3BK M3BM M3BN M3BO M3BR M3BV M3BW M3BZ M3Ba M3Bb M3Bc M3Bd M3Bh M3Bi M3Bl M3B\ -p M3Bq M3Br M3Bs M3Bt M3Bx M3By M3B$ M3B% M3B& M3B' M3B) M3B* M3B/ M3B: M3B< \ -M3B= M3B[ M3B] M3B` M3B{ M3B~ M3C0 M3C1 M3C2 M3C3 M3C4 M3C7 M3C8 M3CC M3CD M3\ -CE M3CX M3CY M3CZ M3Ca M3Cf M3Cg M3Ch M3Ci M3Cl M3Cp M3Cr M3C% M3C: M3C; M3C<\ - M3C= M3C> M3C? M3C@ M3C[ M3C] M3DF M3DL M3DN M3DP M3Dn M3Do M3Dp M3Ds M3Dt M\ -3Dv M3D$ M3D: M3D< M3D^ M3D} M3D~ M3E0 M3E1 M3E2 M3E4 M3E5 M3E6 M3E9 M3EB M3E\ -C M3EF M3EJ M3EK M3EL M3EQ M3ET M3EU M3EV M3EW M3EX M3EY M3EZ M3Ei M3Ej M3El \ -M3Em M3En M3Ep M3Et M3Ew M3Ex M3Ey M3E# M3E$ M3E% M3E& M3E+ M3E- M3E; M3E> M3\ -E? M3E@ M3E| M3E~ M3F9 M3FA M3FB M3FX M3FY M3FZ M3Fj M3Fk M3Fl M3Fn M3Fo M3Fs\ - M3Fw M3Fx M3Fy M3F# M3F: M3F; M3F< M3F= M3F? M3F@ M3F[ M3F^ M3F_ M3F} M3G8 M\ -3GA M3GF M3GW M3GX M3GY M3Gc M3Gd M3Gh M3Gk M3Gm M3Gq M3Gr M3Gt M3G( M3G) M3G\ -* M3G+ M3G? M3G@ M3G[ M3G] M3G_ M3G| M3H0 M3H8 M3H9 M3HD M3HE M3HG M3HH M3HJ \ -M3HW M3He M3Hf M3Hj M3Hl M3Hm M3Hn M3Hp M3Hx M3H# M3H, M3H= M3H? M3H] M3H^ M3\ -H_ M3H` M3H{ M3H} M3I1 M3I2 M3I4 M3I5 M3IF M3IG M3IL M3IM M3IN M3IP M3IQ M3IS\ - M3IT M3Ig M3Ih M3Ii M3Ik M3Il M3Ir M3Iu M3Iv M3Ix M3I/ M3I< M3I~ M3J0 M3J1 M\ -3J5 M3J6 M3JX M3JZ M3Ja M3Jb M3Jq M3Ju M3Jv M3Jw M3J- M3J. M3J/ M3J: M3J= M3J\ -] M3J_ M3KE M3KG M3KH M3KN M3Kc M3Kp M3Kq M3Kr M3Ks M3Kv M3Kw M3Kx M3K# M3K& \ -M3K> M3K? M3K@ M3K[ M3K^ M3K_ M3K` M3K} M3L1 M3L2 M3LC M3LD M3LI M3LJ M3LK M3\ -LN M3LP M3LQ M3LT M3Lf M3Li M3Lv M3Lw M3Lx M3Lz M3L- M3L. M3L] M3L} M3M2 M3M3\ - M3M4 M3MF M3MN M3MO M3MP M3MQ M3MR M3Mc M3Me M3Mf M3Mh M3Mk M3Mp M3Mq M3Mr M\ -3Mt M3M( M3M: M3M; M3M_ M3N4 M3N8 M3N9 M3NG M3NJ M3NK M3NL M3NN M3NO M3NP M3N\ -S M3NU M3NV M3NY M3Na M3Nk M3Nl M3Nm M3Nn M3No M3Nu M3Ny M3N$ M3N% M3N& M3N; \ -M3N< M3N= M3N? M3N@ M3N[ M3N} M3O5 M3OA M3OE M3OX M3OY M3OZ M3Od M3Of M3Ok M3\ -Om M3Or M3Ot M3Ou M3Ow M3Oy M3O% M3O( M3O* M3O+ M3O, M3O< M3O> M3O@ M3O[ M3O]\ - M3O_ M3O| M3P0 M3P8 M3P9 M3PD M3PF M3PG M3PH M3PJ M3PK M3PM M3Pl M3Po M3Pw M\ -3P# M3P% M3P' M3P[ M3P] M3P_ M3P` M3P{ M3P| M3Q1 M3Q4 M3Q5 M3QB M3QC M3QG M3Q\ -I M3QM M3QN M3QO M3QR M3QT M3QW M3Qh M3Qi M3Qj M3Qk M3Ql M3Qo M3Qr M3Qu M3Qx \ -M3Qy M3Q/ M3Q= M3R0 M3R1 M3R2 M3R3 M3R6 M3R8 M3RE M3RM M3Ra M3Rb M3Rc M3Ro M3\ -Rp M3Rq M3Rt M3Rv M3Rw M3Rx M3R+ M3R- M3R/ M3R: M3R< M3R= M3R> M3R[ M3R_ M3R`\ - M3S1 M3S5 M3S8 M3SC M3SE M3SG M3SI M3SJ M3ST M3Sc M3Se M3Sf M3Si M3Sp M3Sr M\ -3Ss M3St M3Sv M3Sw M3Sx M3Sz M3S# M3S% M3S' M3S( M3S? M3S@ M3S[ M3S^ M3S_ M3S\ -` M3S| M3T0 M3T2 M3T3 M3TD M3TF M3TJ M3TK M3TL M3TN M3TP M3TQ M3TS M3Ti M3Tj \ -M3Tp M3Tu M3Tw M3Tx M3Ty M3T, M3T. M3T: M3U3 M3U4 M3U5 M3UE M3UJ M3UO M3UP M3\ -UQ M3UR M3UV M3Ud M3Ue M3Uh M3Ui M3Ul M3Uq M3Ut M3Uu M3Ux M3U( M3U: M3U< M3U>\ - M3U] M3U_ M3U{ M3V7 M3VB M3VF M3VH M3VK M3VL M3VM M3VO M3VR M3VS M3VU M3VY M\ -3Va M3Vb M3Vl M3Vm M3Vn M3Vo M3Vq M3Vz M3V$ M3V& M3V( M3V- M3V< M3V= M3V> M3V\ -? M3V@ M3V_ M3V{ M3W0 M3W5 M3WA M3WY M3WZ M3Wa M3Wf M3Wg M3W) M3W+ M3W, M3W- \ -M3W[ M3W] M3W^ M3W_ M3W} M3X9 M3XB M3XE M3XF M3XH M3XJ M3XK M3XM M3XN M3XQ M3\ -XR M3XV M3XX M3Xb M3Xe M3Xh M3Xi M3Xl M3Xm M3Xq M3X# M3X% M3X& M3X/ M3X> M3X[\ - M3X] M3X^ M3X_ M3X{ M3X| M3X} M3Y4 M3Y5 M3Y7 M3YI M3YJ M3YM M3YN M3YO M3YP M\ -3YR M3YS M3YT M3YV M3YY M3Yi M3Yj M3Yk M3Yl M3Yn M3Ys M3Yw M3Yy M3Y/ M3Y< M3Y\ -= M3Y[ M3Y^ M3Z1 M3Z2 M3Z3 M3Z8 M3Z9 M3ZE M3ZM M3ZU M3ZW M3Za M3Zb M3Zc M3Zd \ -M3Ze M3Zo M3Zq M3Zs M3Zv M3Zw M3Zx M3Zy M3Z# M3Z* M3Z, M3Z. M3Z/ M3Z< M3Z= M3\ -Z@ M3Z` M3a8 M3aB M3aG M3aI M3aK M3aZ M3ae M3af M3ag M3as M3at M3au M3aw M3az\ - M3a# M3a& M3a) M3a/ M3a@ M3a[ M3a] M3a^ M3a_ M3a| M3a} M3b0 M3b4 M3bF M3bG M\ -3bK M3bL M3bM M3bO M3bP M3bQ M3bS M3bV M3bj M3bx M3by M3bz M3b) M3b- M3b: M3b\ -; M3b= M3b` M3c0 M3c4 M3c5 M3c6 M3cC M3cI M3cL M3cN M3cO M3cP M3cQ M3cR M3cT \ -M3cU M3cZ M3cd M3cf M3cg M3ch M3ci M3cm M3cq M3ct M3cu M3c; M3c< M3c[ M3c] M3\ -d1 M3d2 M3d7 M3d8 M3dL M3dM M3dN M3dQ M3dT M3dZ M3da M3db M3ds M3dt M3du M3dw\ - M3d: M3d{ M3d} M3d~ M3eE M3eG M3eH M3eU M3eZ M3ea M3ec M3ed M3ee M3ef M3eg M\ -3ek M3em M3ep M3es M3eu M3ev M3ew M3ez M3e* M3e+ M3e- M3e. M3e< M3e= M3e> M3e\ -@ M3e_ M3e| M3fI M3fK M3fP M3fQ M3fY M3fa M3fb M3fc M3ff M3fg M3fl M3fm M3ft \ -M3fu M3f) M3f* M3f: M3f; M3f< M3f= M3f@ M3f] M3f_ M3f{ M3f} M3f~ M3g0 M3g1 M3\ -g2 M3g7 M3g8 M3gI M3gL M3gM M3gN M3gU M3gX M3gZ M3gp M3gs M3gu M3gv M3g( M3g.\ - M3g; M3h2 M3h4 M3h9 M3hA M3hD M3hE M3hF M3hG M3hI M3hW M3hX M3hY M3hZ M3ha M\ -3hc M3he M3hi M3hj M3hk M3hn M3hr M3hy M3h. M3h] M3h_ M3i1 M3i7 M3iH M3iJ M3i\ -M M3iO M3iT M3iU M3iV M3ia M3ir M3iu M3iv M3iw M3i& M3i( M3i) M3i* M3i> M3i? \ -M3i@ M3i_ M3i~ M3j1 M3jJ M3jP M3jQ M3jU M3jW M3jm M3jn M3j' M3j- M3j. M3j/ M3\ -j: M3j< M3j~ M3k0 M3k1 M3k5 M3k6 M3k9 M3kB M3kD M3kK M3kL M3kM M3kT M3kU M3kp\ - M3kq M3k/ M3k; M3k? M3k@ M3l0 M3l6 M3lN M3lS M3lT M3lV M3lY M3lZ M3la M3lc M\ -3lq M3lt M3lu M3lv M3lx M3l& M3l- M3l: M3l; M3l@ M3l{ M3l~ M3m5 M3m8 M3mD M3m\ -H M3mK M3mW M3ma M3mb M3md M3me M3mf M3mh M3mi M3mk M3ml M3mn M3mq M3mr M3mt \ -M3mv M3mw M3mx M3m# M3m+ M3m, M3m- M3m/ M3m= M3m> M3m? M3m` M3m{ M3m| M3m~ M3\ -n9 M3nB M3nI M3nQ M3nR M3nl M3nm M3nu M3nv M3n$ M3n, M3n_ M3n| M3o1 M3o2 M3o3\ - M3o8 M3o9 M3oM M3oN M3oO M3oa M3op M3ou M3ov M3o) M3o* M3o: M3p1 M3p9 M3pB M\ -3pC M3pE M3pF M3pG M3pH M3pJ M3pO M3pS M3pV M3pX M3pY M3pZ M3pa M3pb M3pd M3p\ -e M3pj M3pk M3pl M3p= M3p^ M3p` M3p{ M3q4 M3q6 M3q9 M3qG M3qI M3qK M3qO M3qP \ -M3qY M3qa M3qb M3qc M3qj M3qk M3qp M3qs M3qt M3qv M3qw M3qx M3qy M3q' M3q) M3\ -q* M3q+ M3q? M3q@ M3q[ M3r3 M3rX M3ri M3rj M3rn M3ro M3rs M3rt M3rv M3rx M3ry\ - M3r# M3r$ M3r+ M3r, M3r. M3r/ M3r: M3r; M3r< M3s0 M3s1 M3s2 M3s7 M3s8 M3sA M\ -3sB M3sC M3sE M3sG M3sL M3sM M3sN M3sU M3sW M3sq M3sr M3sz M3s% M3s) M3s. M3s\ -/ M3s: M3s< M3s= M3s@ M3s] M3t0 M3t1 M3t6 M3t7 M3tB M3tD M3tF M3tL M3tO M3tS \ -M3tT M3tU M3tW M3tY M3tZ M3ta M3tb M3te M3tr M3tu M3tv M3tw M3t% M3t) M3t: M3\ -t= M3t@ M3t~ M3u6 M3u9 M3uI M3uL M3uY M3ue M3uf M3ug M3uh M3uj M3ul M3uw M3ux\ - M3uy M3u, M3u- M3u. M3u/ M3u> M3u? M3u@ M3vQ M3vR M3vS M3vW M3vY M3va M3vd M\ -3ve M3vh M3vi M3vm M3vo M3vr M3vv M3vw M3v, M3v. M3v< M3v> M3v] M3v_ M3v} M3w\ -0 M3w1 M3w2 M3w3 M3w4 M3w9 M3wA M3wN M3wO M3wP M3wS M3wT M3wZ M3wu M3wv M3wx \ -M3w$ M3w+ M3w: M3w; M3w< M3w@ M3w] M3w_ M3w{ M3w~ M3x0 M3x4 M3x6 M3x8 M3xA M3\ -xB M3xF M3xG M3xH M3xI M3xK M3xM M3xR M3xT M3xW M3xY M3xZ M3xa M3xb M3xc M3xf\ - M3xg M3xk M3xl M3xm M3xn M3xp M3xr M3xt M3x# M3x. 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M3,@ M3,{ M3-5 M3-6 M3-\ -A M3-J M3-M M3-Y M3-Z M3-a M3-g M3-k M3-m M3-n M3-o M3-q M3-t M3-% M3-& M3-* \ -M3-+ M3-, M3-: M3-= M3-@ M3-{ M3-} M3.3 M3.4 M3.9 M3.A M3.D M3.E M3.F M3.G M3\ -.J M3.M M3.O M3.P M3.Q M3.R M3.T M3.U M3.W M3.l M3.m M3.n M3.o M3.r M3.s M3.t\ - M3.u M3.v M3.w M3.z M3.% M3.; M3/B M3/a M3/d M3/p M3/u M3/& M3/, M3/; M3/< M\ -3/> M3:4 M3:F M3:G M3:H M3:N M3:g M3:j M3:k M3:l M3:y M3:z M3:% M3:& M3:< M3:\ -> M3:@ M3:[ M3:] M3:_ M3:` M3:} M3;0 M3;1 M3;4 M3;6 M3;9 M3;A M3;E M3;F M3;G \ -M3;H M3;K M3;L M3;M M3;N M3;O M3;P M3;U M3;V M3;W M3;e M3;i M3;j M3;k M3;u M3\ -;- M3;] M3;| M3<0 M3<5 M3<6 M3<7 M3<9 M30 \ -M3>1 M3>5 M3>6 M3>B M3>C M3>D M3>G M3>H M3>W M3>a M3>e M3>h M3>s M3>z M3>$ M3\ ->* M3>. M3>? M3>[ M3>| M3?3 M3?7 M3?C M3?H M3?L M3?O M3?b M3?n M3?o M3?p M3?(\ - M3?+ M3?, M3?- M3?| M3?} M3@8 M3@F M3@G M3@H M3@I M3@P M3@Q M3@R M3@S M3@V M\ -3@W M3@d M3@h M3@m M3@n M3@o M3@q M3@r M3@s M3@t M3@u M3@v M3@w M3@x M3@% M3@\ -( M3@) M3@* M3@+ M3@, M3@} M3[3 M3[A M3[D M3[O M3[U M3[r M3[w M3[- M3[. M3[> \ -M3[@ M3[_ M3[| M3[~ M3]2 M3]4 M3]6 M3]B M3]C M3]E M3]G M3]H M3]I M3]M M3]T M3\ -]W M3]Y M3]e M3]h M3]k M3]l M3]m M3]t M3]x M3]$ M3]% M3]' M3]) M3]; M3]= M3]@\ - M3][ M3]] M3]^ M3]` M3]{ M3]| M3^1 M3^2 M3^B M3^F M3^G M3^H M3^J M3^L M3^M M\ -3^N M3^O M3^P M3^Q M3^U M3^W M3^X M3^Y M3^h M3^x M3^# M3^[ M3_S M3_n M3_p M3_\ -s M3_* M3_- M3_. M3_/ M3_: M3_; M3_^ M3_~ M3`2 M3`4 M3`7 M3`8 M3`A M3`D M3`E \ -M3`F M3`H M3`K M3`O M3`S M3`T M3`X M3`a M3`d M3`h M3`i M3`j M3`m M3`n M3`o M3\ -`p M3`r M3`s M3`t M3`x M3`y M3`z M3`$ M3`) M3`- M3`. M3`/ M3`: M3`[ M3`] M3`^\ - M3`| M3`} M3`~ M3{4 M3{8 M3{C M3{D M3{E M3{F M3{c M3{e M3{v M3{w M3{x M3{$ M\ -3{% M3{@ M3{{ M3{} M3|U M3|W M3|X M3|a M3|c M3|e M3|i M3|j M3|k M3|n M3|o M3|\ -q M3|u M3|$ M3|* M3|_ M3|} M3|~ M3}0 M3}5 M3}8 M3}9 M3}A M3}B M3}D M3}E M3}I \ -M3}M M3}N M3}O M3}Q M3}S M3}U M3}b M3}c M3}n M3}p M3}r M3}t M3}y M3}& M3}' M3\ -}( M3}* M3}+ M3}, M3}- M3}. M3}: M3}? M3}@ M3}` M3}} M3~C M3~E M3~O M3~P M3~Q\ - M3~S M3~c M3~d M3~t M3~u M3~_ M3~} M400 M401 M40H M40J M40K M40L M40M M40S M\ -40V M40Z M40a M40x M40& M40' M40( M40) M40* M40, M40. M40? M40@ M40[ M40{ M40\ -| M41H M41I M41L M41X M41a M41j M41k M41l M41m M41u M41v M41& M41* M41{ M420 \ -M421 M422 M427 M42J M42L M42P M42p M42x M42% M42- M42. M42: M42< M42= M42> M4\ -2? M42[ M433 M437 M43L M43W M43X M43Y M43d M43e M43i M43j M43l M43m M43n M43#\ - M43$ M43. M43/ M446 M448 M44D M44E M44F M44H M44N M44O M44R M44V M44Z M44a M\ -44j M44w M44x M44y M44z M44- M44/ M44@ M44` M44~ M45A M45D M45G M45K M45V M45\ -X M45c M45d M45f M45j M45k M45l M45n M45o M45p M45q M45v M45% M45* M45, M45@ \ -M45~ M460 M461 M466 M469 M46A M46C M46D M46E M46F M46L M46N M46O M46P M46T M4\ -6V M46# M46$ M46+ M46, M46- M46. M46/ M46; M46? M46@ M46~ M470 M473 M47A M47P\ - M47Q M47R M47X M47d M47e M47g M47s M47u M47v M47# M47% M47' M47) M47* M481 M\ -484 M487 M488 M48G M48H M48I M48J M48L M48M M48N M48S M48Z M48a M48c M48s M48\ -' M48( M48) M48+ M48, M48- M48/ M48@ M48[ M48] M48| M48} M493 M496 M499 M49C \ -M49G M49I M49J M49K M49M M49N M49S M49Y M49a M49b M49c M49g M49h M49l M49m M4\ -9n M49p M49u M49v M49& M49' M49) M49- M49. M4A1 M4A2 M4A3 M4A9 M4AK M4AL M4AN\ - M4AR M4Ao M4Au M4Ax M4A; M4A< M4A> M4A? M4A@ M4A] M4A^ M4A_ M4A} M4BQ M4BW M\ -4BX M4BY M4BZ M4Ba M4Be M4Bf M4Bk M4Bl M4Bm M4Bn M4Bo M4Bw M4B$ M4B% M4B, M4B\ -. M4B/ M4B; M4B> M4B? 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M4I@ M4I[ M4I^ M4I~ M4J0 \ -M4J2 M4J5 M4J9 M4JR M4JX M4JY M4JZ M4Ja M4Jf M4Jg M4Jk M4Jm M4Jn M4Jo M4Jp M4\ -Ju M4Jv M4J% M4J& M4J~ M4K4 M4K8 M4KA M4KE M4KF M4KG M4KH M4KI M4KJ M4KO M4KQ\ - M4KZ M4K' M4K_ M4K{ M4K} M4K~ M4L0 M4LK M4LW M4LY M4LZ M4Ld M4Le M4Lo M4Lp M\ -4Lq M4Ls M4L& M4L* M4L> M4L@ M4L] M4L^ M4L_ M4L~ M4M0 M4M4 M4MA M4MB M4MC M4M\ -K M4MT M4MU M4MX M4MZ M4Ma M4Me M4Mk M4Mn M4Mo M4Mp M4M_ M4M` M4M{ M4M| M4M} \ -M4M~ M4N4 M4N6 M4N9 M4NA M4NB M4Ne M4Nu M4Nv M4Nx M4Nz M4N{ M4N} M4O2 M4OB M4\ -OD M4OH M4OI M4OJ M4OZ M4Oa M4Of M4Os M4Ou M4Ov M4Ox M4Oy M4Oz M4O: M4O< M4O=\ - M4O> M4P0 M4P2 M4P3 M4P4 M4P6 M4PF M4PG M4PH M4PI M4Pd M4Pk M4Pq M4Pr M4Ps M\ -4Pt M4Pu M4Pv M4Pz M4P& M4P' M4Q5 M4Q6 M4QA M4QN M4QP M4QU M4QW M4Qt M4Q, M4Q\ -- M4Q/ M4Q^ M4Q_ M4Q` M4R5 M4RB M4RE M4RJ M4RQ M4RR M4RS M4Re M4Ri M4Rj M4Rk \ -M4Rr M4Ry M4Rz M4R# M4R$ M4R' M4R] M4R^ M4R_ M4SE M4SM M4SN M4SO M4SS M4ST M4\ -SU M4SV M4Sf M4Sh M4Si M4Sj M4Sx M4S# M4S$ M4S* M4S- M4S/ M4S= M4S` M4S| M4T1\ - M4TD M4TI M4TM M4TN M4TO M4Td M4Tf M4Tl M4Tp M4Tq M4Tr M4Tx M4T% M4T( M4T) M\ -4T* M4T, M4T@ M4T[ M4T^ M4T_ M4T` M4T| M4U1 M4U3 M4U6 M4U8 M4UA M4UB M4UC M4U\ -D M4UG M4UM M4UO M4UU M4UV M4UW M4UX M4Ua M4Ub M4Uo M4Up M4Uq M4U> M4U` M4U{ \ -M4U| M4U} M4U~ M4V0 M4V2 M4V7 M4VX M4Va M4Vg M4Vu M4Vx M4V& M4V) M4V[ M4V| M4\ -W2 M4WD M4WI M4WJ M4WK M4Wb M4Wg M4Wh M4Wm M4Wn M4Wo M4Wq M4Wr M4Wu M4Wx M4Wy\ - M4Wz M4W# M4W= M4W> M4W? M4W~ M4X1 M4X3 M4X4 M4X5 M4X7 M4X8 M4XE M4XH M4XI M\ -4XJ M4Xd M4Xh M4Xi M4Xr M4Xs M4Xt M4Xu M4Xv M4Xw M4X$ M4X% M4X& M4X( M4X: M4X\ -< M4X= M4X> M4YN M4YP M4YW M4Ys M4Yt M4Y$ M4Y) M4Y- M4Y_ M4Y` M4Y{ M4Y} M4ZB \ -M4ZC M4ZD M4ZP M4ZR M4ZS M4ZT M4Zj M4Zk M4Zl M4Zn M4Zz M4Z# M4Z$ M4Z% M4Z( M4\ -Z* M4Z+ M4Z. M4Z: M4Z> M4Z@ M4Z^ M4Z_ M4Z` M4Z} M4a7 M4a8 M4aD M4aG M4aJ M4aN\ - M4aO M4aP M4aR M4aT M4aU M4aV M4aX M4aY M4ad M4ah M4ai M4aj M4ak M4ax M4a# M\ -4a; M4a> M4a_ M4a| M4a~ M4b3 M4bM M4bO M4bP M4bZ M4bm M4bp M4bq M4br M4bs M4b\ -* M4b< M4b_ M4b` M4b{ M4c0 M4cC M4cD M4cE M4cV M4cW M4cY M4cZ M4cb M4cc M4cf \ -M4cg M4co M4cp M4cq M4cr M4cu M4cv M4cz M4c% M4c+ M4c; M4c= M4c] M4c{ M4c| M4\ -c} M4c~ M4d0 M4d1 M4d5 M4d6 M4dA M4dB M4dC M4dD M4de M4dw M4dz M4d{ M4eE M4eF\ - M4eG M4eJ M4eK M4eL M4eO M4eX M4eb M4ed M4ee M4ej M4el M4en M4eo M4ep M4ew M\ -4ey M4ez M4e# M4e$ M4e& M4e' M4e( M4e* M4e. M4e> M4e? 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M4k] M4k^ M4k| M4k~ M4l6 M\ -4lD M4lY M4lZ M4la M4lb M4lc M4lf M4lh M4l% M4l^ M4l_ M4l{ M4l| M4l} M4m2 M4m\ -9 M4mB M4mC M4mD M4mI M4mJ M4mM M4mO M4mP M4mX M4me M4mi M4mj M4mk M4mu M4mw \ -M4m# M4m$ M4m/ M4m: M4m; M4m~ M4n4 M4n6 M4n7 M4nW M4nb M4nc M4nd M4nh M4nk M4\ -nl M4nw M4nz M4n' M4n; M4n= M4n? M4o0 M4o1 M4o3 M4o4 M4o5 M4oB M4oG M4oW M4os\ - M4ot M4ou M4oy M4o# M4o' M4o+ M4o= M4o> M4o? M4o@ M4o] M4p9 M4pB M4pC M4pD M\ -4pO M4pT M4pV M4pW M4pY M4po M4pp M4pq M4p& M4p( M4q7 M4qB M4qC M4qD M4qE M4q\ -F M4qG M4qK M4qL M4qa M4qk M4qz M4q# M4q$ M4q) M4q* M4q. M4q< M4q~ M4rF M4rH \ -M4rJ M4rN M4rR M4rS M4rU M4rV M4rW M4rZ M4rf M4rj M4rk M4rl M4rv M4rx M4r# M4\ -r( M4r* M4r+ M4r, M4r; M4r> M4r{ M4r| M4r~ M4s0 M4s4 M4s7 M4sF M4sH M4sI M4sJ\ - M4sQ M4sU M4sd M4s) M4s+ M4s, M4s- M4s. M4s: M4s; M4s= M4s? 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NDH NO_ \ -NO` NO} NP3 NP4 NP7 NPC NPD NP/ NP: NP; NP^ NP{ NQ1 NQ2 NQ3 NQ4 NQ5 NQ6 NQA N\ -QJ NQK NQL NQQ NQR NQV NQW NQX NRs NRv NRw NRz NR$ NR+ NR> NSm NSo NSp NSq NS\ -v NS# NS$ NS% NS& NS' NS( NS) NS* NS+ NS] NS^ NS` NS{ NS| NS} NS~ NT0 NTH NTI\ - NTM NTN NTO NTR NTS NTT NTU NWD NWE NWF NWG NWH NWI NWM NWN NWP NWQ NWf NWh \ -NWm NWn NWs NWu NXM NXQ NXS NXT NXU NXV NXc NXf NXg NXh NXi NXk NX: NX; NX< N\ -X= NX? NY2 NY3 NY4 NY5 NY6 NY7 NYK NYL NYM NYQ NYR NYW NYX NYY NYZ NYa NY/ NY\ -: NY; NY< NY= NY> NY? 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Y2mK Y2mY Y2mt Y2nb Y2n% Y2oA Y2oL Y2xo Y2x@ Y2x[ Y\ -2zZ Y2z[ Y2z| Y2#o Y2#( Y2%T Y2%q Y2%r Y2%] Y2&C Y2(l Y2(p Y2(r Y2() Y2([ Y2)\ -4 Y2): Y2*H Y2*Z Y2*a Y2*g Y2*^ Y2+9 Y2+q Y2,D Y2,T Y2-T Y2-U Y2-f Y2-r Y2-t \ -Y2-@ Y2-] Y2-^ Y2/V Y2:s Y2:) Y2:^ Y2;4 Y2W Y2>o Y2?U Y2?f Y2?t Y2?^ Y2@F Y2@W Y2[V Y3GR Y3GS Y3Gr Y3G; Y3Hf Y3H@\ - Y3JR Y3Jp Y3KT Y3MS Y3OS Y3OY Y3PU Y3P+ Y3Ql Y3RT Y3Rn Y3ST Y3Sv Y3T$ Y3T% Y\ -3T< Y3T= Y3US Y3UT Y3Uw Y3WU Y3XH Y3XU Y3Xx Y3X| Y3Y/ Y3ZR Y3ZT Y3ZU Y3Ze Y3Z\ -< Y3bS Y3bj Y3bm Y3cL Y3cT Y3cy Y3eX Y3fN Y3fT Y3fa Y3fn Y3fo Y3iP Y3iQ Y3lR \ -Y3mY Y3my Y3na Y3nb Y3o1 Y3qQ Y3qr Y3qv Y3r$ Y3r= Y3sQ Y3sr Y3tQ Y3u# Y3vb Y3\ -v% Y3w; Y3x$ Y3x% Y3yS Y3yr Y3zn Y3zp Y3#R Y3#( Y3$R Y3$T Y3$W Y3&C Y3'3 Y3)C\ - Y3,E Y3,/ Y3,: Y3-k Y3.5 Y3.B Y3/5 Y3/o Y3/r Y3:E Y3:: Y3;, Y3;| Y3<0 Y3=n Y\ -3>1 Y3>/ Y3>; Y3?{ Y3[= Y3[@ Y3]A Y3]D Y3_p Y3_s Y3`I Y3`# Y3{F Z ZPj ZV+ ZWD\ - ZWE ZWF ZWG ZWH ZWI ZWJ ZWK ZWL ZY< ZY@ Zb0 Zbi Zbn Ze0 ZeE ZeF ZeG ZeH ZeI \ -ZeJ ZeK ZeL ZeM Zg: Zg] Zjx Z-W Z-Y Z Z3=? Z3>[ Z3[^ Z3]? Z3_% Z3_@ Z3_[ Z3`/ Z3`: a aSt aS$ aS- aZ3 ah3 \ -ahM a;. a?( a_a a12K a1G( a1O+ a2Yh a2Yi a2b^ a2b_ a2b` a2c2 a2c3 a2c4 a2cB a\ -2cC a2cD a2e/ a2gr a2gs a2j_ a2j` a2j{ a2k3 a2k4 a2k5 a2kC a2kD a2kE a2lc a2l\ -d a2le a2ll a2lm a2ln a2lu a2lv a2lw a2m/ a2na a2#z a2,z a2/n a2;S a2=, a3OI \ -a3Rg a3W1 a3X@ a3a+ a3i8 a3mm a3qk a3tY a3ug a3y2 a3&V a3(u a3(v a3(w a3(& a3\ -(' a3(( a3(/ a3(: a3(; a3)J a3)K a3)L a3)S a3)T a3)U a3)b a3)c a3)d a3-6 a3.g\ - a3:v a3:w a3:x a3:' a3:( a3:) a3:: a3:; a3:< a3;K a3;L a3;M a3;T a3;U a3;V a\ -3;c a3;d a3;e a3<3 a3?G a3@Q a3]w a3]x a3]y a3]( a3]) a3]* a3]; a3]< a3]= a3^\ -L a3^M a3^N a3^U a3^V a3^W a3^d a3^e a3^f a3`2 a3{9 b b2b^ b2b_ b2b` b2j_ b2j\ -` b2j{ b2lc b2ld b2le b2l& b2)~ b2,| b2;J b2>z b3(u b3(v b3(w b3)J b3)K b3)L \ -b3:v b3:w b3:x b3;K b3;L b3;M b3;; b3]w b3]x b3]y b3^L b3^M b3^N c cWD c2ZN c\ -2ZP c2cT c2hO c2hP c2iN c2iO c2kU c2lU c2&B c2._ c3%` c3%| c3&_ c3&` c3(B c3)\ -A c3-r c3-{ c3-| c3.` c3.{ c3:C c3;C c3?| c3?} c3@{ c3@} c3]E c3^C d d2ZN d2Z\ -O d2cT d2hO d2hQ d2iN d2iO d2kV d2lV d2>i d3%` d3%{ d3&_ d3&{ d3(B d3)B d3-{ \ -d3-} d3.` d3.{ d3:D d3;D d3?| d3?} d3@{ d3@| d3]F d3^C e eQj elh f fQi flv f2\ -xT f2xU f2xV f2xW f2xX f2xY f2xZ f2xa f2xb f2#s f2&x f2&y f2&z f2&# f2&$ f2&%\ - f2&& f2&' f2&( f2(U f2(V f2(W f2(X f2(Y f2(Z f2(a f2(b f2(c f2)^ f2.y f2.z f\ -2.# f2.$ f2.% f2.& f2.' f2.( f2.) f2:V f2:W f2:X f2:Y f2:Z f2:a f2:b f2:c f2:\ -d f2@z f2@# f2@$ f2@% f2@& f2@' f2@( f2@) f2@* g g2xc g2xd g2xe g2xg g2xh g2x\ -i g2xk g2#? g2#@ g2#[ g2#^ g2#_ g2#` g2#| g2(e g2+[ g2:e g2:i g2:m g2=[ g2=` \ -g2=~ g3G? g3G@ g3G[ g3G^ g3G_ g3G` g3G| g3Kw g3Kx g3Ky g3K# g3K$ g3K% g3K' g3\ -O[ g3Sy g3W[ g3W` g3W~ g3ay g3a% g3a) g4j< g4j= g4j> g4j@ g4j[ g4j] g4j_ g4nS\ - g4nT g4nU g4nW g4nX g4nY g4na g4r> g4vU g4z> g4z] g4z{ g4&U g4&Y g4&c h h1T=\ - h1T> h1T? h1T@ h1T[ h1T^ h1T_ h1T` h1b> h1b[ h1b] h1b^ h1b` h1b{ h1j@ h1j^ h\ -1j_ h1j` h1j| i i1T@ i1b: i1c2 i1j; i1k2 j j1T- k l m1 m3 m9 mA mC mF mR mS m\ -T mU n9 nA nC nF o3 o4 oC oD oF oG oR oS oT oa p9 pA pB q3 q4 qC qF qR qS qT \ -qU qV qW r3 rR rS rT s3 s4 s5 sC sU sV sW sd sm w3 w4 wA wB wC wD wE wV wY we\ - wf wh y1 y4 y5 yA yB yG $B $G %3 %C %D %F %T %U %V %W &B 'B 'G -1", -]; diff --git a/data/cc.tbl b/data/cc.tbl index c38a7c2..50911c8 100644 --- a/data/cc.tbl +++ b/data/cc.tbl @@ -1,31 +1,52 @@ ############################################################################# ## -#W cc.tbl CC-loops p^2, 2p, for p odd prime G. P. Nagy / P. Vojtechovsky +#W cc.tbl Library of CC loops G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: cc.tbl, v 3.0.0 2015/06/10 gap Exp $ +#H @(#)$Id: cc.tbl, v 3.4.0 2015/06/10 gap Exp $ ## #Y Copyright (C) 2005, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) ## +############################################################################# +## Binding global variables +## LOOPS_cc_used_factors +## LOOPS_cc_cocycles +## LOOPS_cc_bases +## LOOPS_cc_coordinates + # CC loops are activated as follows: -# If n = 2p or p^2, where p is a prime, then we call a method for -# cosntructing these loops. +# If n = 2p, where p is an odd prime, then we call an algebraic method for +# constructing these loops. +# If n = p^2, where p>3 is a prime, then we call an algebraic method for +# construction these loops. +# If n is a power of 2 or 3, then we use cocycles located in cc/cc_cocycles_n.tbl. # For all other orders, we point to the library of RCC loops. LOOPS_cc_data := [ #implemented orders -[ 8, 12, 16, 18, 20, 21, 24, 27], -#number of nonassociative loops of given order -[ 2, 3, 28, 7, 3, 1, 14, 55], -#the numbers of the loops in the RCC library +[ 2, 3, 4, 5, 7, 8, 9, 12, 16, 18, 20, 21, 24, 25, 27, 32, 49, 64, 81, 125, 343], +#number of loops of given order in the library +[ 1, 1, 2, 1, 1, 7, 5, 3, 42, 7, 3, 1, 14, 5, 60, 437, 5, 14854, 5406, 84, 122], [ -#order 8 -[2,7], +#order 2 (Z_2) +["010"], +#order 3 (Z_3) +["201"], +#order 4 (placeholder only) +, +# order 5 (Z_5) +["2340401123"], +# order 7 (Z_7) +["234560456016012123345"], +#order 8 (placeholder only) +, +#order 9 (placeholder only) +, #order 12 [53,73,89], -#order 16 -[9,35,107,228,243,292,437,440,1043,1883,1936,2332,2420,2636,2645,2750,2753,2794,2797,2847,3682,3730,3739,3848,3949,4735,4904,4925], +#order 16 (placeholder only) +, #order 18 [22,29,77,292,360,377,1133], #order 20 @@ -33,18 +54,12 @@ LOOPS_cc_data := [ #order 21 [104], #order 24 -[302,1025,2119,2182,2335,3066,4569,5176,5589,5997,7495,194830,225705,243216], -#order 27 -[78,86,317,319,361,571,711,1080,1085,1624,1665,2217,2219,3614,3624,8579,8582,15059,15072,15503,15512,19439,23177,23214,26331,26348,52978,55027,55055,59116,59123,75864,78970,79011,83042,83104,83155,104913,106081,106144,110854,110892,110930,114102,117212,119407,134858,136370,140791,148160,148892,149330,151792,152090,152515] +[302,1025,2119,2182,2335,3066,4569,5176,5589,5997,7495,194830,225705,243216] ] ]; -# The following can be used to point to CC loops of order 2p and p^2 in the library of RCC loops. -# order 6, [3] -# order 9, [5,4,3] -# order 10, [16] -# order 14, [97] -# order 22, [10346] -# order 25, [86,93,118] -# order 26, [151964] +LOOPS_cc_used_factors := []; +LOOPS_cc_cocycles := []; +LOOPS_cc_bases := []; +LOOPS_cc_coordinates := []; diff --git a/doc/chap0.txt b/doc/chap0.txt index 04b040b..604f2aa 100644 --- a/doc/chap0.txt +++ b/doc/chap0.txt @@ -6,7 +6,7 @@ Computing with quasigroups and loops in GAP - Version 3.3.0 + Version 3.4.0 Gábor P. Nagy @@ -28,7 +28,7 @@ ------------------------------------------------------- Copyright - © 2016 Gábor P. Nagy and Petr Vojtěchovský. + © 2017 Gábor P. Nagy and Petr Vojtěchovský. ------------------------------------------------------- @@ -167,10 +167,12 @@ 6.11-3 QuasigroupsUpToIsomorphism 6.11-4 LoopsUpToIsomorphism 6.11-5 AutomorphismGroup - 6.11-6 IsomorphicCopyByPerm - 6.11-7 IsomorphicCopyByNormalSubloop - 6.11-8 Discriminator - 6.11-9 AreEqualDiscriminators + 6.11-6 QuasigroupIsomorph + 6.11-7 LoopIsomorph + 6.11-8 IsomorphicCopyByPerm + 6.11-9 IsomorphicCopyByNormalSubloop + 6.11-10 Discriminator + 6.11-11 AreEqualDiscriminators 6.12 Isotopisms 6.12-1 IsotopismLoops 6.12-2 LoopsUpToIsotopism @@ -256,28 +258,31 @@ 9.2 Left Bol Loops and Right Bol Loops 9.2-1 LeftBolLoop 9.2-2 RightBolLoop - 9.3 Moufang Loops - 9.3-1 MoufangLoop - 9.4 Code Loops - 9.4-1 CodeLoop - 9.5 Steiner Loops - 9.5-1 SteinerLoop - 9.6 Conjugacy Closed Loops - 9.6-1 RCCLoop and RightConjugacyClosedLoop - 9.6-2 LCCLoop and LeftConjugacyClosedLoop - 9.6-3 CCLoop and ConjugacyClosedLoop - 9.7 Small Loops - 9.7-1 SmallLoop - 9.8 Paige Loops - 9.8-1 PaigeLoop - 9.9 Nilpotent Loops - 9.9-1 NilpotentLoop - 9.10 Automorphic Loops - 9.10-1 AutomorphicLoop - 9.11 Interesting Loops - 9.11-1 InterestingLoop - 9.12 Libraries of Loops Up To Isotopism - 9.12-1 ItpSmallLoop + 9.3 Left Bruck Loops and Right Bruck Loops + 9.3-1 LeftBruckLoop + 9.3-2 RightBruckLoop + 9.4 Moufang Loops + 9.4-1 MoufangLoop + 9.5 Code Loops + 9.5-1 CodeLoop + 9.6 Steiner Loops + 9.6-1 SteinerLoop + 9.7 Conjugacy Closed Loops + 9.7-1 RCCLoop and RightConjugacyClosedLoop + 9.7-2 LCCLoop and LeftConjugacyClosedLoop + 9.7-3 CCLoop and ConjugacyClosedLoop + 9.8 Small Loops + 9.8-1 SmallLoop + 9.9 Paige Loops + 9.9-1 PaigeLoop + 9.10 Nilpotent Loops + 9.10-1 NilpotentLoop + 9.11 Automorphic Loops + 9.11-1 AutomorphicLoop + 9.12 Interesting Loops + 9.12-1 InterestingLoop + 9.13 Libraries of Loops Up To Isotopism + 9.13-1 ItpSmallLoop A Files B Filters diff --git a/doc/chap0_mj.html b/doc/chap0_mj.html index c1e0f72..c329e99 100644 --- a/doc/chap0_mj.html +++ b/doc/chap0_mj.html @@ -31,7 +31,7 @@

Computing with quasigroups and loops in GAP

-

Version 3.3.0

+

Version 3.4.0

Gábor P. Nagy @@ -50,7 +50,7 @@

Copyright

-

© 2016 Gábor P. Nagy and Petr Vojtěchovský.

+

© 2017 Gábor P. Nagy and Petr Vojtěchovský.

@@ -331,10 +331,12 @@
  6.11-3 QuasigroupsUpToIsomorphism

  6.11-4 LoopsUpToIsomorphism

  6.11-5 AutomorphismGroup
-
  6.11-6 IsomorphicCopyByPerm
-
  6.11-7 IsomorphicCopyByNormalSubloop
-
  6.11-8 Discriminator
-
  6.11-9 AreEqualDiscriminators
+
  6.11-6 QuasigroupIsomorph
+
  6.11-7 LoopIsomorph
+
  6.11-8 IsomorphicCopyByPerm
+
  6.11-9 IsomorphicCopyByNormalSubloop
+
  6.11-10 Discriminator
+
  6.11-11 AreEqualDiscriminators
 6.12 Isotopisms @@ -474,60 +476,66 @@
  9.2-1 LeftBolLoop

  9.2-2 RightBolLoop
-
 9.3 Moufang Loops + -
 9.4 Code Loops + -
 9.5 Steiner Loops + -
 9.6 Conjugacy Closed Loops + + -
 9.7 Small Loops + -
 9.8 Paige Loops + -
 9.9 Nilpotent Loops + -
 9.10 Automorphic Loops + -
 9.11 Interesting Loops + -
A Files diff --git a/doc/chap1.txt b/doc/chap1.txt index 96b78b5..6d27195 100644 --- a/doc/chap1.txt +++ b/doc/chap1.txt @@ -20,7 +20,7 @@ 1.2 Installation - Have GAP 4.7 or newer installed on your computer. + Have GAP 4.8 or newer installed on your computer. If you do not see the subfolder pkg/loops in the main directory of GAP then download the LOOPS package from the distribution website @@ -85,14 +85,15 @@ We thank the following people for sending us remarks and comments, and for suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, - Andreas Distler, Aleš Drápal, Steve Flammia, Kenneth W. Johnson, Michael K. - Kinyon, Alexander Konovalov, Frank Lübeck and Jonathan D.H. Smith. + Andreas Distler, Aleš Drápal, Graham Ellis, Steve Flammia, Kenneth W. + Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Lübeck, Jonathan D.H. + Smith, David Stanovský and Glen Whitney. The library of Moufang loops of order 243 was generated from data provided by Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy closed loops of order less than 28 was generated from data provided by - Katharina Artic. The library of commutative automorphic loops of order 27, - 81 and 243 was obtained jointly with Izabella Stuhl. + Katharina Artic. The library of right Bruck loops of order 27, 81 was + obtained jointly with Izabella Stuhl. Gábor P. Nagy was supported by OTKA grants F042959 and T043758, and Petr Vojtěchovský was supported by the 2006 and 2016 University of Denver PROF diff --git a/doc/chap1_mj.html b/doc/chap1_mj.html index f7f1272..07113b6 100644 --- a/doc/chap1_mj.html +++ b/doc/chap1_mj.html @@ -73,7 +73,7 @@

1.2 Installation

-

Have GAP 4.7 or newer installed on your computer.

+

Have GAP 4.8 or newer installed on your computer.

If you do not see the subfolder pkg/loops in the main directory of GAP then download the LOOPS package from the distribution website http://www.math.du.edu/loops and unpack the downloaded file into the pkg subfolder.

@@ -127,9 +127,9 @@ gap> WriteGapIniFile();;

1.7 Acknowledgment

-

We thank the following people for sending us remarks and comments, and for suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, Andreas Distler, Aleš Drápal, Steve Flammia, Kenneth W. Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Lübeck and Jonathan D.H. Smith.

+

We thank the following people for sending us remarks and comments, and for suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, Andreas Distler, Aleš Drápal, Graham Ellis, Steve Flammia, Kenneth W. Johnson, Michael K. Kinyon, Alexander Konovalov, Frank Lübeck, Jonathan D.H. Smith, David Stanovský and Glen Whitney.

-

The library of Moufang loops of order 243 was generated from data provided by Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy closed loops of order less than 28 was generated from data provided by Katharina Artic. The library of commutative automorphic loops of order 27, 81 and 243 was obtained jointly with Izabella Stuhl.

+

The library of Moufang loops of order 243 was generated from data provided by Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy closed loops of order less than 28 was generated from data provided by Katharina Artic. The library of right Bruck loops of order 27, 81 was obtained jointly with Izabella Stuhl.

Gábor P. Nagy was supported by OTKA grants F042959 and T043758, and Petr Vojtěchovský was supported by the 2006 and 2016 University of Denver PROF grants and the Simons Foundation Collaboration Grant 210176.

diff --git a/doc/chap3.txt b/doc/chap3.txt index 0cea0a0..873329c 100644 --- a/doc/chap3.txt +++ b/doc/chap3.txt @@ -40,8 +40,8 @@ DeclareRepresentation( "IsLoopElmRep", IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] ); ## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup) - DeclareCategory( "IsLatin", IsObject ); - DeclareCategory( "IsQuasigroup", IsMagma and IsLatin ); + DeclareCategory( "IsLatinMagma", IsObject ); + DeclareCategory( "IsQuasigroup", IsMagma and IsLatinMagma ); DeclareCategory( "IsLoop", IsQuasigroup and IsMultiplicativeElementWithInverseCollection); diff --git a/doc/chap3_mj.html b/doc/chap3_mj.html index 5c436ed..75c294a 100644 --- a/doc/chap3_mj.html +++ b/doc/chap3_mj.html @@ -72,19 +72,19 @@
-
-DeclareCategory( "IsQuasigroupElement", IsMultiplicativeElement );
-DeclareRepresentation( "IsQuasigroupElmRep",
-    IsPositionalObjectRep and IsMultiplicativeElement, [1] );
-DeclareCategory( "IsLoopElement",
-    IsQuasigroupElement and IsMultiplicativeElementWithInverse );
-DeclareRepresentation( "IsLoopElmRep",
-    IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] );
-## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup)
-DeclareCategory( "IsLatin", IsObject );
-DeclareCategory( "IsQuasigroup", IsMagma and IsLatin );
-DeclareCategory( "IsLoop", IsQuasigroup and
-    IsMultiplicativeElementWithInverseCollection);
+
+DeclareCategory( "IsQuasigroupElement", IsMultiplicativeElement );
+DeclareRepresentation( "IsQuasigroupElmRep",
+    IsPositionalObjectRep and IsMultiplicativeElement, [1] );
+DeclareCategory( "IsLoopElement",
+    IsQuasigroupElement and IsMultiplicativeElementWithInverse );
+DeclareRepresentation( "IsLoopElmRep",
+    IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] );
+## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup)
+DeclareCategory( "IsLatinMagma", IsObject );
+DeclareCategory( "IsQuasigroup", IsMagma and IsLatinMagma );
+DeclareCategory( "IsLoop", IsQuasigroup and
+    IsMultiplicativeElementWithInverseCollection);
 
 
@@ -162,15 +162,15 @@ DeclareCategory( "IsLoop", IsQuasigroup and

In the following example, L is a loop with two elements.

-
-gap> L;

-<loop of order 2>
-gap> Print( L );

-<loop with multiplication table [ [ 1,  2 ], [  2,  1 ] ]>
-gap> Elements( L );

-[ l1, l2 ]
-gap> SetLoopElmName( L, "loop_element" );; Elements( L );

-[ loop_element1, loop_element2 ]
+
+gap> L;
+<loop of order 2>
+gap> Print( L );
+<loop with multiplication table [ [ 1,  2 ], [  2,  1 ] ]>
+gap> Elements( L );
+[ l1, l2 ]
+gap> SetLoopElmName( L, "loop_element" );; Elements( L );
+[ loop_element1, loop_element2 ]
 
diff --git a/doc/chap4_mj.html b/doc/chap4_mj.html index aab30dc..1699a40 100644 --- a/doc/chap4_mj.html +++ b/doc/chap4_mj.html @@ -188,15 +188,15 @@

Since CanonicalCayleyTable is called within the above operation, the resulting quasigroup will have Cayley table with distinct entries \(1\), \(\dots\), \(n\).

-
-gap> ct := CanonicalCayleyTable( [[5,3],[3,5]] );

-[ [ 2, 1 ], [ 1, 2 ] ]
-gap> NormalizedQuasigroupTable( ct );

-[ [ 1, 2 ], [ 2, 1 ] ]
-gap> LoopByCayleyTable( last );

-<loop of order 2>
-gap> [ IsQuasigroupTable( ct ), IsLoopTable( ct ) ];

-[ true, false ]
+
+gap> ct := CanonicalCayleyTable( [[5,3],[3,5]] );
+[ [ 2, 1 ], [ 1, 2 ] ]
+gap> NormalizedQuasigroupTable( ct );
+[ [ 1, 2 ], [ 2, 1 ] ]
+gap> LoopByCayleyTable( last );
+<loop of order 2>
+gap> [ IsQuasigroupTable( ct ), IsLoopTable( ct ) ];
+[ true, false ]
 

@@ -235,56 +235,56 @@

Example: Data does not have to be arranged into an array of any kind.

-

\[ - \begin{array}{cccc} - 0&1&2&1\\ - 2&0&2& \\ - 0&1& & - \end{array}\quad + \quad "" \quad \Longrightarrow\quad - \begin{array}{ccc} - 1&2&3\\ - 2&3&1\\ - 3&1&2 - \end{array} +

\[ + \begin{array}{cccc} + 0&1&2&1\\ + 2&0&2& \\ + 0&1& & + \end{array}\quad + \quad "" \quad \Longrightarrow\quad + \begin{array}{ccc} + 1&2&3\\ + 2&3&1\\ + 3&1&2 + \end{array} \]

Example: Chunks can be any strings.

-

\[ - \begin{array}{cc} - {\rm red}&{\rm green}\\ - {\rm green}&{\rm red}\\ - \end{array}\quad + \quad "" \quad \Longrightarrow\quad - \begin{array}{cc} - 1& 2\\ - 2& 1 - \end{array} +

\[ + \begin{array}{cc} + {\rm red}&{\rm green}\\ + {\rm green}&{\rm red}\\ + \end{array}\quad + \quad "" \quad \Longrightarrow\quad + \begin{array}{cc} + 1& 2\\ + 2& 1 + \end{array} \]

Example: A typical table produced by GAP is easily parsed by deleting brackets and commas.

-

\[ - [ [0, 1], [1, 0] ] \quad + \quad "[,]" \quad \Longrightarrow\quad - \begin{array}{cc} - 1& 2\\ - 2& 1 - \end{array} +

\[ + [ [0, 1], [1, 0] ] \quad + \quad "[,]" \quad \Longrightarrow\quad + \begin{array}{cc} + 1& 2\\ + 2& 1 + \end{array} \]

Example: A typical TeX table with rows separated by lines is also easily converted. Note that we have to use \(\backslash\backslash\) to ensure that every occurrence of \(\backslash\) is deleted, since \(\backslash\backslash\) represents the character \(\backslash\) in GAP

-

\[ - \begin{array}{lll} - x\&& y\&&\ z\backslash\backslash\cr - y\&& z\&&\ x\backslash\backslash\cr - z\&& x\&&\ y - \end{array} - \quad + \quad "\backslash\backslash\&" \quad \Longrightarrow\quad - \begin{array}{ccc} - 1&2&3\cr - 2&3&1\cr - 3&1&2 - \end{array} +

\[ + \begin{array}{lll} + x\&& y\&&\ z\backslash\backslash\cr + y\&& z\&&\ x\backslash\backslash\cr + z\&& x\&&\ y + \end{array} + \quad + \quad "\backslash\backslash\&" \quad \Longrightarrow\quad + \begin{array}{ccc} + 1&2&3\cr + 2&3&1\cr + 3&1&2 + \end{array} \]

@@ -329,14 +329,14 @@

These are the dual operations to QuasigroupByLeftSection and LoopByLeftSection.

-
-gap> S := Subloop( MoufangLoop( 12, 1 ), [ 3 ] );;

-gap> ls := LeftSection( S );

-[ (), (1,3,5), (1,5,3) ]
-gap> CayleyTableByPerms( ls );

-[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
-gap> CayleyTable( LoopByLeftSection( ls ) );

-[ [ 1, 2, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ] ]
+
+gap> S := Subloop( MoufangLoop( 12, 1 ), [ 3 ] );;
+gap> ls := LeftSection( S );
+[ (), (1,3,5), (1,5,3) ]
+gap> CayleyTableByPerms( ls );
+[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
+gap> CayleyTable( LoopByLeftSection( ls ) );
+[ [ 1, 2, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ] ]
 

@@ -360,11 +360,11 @@

Here is a simple example in which \(T\) is actually the right section of the resulting loop.

-
-gap> T := [ (), (1,2)(3,4,5), (1,3,5)(2,4), (1,4,3)(2,5), (1,5,4)(2,3) ];;

-gap> G := Group( T );; H := Stabilizer( G, 1 );;

-gap> LoopByRightFolder( G, H, T );

-<loop of order 5>
+
+gap> T := [ (), (1,2)(3,4,5), (1,3,5)(2,4), (1,4,3)(2,5), (1,5,4)(2,3) ];;
+gap> G := Group( T );; H := Stabilizer( G, 1 );;
+gap> LoopByRightFolder( G, H, T );
+<loop of order 5>
 

@@ -394,16 +394,16 @@

Returns: The extension of an abelian group K by a loop F, using action f and cocycle t. The arguments must be formatted as the output of NuclearExtension.

-
-gap> F := IntoLoop( Group( (1,2) ) );

-<loop of order 2>
-gap> K := DirectProduct( F, F );;

-gap> phi := [ (), (2,3) ];;

-gap> theta := [ [ 1, 1 ], [ 1, 3 ] ];;

-gap> LoopByExtension( K, F, phi, theta );

-<loop of order 8>
-gap> IsAssociative( last );

-false
+
+gap> F := IntoLoop( Group( (1,2) ) );
+<loop of order 2>
+gap> K := DirectProduct( F, F );;
+gap> phi := [ (), (2,3) ];;
+gap> theta := [ [ 1, 1 ], [ 1, 3 ] ];;
+gap> LoopByExtension( K, F, phi, theta );
+<loop of order 8>
+gap> IsAssociative( last );
+false
 

diff --git a/doc/chap5_mj.html b/doc/chap5_mj.html index 5506081..cedfb9e 100644 --- a/doc/chap5_mj.html +++ b/doc/chap5_mj.html @@ -167,17 +167,17 @@

Returns: The left inverse, right inverse and inverse, respectively, of the quasigroup element x.

-
-gap> CayleyTable( Q );

-[ [ 1, 2, 3, 4, 5 ],
-  [ 2, 1, 4, 5, 3 ],
-  [ 3, 4, 5, 1, 2 ],
-  [ 4, 5, 2, 3, 1 ],
-  [ 5, 3, 1, 2, 4 ] ]
-gap> elms := Elements( Q );

-gap> [ l1, l2, l3, l4, l5 ];

-gap> [ LeftInverse( elms[3] ), RightInverse( elms[3] ), Inverse( elms[3] ) ];

-[ l5, l4, fail ]
+
+gap> CayleyTable( Q );
+[ [ 1, 2, 3, 4, 5 ],
+  [ 2, 1, 4, 5, 3 ],
+  [ 3, 4, 5, 1, 2 ],
+  [ 4, 5, 2, 3, 1 ],
+  [ 5, 3, 1, 2, 4 ] ]
+gap> elms := Elements( Q );
+gap> [ l1, l2, l3, l4, l5 ];
+gap> [ LeftInverse( elms[3] ), RightInverse( elms[3] ), Inverse( elms[3] ) ];
+[ l5, l4, fail ]
 

diff --git a/doc/chap6.txt b/doc/chap6.txt index 52ef574..3c22b5f 100644 --- a/doc/chap6.txt +++ b/doc/chap6.txt @@ -488,17 +488,28 @@ the elements of the underlying quasigroup without changing the isomorphism type of the quasigroups. LOOPS contains several functions for this purpose. - 6.11-6 IsomorphicCopyByPerm + 6.11-6 QuasigroupIsomorph + + QuasigroupIsomorph( Q, f )  operation + Returns: When Q is a quasigroup and f is a permutation of 1,dots,|Q|, + returns the quasigroup defined on the same set as Q with + multiplication * defined by x*y =f(f^-1(x)f^-1(y)). + + 6.11-7 LoopIsomorph + + LoopIsomorph( Q, f )  operation + Returns: When Q is a loop and f is a permutation of 1,dots,|Q| fixing 1, + returns the loop defined on the same set as Q with multiplication + * defined by x*y =f(f^-1(x)f^-1(y)). If f(1)=cne 1, the + isomorphism (1,c) is applied after f. + + 6.11-8 IsomorphicCopyByPerm IsomorphicCopyByPerm( Q, f )  operation - Returns: When Q is a quasigroup and f is a permutation of 1,dots,|Q|, - returns a quasigroup defined on the same set as Q with - multiplication * defined by x*y =f(f^-1(x)f^-1(y)). When Q is a - declared loop, a loop is returned. Consequently, when Q is a - declared loop and f(1) = kne 1, then f is first replaced with f∘ - (1,k), to make sure that the resulting Cayley table is normalized. + Returns: LoopIsomorphism(Q,f) if Q is a loop, and + QuasigroupIsomorphism(Q,f) if Q is a quasigroup. - 6.11-7 IsomorphicCopyByNormalSubloop + 6.11-9 IsomorphicCopyByNormalSubloop IsomorphicCopyByNormalSubloop( Q, S )  operation Returns: When S is a normal subloop of a loop Q, returns an isomorphic copy @@ -511,7 +522,7 @@ these invariants to partition the loop into blocks of elements preserved under isomorphisms. The following two operations are used in the search. - 6.11-8 Discriminator + 6.11-10 Discriminator Discriminator( Q )  operation Returns: A data structure with isomorphism invariants of a loop Q. @@ -523,7 +534,7 @@ If two loops have different discriminators, they are not isomorphic. If they have identical discriminators, they may or may not be isomorphic. - 6.11-9 AreEqualDiscriminators + 6.11-11 AreEqualDiscriminators AreEqualDiscriminators( D1, D2 )  operation Returns: true if D1, D2 are equal discriminators for the purposes of diff --git a/doc/chap6_mj.html b/doc/chap6_mj.html index ffd0b44..a939b78 100644 --- a/doc/chap6_mj.html +++ b/doc/chap6_mj.html @@ -120,10 +120,12 @@
  6.11-3 QuasigroupsUpToIsomorphism

  6.11-4 LoopsUpToIsomorphism

  6.11-5 AutomorphismGroup
-
  6.11-6 IsomorphicCopyByPerm
-
  6.11-7 IsomorphicCopyByNormalSubloop
-
  6.11-8 Discriminator
-
  6.11-9 AreEqualDiscriminators
+
  6.11-6 QuasigroupIsomorph
+
  6.11-7 LoopIsomorph
+
  6.11-8 IsomorphicCopyByPerm
+
  6.11-9 IsomorphicCopyByNormalSubloop
+
  6.11-10 Discriminator
+
  6.11-11 AreEqualDiscriminators
 6.12 Isotopisms @@ -265,28 +267,28 @@

Note how the Cayley table of a subquasigroup is created only upon explicit demand. Also note that changing the names of elements of a subquasigroup (subloop) automatically changes the names of the elements of the parent subquasigroup (subloop). This is because the elements are shared.

-
-gap> M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.5 ] );

-<loop of order 3>
-gap> [ Parent( S ) = M, Elements( S ), PosInParent( S ) ];

-[ true, [ l1, l3, l5], [ 1, 3, 5 ] ]
-gap> HasCayleyTable( S );

-false
-gap> SetLoopElmName( S, "s" );; Elements( S ); Elements( M );

-[ s1, s3, s5 ]
-[ s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12 ]
-gap> CayleyTable( S );

-[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
-gap> LeftSection( S );

-[ (), (1,3,5), (1,5,3) ]
-gap> [ HasCayleyTable( S ), Parent( S ) = M ];

-[ true, true ]
-gap> L := LoopByCayleyTable( CayleyTable( S ) );; Elements( L );

-[ l1, l2, l3 ]
-gap> [ Parent( L ) = L, IsSubloop( M, S ), IsSubloop( M, L ) ];

-[ true, true, false ]
-gap> LeftSection( L );

-[ (), (1,2,3), (1,3,2) ]
+
+gap> M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.5 ] );
+<loop of order 3>
+gap> [ Parent( S ) = M, Elements( S ), PosInParent( S ) ];
+[ true, [ l1, l3, l5], [ 1, 3, 5 ] ]
+gap> HasCayleyTable( S );
+false
+gap> SetLoopElmName( S, "s" );; Elements( S ); Elements( M );
+[ s1, s3, s5 ]
+[ s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12 ]
+gap> CayleyTable( S );
+[ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ]
+gap> LeftSection( S );
+[ (), (1,3,5), (1,5,3) ]
+gap> [ HasCayleyTable( S ), Parent( S ) = M ];
+[ true, true ]
+gap> L := LoopByCayleyTable( CayleyTable( S ) );; Elements( L );
+[ l1, l2, l3 ]
+gap> [ Parent( L ) = L, IsSubloop( M, S ), IsSubloop( M, L ) ];
+[ true, true, false ]
+gap> LeftSection( L );
+[ (), (1,2,3), (1,3,2) ]
 

@@ -349,16 +351,16 @@ false

Here is an example for multiplication groups and inner mapping groups:

-
-gap> M := MoufangLoop(12,1);

-<Moufang loop 12/1>
-gap> LeftSection(M)[2];

-(1,2)(3,4)(5,6)(7,8)(9,12)(10,11)
-gap> Mlt := MultiplicationGroup(M); Inn := InnerMappingGroup(M);

-<permutation group of size 2592 with 23 generators>
-Group([ (4,6)(7,11), (7,11)(8,10), (2,6,4)(7,9,11), (3,5)(9,11), (8,12,10) ])
-gap> Size(Inn);

-216
+
+gap> M := MoufangLoop(12,1);
+<Moufang loop 12/1>
+gap> LeftSection(M)[2];
+(1,2)(3,4)(5,6)(7,8)(9,12)(10,11)
+gap> Mlt := MultiplicationGroup(M); Inn := InnerMappingGroup(M);
+<permutation group of size 2592 with 23 generators>
+Group([ (4,6)(7,11), (7,11)(8,10), (2,6,4)(7,9,11), (3,5)(9,11), (8,12,10) ])
+gap> Size(Inn);
+216
 

@@ -464,16 +466,16 @@ Group([ (4,6)(7,11), (7,11)(8,10), (2,6,4)(7,9,11), (3,5)(9,11), (8,12,10) ])

Returns: When S is a normal subloop of a loop Q, returns the natural projection from Q onto Q\(/\)S.

-
-gap> M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.3 ] );

-<loop of order 3>
-gap> IsNormal( M, S );

-true
-gap> F := FactorLoop( M, S );

-<loop of order 4>
-gap> NaturalHomomorphismByNormalSubloop( M, S );

-MappingByFunction( <loop of order 12>, <loop of order 4>,
-    function( x ) ... end )
+
+gap> M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.3 ] );
+<loop of order 3>
+gap> IsNormal( M, S );
+true
+gap> F := FactorLoop( M, S );
+<loop of order 4>
+gap> NaturalHomomorphismByNormalSubloop( M, S );
+MappingByFunction( <loop of order 12>, <loop of order 4>,
+    function( x ) ... end )
 

@@ -607,16 +609,30 @@ MappingByFunction( <loop of order 12>, <loop of order 4>,

While dealing with Cayley tables, it is often useful to rename or reorder the elements of the underlying quasigroup without changing the isomorphism type of the quasigroups. LOOPS contains several functions for this purpose.

+

+ +
6.11-6 QuasigroupIsomorph
+ +
‣ QuasigroupIsomorph( Q, f )( operation )
+

Returns: When Q is a quasigroup and f is a permutation of \(1,\dots,|\)Q\(|\), returns the quasigroup defined on the same set as Q with multiplication \(*\) defined by \(x*y = \)f\((\)f\({}^{-1}(x)\)f\({}^{-1}(y))\).

+ +

+ +
6.11-7 LoopIsomorph
+ +
‣ LoopIsomorph( Q, f )( operation )
+

Returns: When Q is a loop and f is a permutation of \(1,\dots,|\)Q\(|\) fixing \(1\), returns the loop defined on the same set as Q with multiplication \(*\) defined by \(x*y = \)f\((\)f\({}^{-1}(x)\)f\({}^{-1}(y))\). If f\((1)=c\ne 1\), the isomorphism \((1,c)\) is applied after f.

+

-
6.11-6 IsomorphicCopyByPerm
+
6.11-8 IsomorphicCopyByPerm
‣ IsomorphicCopyByPerm( Q, f )( operation )
-

Returns: When Q is a quasigroup and f is a permutation of \(1,\dots,|\)Q\(|\), returns a quasigroup defined on the same set as Q with multiplication \(*\) defined by \(x*y = \)f\((\)f\({}^{-1}(x)\)f\({}^{-1}(y))\). When Q is a declared loop, a loop is returned. Consequently, when Q is a declared loop and f\((1) = k\ne 1\), then f is first replaced with f\(\circ (1,k)\), to make sure that the resulting Cayley table is normalized.

+

Returns: LoopIsomorphism(Q,f) if Q is a loop, and QuasigroupIsomorphism(Q,f) if Q is a quasigroup.

-
6.11-7 IsomorphicCopyByNormalSubloop
+
6.11-9 IsomorphicCopyByNormalSubloop
‣ IsomorphicCopyByNormalSubloop( Q, S )( operation )

Returns: When S is a normal subloop of a loop Q, returns an isomorphic copy of Q in which the elements are ordered according to the right cosets of S. In particular, the Cayley table of S will appear in the top left corner of the Cayley table of the resulting loop.

@@ -625,7 +641,7 @@ MappingByFunction( <loop of order 12>, <loop of order 4>,

-
6.11-8 Discriminator
+
6.11-10 Discriminator
‣ Discriminator( Q )( operation )

Returns: A data structure with isomorphism invariants of a loop Q.

@@ -636,7 +652,7 @@ MappingByFunction( <loop of order 12>, <loop of order 4>,

-
6.11-9 AreEqualDiscriminators
+
6.11-11 AreEqualDiscriminators
‣ AreEqualDiscriminators( D1, D2 )( operation )

Returns: true if D1, D2 are equal discriminators for the purposes of isomorphism searches.

diff --git a/doc/chap7_mj.html b/doc/chap7_mj.html index cd2a8b7..6f0f8c2 100644 --- a/doc/chap7_mj.html +++ b/doc/chap7_mj.html @@ -444,19 +444,19 @@

The following trivial example shows some of the implications and the naming conventions of LOOPS at work:

-
-gap> L := LoopByCayleyTable( [ [ 1, 2 ], [ 2, 1 ] ] );

-<loop of order 2>
-gap> [ IsLeftBolLoop( L ), L ]

-[ true, <left Bol loop of order 2> ]
-gap> [ HasIsLeftAlternativeLoop( L ), IsLeftAlternativeLoop( L ) ];

-[ true, true ]
-gap> [ HasIsRightBolLoop( L ), IsRightBolLoop( L ) ];

-[ false, true ]
-gap> L;

-<Moufang loop of order 2>
-gap> [ IsAssociative( L ), L ];

-[ true, <associative loop of order 2> ]
+
+gap> L := LoopByCayleyTable( [ [ 1, 2 ], [ 2, 1 ] ] );
+<loop of order 2>
+gap> [ IsLeftBolLoop( L ), L ]
+[ true, <left Bol loop of order 2> ]
+gap> [ HasIsLeftAlternativeLoop( L ), IsLeftAlternativeLoop( L ) ];
+[ true, true ]
+gap> [ HasIsRightBolLoop( L ), IsRightBolLoop( L ) ];
+[ false, true ]
+gap> L;
+<Moufang loop of order 2>
+gap> [ IsAssociative( L ), L ];
+[ true, <associative loop of order 2> ]
 

The analogous terminology for quasigroups of Bol-Moufang type is not standard yet, and hence is not supported in LOOPS except for the situations explicitly noted above.

diff --git a/doc/chap8_mj.html b/doc/chap8_mj.html index 5f4f0fb..faad0e4 100644 --- a/doc/chap8_mj.html +++ b/doc/chap8_mj.html @@ -202,13 +202,13 @@

Returns: One loop (given as a section) whose multiplication group is equal to the transitive permutation group G.

-
-gap> g:=PGL(3,3);

-Group([ (6,7)(8,11)(9,13)(10,12), (1,2,5,7,13,3,8,6,10,9,12,4,11) ])
-gap> a:=AllLoopTablesInGroup(g,3,0);; Size(a);

-56
-gap> a:=AllLoopsWithMltGroup(g,3,0);; Size(a);

-52
+
+gap> g:=PGL(3,3);
+Group([ (6,7)(8,11)(9,13)(10,12), (1,2,5,7,13,3,8,6,10,9,12,4,11) ])
+gap> a:=AllLoopTablesInGroup(g,3,0);; Size(a);
+56
+gap> a:=AllLoopsWithMltGroup(g,3,0);; Size(a);
+52
 
diff --git a/doc/chap9.txt b/doc/chap9.txt index bf918b0..abb69bc 100644 --- a/doc/chap9.txt +++ b/doc/chap9.txt @@ -78,12 +78,34 @@ retrieved by calling Opposite on left Bol loops. - 9.3 Moufang Loops + 9.3 Left Bruck Loops and Right Bruck Loops + + The emmerging library named left Bruck contains all left Bruck loops of + orders 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops, respectively). + + For an odd prime p, left Bruck loops of order p^k are centrally nilpotent + and hence central extensions of the cyclic group of order p by a left Bruck + loop of order p^k-1. It is known that left Bruck loops of order p and p^2 + are abelian groups; we have included them in the library because of the + iterative nature of the construction of nilpotent loops. + + 9.3-1 LeftBruckLoop + + LeftBruckLoop( n, m )  function + Returns: The mth left Bruck loop of order n in the library. + + 9.3-2 RightBruckLoop + + RightBruckLoop( n, m )  function + Returns: The mth right Bruck loop of order n in the library. + + + 9.4 Moufang Loops The library named Moufang contains all nonassociative Moufang loops of order nle 64 and n∈{81,243}. - 9.3-1 MoufangLoop + 9.4-1 MoufangLoop MoufangLoop( n, m )  function Returns: The mth Moufang loop of order n in the library. @@ -107,20 +129,20 @@ obtained as MoufangLoop(16,3). - 9.4 Code Loops + 9.5 Code Loops The library named code contains all nonassociative code loops of order less than 65. There are 5 such loops of order 16, 16 of order 32, and 80 of order 64, all Moufang. The library merely points to the corresponding Moufang loops. See [NV07] for a classification of small code loops. - 9.4-1 CodeLoop + 9.5-1 CodeLoop CodeLoop( n, m )  function Returns: The mth code loop of order n in the library. - 9.5 Steiner Loops + 9.6 Steiner Loops Here is how the libary named Steiner is described within LOOPS: @@ -141,13 +163,13 @@ Our labeling of Steiner loops of order 16 coincides with the labeling of Steiner triple systems of order 15 in [CR99]. - 9.5-1 SteinerLoop + 9.6-1 SteinerLoop SteinerLoop( n, m )  function Returns: The mth Steiner loop of order n in the library. - 9.6 Conjugacy Closed Loops + 9.7 Conjugacy Closed Loops The library named RCC contains all nonassocitive right conjugacy closed loops of order nle 27 up to isomorphism. The data for the library was @@ -171,14 +193,14 @@ - 9.6-1 RCCLoop and RightConjugacyClosedLoop + 9.7-1 RCCLoop and RightConjugacyClosedLoop RCCLoop( n, m )  function RightConjugacyClosedLoop( n, m )  function Returns: The mth right conjugacy closed loop of order n in the library. - 9.6-2 LCCLoop and LeftConjugacyClosedLoop + 9.7-2 LCCLoop and LeftConjugacyClosedLoop LCCLoop( n, m )  function LeftConjugacyClosedLoop( n, m )  function @@ -188,8 +210,10 @@ Left conjugacy closed loops are obtained from right conjugacy closed loops via Opposite. - The library named CC contains all nonassociative conjugacy closed loops of - order nle 27 and also of orders 2p and p^2 for all primes p. + The library named CC contains all CC loops of order 2le 2^kle 64, 3le 3^kle + 81, 5le 5^kle 125, 7le 7^kle 343, all nonassociative CC loops of order less + than 28, and all nonassociative CC loops of order p^2 and 2p for any odd + prime p. By results of Kunen [Kun00], for every odd prime p there are precisely 3 nonassociative conjugacy closed loops of order p^2. Csörgő and Drápal [CD05] @@ -215,25 +239,25 @@ m + n ). - 9.6-3 CCLoop and ConjugacyClosedLoop + 9.7-3 CCLoop and ConjugacyClosedLoop CCLoop( n, m )  function ConjugacyClosedLoop( n, m )  function Returns: The mth conjugacy closed loop of order n in the library. - 9.7 Small Loops + 9.8 Small Loops The library named small contains all nonassociative loops of order 5 and 6. There are 5 and 107 such loops, respectively. - 9.7-1 SmallLoop + 9.8-1 SmallLoop SmallLoop( n, m )  function Returns: The mth loop of order n in the library. - 9.8 Paige Loops + 9.9 Paige Loops Paige loops are nonassociative finite simple Moufang loops. By [Lie87], there is precisely one Paige loop for every finite field. @@ -241,14 +265,14 @@ The library named Paige contains the smallest nonassociative simple Moufang loop. - 9.8-1 PaigeLoop + 9.9-1 PaigeLoop PaigeLoop( q )  function Returns: The Paige loop constructed over the finite field of order q. Only the case q=2 is implemented. - 9.9 Nilpotent Loops + 9.10 Nilpotent Loops The library named nilpotent contains all nonassociative nilpotent loops of order less than 12 up to isomorphism. There are 2 nonassociative nilpotent @@ -258,30 +282,32 @@ are 2623755 nilpotent loops of order 12, and 123794003928541545927226368 nilpotent loops of order 22. - 9.9-1 NilpotentLoop + 9.10-1 NilpotentLoop NilpotentLoop( n, m )  function Returns: The mth nilpotent loop of order n in the library. - 9.10 Automorphic Loops + 9.11 Automorphic Loops The library named automorphic contains all nonassociative automorphic loops of order less than 16 up to isomorphism (there is 1 such loop of order 6, 7 - of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15), - all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, 2, - 7 and 72 such loops, respectively, including abelian groups), and - commutative automorphic loops Q of order 243 possessing a central subloop S - of order 3 such that Q/S is not the elementary abelian group of order 81 - (there are 118451 such loops). + of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15) + and all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, + 2, 7 and 72 such loops). - 9.10-1 AutomorphicLoop + It turns out that commutative automorphic loops of order 3, 9, 27 and 81 + (but not 243) are in one-to-on correspondence with left Bruck loops of the + respective orders, see [Gre14], [SV17]. Only the left Bruck loops are stored + in the library. + + 9.11-1 AutomorphicLoop AutomorphicLoop( n, m )  function Returns: The mth automorphic loop of order n in the library. - 9.11 Interesting Loops + 9.12 Interesting Loops The library named interesting contains some loops that are illustrative in the theory of loops. At this point, the library contains a nonassociative @@ -290,20 +316,20 @@ generalize octonions), and the unique nonassociative simple right Bol loop of order 96 and exponent 2. - 9.11-1 InterestingLoop + 9.12-1 InterestingLoop InterestingLoop( n, m )  function Returns: The mth interesting loop of order n in the library. - 9.12 Libraries of Loops Up To Isotopism + 9.13 Libraries of Loops Up To Isotopism For the library named small we also provide the corresponding library of loops up to isotopism. In general, given a library named libname, the corresponding library of loops up to isotopism is named itp lib, and the loops can be retrieved by the template ItpLibLoop(n,m). - 9.12-1 ItpSmallLoop + 9.13-1 ItpSmallLoop ItpSmallLoop( n, m )  function Returns: The mth small loop of order n up to isotopism in the library. diff --git a/doc/chap9_mj.html b/doc/chap9_mj.html index d2a086f..2193e85 100644 --- a/doc/chap9_mj.html +++ b/doc/chap9_mj.html @@ -38,60 +38,66 @@
  9.2-1 LeftBolLoop

  9.2-2 RightBolLoop
-
 9.3 Moufang Loops + -
 9.4 Code Loops + -
 9.5 Steiner Loops + -
 9.6 Conjugacy Closed Loops + + -
 9.7 Small Loops + -
 9.8 Paige Loops + -
 9.9 Nilpotent Loops + -
 9.10 Automorphic Loops + -
 9.11 Interesting Loops + - @@ -170,15 +176,37 @@

Remark: Only left Bol loops are stored in the library. Right Bol loops are retrieved by calling Opposite on left Bol loops.

+

+ +

9.3 Left Bruck Loops and Right Bruck Loops

+ +

The emmerging library named left Bruck contains all left Bruck loops of orders \(3\), \(9\), \(27\) and \(81\) (there are \(1\), \(2\), \(7\) and \(72\) such loops, respectively).

+ +

For an odd prime \(p\), left Bruck loops of order \(p^k\) are centrally nilpotent and hence central extensions of the cyclic group of order \(p\) by a left Bruck loop of order \(p^{k-1}\). It is known that left Bruck loops of order \(p\) and \(p^2\) are abelian groups; we have included them in the library because of the iterative nature of the construction of nilpotent loops.

+ +

+ +
9.3-1 LeftBruckLoop
+ +
‣ LeftBruckLoop( n, m )( function )
+

Returns: The mth left Bruck loop of order n in the library.

+ +

+ +
9.3-2 RightBruckLoop
+ +
‣ RightBruckLoop( n, m )( function )
+

Returns: The mth right Bruck loop of order n in the library.

+

-

9.3 Moufang Loops

+

9.4 Moufang Loops

The library named Moufang contains all nonassociative Moufang loops of order \(n\le 64\) and \(n\in\{81,243\}\).

-
9.3-1 MoufangLoop
+
9.4-1 MoufangLoop
‣ MoufangLoop( n, m )( function )

Returns: The mth Moufang loop of order n in the library.

@@ -187,79 +215,79 @@

The extent of the library is summarized below:

-

\[ -\begin{array}{r|rrrrrrrrrrrrrrrrrr} - order&12&16&20&24&28&32&36&40&42&44&48&52&54&56&60&64&81&243\cr - loops&1 &5 &1 &5 &1 &71&4 &5 &1 &1 &51&1 &2 &4 &5 &4262& 5 &72 -\end{array} +

\[ +\begin{array}{r|rrrrrrrrrrrrrrrrrr} + order&12&16&20&24&28&32&36&40&42&44&48&52&54&56&60&64&81&243\cr + loops&1 &5 &1 &5 &1 &71&4 &5 &1 &1 &51&1 &2 &4 &5 &4262& 5 &72 +\end{array} \]

The octonion loop of order 16 (i.e., the multiplication loop of the basis elements in the 8-dimensional standard real octonion algebra) can be obtained as MoufangLoop(16,3).

-

9.4 Code Loops

+

9.5 Code Loops

The library named code contains all nonassociative code loops of order less than 65. There are 5 such loops of order 16, 16 of order 32, and 80 of order 64, all Moufang. The library merely points to the corresponding Moufang loops. See [NV07] for a classification of small code loops.

-
9.4-1 CodeLoop
+
9.5-1 CodeLoop
‣ CodeLoop( n, m )( function )

Returns: The mth code loop of order n in the library.

-

9.5 Steiner Loops

+

9.6 Steiner Loops

Here is how the libary named Steiner is described within LOOPS:

-
-gap> DisplayLibraryInfo( "Steiner" );

-The library contains all nonassociative Steiner loops of order less or equal to 16.
-It also contains the associative Steiner loops of order 4 and 8.
-------
-Extent of the library:
-   1 loop of order 4
-   1 loop of order 8
-   1 loop of order 10
-   2 loops of order 14
-   80 loops of order 16
-true
+
+gap> DisplayLibraryInfo( "Steiner" );
+The library contains all nonassociative Steiner loops of order less or equal to 16.
+It also contains the associative Steiner loops of order 4 and 8.
+------
+Extent of the library:
+   1 loop of order 4
+   1 loop of order 8
+   1 loop of order 10
+   2 loops of order 14
+   80 loops of order 16
+true
 

Our labeling of Steiner loops of order 16 coincides with the labeling of Steiner triple systems of order 15 in [CR99].

-
9.5-1 SteinerLoop
+
9.6-1 SteinerLoop
‣ SteinerLoop( n, m )( function )

Returns: The mth Steiner loop of order n in the library.

-

9.6 Conjugacy Closed Loops

+

9.7 Conjugacy Closed Loops

The library named RCC contains all nonassocitive right conjugacy closed loops of order \(n\le 27\) up to isomorphism. The data for the library was generated by Katharina Artic [Art15] who can also provide additional data for all right conjugacy closed loops of order \(n\le 31\).

Let \(Q\) be a right conjugacy closed loop, \(G\) its right multiplication group and \(T\) its right section. Then \(\langle T\rangle = G\) is a transitive group, and \(T\) is a union of conjugacy classes of \(G\). Every right conjugacy closed loop of order \(n\) can therefore be represented as a union of certain conjugacy classes of a transitive group of degree \(n\). This is how right conjugacy closed loops of order less than \(28\) are represented in LOOPS. The following table summarizes the number of right conjugacy closed loops of a given order up to isomorphism:

-

\[ -\begin{array}{r|rrrrrrrrrrrrrrrr} - order &6& 8&9&10& 12&14&15& 16& 18& 20&\cr - loops &3&19&5&16&155&97& 17&6317&1901&8248&\cr - \hline - order &21& 22& 24& 25& 26& 27\cr - loops &119&10487&471995& 119&151971&152701 -\end{array} +

\[ +\begin{array}{r|rrrrrrrrrrrrrrrr} + order &6& 8&9&10& 12&14&15& 16& 18& 20&\cr + loops &3&19&5&16&155&97& 17&6317&1901&8248&\cr + \hline + order &21& 22& 24& 25& 26& 27\cr + loops &119&10487&471995& 119&151971&152701 +\end{array} \]

-
9.6-1 RCCLoop and RightConjugacyClosedLoop
+
9.7-1 RCCLoop and RightConjugacyClosedLoop
‣ RCCLoop( n, m )( function )
‣ RightConjugacyClosedLoop( n, m )( function )
@@ -267,7 +295,7 @@ true

-
9.6-2 LCCLoop and LeftConjugacyClosedLoop
+
9.7-2 LCCLoop and LeftConjugacyClosedLoop
‣ LCCLoop( n, m )( function )
‣ LeftConjugacyClosedLoop( n, m )( function )
@@ -275,7 +303,7 @@ true

Remark: Only the right conjugacy closed loops are stored in the library. Left conjugacy closed loops are obtained from right conjugacy closed loops via Opposite.

-

The library named CC contains all nonassociative conjugacy closed loops of order \(n\le 27\) and also of orders \(2p\) and \(p^2\) for all primes \(p\).

+

The library named CC contains all CC loops of order \(2\le 2^k\le 64\), \(3\le 3^k\le 81\), \(5\le 5^k\le 125\), \(7\le 7^k\le 343\), all nonassociative CC loops of order less than 28, and all nonassociative CC loops of order \(p^2\) and \(2p\) for any odd prime \(p\).

By results of Kunen [Kun00], for every odd prime \(p\) there are precisely 3 nonassociative conjugacy closed loops of order \(p^2\). Csörgő and Drápal [CD05] described these 3 loops by multiplicative formulas on \(\mathbb{Z}_{p^2}\) and \(\mathbb{Z}_p \times \mathbb{Z}_p\) as follows:

@@ -295,7 +323,7 @@ true

-
9.6-3 CCLoop and ConjugacyClosedLoop
+
9.7-3 CCLoop and ConjugacyClosedLoop
‣ CCLoop( n, m )( function )
‣ ConjugacyClosedLoop( n, m )( function )
@@ -303,20 +331,20 @@ true

-

9.7 Small Loops

+

9.8 Small Loops

The library named small contains all nonassociative loops of order 5 and 6. There are 5 and 107 such loops, respectively.

-
9.7-1 SmallLoop
+
9.8-1 SmallLoop
‣ SmallLoop( n, m )( function )

Returns: The mth loop of order n in the library.

-

9.8 Paige Loops

+

9.9 Paige Loops

Paige loops are nonassociative finite simple Moufang loops. By [Lie87], there is precisely one Paige loop for every finite field.

@@ -324,14 +352,14 @@ true

-
9.8-1 PaigeLoop
+
9.9-1 PaigeLoop
‣ PaigeLoop( q )( function )

Returns: The Paige loop constructed over the finite field of order q. Only the case q=2 is implemented.

-

9.9 Nilpotent Loops

+

9.10 Nilpotent Loops

The library named nilpotent contains all nonassociative nilpotent loops of order less than 12 up to isomorphism. There are 2 nonassociative nilpotent loops of order 6, 134 of order 8, 8 of order 9 and 1043 of order 10.

@@ -339,58 +367,60 @@ true

-
9.9-1 NilpotentLoop
+
9.10-1 NilpotentLoop
‣ NilpotentLoop( n, m )( function )

Returns: The mth nilpotent loop of order n in the library.

-

9.10 Automorphic Loops

+

9.11 Automorphic Loops

-

The library named automorphic contains all nonassociative automorphic loops of order less than 16 up to isomorphism (there is 1 such loop of order 6, 7 of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15), all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops, respectively, including abelian groups), and commutative automorphic loops \(Q\) of order 243 possessing a central subloop \(S\) of order 3 such that \(Q/S\) is not the elementary abelian group of order 81 (there are 118451 such loops).

+

The library named automorphic contains all nonassociative automorphic loops of order less than 16 up to isomorphism (there is 1 such loop of order 6, 7 of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15) and all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops).

+ +

It turns out that commutative automorphic loops of order 3, 9, 27 and 81 (but not 243) are in one-to-on correspondence with left Bruck loops of the respective orders, see [Gre14], [SV17]. Only the left Bruck loops are stored in the library.

-
9.10-1 AutomorphicLoop
+
9.11-1 AutomorphicLoop
‣ AutomorphicLoop( n, m )( function )

Returns: The mth automorphic loop of order n in the library.

-

9.11 Interesting Loops

+

9.12 Interesting Loops

The library named interesting contains some loops that are illustrative in the theory of loops. At this point, the library contains a nonassociative loop of order 5, a nonassociative nilpotent loop of order 6, a non-Moufang left Bol loop of order 16, the loop of sedenions of order 32 (sedenions generalize octonions), and the unique nonassociative simple right Bol loop of order 96 and exponent 2.

-
9.11-1 InterestingLoop
+
9.12-1 InterestingLoop
‣ InterestingLoop( n, m )( function )

Returns: The mth interesting loop of order n in the library.

-

9.12 Libraries of Loops Up To Isotopism

+

9.13 Libraries of Loops Up To Isotopism

For the library named small we also provide the corresponding library of loops up to isotopism. In general, given a library named libname, the corresponding library of loops up to isotopism is named itp lib, and the loops can be retrieved by the template ItpLibLoop(n,m).

-
9.12-1 ItpSmallLoop
+
9.13-1 ItpSmallLoop
‣ ItpSmallLoop( n, m )( function )

Returns: The mth small loop of order n up to isotopism in the library.

-
-gap> SmallLoop( 6, 14 );

-<small loop 6/14>
-gap> ItpSmallLoop( 6, 14 );

-<small loop 6/42>
-gap> LibraryLoop( "itp small", 6, 14 );

-<small loop 6/42>
+
+gap> SmallLoop( 6, 14 );
+<small loop 6/14>
+gap> ItpSmallLoop( 6, 14 );
+<small loop 6/42>
+gap> LibraryLoop( "itp small", 6, 14 );
+<small loop 6/42>
 

Note that loops up to isotopism form a subset of the corresponding library of loops up to isomorphism. For instance, the above example shows that the 14th small loop of order 6 up to isotopism is in fact the 42nd small loop of order 6 up to isomorphism.

diff --git a/doc/chapB.txt b/doc/chapB.txt index b546b8e..7b15ddd 100644 --- a/doc/chapB.txt +++ b/doc/chapB.txt @@ -105,9 +105,6 @@ ( IsLeftAutomorphicLoop, IsAutomorphicLoop ) ( IsRightAutomorphicLoop, IsAutomorphicLoop ) ( IsMiddleAutomorphicLoop, IsAutomorphicLoop ) - ( IsMiddleAutomorphicLoop, IsCommutative ) - ( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsCommutative ) - ( IsAutomorphicLoop, IsRightAutomorphicLoop and IsCommutative ) ( IsLeftAutomorphicLoop, IsRightAutomorphicLoop and HasAntiautomorphicInverseProperty ) ( IsRightAutomorphicLoop, IsLeftAutomorphicLoop and @@ -120,9 +117,13 @@ ( IsMoufangLoop, IsAutomorphicLoop and HasLeftInverseProperty ) ( IsMoufangLoop, IsAutomorphicLoop and HasRightInverseProperty ) ( IsMoufangLoop, IsAutomorphicLoop and HasWeakInverseProperty ) + ( IsMiddleAutomorphicLoop, IsCommutative ) ( IsLeftAutomorphicLoop, IsLeftBruckLoop ) ( IsLeftAutomorphicLoop, IsLCCLoop ) ( IsRightAutomorphicLoop, IsRightBruckLoop ) ( IsRightAutomorphicLoop, IsRCCLoop ) ( IsAutomorphicLoop, IsCommutative and IsMoufangLoop ) + ( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsMiddleAutomorphicLoop ) + ( IsAutomorphicLoop, IsRightAutomorphicLoop and IsMiddleAutomorphicLoop ) + ( IsAutomorphicLoop, IsAssociative ) diff --git a/doc/chapB_mj.html b/doc/chapB_mj.html index 0b897e5..54b8a13 100644 --- a/doc/chapB_mj.html +++ b/doc/chapB_mj.html @@ -31,7 +31,7 @@

Many implications among properties of loops are built directly into LOOPS. A sizeable portion of these properties are of trivial character or are based on definitions (e.g., alternative loops \(=\) left alternative loops \(+\) right alternative loops). The remaining implications are theorems.

-

All filters of LOOPS are summarized below, using the GAP convention that the property on the left is implied by the property (properties) on the right.

( IsExtraLoop, IsAssociative and IsLoop )
( IsExtraLoop, IsCodeLoop )
( IsCCLoop, IsCodeLoop )
( HasTwosidedInverses, IsPowerAssociative and IsLoop )
( IsPowerAlternative, IsDiassociative )
( IsFlexible, IsDiassociative )
( HasAntiautomorphicInverseProperty, HasAutomorphicInverseProperty and IsCommutative )
( HasAutomorphicInverseProperty, HasAntiautomorphicInverseProperty and IsCommutative )
( HasLeftInverseProperty, HasInverseProperty )
( HasRightInverseProperty, HasInverseProperty )
( HasWeakInverseProperty, HasInverseProperty )
( HasAntiautomorphicInverseProperty, HasInverseProperty )
( HasTwosidedInverses, HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and IsCommutative )
( HasInverseProperty, HasRightInverseProperty and IsCommutative )
( HasInverseProperty, HasLeftInverseProperty and HasRightInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and HasWeakInverseProperty )
( HasInverseProperty, HasRightInverseProperty and HasWeakInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasRightInverseProperty and HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasWeakInverseProperty and HasAntiautomorphicInverseProperty )
( HasTwosidedInverses, HasLeftInverseProperty )
( HasTwosidedInverses, HasRightInverseProperty )
( HasTwosidedInverses, IsFlexible and IsLoop )
( IsMoufangLoop, IsExtraLoop )
( IsCLoop, IsExtraLoop )
( IsExtraLoop, IsMoufangLoop and IsLeftNuclearSquareLoop )
( IsExtraLoop, IsMoufangLoop and IsMiddleNuclearSquareLoop )
( IsExtraLoop, IsMoufangLoop and IsRightNuclearSquareLoop )
( IsLeftBolLoop, IsMoufangLoop )
( IsRightBolLoop, IsMoufangLoop )
( IsDiassociative, IsMoufangLoop )
( IsMoufangLoop, IsLeftBolLoop and IsRightBolLoop )
( IsLCLoop, IsCLoop )
( IsRCLoop, IsCLoop )
( IsDiassociative, IsCLoop and IsFlexible)
( IsCLoop, IsLCLoop and IsRCLoop )
( IsRightBolLoop, IsLeftBolLoop and IsCommutative )
( IsLeftPowerAlternative, IsLeftBolLoop )
( IsLeftBolLoop, IsRightBolLoop and IsCommutative )
( IsRightPowerAlternative, IsRightBolLoop )
( IsLeftPowerAlternative, IsLCLoop )
( IsLeftNuclearSquareLoop, IsLCLoop )
( IsMiddleNuclearSquareLoop, IsLCLoop )
( IsRCLoop, IsLCLoop and IsCommutative )
( IsRightPowerAlternative, IsRCLoop )
( IsRightNuclearSquareLoop, IsRCLoop )
( IsMiddleNuclearSquareLoop, IsRCLoop )
( IsLCLoop, IsRCLoop and IsCommutative )
( IsRightNuclearSquareLoop, IsLeftNuclearSquareLoop and IsCommutative )
( IsLeftNuclearSquareLoop, IsRightNuclearSquareLoop and IsCommutative )
( IsLeftNuclearSquareLoop, IsNuclearSquareLoop )
( IsRightNuclearSquareLoop, IsNuclearSquareLoop )
( IsMiddleNuclearSquareLoop, IsNuclearSquareLoop )
( IsNuclearSquareLoop, IsLeftNuclearSquareLoop and IsRightNuclearSquareLoop
and IsMiddleNuclearSquareLoop )
( IsFlexible, IsCommutative )
( IsRightAlternative, IsLeftAlternative and IsCommutative )
( IsLeftAlternative, IsRightAlternative and IsCommutative )
( IsLeftAlternative, IsAlternative )
( IsRightAlternative, IsAlternative )
( IsAlternative, IsLeftAlternative and IsRightAlternative )
( IsLeftAlternative, IsLeftPowerAlternative )
( HasLeftInverseProperty, IsLeftPowerAlternative )
( IsPowerAssociative, IsLeftPowerAlternative )
( IsRightAlternative, IsRightPowerAlternative )
( HasRightInverseProperty, IsRightPowerAlternative )
( IsPowerAssociative, IsRightPowerAlternative )
( IsLeftPowerAlternative, IsPowerAlternative )
( IsRightPowerAlternative, IsPowerAlternative )
( IsAssociative, IsLCCLoop and IsCommutative )
( IsExtraLoop, IsLCCLoop and IsMoufangLoop )
( IsAssociative, IsRCCLoop and IsCommutative )
( IsExtraLoop, IsRCCLoop and IsMoufangLoop )
( IsLCCLoop, IsCCLoop )
( IsRCCLoop, IsCCLoop )
( IsCCLoop, IsLCCLoop and IsRCCLoop )
( IsOsbornLoop, IsMoufangLoop )
( IsOsbornLoop, IsCCLoop )
( HasAutomorphicInverseProperty, IsLeftBruckLoop )
( IsLeftBolLoop, IsLeftBruckLoop )
( IsRightBruckLoop, IsLeftBruckLoop and IsCommutative )
( IsLeftBruckLoop, IsLeftBolLoop and HasAutomorphicInverseProperty )
( HasAutomorphicInverseProperty, IsRightBruckLoop )
( IsRightBolLoop, IsRightBruckLoop )
( IsLeftBruckLoop, IsRightBruckLoop and IsCommutative )
( IsRightBruckLoop, IsRightBolLoop and HasAutomorphicInverseProperty )
( IsCommutative, IsSteinerLoop )
( IsCLoop, IsSteinerLoop )
( IsLeftAutomorphicLoop, IsAutomorphicLoop )
( IsRightAutomorphicLoop, IsAutomorphicLoop )
( IsMiddleAutomorphicLoop, IsAutomorphicLoop )
( IsMiddleAutomorphicLoop, IsCommutative )
( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsCommutative )
( IsAutomorphicLoop, IsRightAutomorphicLoop and IsCommutative )
( IsLeftAutomorphicLoop, IsRightAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsRightAutomorphicLoop, IsLeftAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsFlexible, IsMiddleAutomorphicLoop )
( HasAntiautomorphicInverseProperty, IsFlexible and IsLeftAutomorphicLoop )
( HasAntiautomorphicInverseProperty, IsFlexible and IsRightAutomorphicLoop )
( IsMoufangLoop, IsAutomorphicLoop and IsLeftAlternative )
( IsMoufangLoop, IsAutomorphicLoop and IsRightAlternative )
( IsMoufangLoop, IsAutomorphicLoop and HasLeftInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasRightInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasWeakInverseProperty )
( IsLeftAutomorphicLoop, IsLeftBruckLoop )
( IsLeftAutomorphicLoop, IsLCCLoop )
( IsRightAutomorphicLoop, IsRightBruckLoop )
( IsRightAutomorphicLoop, IsRCCLoop )
( IsAutomorphicLoop, IsCommutative and IsMoufangLoop )

+

All filters of LOOPS are summarized below, using the GAP convention that the property on the left is implied by the property (properties) on the right.

( IsExtraLoop, IsAssociative and IsLoop )
( IsExtraLoop, IsCodeLoop )
( IsCCLoop, IsCodeLoop )
( HasTwosidedInverses, IsPowerAssociative and IsLoop )
( IsPowerAlternative, IsDiassociative )
( IsFlexible, IsDiassociative )
( HasAntiautomorphicInverseProperty, HasAutomorphicInverseProperty and IsCommutative )
( HasAutomorphicInverseProperty, HasAntiautomorphicInverseProperty and IsCommutative )
( HasLeftInverseProperty, HasInverseProperty )
( HasRightInverseProperty, HasInverseProperty )
( HasWeakInverseProperty, HasInverseProperty )
( HasAntiautomorphicInverseProperty, HasInverseProperty )
( HasTwosidedInverses, HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and IsCommutative )
( HasInverseProperty, HasRightInverseProperty and IsCommutative )
( HasInverseProperty, HasLeftInverseProperty and HasRightInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and HasWeakInverseProperty )
( HasInverseProperty, HasRightInverseProperty and HasWeakInverseProperty )
( HasInverseProperty, HasLeftInverseProperty and HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasRightInverseProperty and HasAntiautomorphicInverseProperty )
( HasInverseProperty, HasWeakInverseProperty and HasAntiautomorphicInverseProperty )
( HasTwosidedInverses, HasLeftInverseProperty )
( HasTwosidedInverses, HasRightInverseProperty )
( HasTwosidedInverses, IsFlexible and IsLoop )
( IsMoufangLoop, IsExtraLoop )
( IsCLoop, IsExtraLoop )
( IsExtraLoop, IsMoufangLoop and IsLeftNuclearSquareLoop )
( IsExtraLoop, IsMoufangLoop and IsMiddleNuclearSquareLoop )
( IsExtraLoop, IsMoufangLoop and IsRightNuclearSquareLoop )
( IsLeftBolLoop, IsMoufangLoop )
( IsRightBolLoop, IsMoufangLoop )
( IsDiassociative, IsMoufangLoop )
( IsMoufangLoop, IsLeftBolLoop and IsRightBolLoop )
( IsLCLoop, IsCLoop )
( IsRCLoop, IsCLoop )
( IsDiassociative, IsCLoop and IsFlexible)
( IsCLoop, IsLCLoop and IsRCLoop )
( IsRightBolLoop, IsLeftBolLoop and IsCommutative )
( IsLeftPowerAlternative, IsLeftBolLoop )
( IsLeftBolLoop, IsRightBolLoop and IsCommutative )
( IsRightPowerAlternative, IsRightBolLoop )
( IsLeftPowerAlternative, IsLCLoop )
( IsLeftNuclearSquareLoop, IsLCLoop )
( IsMiddleNuclearSquareLoop, IsLCLoop )
( IsRCLoop, IsLCLoop and IsCommutative )
( IsRightPowerAlternative, IsRCLoop )
( IsRightNuclearSquareLoop, IsRCLoop )
( IsMiddleNuclearSquareLoop, IsRCLoop )
( IsLCLoop, IsRCLoop and IsCommutative )
( IsRightNuclearSquareLoop, IsLeftNuclearSquareLoop and IsCommutative )
( IsLeftNuclearSquareLoop, IsRightNuclearSquareLoop and IsCommutative )
( IsLeftNuclearSquareLoop, IsNuclearSquareLoop )
( IsRightNuclearSquareLoop, IsNuclearSquareLoop )
( IsMiddleNuclearSquareLoop, IsNuclearSquareLoop )
( IsNuclearSquareLoop, IsLeftNuclearSquareLoop and IsRightNuclearSquareLoop
and IsMiddleNuclearSquareLoop )
( IsFlexible, IsCommutative )
( IsRightAlternative, IsLeftAlternative and IsCommutative )
( IsLeftAlternative, IsRightAlternative and IsCommutative )
( IsLeftAlternative, IsAlternative )
( IsRightAlternative, IsAlternative )
( IsAlternative, IsLeftAlternative and IsRightAlternative )
( IsLeftAlternative, IsLeftPowerAlternative )
( HasLeftInverseProperty, IsLeftPowerAlternative )
( IsPowerAssociative, IsLeftPowerAlternative )
( IsRightAlternative, IsRightPowerAlternative )
( HasRightInverseProperty, IsRightPowerAlternative )
( IsPowerAssociative, IsRightPowerAlternative )
( IsLeftPowerAlternative, IsPowerAlternative )
( IsRightPowerAlternative, IsPowerAlternative )
( IsAssociative, IsLCCLoop and IsCommutative )
( IsExtraLoop, IsLCCLoop and IsMoufangLoop )
( IsAssociative, IsRCCLoop and IsCommutative )
( IsExtraLoop, IsRCCLoop and IsMoufangLoop )
( IsLCCLoop, IsCCLoop )
( IsRCCLoop, IsCCLoop )
( IsCCLoop, IsLCCLoop and IsRCCLoop )
( IsOsbornLoop, IsMoufangLoop )
( IsOsbornLoop, IsCCLoop )
( HasAutomorphicInverseProperty, IsLeftBruckLoop )
( IsLeftBolLoop, IsLeftBruckLoop )
( IsRightBruckLoop, IsLeftBruckLoop and IsCommutative )
( IsLeftBruckLoop, IsLeftBolLoop and HasAutomorphicInverseProperty )
( HasAutomorphicInverseProperty, IsRightBruckLoop )
( IsRightBolLoop, IsRightBruckLoop )
( IsLeftBruckLoop, IsRightBruckLoop and IsCommutative )
( IsRightBruckLoop, IsRightBolLoop and HasAutomorphicInverseProperty )
( IsCommutative, IsSteinerLoop )
( IsCLoop, IsSteinerLoop )
( IsLeftAutomorphicLoop, IsAutomorphicLoop )
( IsRightAutomorphicLoop, IsAutomorphicLoop )
( IsMiddleAutomorphicLoop, IsAutomorphicLoop )
( IsLeftAutomorphicLoop, IsRightAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsRightAutomorphicLoop, IsLeftAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsFlexible, IsMiddleAutomorphicLoop )
( HasAntiautomorphicInverseProperty, IsFlexible and IsLeftAutomorphicLoop )
( HasAntiautomorphicInverseProperty, IsFlexible and IsRightAutomorphicLoop )
( IsMoufangLoop, IsAutomorphicLoop and IsLeftAlternative )
( IsMoufangLoop, IsAutomorphicLoop and IsRightAlternative )
( IsMoufangLoop, IsAutomorphicLoop and HasLeftInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasRightInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasWeakInverseProperty )
( IsMiddleAutomorphicLoop, IsCommutative )
( IsLeftAutomorphicLoop, IsLeftBruckLoop )
( IsLeftAutomorphicLoop, IsLCCLoop )
( IsRightAutomorphicLoop, IsRightBruckLoop )
( IsRightAutomorphicLoop, IsRCCLoop )
( IsAutomorphicLoop, IsCommutative and IsMoufangLoop )
( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsMiddleAutomorphicLoop )
( IsAutomorphicLoop, IsRightAutomorphicLoop and IsMiddleAutomorphicLoop )
( IsAutomorphicLoop, IsAssociative )

diff --git a/doc/chapBib.txt b/doc/chapBib.txt index 30f8cdb..a740990 100644 --- a/doc/chapBib.txt +++ b/doc/chapBib.txt @@ -42,6 +42,9 @@ less than 64, Nova Science Publishers Inc., Commack, NY (1999), xviii+287 pages. + [Gre14] Greer, M., A class of loops categorically isomorphic to Bruck loops + of odd order, Comm. Algebra, 42, 8 (2014), 3682–3697. + [GKN14] Grishkov, A., Kinyon, M. and Nagy, G. P., Solvability of commutative automorphic loops, Proc. Amer. Math. Soc., 142, 9 (2014), 3029–3037. @@ -89,6 +92,10 @@ [SZ12] Slattery, M. and Zenisek, A., Moufang loops of order 243, Commentationes Mathematicae Universitatis Carolinae, 53, 3 (2012), 423–428. + [SV17] Stuhl, I. and Vojtěchovský, P., Involutory latin quandles, Bruck + loops and commutative automorphic loops of odd prime power order,  (2017), + ((preprint)). + [Voj06] Vojtěchovský, P., Toward the classification of Moufang loops of order 64, European J. Combin., 27, 3 (2006), 444–460. diff --git a/doc/chapBib_mj.html b/doc/chapBib_mj.html index c7aa44f..54165df 100644 --- a/doc/chapBib_mj.html +++ b/doc/chapBib_mj.html @@ -164,6 +164,18 @@

+

+

+[Gre14] Greer, M., + A class of loops categorically isomorphic to Bruck loops of + odd order, + Comm. Algebra, + 42 (8) + (2014), + 3682–3697. +

+ +

[GKN14] Grishkov, A., Kinyon, M. and Nagy, G. P., @@ -327,6 +339,17 @@

+

+

+[SV17] Stuhl, I. and Vojtěchovský, P., + Involutory latin quandles, Bruck loops and commutative automorphic + loops of odd prime power order, + + (2017)
+(preprint). +

+ +

[Voj06] Vojtěchovský, P., diff --git a/doc/chapInd.txt b/doc/chapInd.txt index 998843a..0849df7 100644 --- a/doc/chapInd.txt +++ b/doc/chapInd.txt @@ -11,7 +11,7 @@ alternative loop, left 7.4 alternative loop, right 7.4 antiautomorphic inverse property 7.2-5 - AreEqualDiscriminators 6.11-9 + AreEqualDiscriminators 6.11-11 AssociatedLeftBruckLoop 8.1-1 AssociatedRightBruckLoop 8.1-1 associator 2.5 @@ -23,7 +23,7 @@ automorphic loop, left 7.7 automorphic loop, middle 7.7 automorphic loop, right 7.7 - AutomorphicLoop 9.10-1 + AutomorphicLoop 9.11-1 AutomorphismGroup 6.11-5 Bol loop, left 3.3 Bol loop, left 7.4 @@ -39,7 +39,7 @@ Cayley table, canonical 4.3-1 CayleyTable 5.1-2 CayleyTableByPerms 4.6-1 - CCLoop 9.6-3 + CCLoop 9.7-3 center 2.3 Center 6.6-4 central series, lower 6.9-5 @@ -47,7 +47,7 @@ Chein loop 8.2-3 cocycle 4.8 code loop 7.8-1 - CodeLoop 9.4-1 + CodeLoop 9.5-1 commutant 2.3 Commutant 6.6-3 commutator 2.5 @@ -55,7 +55,7 @@ conjugacy closed loop 7.6 conjugacy closed loop, left 7.6 conjugacy closed loop, right 7.6 - ConjugacyClosedLoop 9.6-3 + ConjugacyClosedLoop 9.7-3 conjugation 6.5 coset 6.2-6 derived series 2.4 @@ -64,7 +64,7 @@ DerivedSubloop 6.10-2 diassociative quasigroup 7.1-4 DirectProduct 4.11-1 - Discriminator 6.11-8 + Discriminator 6.11-10 DisplayLibraryInfo 9.1-3 distributive quasigroup 7.3-6 distributive quasigroup, left 7.3-6 @@ -111,7 +111,7 @@ inner mapping group, middle 6.5 inner mapping group, right 2.2 InnerMappingGroup 6.5-3 - InterestingLoop 9.11-1 + InterestingLoop 9.12-1 IntoGroup 4.10-4 IntoLoop 4.10-3 IntoQuasigroup 4.10-1 @@ -169,8 +169,8 @@ IsNilpotent 6.9-1 IsNormal 6.7-1 IsNuclearSquareLoop 7.4-11 - IsomorphicCopyByNormalSubloop 6.11-7 - IsomorphicCopyByPerm 6.11-6 + IsomorphicCopyByNormalSubloop 6.11-9 + IsomorphicCopyByPerm 6.11-8 isomorphism 2.6 IsomorphismLoops 6.11-2 IsomorphismQuasigroups 6.11-1 @@ -206,16 +206,17 @@ IsSubquasigroup 6.2-3 IsTotallySymmetric 7.3-2 IsUnipotent 7.3-5 - ItpSmallLoop 9.12-1 + ItpSmallLoop 9.13-1 K loop, left 7.8-3 K loop, right 7.8-4 latin square 2.1 latin square 4.1 latin square, random 4.9 LC loop 7.4 - LCCLoop 9.6-2 + LCCLoop 9.7-2 LeftBolLoop 9.2-1 - LeftConjugacyClosedLoop 9.6-2 + LeftBruckLoop 9.3-1 + LeftConjugacyClosedLoop 9.7-2 LeftDivision 5.2-1 LeftDivision 5.2-1 LeftDivision 5.2-1 @@ -234,7 +235,7 @@ loop, LC 7.4 loop, Moufang 7.4 loop, Osborn 7.6-4 - loop, Paige 9.8 + loop, Paige 9.9 loop, RC 7.4 loop, Steiner 7.8-2 loop, alternative 7.4 @@ -259,7 +260,7 @@ loop, nilpotent 2.4 loop, nilpotent 4.9-2 loop, nuclear square 7.4 - loop, octonion 9.3-1 + loop, octonion 9.4-1 loop, of Bol-Moufang type 7.4 loop, power alternative 7.5 loop, power associative 5.1-5 @@ -271,7 +272,7 @@ loop, right conjugacy closed 7.6 loop, right nuclear square 7.4 loop, right power alternative 7.5 - loop, sedenion 9.11 + loop, sedenion 9.12 loop, simple 3.3 loop, simple 6.7-3 loop, solvable 2.4 @@ -286,6 +287,7 @@ LoopByRightFolder 4.7-1 LoopByRightSection 4.6-3 LoopFromFile 4.5-1 + LoopIsomorph 6.11-7 LoopMG2 8.2-3 LoopsUpToIsomorphism 6.11-4 LoopsUpToIsotopism 6.12-2 @@ -299,7 +301,7 @@ modification, cyclic 8.2-1 modification, dihedral 8.2-2 Moufang loop 7.4 - MoufangLoop 9.3-1 + MoufangLoop 9.4-1 multiplication group 2.2 multiplication group, left 2.2 multiplication group, relative 6.4-2 @@ -315,7 +317,7 @@ NilpotencyClassOfLoop 6.9-2 nilpotent loop 2.4 nilpotent loop, strongly 6.9-3 - NilpotentLoop 9.9-1 + NilpotentLoop 9.10-1 normal closure 6.7-2 normal subloop 6.7-1 NormalClosure 6.7-2 @@ -332,7 +334,7 @@ nucleus, right 2.3 NucleusOfLoop 6.6-2 NucleusOfQuasigroup 6.6-2 - octonion loop 9.3-1 + octonion loop 9.4-1 One 5.1-3 OneLoopTableInGroup 8.4-3 OneLoopWithMltGroup 8.4-6 @@ -342,8 +344,8 @@ OppositeLoop 4.12-1 OppositeQuasigroup 4.12-1 Osborn loop 7.6-4 - Paige loop 9.8 - PaigeLoop 9.8-1 + Paige loop 9.9 + PaigeLoop 9.9-1 Parent 6.1-1 PosInParent 6.1-3 Position 6.1-2 @@ -373,18 +375,20 @@ QuasigroupByRightFolder 4.7-1 QuasigroupByRightSection 4.6-3 QuasigroupFromFile 4.5-1 + QuasigroupIsomorph 6.11-6 QuasigroupsUpToIsomorphism 6.11-3 RandomLoop 4.9-1 RandomNilpotentLoop 4.9-2 RandomQuasigroup 4.9-1 RC loop 7.4 - RCCLoop 9.6-1 + RCCLoop 9.7-1 RelativeLeftMultiplicationGroup 6.4-2 RelativeMultiplicationGroup 6.4-2 RelativeRightMultiplicationGroup 6.4-2 RightBolLoop 9.2-2 RightBolLoopByExactGroupFactorization 8.1-3 - RightConjugacyClosedLoop 9.6-1 + RightBruckLoop 9.3-2 + RightConjugacyClosedLoop 9.7-1 RightCosets 6.2-6 RightDivision 5.2-1 RightDivision 5.2-1 @@ -400,7 +404,7 @@ RightTransversal 6.2-7 section, left 2.2 section, right 2.2 - sedenion loop 9.11 + sedenion loop 9.12 semisymmetric quasigroup 7.3-1 SetLoopElmName 3.4-1 SetQuasigroupElmName 3.4-1 @@ -408,12 +412,12 @@ simple loop 6.7-3 Size 5.1-4 SmallGeneratingSet 5.5-3 - SmallLoop 9.7-1 + SmallLoop 9.8-1 solvability class 2.4 solvable loop 2.4 Steiner loop 7.8-2 Steiner quasigroup 7.3-4 - SteinerLoop 9.5-1 + SteinerLoop 9.6-1 strongly nilpotent loop 6.9-3 subloop 2.3 Subloop 6.2-2 diff --git a/doc/chapInd_mj.html b/doc/chapInd_mj.html index 3c09f07..93fb458 100644 --- a/doc/chapInd_mj.html +++ b/doc/chapInd_mj.html @@ -37,7 +37,7 @@ alternative loop 7.4
alternative loop, left 7.4
alternative loop, right 7.4
antiautomorphic inverse property 7.2-5
-AreEqualDiscriminators 6.11-9
+AreEqualDiscriminators 6.11-11
AssociatedLeftBruckLoop 8.1-1
AssociatedRightBruckLoop 8.1-1
associator 2.5
@@ -49,7 +49,7 @@ automorphic loop 7.7
automorphic loop, left 7.7
automorphic loop, middle 7.7
automorphic loop, right 7.7
-AutomorphicLoop 9.10-1
+AutomorphicLoop 9.11-1
AutomorphismGroup 6.11-5
Bol loop, left 3.3
Bol loop, left 7.4
@@ -65,7 +65,7 @@ Cayley table 4.1
Cayley table, canonical 4.3-1
CayleyTable 5.1-2
CayleyTableByPerms 4.6-1
-CCLoop 9.6-3
+CCLoop 9.7-3
center 2.3
Center 6.6-4
central series, lower 6.9-5
@@ -73,7 +73,7 @@ central series, upper 2.4
Chein loop 8.2-3
cocycle 4.8
code loop 7.8-1
-CodeLoop 9.4-1
+CodeLoop 9.5-1
commutant 2.3
Commutant 6.6-3
commutator 2.5
@@ -81,7 +81,7 @@ commutator 2.5
conjugacy closed loop 7.6
conjugacy closed loop, left 7.6
conjugacy closed loop, right 7.6
-ConjugacyClosedLoop 9.6-3
+ConjugacyClosedLoop 9.7-3
conjugation 6.5
coset 6.2-6
derived series 2.4
@@ -90,7 +90,7 @@ derived subloop 2.4
DerivedSubloop 6.10-2
diassociative quasigroup 7.1-4
DirectProduct 4.11-1
-Discriminator 6.11-8
+Discriminator 6.11-10
DisplayLibraryInfo 9.1-3
distributive quasigroup 7.3-6
distributive quasigroup, left 7.3-6
@@ -137,7 +137,7 @@ inner mapping group, left 2.2
6.5
inner mapping group, right 2.2
InnerMappingGroup 6.5-3
-InterestingLoop 9.11-1
+InterestingLoop 9.12-1
IntoGroup 4.10-4
IntoLoop 4.10-3
IntoQuasigroup 4.10-1
@@ -195,8 +195,8 @@ IsLoopElement 3.1
IsNilpotent 6.9-1
IsNormal 6.7-1
IsNuclearSquareLoop 7.4-11
-IsomorphicCopyByNormalSubloop 6.11-7
-IsomorphicCopyByPerm 6.11-6
+IsomorphicCopyByNormalSubloop 6.11-9
+IsomorphicCopyByPerm 6.11-8
isomorphism 2.6
IsomorphismLoops 6.11-2
IsomorphismQuasigroups 6.11-1
@@ -232,16 +232,17 @@ IsQuasigroupElement 3.1
IsSubquasigroup 6.2-3
IsTotallySymmetric 7.3-2
IsUnipotent 7.3-5
-ItpSmallLoop 9.12-1
+ItpSmallLoop 9.13-1
K loop, left 7.8-3
K loop, right 7.8-4
latin square 2.1
latin square 4.1
latin square, random 4.9
LC loop 7.4
-LCCLoop 9.6-2
+LCCLoop 9.7-2
LeftBolLoop 9.2-1
-LeftConjugacyClosedLoop 9.6-2
+LeftBruckLoop 9.3-1
+LeftConjugacyClosedLoop 9.7-2
LeftDivision 5.2-1
LeftDivision 5.2-1
LeftDivision 5.2-1
@@ -260,7 +261,7 @@ loop, Chein 8.2-3
loop, LC 7.4
loop, Moufang 7.4
loop, Osborn 7.6-4
-loop, Paige 9.8
+loop, Paige 9.9
loop, RC 7.4
loop, Steiner 7.8-2
loop, alternative 7.4
@@ -285,7 +286,7 @@ loop, middle nuclear square 7.42.4
loop, nilpotent 4.9-2
loop, nuclear square 7.4
-loop, octonion 9.3-1
+loop, octonion 9.4-1
loop, of Bol-Moufang type 7.4
loop, power alternative 7.5
loop, power associative 5.1-5
@@ -297,7 +298,7 @@ loop, right automorphic 7.7
loop, right conjugacy closed 7.6
loop, right nuclear square 7.4
loop, right power alternative 7.5
-loop, sedenion 9.11
+loop, sedenion 9.12
loop, simple 3.3
loop, simple 6.7-3
loop, solvable 2.4
@@ -312,6 +313,7 @@ loop table 4.1
LoopByRightFolder 4.7-1
LoopByRightSection 4.6-3
LoopFromFile 4.5-1
+LoopIsomorph 6.11-7
LoopMG2 8.2-3
LoopsUpToIsomorphism 6.11-4
LoopsUpToIsotopism 6.12-2
@@ -325,7 +327,7 @@ modification, Moufang 8.2
modification, cyclic 8.2-1
modification, dihedral 8.2-2
Moufang loop 7.4
-MoufangLoop 9.3-1
+MoufangLoop 9.4-1
multiplication group 2.2
multiplication group, left 2.2
multiplication group, relative 6.4-2
@@ -341,7 +343,7 @@ nilpotence class 2.4
NilpotencyClassOfLoop 6.9-2
nilpotent loop 2.4
nilpotent loop, strongly 6.9-3
-NilpotentLoop 9.9-1
+NilpotentLoop 9.10-1
normal closure 6.7-2
normal subloop 6.7-1
NormalClosure 6.7-2
@@ -358,7 +360,7 @@ nucleus, middle 2.3
nucleus, right 2.3
NucleusOfLoop 6.6-2
NucleusOfQuasigroup 6.6-2
-octonion loop 9.3-1
+octonion loop 9.4-1
One 5.1-3
OneLoopTableInGroup 8.4-3
OneLoopWithMltGroup 8.4-6
@@ -368,8 +370,8 @@ opposite quasigroup 4.12
OppositeLoop 4.12-1
OppositeQuasigroup 4.12-1
Osborn loop 7.6-4
-Paige loop 9.8
-PaigeLoop 9.8-1
+Paige loop 9.9
+PaigeLoop 9.9-1
Parent 6.1-1
PosInParent 6.1-3
Position 6.1-2
@@ -399,18 +401,20 @@ quasigroup table 4.1
QuasigroupByRightFolder 4.7-1
QuasigroupByRightSection 4.6-3
QuasigroupFromFile 4.5-1
+QuasigroupIsomorph 6.11-6
QuasigroupsUpToIsomorphism 6.11-3
RandomLoop 4.9-1
RandomNilpotentLoop 4.9-2
RandomQuasigroup 4.9-1
RC loop 7.4
-RCCLoop 9.6-1
+RCCLoop 9.7-1
RelativeLeftMultiplicationGroup 6.4-2
RelativeMultiplicationGroup 6.4-2
RelativeRightMultiplicationGroup 6.4-2
RightBolLoop 9.2-2
RightBolLoopByExactGroupFactorization 8.1-3
-RightConjugacyClosedLoop 9.6-1
+RightBruckLoop 9.3-2
+RightConjugacyClosedLoop 9.7-1
RightCosets 6.2-6
RightDivision 5.2-1
RightDivision 5.2-1
@@ -426,7 +430,7 @@ RC loop 7.4
RightTransversal 6.2-7
section, left 2.2
section, right 2.2
-sedenion loop 9.11
+sedenion loop 9.12
semisymmetric quasigroup 7.3-1
SetLoopElmName 3.4-1
SetQuasigroupElmName 3.4-1
@@ -434,12 +438,12 @@ simple loop 3.3
simple loop 6.7-3
Size 5.1-4
SmallGeneratingSet 5.5-3
-SmallLoop 9.7-1
+SmallLoop 9.8-1
solvability class 2.4
solvable loop 2.4
Steiner loop 7.8-2
Steiner quasigroup 7.3-4
-SteinerLoop 9.5-1
+SteinerLoop 9.6-1
strongly nilpotent loop 6.9-3
subloop 2.3
Subloop 6.2-2
diff --git a/doc/loops.bbl b/doc/loops.bbl deleted file mode 100644 index da2eb9c..0000000 --- a/doc/loops.bbl +++ /dev/null @@ -1,161 +0,0 @@ -\begin{thebibliography}{DBGV12} - -\bibitem[Art59]{Ar} -R.~Artzy. -\newblock On automorphic-inverse properties in loops. -\newblock {\em Proc. Amer. Math. Soc.}, 10:588{\textendash}591, 1959. - -\bibitem[Art15]{Artic} -K.~Artic. -\newblock {\em On conjugacy closed loops and conjugacy closed loop folders}. -\newblock PhD thesis, RWTH Aachen University, 2015. - -\bibitem[BP56]{BrPa} -R.~H. Bruck and L.~J. Paige. -\newblock Loops whose inner mappings are automorphisms. -\newblock {\em Ann. of Math. (2)}, 63:308{\textendash}323, 1956. - -\bibitem[Bru58]{Br} -R.~H. Bruck. -\newblock {\em A survey of binary systems}. -\newblock Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Heft - 20. Reihe: Gruppentheorie. Springer Verlag, Berlin, 1958. - -\bibitem[CD05]{CsDr} -P.~Cs{\"o}rg{\H o} and A.~Dr{\a'a}pal. -\newblock Left conjugacy closed loops of nilpotency class two. -\newblock {\em Results Math.}, 47(3-4):242{\textendash}265, 2005. - -\bibitem[CR99]{CoRo} -C.~J. Colbourn and A.~Rosa. -\newblock {\em Triple systems}. -\newblock Oxford Mathematical Monographs. The Clarendon Press Oxford University - Press, New York, 1999. - -\bibitem[DBGV12]{BaGrVo} -D.~A.~S. De~Barros, A.~Grishkov, and P.~Vojt{\v e}chovsk{\a'y}. -\newblock Commutative automorphic loops of order {$p^3$}. -\newblock {\em J. Algebra Appl.}, 11(5):1250100, 15, 2012. - -\bibitem[Dr{\a'a}03]{DrapalCD} -A.~Dr{\a'a}pal. -\newblock Cyclic and dihedral constructions of even order. -\newblock {\em Comment. Math. Univ. 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Goodaire, S.~May, and M.~Raman. -\newblock {\em The {M}oufang loops of order less than 64}. -\newblock Nova Science Publishers Inc., Commack, NY, 1999. - -\bibitem[JKNV11]{JoKiNaVo} -K.~W. Johnson, M.~K. Kinyon, G.~P. Nagy, and P.~Vojt{\v e}chovsk{\a'y}. -\newblock Searching for small simple automorphic loops. -\newblock {\em LMS J. Comput. Math.}, 14:200{\textendash}213, 2011. - -\bibitem[JKV12]{JeKiVo} -P.~Jedli{\v c}ka, M.~Kinyon, and P.~Vojt{\v e}chovsk{\a'y}. -\newblock Nilpotency in automorphic loops of prime power order. -\newblock {\em J. Algebra}, 350:64{\textendash}76, 2012. - -\bibitem[JM96]{JaMa} -M.~T. Jacobson and P.~Matthews. -\newblock Generating uniformly distributed random {L}atin squares. -\newblock {\em J. Combin. Des.}, 4(6):405{\textendash}437, 1996. - -\bibitem[KKP02]{KiKuPh} -M.~K. Kinyon, K.~Kunen, and J.~D. Phillips. -\newblock Every diassociative {$A$}-loop is {M}oufang. -\newblock {\em Proc. Amer. Math. Soc.}, 130(3):619{\textendash}624, 2002. - -\bibitem[KKPV16]{KiKuPhVo} -M.~K. Kinyon, K.~Kunen, J.~D. Phillips, and P.~Vojt{\v e}chovsk{\a'y}. -\newblock The structure of automorphic loops. -\newblock {\em Trans. Amer. Math. Soc.}, 368(12):8901{\textendash}8927, 2016. - -\bibitem[KNV15]{KiNaVo2015} -M.~K. Kinyon, G.~P. Nagy, and P.~Vojt{\v e}chovsk{\a'y}. -\newblock Bol loops and bruck loops of order $pq$. -\newblock 2015. -\newblock preprint. - -\bibitem[Kun00]{Kun} -K.~Kunen. -\newblock The structure of conjugacy closed loops. -\newblock {\em Trans. Amer. Math. Soc.}, 352(6):2889{\textendash}2911, 2000. - -\bibitem[Lie87]{Li} -M.~W. Liebeck. -\newblock The classification of finite simple {M}oufang loops. -\newblock {\em Math. Proc. Cambridge Philos. Soc.}, 102(1):33{\textendash}47, - 1987. - -\bibitem[Moo]{Mo} -G.~E. Moorhouse. -\newblock Bol loops of small order. -\newblock http://www.uwyo.edu/moorhouse/pub/bol/. - -\bibitem[NV03]{NaVo2003} -G.~P. Nagy and P.~Vojt{\v e}chovsk{\a'y}. -\newblock Octonions, simple {M}oufang loops and triality. -\newblock {\em Quasigroups Related Systems}, 10:65{\textendash}94, 2003. - -\bibitem[NV07]{NaVo2007} -G.~P. Nagy and P.~Vojt{\v e}chovsk{\a'y}. -\newblock The {M}oufang loops of order 64 and 81. -\newblock {\em J. Symbolic Comput.}, 42(9):871{\textendash}883, 2007. - -\bibitem[Pfl90]{Pf} -H.~O. Pflugfelder. -\newblock {\em Quasigroups and loops: introduction}, volume~7 of {\em Sigma - Series in Pure Mathematics}. -\newblock Heldermann Verlag, Berlin, 1990. - -\bibitem[PV05]{PhiVoj} -J.~D. Phillips and P.~Vojt{\v e}chovsk{\a'y}. -\newblock The varieties of loops of {B}ol-{M}oufang type. -\newblock {\em Algebra Universalis}, 54(3):259{\textendash}271, 2005. - -\bibitem[SZ12]{SlZe2011} -M.~Slattery and A.~Zenisek. -\newblock Moufang loops of order 243. -\newblock {\em Commentationes Mathematicae Universitatis Carolinae}, - 53(3):423{\textendash}428, 2012. - -\bibitem[Voj06]{Vo} -P.~Vojt{\v e}chovsk{\a'y}. -\newblock Toward the classification of {M}oufang loops of order 64. -\newblock {\em European J. Combin.}, 27(3):444{\textendash}460, 2006. - -\bibitem[Voj15]{VoQRS} -P.~Vojt{\v e}chovsk{\a'y}. -\newblock Three lectures on automorphic loops. -\newblock {\em Quasigroups Related Systems}, 23(1):129{\textendash}163, 2015. - -\bibitem[WJ75]{Wi} -R.~L. Wilson~Jr. -\newblock Quasidirect products of quasigroups. -\newblock {\em Comm. Algebra}, 3(9):835{\textendash}850, 1975. - -\end{thebibliography} diff --git a/doc/loops.bib b/doc/loops.bib index e9a72e1..1cd3b01 100644 --- a/doc/loops.bib +++ b/doc/loops.bib @@ -260,6 +260,27 @@ Publishers, 1999. MRNUMBER = {1689624 (2000a:20147)}, } +\bibitem{Greer} +Mark Greer. +\newblock{\it A class of loops categorically isomorphic to Bruck loops of odd order}, +Comm. Algebra {42} (2014), 3682--3697. + +@article {Greer, + AUTHOR = {Greer, Mark}, + TITLE = {A class of loops categorically isomorphic to {B}ruck loops of odd order}, + JOURNAL = {Comm. Algebra}, + FJOURNAL = {Communications in Algebra}, + VOLUME = {42}, + YEAR = {2014}, + NUMBER = {8}, + PAGES = {3682--3697}, + ISSN = {0092-7872}, + MRCLASS = {20N05}, + MRNUMBER = {3196069}, +MRREVIEWER = {Anil Kumar V.}, + URL = {https://doi.org/10.1080/00927872.2013.791304}, +} + \bibitem{GrKiNa} Alexander Grishkov, Michael Kinyon and G\'abor Nagy. \newblock {\it Solvability of commutative automorphic loops}, @@ -591,6 +612,19 @@ preprint. PAGES = {423--428}, } +\bibitem{StuhlVojtechovsky} +Izabella Stuhl and Petr Vojt\v{e}chovsk\'y. +\newblock {\it Involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order}, +preprint, 2017. + +@article {StuhlVojtechovsky, + AUTHOR = {Stuhl, Izabella and Vojt{\v{e}}chovsk{\'y}, Petr}, + TITLE = {Involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order}, + JOURNAL = {}, + YEAR = {2017}, + NOTE = {preprint}, +} + \bibitem{Vo} Petr Vojt\v{e}chovsk\'y. \newblock {\it Toward the classification of Moufang loops of order $64$}, diff --git a/doc/loops.blg b/doc/loops.blg deleted file mode 100644 index bf6477f..0000000 --- a/doc/loops.blg +++ /dev/null @@ -1,5 +0,0 @@ -This is BibTeX, Version 0.99dThe top-level auxiliary file: loops.aux -The style file: alpha.bst -Database file #1: loops_bib.xml.bib -Warning--empty journal in KiNaVo2015 -(There was 1 warning) diff --git a/doc/loops.brf b/doc/loops.brf deleted file mode 100644 index 4bff5b2..0000000 --- a/doc/loops.brf +++ /dev/null @@ -1,35 +0,0 @@ -\backcite {Br}{{8}{2}{chapter.2}} -\backcite {Pf}{{8}{2}{chapter.2}} -\backcite {JaMa}{{19}{4.9}{section.4.9}} -\backcite {Vo}{{35}{6.11.8}{subsection.6.11.8}} -\backcite {Ar}{{37}{7.2.4}{subsection.7.2.4}} -\backcite {Fe}{{39}{7.4}{section.7.4}} -\backcite {PhiVoj}{{39}{7.4}{section.7.4}} -\backcite {PhiVoj}{{39}{7.4}{section.7.4}} -\backcite {BrPa}{{43}{7.7}{section.7.7}} -\backcite {BrPa}{{43}{7.7}{section.7.7}} -\backcite {JoKiNaVo}{{43}{7.7}{section.7.7}} -\backcite {KiKuPh}{{43}{7.7}{section.7.7}} -\backcite {KiKuPhVo}{{43}{7.7}{section.7.7}} -\backcite {GrKiNa}{{43}{7.7}{section.7.7}} -\backcite {VoQRS}{{43}{7.7}{section.7.7}} -\backcite {JeKiVo}{{43}{7.7}{section.7.7}} -\backcite {BaGrVo}{{43}{7.7}{section.7.7}} -\backcite {VoQRS}{{43}{7.7}{section.7.7}} -\backcite {DrapalCD}{{46}{8.2}{section.8.2}} -\backcite {DrVo}{{46}{8.2}{section.8.2}} -\backcite {NaVo2003}{{46}{8.3}{section.8.3}} -\backcite {Mo}{{50}{9.2}{section.9.2}} -\backcite {KiNaVo2015}{{50}{9.2}{section.9.2}} -\backcite {Go}{{50}{9.3.1}{subsection.9.3.1}} -\backcite {NaVo2007}{{50}{9.3.1}{subsection.9.3.1}} -\backcite {SlZe2011}{{50}{9.3.1}{subsection.9.3.1}} -\backcite {NaVo2007}{{51}{9.4}{section.9.4}} -\backcite {CoRo}{{51}{9.5}{section.9.5}} -\backcite {Artic}{{51}{9.6}{section.9.6}} -\backcite {Kun}{{52}{9.6.2}{subsection.9.6.2}} -\backcite {CsDr}{{52}{9.6.2}{subsection.9.6.2}} -\backcite {Wi}{{52}{9.6.2}{subsection.9.6.2}} -\backcite {Kun}{{52}{9.6.2}{subsection.9.6.2}} -\backcite {Li}{{53}{9.8}{section.9.8}} -\backcite {DaVo}{{53}{9.9}{section.9.9}} diff --git a/doc/loops.idx b/doc/loops.idx deleted file mode 100644 index 510d27e..0000000 --- a/doc/loops.idx +++ /dev/null @@ -1,427 +0,0 @@ -\indexentry{groupoid|hyperpage}{8} -\indexentry{magma|hyperpage}{8} -\indexentry{neutral element|hyperpage}{8} -\indexentry{identity!element|hyperpage}{8} -\indexentry{inverse!two-sided|hyperpage}{8} -\indexentry{group|hyperpage}{8} -\indexentry{quasigroup|hyperpage}{8} -\indexentry{latin square|hyperpage}{8} -\indexentry{loop|hyperpage}{8} -\indexentry{translation!left|hyperpage}{8} -\indexentry{translation!right|hyperpage}{8} -\indexentry{division!left|hyperpage}{8} -\indexentry{division!right|hyperpage}{8} -\indexentry{section!left|hyperpage}{8} -\indexentry{section!right|hyperpage}{8} -\indexentry{multiplication group!left|hyperpage}{9} -\indexentry{multiplication group!right|hyperpage}{9} -\indexentry{multiplication group|hyperpage}{9} -\indexentry{inner mapping group!left|hyperpage}{9} -\indexentry{inner mapping group!right|hyperpage}{9} -\indexentry{inner mapping group|hyperpage}{9} -\indexentry{subquasigroup|hyperpage}{9} -\indexentry{subloop|hyperpage}{9} -\indexentry{nucleus!left|hyperpage}{9} -\indexentry{nucleus!middle|hyperpage}{9} -\indexentry{nucleus!right|hyperpage}{9} -\indexentry{nucleus|hyperpage}{9} -\indexentry{commutant|hyperpage}{9} -\indexentry{center|hyperpage}{9} -\indexentry{subloop!normal|hyperpage}{9} -\indexentry{nilpotence class|hyperpage}{9} -\indexentry{nilpotent loop|hyperpage}{9} -\indexentry{loop!nilpotent|hyperpage}{9} -\indexentry{central series!upper|hyperpage}{9} -\indexentry{derived subloop|hyperpage}{9} -\indexentry{solvability class|hyperpage}{9} -\indexentry{solvable loop|hyperpage}{9} -\indexentry{loop!solvable|hyperpage}{9} -\indexentry{derived series|hyperpage}{9} -\indexentry{commutator|hyperpage}{9} -\indexentry{associator|hyperpage}{9} -\indexentry{associator subloop|hyperpage}{9} -\indexentry{homomorphism|hyperpage}{9} -\indexentry{isomorphism|hyperpage}{9} -\indexentry{homotopism|hyperpage}{10} -\indexentry{isotopism|hyperpage}{10} -\indexentry{isotopism!principal|hyperpage}{10} -\indexentry{loop isotope!principal|hyperpage}{10} -\indexentry{IsQuasigroupElement|hyperpage}{11} -\indexentry{IsLoopElement|hyperpage}{11} -\indexentry{IsQuasigroup|hyperpage}{11} -\indexentry{IsLoop|hyperpage}{11} -\indexentry{Bol loop!left|hyperpage}{12} -\indexentry{loop!left Bol|hyperpage}{12} -\indexentry{simple loop|hyperpage}{12} -\indexentry{loop!simple|hyperpage}{12} -\indexentry{SetQuasigroupElmName@\texttt {SetQuasigroupElmName}|hyperpage}{13} -\indexentry{SetLoopElmName@\texttt {SetLoopElmName}|hyperpage}{13} -\indexentry{Cayley table|hyperpage}{14} -\indexentry{multiplication table|hyperpage}{14} -\indexentry{quasigroup table|hyperpage}{14} -\indexentry{latin square|hyperpage}{14} -\indexentry{loop table|hyperpage}{14} -\indexentry{IsQuasigroupTable@\texttt {IsQuasigroupTable}|hyperpage}{14} -\indexentry{IsQuasigroupCayleyTable@\texttt {IsQuasigroupCayleyTable}|hyperpage}{14} -\indexentry{IsLoopTable@\texttt {IsLoopTable}|hyperpage}{14} -\indexentry{IsLoopCayleyTable@\texttt {IsLoopCayleyTable}|hyperpage}{14} -\indexentry{CanonicalCayleyTable@\texttt {CanonicalCayleyTable}|hyperpage}{15} -\indexentry{Cayley table!canonical|hyperpage}{15} -\indexentry{CanonicalCopy@\texttt {CanonicalCopy}|hyperpage}{15} -\indexentry{NormalizedQuasigroupTable@\texttt {NormalizedQuasigroupTable}|hyperpage}{15} -\indexentry{QuasigroupByCayleyTable@\texttt {QuasigroupByCayleyTable}|hyperpage}{15} -\indexentry{LoopByCayleyTable@\texttt {LoopByCayleyTable}|hyperpage}{15} -\indexentry{QuasigroupFromFile@\texttt {QuasigroupFromFile}|hyperpage}{17} -\indexentry{LoopFromFile@\texttt {LoopFromFile}|hyperpage}{17} -\indexentry{CayleyTableByPerms@\texttt {CayleyTableByPerms}|hyperpage}{17} -\indexentry{QuasigroupByLeftSection@\texttt {QuasigroupByLeftSection}|hyperpage}{17} -\indexentry{LoopByLeftSection@\texttt {LoopByLeftSection}|hyperpage}{17} -\indexentry{QuasigroupByRightSection@\texttt {QuasigroupByRightSection}|hyperpage}{17} -\indexentry{LoopByRightSection@\texttt {LoopByRightSection}|hyperpage}{17} -\indexentry{folder!quasigroup|hyperpage}{18} -\indexentry{QuasigroupByRightFolder@\texttt {QuasigroupByRightFolder}|hyperpage}{18} -\indexentry{LoopByRightFolder@\texttt {LoopByRightFolder}|hyperpage}{18} -\indexentry{extension|hyperpage}{18} -\indexentry{extension!nuclear|hyperpage}{18} -\indexentry{cocycle|hyperpage}{18} -\indexentry{NuclearExtension@\texttt {NuclearExtension}|hyperpage}{18} -\indexentry{LoopByExtension@\texttt {LoopByExtension}|hyperpage}{18} -\indexentry{latin square!random|hyperpage}{19} -\indexentry{RandomQuasigroup@\texttt {RandomQuasigroup}|hyperpage}{19} -\indexentry{RandomLoop@\texttt {RandomLoop}|hyperpage}{19} -\indexentry{RandomNilpotentLoop@\texttt {RandomNilpotentLoop}|hyperpage}{19} -\indexentry{loop!nilpotent|hyperpage}{19} -\indexentry{IntoQuasigroup@\texttt {IntoQuasigroup}|hyperpage}{20} -\indexentry{PrincipalLoopIsotope@\texttt {PrincipalLoopIsotope}|hyperpage}{20} -\indexentry{IntoLoop@\texttt {IntoLoop}|hyperpage}{20} -\indexentry{IntoGroup@\texttt {IntoGroup}|hyperpage}{20} -\indexentry{DirectProduct@\texttt {DirectProduct}|hyperpage}{21} -\indexentry{opposite quasigroup|hyperpage}{21} -\indexentry{quasigroup!opposite|hyperpage}{21} -\indexentry{Opposite@\texttt {Opposite}|hyperpage}{21} -\indexentry{OppositeQuasigroup@\texttt {OppositeQuasigroup}|hyperpage}{21} -\indexentry{OppositeLoop@\texttt {OppositeLoop}|hyperpage}{21} -\indexentry{Elements@\texttt {Elements}|hyperpage}{22} -\indexentry{CayleyTable@\texttt {CayleyTable}|hyperpage}{22} -\indexentry{One@\texttt {One}|hyperpage}{22} -\indexentry{Size@\texttt {Size}|hyperpage}{22} -\indexentry{Exponent@\texttt {Exponent}|hyperpage}{23} -\indexentry{loop!power associative|hyperpage}{23} -\indexentry{power associative loop|hyperpage}{23} -\indexentry{exponent|hyperpage}{23} -\indexentry{LeftDivision@\texttt {LeftDivision}|hyperpage}{23} -\indexentry{RightDivision@\texttt {RightDivision}|hyperpage}{23} -\indexentry{LeftDivision@\texttt {LeftDivision}|hyperpage}{23} -\indexentry{LeftDivision@\texttt {LeftDivision}|hyperpage}{23} -\indexentry{RightDivision@\texttt {RightDivision}|hyperpage}{23} 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{Parent}|hyperpage}{26} -\indexentry{Position@\texttt {Position}|hyperpage}{26} -\indexentry{PosInParent@\texttt {PosInParent}|hyperpage}{27} -\indexentry{Subquasigroup@\texttt {Subquasigroup}|hyperpage}{27} -\indexentry{Subloop@\texttt {Subloop}|hyperpage}{27} -\indexentry{IsSubquasigroup@\texttt {IsSubquasigroup}|hyperpage}{27} -\indexentry{IsSubloop@\texttt {IsSubloop}|hyperpage}{27} -\indexentry{AllSubquasigroups@\texttt {AllSubquasigroups}|hyperpage}{27} -\indexentry{AllSubloops@\texttt {AllSubloops}|hyperpage}{28} -\indexentry{RightCosets@\texttt {RightCosets}|hyperpage}{28} -\indexentry{coset|hyperpage}{28} -\indexentry{RightTransversal@\texttt {RightTransversal}|hyperpage}{28} -\indexentry{transversal|hyperpage}{28} -\indexentry{LeftTranslation@\texttt {LeftTranslation}|hyperpage}{28} -\indexentry{RightTranslation@\texttt {RightTranslation}|hyperpage}{28} -\indexentry{LeftSection@\texttt {LeftSection}|hyperpage}{28} -\indexentry{RightSection@\texttt 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group!middle|hyperpage}{30} -\indexentry{LeftInnerMapping@\texttt {LeftInnerMapping}|hyperpage}{30} -\indexentry{RightInnerMapping@\texttt {RightInnerMapping}|hyperpage}{30} -\indexentry{MiddleInnerMapping@\texttt {MiddleInnerMapping}|hyperpage}{30} -\indexentry{LeftInnerMappingGroup@\texttt {LeftInnerMappingGroup}|hyperpage}{30} -\indexentry{RightInnerMappingGroup@\texttt {RightInnerMappingGroup}|hyperpage}{30} -\indexentry{MiddleInnerMappingGroup@\texttt {MiddleInnerMappingGroup}|hyperpage}{30} -\indexentry{InnerMappingGroup@\texttt {InnerMappingGroup}|hyperpage}{30} -\indexentry{LeftNucleus@\texttt {LeftNucleus}|hyperpage}{30} -\indexentry{MiddleNucleus@\texttt {MiddleNucleus}|hyperpage}{30} -\indexentry{RightNucleus@\texttt {RightNucleus}|hyperpage}{30} -\indexentry{Nuc@\texttt {Nuc}|hyperpage}{31} -\indexentry{NucleusOfQuasigroup@\texttt {NucleusOfQuasigroup}|hyperpage}{31} -\indexentry{NucleusOfLoop@\texttt {NucleusOfLoop}|hyperpage}{31} -\indexentry{Commutant@\texttt {Commutant}|hyperpage}{31} -\indexentry{Center@\texttt {Center}|hyperpage}{31} -\indexentry{AssociatorSubloop@\texttt {AssociatorSubloop}|hyperpage}{31} -\indexentry{IsNormal@\texttt {IsNormal}|hyperpage}{31} -\indexentry{subloop!normal|hyperpage}{31} -\indexentry{normal subloop|hyperpage}{31} -\indexentry{NormalClosure@\texttt {NormalClosure}|hyperpage}{31} -\indexentry{normal closure|hyperpage}{31} -\indexentry{IsSimple@\texttt {IsSimple}|hyperpage}{32} -\indexentry{simple loop|hyperpage}{32} -\indexentry{loop!simple|hyperpage}{32} -\indexentry{FactorLoop@\texttt {FactorLoop}|hyperpage}{32} -\indexentry{NaturalHomomorphismByNormalSubloop@\texttt {NaturalHomomorphismByNormalSubloop}|hyperpage}{32} -\indexentry{IsNilpotent@\texttt {IsNilpotent}|hyperpage}{32} -\indexentry{NilpotencyClassOfLoop@\texttt {NilpotencyClassOfLoop}|hyperpage}{32} -\indexentry{IsStronglyNilpotent@\texttt {IsStronglyNilpotent}|hyperpage}{32} -\indexentry{strongly nilpotent loop|hyperpage}{32} -\indexentry{nilpotent loop!strongly|hyperpage}{32} -\indexentry{loop!strongly nilpotent|hyperpage}{32} -\indexentry{UpperCentralSeries@\texttt {UpperCentralSeries}|hyperpage}{33} -\indexentry{LowerCentralSeries@\texttt {LowerCentralSeries}|hyperpage}{33} -\indexentry{central series!lower|hyperpage}{33} -\indexentry{IsSolvable@\texttt {IsSolvable}|hyperpage}{33} -\indexentry{DerivedSubloop@\texttt {DerivedSubloop}|hyperpage}{33} -\indexentry{DerivedLength@\texttt {DerivedLength}|hyperpage}{33} -\indexentry{FrattiniSubloop@\texttt {FrattiniSubloop}|hyperpage}{33} -\indexentry{Frattini subloop|hyperpage}{33} -\indexentry{FrattinifactorSize@\texttt {FrattinifactorSize}|hyperpage}{33} -\indexentry{IsomorphismQuasigroups@\texttt {IsomorphismQuasigroups}|hyperpage}{33} -\indexentry{IsomorphismLoops@\texttt {IsomorphismLoops}|hyperpage}{34} -\indexentry{QuasigroupsUpToIsomorphism@\texttt {QuasigroupsUpToIsomorphism}|hyperpage}{34} -\indexentry{LoopsUpToIsomorphism@\texttt {LoopsUpToIsomorphism}|hyperpage}{34} -\indexentry{AutomorphismGroup@\texttt {AutomorphismGroup}|hyperpage}{34} -\indexentry{IsomorphicCopyByPerm@\texttt {IsomorphicCopyByPerm}|hyperpage}{34} -\indexentry{IsomorphicCopyByNormalSubloop@\texttt {IsomorphicCopyByNormalSubloop}|hyperpage}{34} -\indexentry{Discriminator@\texttt {Discriminator}|hyperpage}{35} -\indexentry{AreEqualDiscriminators@\texttt {AreEqualDiscriminators}|hyperpage}{35} -\indexentry{IsotopismLoops@\texttt {IsotopismLoops}|hyperpage}{35} -\indexentry{LoopsUpToIsotopism@\texttt {LoopsUpToIsotopism}|hyperpage}{35} -\indexentry{IsAssociative@\texttt {IsAssociative}|hyperpage}{36} -\indexentry{IsCommutative@\texttt {IsCommutative}|hyperpage}{36} -\indexentry{IsPowerAssociative@\texttt {IsPowerAssociative}|hyperpage}{36} -\indexentry{quasigroup!power associative|hyperpage}{36} -\indexentry{power associative quasigroup|hyperpage}{36} -\indexentry{IsDiassociative@\texttt {IsDiassociative}|hyperpage}{36} -\indexentry{quasigroup!diassociative|hyperpage}{37} -\indexentry{diassociative quasigroup|hyperpage}{37} -\indexentry{inverse!left|hyperpage}{37} -\indexentry{inverse!right|hyperpage}{37} -\indexentry{HasLeftInverseProperty@\texttt {HasLeftInverseProperty}|hyperpage}{37} -\indexentry{HasRightInverseProperty@\texttt {HasRightInverseProperty}|hyperpage}{37} -\indexentry{HasInverseProperty@\texttt {HasInverseProperty}|hyperpage}{37} -\indexentry{inverse property!left|hyperpage}{37} -\indexentry{inverse property!right|hyperpage}{37} -\indexentry{inverse property|hyperpage}{37} -\indexentry{HasTwosidedInverses@\texttt {HasTwosidedInverses}|hyperpage}{37} -\indexentry{inverse!two-sided|hyperpage}{37} -\indexentry{HasWeakInverseProperty@\texttt {HasWeakInverseProperty}|hyperpage}{37} -\indexentry{inverse property!weak|hyperpage}{37} -\indexentry{HasAutomorphicInverseProperty@\texttt {HasAutomorphicInverseProperty}|hyperpage}{37} -\indexentry{automorphic inverse property|hyperpage}{37} -\indexentry{inverse property!automorphic|hyperpage}{37} -\indexentry{HasAntiautomorphicInverseProperty@\texttt {HasAntiautomorphicInverseProperty}|hyperpage}{37} -\indexentry{antiautomorphic inverse property|hyperpage}{37} -\indexentry{inverse property!antiautomorphic|hyperpage}{37} -\indexentry{IsSemisymmetric@\texttt {IsSemisymmetric}|hyperpage}{38} -\indexentry{semisymmetric quasigroup|hyperpage}{38} -\indexentry{quasigroup!semisymmetric|hyperpage}{38} -\indexentry{IsTotallySymmetric@\texttt {IsTotallySymmetric}|hyperpage}{38} -\indexentry{totally symmetric quasigroup|hyperpage}{38} -\indexentry{quasigroup!totally symmetric|hyperpage}{38} -\indexentry{IsIdempotent@\texttt {IsIdempotent}|hyperpage}{38} -\indexentry{idempotent quasigroup|hyperpage}{38} -\indexentry{quasigroup!idempotent|hyperpage}{38} -\indexentry{IsSteinerQuasigroup@\texttt {IsSteinerQuasigroup}|hyperpage}{38} -\indexentry{Steiner quasigroup|hyperpage}{38} -\indexentry{quasigroup!Steiner|hyperpage}{38} -\indexentry{unipotent quasigroup|hyperpage}{38} -\indexentry{quasigroup!unipotent|hyperpage}{38} -\indexentry{IsUnipotent@\texttt {IsUnipotent}|hyperpage}{38} -\indexentry{IsLeftDistributive@\texttt {IsLeftDistributive}|hyperpage}{38} -\indexentry{IsRightDistributive@\texttt {IsRightDistributive}|hyperpage}{38} -\indexentry{IsDistributive@\texttt {IsDistributive}|hyperpage}{38} -\indexentry{quasigroup!left distributive|hyperpage}{38} -\indexentry{distributive quasigroup!left|hyperpage}{38} -\indexentry{quasigroup!right distributive|hyperpage}{38} -\indexentry{distributive quasigroup!right|hyperpage}{38} -\indexentry{quasigroup!distributive|hyperpage}{38} -\indexentry{distributive quasigroup|hyperpage}{38} -\indexentry{IsEntropic@\texttt {IsEntropic}|hyperpage}{39} -\indexentry{IsMedial@\texttt {IsMedial}|hyperpage}{39} -\indexentry{entropic quasigroup|hyperpage}{39} -\indexentry{quasigroup!entropic|hyperpage}{39} -\indexentry{medial quasigroup|hyperpage}{39} -\indexentry{quasigroup!medial|hyperpage}{39} -\indexentry{loop!of Bol-Moufang type|hyperpage}{39} -\indexentry{identity!of Bol-Moufang type|hyperpage}{39} -\indexentry{alternative loop!left|hyperpage}{39} -\indexentry{loop!left alternative|hyperpage}{39} -\indexentry{alternative loop!right|hyperpage}{39} -\indexentry{loop!right alternative|hyperpage}{39} -\indexentry{nuclear square loop!left|hyperpage}{39} -\indexentry{loop!left nuclear square|hyperpage}{39} -\indexentry{nuclear square loop!middle|hyperpage}{39} -\indexentry{loop!middle nuclear square|hyperpage}{39} -\indexentry{nuclear square loop!right|hyperpage}{39} -\indexentry{loop!right nuclear square|hyperpage}{39} -\indexentry{flexible loop|hyperpage}{39} -\indexentry{loop!flexible|hyperpage}{39} -\indexentry{Bol loop!left|hyperpage}{39} -\indexentry{loop!left Bol|hyperpage}{39} -\indexentry{Bol loop!right|hyperpage}{39} -\indexentry{loop!right Bol|hyperpage}{39} -\indexentry{LC loop|hyperpage}{39} -\indexentry{loop!LC|hyperpage}{39} -\indexentry{RC loop|hyperpage}{39} -\indexentry{loop!RC|hyperpage}{39} -\indexentry{Moufang loop|hyperpage}{39} -\indexentry{loop!Moufang|hyperpage}{39} -\indexentry{C loop|hyperpage}{39} -\indexentry{loop!C|hyperpage}{39} -\indexentry{extra loop|hyperpage}{39} -\indexentry{loop!extra|hyperpage}{39} -\indexentry{alternative loop|hyperpage}{39} -\indexentry{loop!alternative|hyperpage}{39} -\indexentry{nuclear square loop|hyperpage}{39} -\indexentry{loop!nuclear square|hyperpage}{39} -\indexentry{IsExtraLoop@\texttt {IsExtraLoop}|hyperpage}{40} -\indexentry{IsMoufangLoop@\texttt {IsMoufangLoop}|hyperpage}{40} -\indexentry{IsCLoop@\texttt {IsCLoop}|hyperpage}{40} -\indexentry{IsLeftBolLoop@\texttt {IsLeftBolLoop}|hyperpage}{40} -\indexentry{IsRightBolLoop@\texttt {IsRightBolLoop}|hyperpage}{40} -\indexentry{IsLCLoop@\texttt {IsLCLoop}|hyperpage}{40} -\indexentry{IsRCLoop@\texttt {IsRCLoop}|hyperpage}{40} -\indexentry{IsLeftNuclearSquareLoop@\texttt {IsLeftNuclearSquareLoop}|hyperpage}{40} -\indexentry{IsMiddleNuclearSquareLoop@\texttt {IsMiddleNuclearSquareLoop}|hyperpage}{40} -\indexentry{IsRightNuclearSquareLoop@\texttt {IsRightNuclearSquareLoop}|hyperpage}{40} -\indexentry{IsNuclearSquareLoop@\texttt {IsNuclearSquareLoop}|hyperpage}{41} -\indexentry{IsFlexible@\texttt {IsFlexible}|hyperpage}{41} -\indexentry{IsLeftAlternative@\texttt {IsLeftAlternative}|hyperpage}{41} -\indexentry{IsRightAlternative@\texttt {IsRightAlternative}|hyperpage}{41} -\indexentry{IsAlternative@\texttt {IsAlternative}|hyperpage}{41} -\indexentry{power alternative loop!left|hyperpage}{42} -\indexentry{loop!left power alternative|hyperpage}{42} -\indexentry{power alternative loop!right|hyperpage}{42} -\indexentry{loop!right power alternative|hyperpage}{42} -\indexentry{power alternative loop|hyperpage}{42} -\indexentry{loop!power alternative|hyperpage}{42} -\indexentry{IsLeftPowerAlternative@\texttt {IsLeftPowerAlternative}|hyperpage}{42} -\indexentry{IsRightPowerAlternative@\texttt {IsRightPowerAlternative}|hyperpage}{42} -\indexentry{IsPowerAlternative@\texttt {IsPowerAlternative}|hyperpage}{42} -\indexentry{conjugacy closed loop!left|hyperpage}{42} -\indexentry{loop!left conjugacy closed|hyperpage}{42} -\indexentry{conjugacy closed loop!right|hyperpage}{42} -\indexentry{loop!right conjugacy closed|hyperpage}{42} -\indexentry{conjugacy closed loop|hyperpage}{42} -\indexentry{loop!conjugacy closed|hyperpage}{42} -\indexentry{IsLCCLoop@\texttt {IsLCCLoop}|hyperpage}{42} -\indexentry{IsLeftConjugacyClosedLoop@\texttt {IsLeftConjugacyClosedLoop}|hyperpage}{42} -\indexentry{IsRCCLoop@\texttt {IsRCCLoop}|hyperpage}{42} -\indexentry{IsRightConjugacyClosedLoop@\texttt {IsRightConjugacyClosedLoop}|hyperpage}{42} -\indexentry{IsCCLoop@\texttt {IsCCLoop}|hyperpage}{42} -\indexentry{IsConjugacyClosedLoop@\texttt {IsConjugacyClosedLoop}|hyperpage}{42} -\indexentry{IsOsbornLoop@\texttt {IsOsbornLoop}|hyperpage}{42} -\indexentry{Osborn loop|hyperpage}{43} -\indexentry{loop!Osborn|hyperpage}{43} -\indexentry{automorphic loop!left|hyperpage}{43} -\indexentry{loop!left automorphic|hyperpage}{43} -\indexentry{automorphic loop!middle|hyperpage}{43} -\indexentry{loop!middle automorphic|hyperpage}{43} -\indexentry{automorphic loop!right|hyperpage}{43} -\indexentry{loop!right automorphic|hyperpage}{43} -\indexentry{automorphic loop|hyperpage}{43} -\indexentry{loop!automorphic|hyperpage}{43} -\indexentry{IsLeftAutomorphicLoop@\texttt {IsLeftAutomorphicLoop}|hyperpage}{43} -\indexentry{IsLeftALoop@\texttt {IsLeftALoop}|hyperpage}{43} -\indexentry{IsMiddleAutomorphicLoop@\texttt {IsMiddleAutomorphicLoop}|hyperpage}{43} -\indexentry{IsMiddleALoop@\texttt {IsMiddleALoop}|hyperpage}{43} -\indexentry{IsRightAutomorphicLoop@\texttt {IsRightAutomorphicLoop}|hyperpage}{44} -\indexentry{IsRightALoop@\texttt {IsRightALoop}|hyperpage}{44} -\indexentry{IsAutomorphicLoop@\texttt {IsAutomorphicLoop}|hyperpage}{44} -\indexentry{IsALoop@\texttt {IsALoop}|hyperpage}{44} -\indexentry{IsCodeLoop@\texttt {IsCodeLoop}|hyperpage}{44} -\indexentry{code loop|hyperpage}{44} -\indexentry{loop!code|hyperpage}{44} -\indexentry{IsSteinerLoop@\texttt {IsSteinerLoop}|hyperpage}{44} -\indexentry{Steiner loop|hyperpage}{44} -\indexentry{loop!Steiner|hyperpage}{44} -\indexentry{IsLeftBruckLoop@\texttt {IsLeftBruckLoop}|hyperpage}{44} -\indexentry{IsLeftKLoop@\texttt {IsLeftKLoop}|hyperpage}{44} -\indexentry{Bruck loop!left|hyperpage}{44} -\indexentry{loop!left Bruck|hyperpage}{44} -\indexentry{K loop!left|hyperpage}{44} -\indexentry{loop!left K|hyperpage}{44} -\indexentry{IsRightBruckLoop@\texttt {IsRightBruckLoop}|hyperpage}{44} -\indexentry{IsRightKLoop@\texttt {IsRightKLoop}|hyperpage}{44} -\indexentry{Bruck loop!right|hyperpage}{44} -\indexentry{loop!right Bruck|hyperpage}{44} -\indexentry{K loop!right|hyperpage}{44} -\indexentry{loop!right K|hyperpage}{44} -\indexentry{AssociatedLeftBruckLoop@\texttt {AssociatedLeftBruckLoop}|hyperpage}{45} -\indexentry{AssociatedRightBruckLoop@\texttt {AssociatedRightBruckLoop}|hyperpage}{45} -\indexentry{loop!left Bol|hyperpage}{45} -\indexentry{Bol loop!left|hyperpage}{45} -\indexentry{Bruck loop!associated left|hyperpage}{45} -\indexentry{loop!associated left Bruck|hyperpage}{45} -\indexentry{IsExactGroupFactorization@\texttt {IsExactGroupFactorization}|hyperpage}{45} -\indexentry{exact group factorization|hyperpage}{45} -\indexentry{RightBolLoopByExactGroupFactorization@\texttt {Right}\discretionary {-}{}{}\texttt {Bol}\discretionary {-}{}{}\texttt {Loop}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Exact}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {Factorization}|hyperpage}{45} -\indexentry{modification!Moufang|hyperpage}{46} -\indexentry{LoopByCyclicModification@\texttt {LoopByCyclicModification}|hyperpage}{46} -\indexentry{modification!cyclic|hyperpage}{46} -\indexentry{LoopByDihedralModification@\texttt {LoopByDihedralModification}|hyperpage}{46} -\indexentry{modification!dihedral|hyperpage}{46} -\indexentry{LoopMG2@\texttt {LoopMG2}|hyperpage}{46} -\indexentry{Chein loop|hyperpage}{46} -\indexentry{loop!Chein|hyperpage}{46} -\indexentry{group with triality|hyperpage}{46} -\indexentry{TrialityPermGroup@\texttt {TrialityPermGroup}|hyperpage}{47} -\indexentry{TrialityPcGroup@\texttt {TrialityPcGroup}|hyperpage}{47} -\indexentry{AllLoopTablesInGroup@\texttt {AllLoopTablesInGroup}|hyperpage}{47} -\indexentry{AllProperLoopTablesInGroup@\texttt {AllProperLoopTablesInGroup}|hyperpage}{47} -\indexentry{OneLoopTableInGroup@\texttt {OneLoopTableInGroup}|hyperpage}{47} -\indexentry{OneProperLoopTableInGroup@\texttt {OneProperLoopTableInGroup}|hyperpage}{48} -\indexentry{AllLoopsWithMltGroup@\texttt {AllLoopsWithMltGroup}|hyperpage}{48} -\indexentry{OneLoopWithMltGroup@\texttt {OneLoopWithMltGroup}|hyperpage}{48} -\indexentry{LibraryLoop@\texttt {LibraryLoop}|hyperpage}{49} -\indexentry{MyLibraryLoop@\texttt {MyLibraryLoop}|hyperpage}{49} -\indexentry{DisplayLibraryInfo@\texttt {DisplayLibraryInfo}|hyperpage}{50} -\indexentry{LeftBolLoop@\texttt {LeftBolLoop}|hyperpage}{50} -\indexentry{RightBolLoop@\texttt {RightBolLoop}|hyperpage}{50} -\indexentry{MoufangLoop@\texttt {MoufangLoop}|hyperpage}{50} -\indexentry{octonion loop|hyperpage}{50} -\indexentry{loop!octonion|hyperpage}{50} -\indexentry{CodeLoop@\texttt {CodeLoop}|hyperpage}{51} -\indexentry{SteinerLoop@\texttt {SteinerLoop}|hyperpage}{51} -\indexentry{RCCLoop@\texttt {RCCLoop}|hyperpage}{52} -\indexentry{RightConjugacyClosedLoop@\texttt {RightConjugacyClosedLoop}|hyperpage}{52} -\indexentry{LCCLoop@\texttt {LCCLoop}|hyperpage}{52} -\indexentry{LeftConjugacyClosedLoop@\texttt {LeftConjugacyClosedLoop}|hyperpage}{52} -\indexentry{CCLoop@\texttt {CCLoop}|hyperpage}{52} -\indexentry{ConjugacyClosedLoop@\texttt {ConjugacyClosedLoop}|hyperpage}{52} -\indexentry{SmallLoop@\texttt {SmallLoop}|hyperpage}{53} -\indexentry{Paige loop|hyperpage}{53} -\indexentry{loop!Paige|hyperpage}{53} -\indexentry{PaigeLoop@\texttt {PaigeLoop}|hyperpage}{53} -\indexentry{NilpotentLoop@\texttt {NilpotentLoop}|hyperpage}{53} -\indexentry{AutomorphicLoop@\texttt {AutomorphicLoop}|hyperpage}{53} -\indexentry{sedenion loop|hyperpage}{54} -\indexentry{loop!sedenion|hyperpage}{54} -\indexentry{InterestingLoop@\texttt {InterestingLoop}|hyperpage}{54} -\indexentry{ItpSmallLoop@\texttt {ItpSmallLoop}|hyperpage}{54} diff --git a/doc/loops.ilg b/doc/loops.ilg deleted file mode 100644 index 382edad..0000000 --- a/doc/loops.ilg +++ /dev/null @@ -1,6 +0,0 @@ -This is makeindex, version 2.15 [MiKTeX 2.9 64-bit] (kpathsea + Thai support). -Scanning input file loops.idx....done (427 entries accepted, 0 rejected). -Sorting entries......done (4056 comparisons). -Generating output file loops.ind....done (485 lines written, 0 warnings). -Output written in loops.ind. -Transcript written in loops.ilg. diff --git a/doc/loops.ind b/doc/loops.ind deleted file mode 100644 index 6068fec..0000000 --- a/doc/loops.ind +++ /dev/null @@ -1,485 +0,0 @@ -\begin{theindex} - - \item \texttt {AllLoopsWithMltGroup}, \hyperpage{48} - \item \texttt {AllLoopTablesInGroup}, \hyperpage{47} - \item \texttt {AllProperLoopTablesInGroup}, \hyperpage{47} - \item \texttt {AllSubloops}, \hyperpage{28} - \item \texttt {AllSubquasigroups}, \hyperpage{27} - \item alternative loop, \hyperpage{39} - \subitem left, \hyperpage{39} - \subitem right, \hyperpage{39} - \item antiautomorphic inverse property, \hyperpage{37} - \item \texttt {AreEqualDiscriminators}, \hyperpage{35} - \item \texttt {AssociatedLeftBruckLoop}, \hyperpage{45} - \item \texttt {AssociatedRightBruckLoop}, \hyperpage{45} - \item \texttt {Associator}, \hyperpage{24} - \item associator, \hyperpage{9} - \item associator subloop, \hyperpage{9} - \item \texttt {AssociatorSubloop}, \hyperpage{31} - \item automorphic inverse property, \hyperpage{37} - \item automorphic loop, \hyperpage{43} - \subitem left, \hyperpage{43} - \subitem middle, \hyperpage{43} - \subitem right, \hyperpage{43} - \item \texttt {AutomorphicLoop}, \hyperpage{53} - \item \texttt {AutomorphismGroup}, \hyperpage{34} - - \indexspace - - \item Bol loop - \subitem left, \hyperpage{12}, \hyperpage{39}, \hyperpage{45} - \subitem right, \hyperpage{39} - \item Bruck loop - \subitem associated left, \hyperpage{45} - \subitem left, \hyperpage{44} - \subitem right, \hyperpage{44} - - \indexspace - - \item C loop, \hyperpage{39} - \item \texttt {CanonicalCayleyTable}, \hyperpage{15} - \item \texttt {CanonicalCopy}, \hyperpage{15} - \item Cayley table, \hyperpage{14} - \subitem canonical, \hyperpage{15} - \item \texttt {CayleyTable}, \hyperpage{22} - \item \texttt {CayleyTableByPerms}, \hyperpage{17} - \item \texttt {CCLoop}, \hyperpage{52} - \item \texttt {Center}, \hyperpage{31} - \item center, \hyperpage{9} - \item central series - \subitem lower, \hyperpage{33} - \subitem upper, \hyperpage{9} - \item Chein loop, \hyperpage{46} - \item cocycle, \hyperpage{18} - \item code loop, \hyperpage{44} - \item \texttt {CodeLoop}, \hyperpage{51} - \item \texttt {Commutant}, \hyperpage{31} - \item commutant, \hyperpage{9} - \item \texttt {Commutator}, \hyperpage{24} - \item commutator, \hyperpage{9} - \item conjugacy closed loop, \hyperpage{42} - \subitem left, \hyperpage{42} - \subitem right, \hyperpage{42} - \item \texttt {ConjugacyClosedLoop}, \hyperpage{52} - \item conjugation, \hyperpage{30} - \item coset, \hyperpage{28} - - \indexspace - - \item derived series, \hyperpage{9} - \item derived subloop, \hyperpage{9} - \item \texttt {DerivedLength}, \hyperpage{33} - \item \texttt {DerivedSubloop}, \hyperpage{33} - \item diassociative quasigroup, \hyperpage{37} - \item \texttt {DirectProduct}, \hyperpage{21} - \item \texttt {Discriminator}, \hyperpage{35} - \item \texttt {DisplayLibraryInfo}, \hyperpage{50} - \item distributive quasigroup, \hyperpage{38} - \subitem left, \hyperpage{38} - \subitem right, \hyperpage{38} - \item division - \subitem left, \hyperpage{8} - \subitem right, \hyperpage{8} - - \indexspace - - \item \texttt {Elements}, \hyperpage{22} - \item entropic quasigroup, \hyperpage{39} - \item exact group factorization, \hyperpage{45} - \item \texttt {Exponent}, \hyperpage{23} - \item exponent, \hyperpage{23} - \item extension, \hyperpage{18} - \subitem nuclear, \hyperpage{18} - \item extra loop, \hyperpage{39} - - \indexspace - - \item \texttt {FactorLoop}, \hyperpage{32} - \item flexible loop, \hyperpage{39} - \item folder - \subitem quasigroup, \hyperpage{18} - \item Frattini subloop, \hyperpage{33} - \item \texttt {FrattinifactorSize}, \hyperpage{33} - \item \texttt {FrattiniSubloop}, \hyperpage{33} - - \indexspace - - \item \texttt {GeneratorsOfLoop}, \hyperpage{24} - \item \texttt {GeneratorsOfQuasigroup}, \hyperpage{24} - \item \texttt {GeneratorsSmallest}, \hyperpage{25} - \item group, \hyperpage{8} - \item group with triality, \hyperpage{46} - \item groupoid, \hyperpage{8} - - \indexspace - - \item \texttt {HasAntiautomorphicInverseProperty}, \hyperpage{37} - \item \texttt {HasAutomorphicInverseProperty}, \hyperpage{37} - \item \texttt {HasInverseProperty}, \hyperpage{37} - \item \texttt {HasLeftInverseProperty}, \hyperpage{37} - \item \texttt {HasRightInverseProperty}, \hyperpage{37} - \item \texttt {HasTwosidedInverses}, \hyperpage{37} - \item \texttt {HasWeakInverseProperty}, \hyperpage{37} - \item homomorphism, \hyperpage{9} - \item homotopism, \hyperpage{10} - - \indexspace - - \item idempotent quasigroup, \hyperpage{38} - \item identity - \subitem element, \hyperpage{8} - \subitem of Bol-Moufang type, \hyperpage{39} - \item inner mapping - \subitem left, \hyperpage{29} - \subitem middle, \hyperpage{30} - \subitem right, \hyperpage{29} - \item inner mapping group, \hyperpage{9} - \subitem left, \hyperpage{9} - \subitem middle, \hyperpage{30} - \subitem right, \hyperpage{9} - \item \texttt {InnerMappingGroup}, \hyperpage{30} - \item \texttt {InterestingLoop}, \hyperpage{54} - \item \texttt {IntoGroup}, \hyperpage{20} - \item \texttt {IntoLoop}, \hyperpage{20} - \item \texttt {IntoQuasigroup}, \hyperpage{20} - \item \texttt {Inverse}, \hyperpage{24} - \item inverse, \hyperpage{24} - \subitem left, \hyperpage{24}, \hyperpage{37} - \subitem right, \hyperpage{24}, \hyperpage{37} - \subitem two-sided, \hyperpage{8}, \hyperpage{37} - \item inverse property, \hyperpage{37} - \subitem antiautomorphic, \hyperpage{37} - \subitem automorphic, \hyperpage{37} - \subitem left, \hyperpage{37} - \subitem right, \hyperpage{37} - \subitem weak, \hyperpage{37} - \item \texttt {IsALoop}, \hyperpage{44} - \item \texttt {IsAlternative}, \hyperpage{41} - \item \texttt {IsAssociative}, \hyperpage{36} - \item \texttt {IsAutomorphicLoop}, \hyperpage{44} - \item \texttt {IsCCLoop}, \hyperpage{42} - \item \texttt {IsCLoop}, \hyperpage{40} - \item \texttt {IsCodeLoop}, \hyperpage{44} - \item \texttt {IsCommutative}, \hyperpage{36} - \item \texttt {IsConjugacyClosedLoop}, \hyperpage{42} - \item \texttt {IsDiassociative}, \hyperpage{36} - \item \texttt {IsDistributive}, \hyperpage{38} - \item \texttt {IsEntropic}, \hyperpage{39} - \item \texttt {IsExactGroupFactorization}, \hyperpage{45} - \item \texttt {IsExtraLoop}, \hyperpage{40} - \item \texttt {IsFlexible}, \hyperpage{41} - \item \texttt {IsIdempotent}, \hyperpage{38} - \item \texttt {IsLCCLoop}, \hyperpage{42} - \item \texttt {IsLCLoop}, \hyperpage{40} - \item \texttt {IsLeftALoop}, \hyperpage{43} - \item \texttt {IsLeftAlternative}, \hyperpage{41} - \item \texttt {IsLeftAutomorphicLoop}, \hyperpage{43} - \item \texttt {IsLeftBolLoop}, \hyperpage{40} - \item \texttt {IsLeftBruckLoop}, \hyperpage{44} - \item \texttt {IsLeftConjugacyClosedLoop}, \hyperpage{42} - \item \texttt {IsLeftDistributive}, \hyperpage{38} - \item \texttt {IsLeftKLoop}, \hyperpage{44} - \item \texttt {IsLeftNuclearSquareLoop}, \hyperpage{40} - \item \texttt {IsLeftPowerAlternative}, \hyperpage{42} - \item IsLoop, \hyperpage{11} - \item \texttt {IsLoopCayleyTable}, \hyperpage{14} - \item IsLoopElement, \hyperpage{11} - \item \texttt {IsLoopTable}, \hyperpage{14} - \item \texttt {IsMedial}, \hyperpage{39} - \item \texttt {IsMiddleALoop}, \hyperpage{43} - \item \texttt {IsMiddleAutomorphicLoop}, \hyperpage{43} - \item \texttt {IsMiddleNuclearSquareLoop}, \hyperpage{40} - \item \texttt {IsMoufangLoop}, \hyperpage{40} - \item \texttt {IsNilpotent}, \hyperpage{32} - \item \texttt {IsNormal}, \hyperpage{31} - \item \texttt {IsNuclearSquareLoop}, \hyperpage{41} - \item \texttt {IsomorphicCopyByNormalSubloop}, \hyperpage{34} - \item \texttt {IsomorphicCopyByPerm}, \hyperpage{34} - \item isomorphism, \hyperpage{9} - \item \texttt {IsomorphismLoops}, \hyperpage{34} - \item \texttt {IsomorphismQuasigroups}, \hyperpage{33} - \item \texttt {IsOsbornLoop}, \hyperpage{42} - \item isotopism, \hyperpage{10} - \subitem principal, \hyperpage{10} - \item \texttt {IsotopismLoops}, \hyperpage{35} - \item \texttt {IsPowerAlternative}, \hyperpage{42} - \item \texttt {IsPowerAssociative}, \hyperpage{36} - \item IsQuasigroup, \hyperpage{11} - \item \texttt {IsQuasigroupCayleyTable}, \hyperpage{14} - \item IsQuasigroupElement, \hyperpage{11} - \item \texttt {IsQuasigroupTable}, \hyperpage{14} - \item \texttt {IsRCCLoop}, \hyperpage{42} - \item \texttt {IsRCLoop}, \hyperpage{40} - \item \texttt {IsRightALoop}, \hyperpage{44} - \item \texttt {IsRightAlternative}, \hyperpage{41} - \item \texttt {IsRightAutomorphicLoop}, \hyperpage{44} - \item \texttt {IsRightBolLoop}, \hyperpage{40} - \item \texttt {IsRightBruckLoop}, \hyperpage{44} - \item \texttt {IsRightConjugacyClosedLoop}, \hyperpage{42} - \item \texttt {IsRightDistributive}, \hyperpage{38} - \item \texttt {IsRightKLoop}, \hyperpage{44} - \item \texttt {IsRightNuclearSquareLoop}, \hyperpage{40} - \item \texttt {IsRightPowerAlternative}, \hyperpage{42} - \item \texttt {IsSemisymmetric}, \hyperpage{38} - \item \texttt {IsSimple}, \hyperpage{32} - \item \texttt {IsSolvable}, \hyperpage{33} - \item \texttt {IsSteinerLoop}, \hyperpage{44} - \item \texttt {IsSteinerQuasigroup}, \hyperpage{38} - \item \texttt {IsStronglyNilpotent}, \hyperpage{32} - \item \texttt {IsSubloop}, \hyperpage{27} - \item \texttt {IsSubquasigroup}, \hyperpage{27} - \item \texttt {IsTotallySymmetric}, \hyperpage{38} - \item \texttt {IsUnipotent}, \hyperpage{38} - \item \texttt {ItpSmallLoop}, \hyperpage{54} - - \indexspace - - \item K loop - \subitem left, \hyperpage{44} - \subitem right, \hyperpage{44} - - \indexspace - - \item latin square, \hyperpage{8}, \hyperpage{14} - \subitem random, \hyperpage{19} - \item LC loop, \hyperpage{39} - \item \texttt {LCCLoop}, \hyperpage{52} - \item \texttt {LeftBolLoop}, \hyperpage{50} - \item \texttt {LeftConjugacyClosedLoop}, \hyperpage{52} - \item \texttt {LeftDivision}, \hyperpage{23} - \item \texttt {LeftDivisionCayleyTable}, \hyperpage{23} - \item \texttt {LeftInnerMapping}, \hyperpage{30} - \item \texttt {LeftInnerMappingGroup}, \hyperpage{30} - \item \texttt {LeftInverse}, \hyperpage{24} - \item \texttt {LeftMultiplicationGroup}, \hyperpage{29} - \item \texttt {LeftNucleus}, \hyperpage{30} - \item \texttt {LeftSection}, \hyperpage{28} - \item \texttt {LeftTranslation}, \hyperpage{28} - \item \texttt {LibraryLoop}, \hyperpage{49} - \item loop, \hyperpage{8} - \subitem alternative, \hyperpage{39} - \subitem associated left Bruck, \hyperpage{45} - \subitem automorphic, \hyperpage{43} - \subitem C, \hyperpage{39} - \subitem Chein, \hyperpage{46} - \subitem code, \hyperpage{44} - \subitem conjugacy closed, \hyperpage{42} - \subitem extra, \hyperpage{39} - \subitem flexible, \hyperpage{39} - \subitem LC, \hyperpage{39} - \subitem left alternative, \hyperpage{39} - \subitem left automorphic, \hyperpage{43} - \subitem left Bol, \hyperpage{12}, \hyperpage{39}, \hyperpage{45} - \subitem left Bruck, \hyperpage{44} - \subitem left conjugacy closed, \hyperpage{42} - \subitem left K, \hyperpage{44} - \subitem left nuclear square, \hyperpage{39} - \subitem left power alternative, \hyperpage{42} - \subitem middle automorphic, \hyperpage{43} - \subitem middle nuclear square, \hyperpage{39} - \subitem Moufang, \hyperpage{39} - \subitem nilpotent, \hyperpage{9}, \hyperpage{19} - \subitem nuclear square, \hyperpage{39} - \subitem octonion, \hyperpage{50} - \subitem of Bol-Moufang type, \hyperpage{39} - \subitem Osborn, \hyperpage{43} - \subitem Paige, \hyperpage{53} - \subitem power alternative, \hyperpage{42} - \subitem power associative, \hyperpage{23} - \subitem RC, \hyperpage{39} - \subitem right alternative, \hyperpage{39} - \subitem right automorphic, \hyperpage{43} - \subitem right Bol, \hyperpage{39} - \subitem right Bruck, \hyperpage{44} - \subitem right conjugacy closed, \hyperpage{42} - \subitem right K, \hyperpage{44} - \subitem right nuclear square, \hyperpage{39} - \subitem right power alternative, \hyperpage{42} - \subitem sedenion, \hyperpage{54} - \subitem simple, \hyperpage{12}, \hyperpage{32} - \subitem solvable, \hyperpage{9} - \subitem Steiner, \hyperpage{44} - \subitem strongly nilpotent, \hyperpage{32} - \item loop isotope - \subitem principal, \hyperpage{10} - \item loop table, \hyperpage{14} - \item \texttt {LoopByCayleyTable}, \hyperpage{15} - \item \texttt {LoopByCyclicModification}, \hyperpage{46} - \item \texttt {LoopByDihedralModification}, \hyperpage{46} - \item \texttt {LoopByExtension}, \hyperpage{18} - \item \texttt {LoopByLeftSection}, \hyperpage{17} - \item \texttt {LoopByRightFolder}, \hyperpage{18} - \item \texttt {LoopByRightSection}, \hyperpage{17} - \item \texttt {LoopFromFile}, \hyperpage{17} - \item \texttt {LoopMG2}, \hyperpage{46} - \item \texttt {LoopsUpToIsomorphism}, \hyperpage{34} - \item \texttt {LoopsUpToIsotopism}, \hyperpage{35} - \item \texttt {LowerCentralSeries}, \hyperpage{33} - - \indexspace - - \item magma, \hyperpage{8} - \item medial quasigroup, \hyperpage{39} - \item \texttt {MiddleInnerMapping}, \hyperpage{30} - \item \texttt {MiddleInnerMappingGroup}, \hyperpage{30} - \item \texttt {MiddleNucleus}, \hyperpage{30} - \item modification - \subitem cyclic, \hyperpage{46} - \subitem dihedral, \hyperpage{46} - \subitem Moufang, \hyperpage{46} - \item Moufang loop, \hyperpage{39} - \item \texttt {MoufangLoop}, \hyperpage{50} - \item multiplication group, \hyperpage{9} - \subitem left, \hyperpage{9} - \subitem relative, \hyperpage{29} - \subitem relative left, \hyperpage{29} - \subitem relative right , \hyperpage{29} - \subitem right, \hyperpage{9} - \item multiplication table, \hyperpage{14} - \item \texttt {MultiplicationGroup}, \hyperpage{29} - \item \texttt {MyLibraryLoop}, \hyperpage{49} - - \indexspace - - \item \texttt {NaturalHomomorphismByNormalSubloop}, \hyperpage{32} - \item neutral element, \hyperpage{8} - \item nilpotence class, \hyperpage{9} - \item \texttt {NilpotencyClassOfLoop}, \hyperpage{32} - \item nilpotent loop, \hyperpage{9} - \subitem strongly, \hyperpage{32} - \item \texttt {NilpotentLoop}, \hyperpage{53} - \item normal closure, \hyperpage{31} - \item normal subloop, \hyperpage{31} - \item \texttt {NormalClosure}, \hyperpage{31} - \item \texttt {NormalizedQuasigroupTable}, \hyperpage{15} - \item \texttt {Nuc}, \hyperpage{31} - \item nuclear square loop, \hyperpage{39} - \subitem left, \hyperpage{39} - \subitem middle, \hyperpage{39} - \subitem right, \hyperpage{39} - \item \texttt {NuclearExtension}, \hyperpage{18} - \item nucleus, \hyperpage{9} - \subitem left, \hyperpage{9} - \subitem middle, \hyperpage{9} - \subitem right, \hyperpage{9} - \item \texttt {NucleusOfLoop}, \hyperpage{31} - \item \texttt {NucleusOfQuasigroup}, \hyperpage{31} - - \indexspace - - \item octonion loop, \hyperpage{50} - \item \texttt {One}, \hyperpage{22} - \item \texttt {OneLoopTableInGroup}, \hyperpage{47} - \item \texttt {OneLoopWithMltGroup}, \hyperpage{48} - \item \texttt {OneProperLoopTableInGroup}, \hyperpage{48} - \item \texttt {Opposite}, \hyperpage{21} - \item opposite quasigroup, \hyperpage{21} - \item \texttt {OppositeLoop}, \hyperpage{21} - \item \texttt {OppositeQuasigroup}, \hyperpage{21} - \item Osborn loop, \hyperpage{43} - - \indexspace - - \item Paige loop, \hyperpage{53} - \item \texttt {PaigeLoop}, \hyperpage{53} - \item \texttt {Parent}, \hyperpage{26} - \item \texttt {PosInParent}, \hyperpage{27} - \item \texttt {Position}, \hyperpage{26} - \item power alternative loop, \hyperpage{42} - \subitem left, \hyperpage{42} - \subitem right, \hyperpage{42} - \item power associative loop, \hyperpage{23} - \item power associative quasigroup, \hyperpage{36} - \item \texttt {PrincipalLoopIsotope}, \hyperpage{20} - - \indexspace - - \item quasigroup, \hyperpage{8} - \subitem diassociative, \hyperpage{37} - \subitem distributive, \hyperpage{38} - \subitem entropic, \hyperpage{39} - \subitem idempotent, \hyperpage{38} - \subitem left distributive, \hyperpage{38} - \subitem medial, \hyperpage{39} - \subitem opposite, \hyperpage{21} - \subitem power associative, \hyperpage{36} - \subitem right distributive, \hyperpage{38} - \subitem semisymmetric, \hyperpage{38} - \subitem Steiner, \hyperpage{38} - \subitem totally symmetric, \hyperpage{38} - \subitem unipotent, \hyperpage{38} - \item quasigroup table, \hyperpage{14} - \item \texttt {QuasigroupByCayleyTable}, \hyperpage{15} - \item \texttt {QuasigroupByLeftSection}, \hyperpage{17} - \item \texttt {QuasigroupByRightFolder}, \hyperpage{18} - \item \texttt {QuasigroupByRightSection}, \hyperpage{17} - \item \texttt {QuasigroupFromFile}, \hyperpage{17} - \item \texttt {QuasigroupsUpToIsomorphism}, \hyperpage{34} - - \indexspace - - \item \texttt {RandomLoop}, \hyperpage{19} - \item \texttt {RandomNilpotentLoop}, \hyperpage{19} - \item \texttt {RandomQuasigroup}, \hyperpage{19} - \item RC loop, \hyperpage{39} - \item \texttt {RCCLoop}, \hyperpage{52} - \item \texttt {RelativeLeftMultiplicationGroup}, \hyperpage{29} - \item \texttt {RelativeMultiplicationGroup}, \hyperpage{29} - \item \texttt {RelativeRightMultiplicationGroup}, \hyperpage{29} - \item \texttt {RightBolLoop}, \hyperpage{50} - \item \texttt {Right}\discretionary {-}{}{}\texttt {Bol}\discretionary {-}{}{}\texttt {Loop}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Exact}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {Factorization}, - \hyperpage{45} - \item \texttt {RightConjugacyClosedLoop}, \hyperpage{52} - \item \texttt {RightCosets}, \hyperpage{28} - \item \texttt {RightDivision}, \hyperpage{23} - \item \texttt {RightDivisionCayleyTable}, \hyperpage{23} - \item \texttt {RightInnerMapping}, \hyperpage{30} - \item \texttt {RightInnerMappingGroup}, \hyperpage{30} - \item \texttt {RightInverse}, \hyperpage{24} - \item \texttt {RightMultiplicationGroup}, \hyperpage{29} - \item \texttt {RightNucleus}, \hyperpage{30} - \item \texttt {RightSection}, \hyperpage{28} - \item \texttt {RightTranslation}, \hyperpage{28} - \item \texttt {RightTransversal}, \hyperpage{28} - - \indexspace - - \item section - \subitem left, \hyperpage{8} - \subitem right, \hyperpage{8} - \item sedenion loop, \hyperpage{54} - \item semisymmetric quasigroup, \hyperpage{38} - \item \texttt {SetLoopElmName}, \hyperpage{13} - \item \texttt {SetQuasigroupElmName}, \hyperpage{13} - \item simple loop, \hyperpage{12}, \hyperpage{32} - \item \texttt {Size}, \hyperpage{22} - \item \texttt {SmallGeneratingSet}, \hyperpage{25} - \item \texttt {SmallLoop}, \hyperpage{53} - \item solvability class, \hyperpage{9} - \item solvable loop, \hyperpage{9} - \item Steiner loop, \hyperpage{44} - \item Steiner quasigroup, \hyperpage{38} - \item \texttt {SteinerLoop}, \hyperpage{51} - \item strongly nilpotent loop, \hyperpage{32} - \item \texttt {Subloop}, \hyperpage{27} - \item subloop, \hyperpage{9} - \subitem normal, \hyperpage{9}, \hyperpage{31} - \item \texttt {Subquasigroup}, \hyperpage{27} - \item subquasigroup, \hyperpage{9} - - \indexspace - - \item totally symmetric quasigroup, \hyperpage{38} - \item translation - \subitem left, \hyperpage{8} - \subitem right, \hyperpage{8} - \item transversal, \hyperpage{28} - \item \texttt {TrialityPcGroup}, \hyperpage{47} - \item \texttt {TrialityPermGroup}, \hyperpage{47} - - \indexspace - - \item unipotent quasigroup, \hyperpage{38} - \item \texttt {UpperCentralSeries}, \hyperpage{33} - -\end{theindex} diff --git a/doc/loops.log b/doc/loops.log deleted file mode 100644 index c3e08fb..0000000 --- a/doc/loops.log +++ /dev/null @@ -1,856 +0,0 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (MiKTeX 2.9 64-bit) (preloaded format=latex 2014.9.18) 27 OCT 2016 11:38 -entering extended mode -**loops.tex -(C:\cygwin64\opt\gap4r7\pkg\loops\doc\loops.tex -LaTeX2e <2011/06/27> -Babel and hyphenation patterns for english, afrikaans, ancientgreek, ar -abic, 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in paragraph at lines 1001--1007 -[]\T1/ptm/b/n/10.95 Returns: \T1/ptm/m/n/10.95 If [] is a de-clared magma that - hap-pens to be a group, the cor-re-spond- - [] - -[20] [21] -Chapter 5. -[22 - -] -Underfull \hbox (badness 10000) in paragraph at lines 1165--1173 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 1175--1190 - - [] - -[23] [24] [25] -Chapter 6. - -Underfull \hbox (badness 10000) in paragraph at lines 1378--1383 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 1401--1407 - - [] - -[26 - -] -Underfull \hbox (badness 10000) in paragraph at lines 1446--1449 - - [] - -[27] -Underfull \hbox (badness 10000) in paragraph at lines 1554--1562 - - [] - -[28] [29] -Underfull \hbox (badness 1221) in paragraph at lines 1685--1685 -[][]\T1/ptm/b/n/12 LeftInnerMappingGroup, Right-In-nerMap-ping-Group, Mid-dleIn --nerMap-ping- - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 1708--1713 - - [] - -[30] [31] [32] -Underfull \hbox (badness 10000) in paragraph at lines 2068--2072 - - [] - -[33] -Underfull \hbox (badness 10000) in paragraph at lines 2139--2144 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 2150--2151 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 2173--2178 - - [] - -[34] [35] -Chapter 7. -[36 - -] -Underfull \hbox (badness 10000) in paragraph at lines 2419--2421 - - [] - -[37] [38] [39] [40] -Underfull \hbox (badness 10000) in paragraph at lines 2769--2774 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 2780--2782 - - [] - -[41] [42] [43] [44] -Chapter 8. -[45 - -] [46] -Underfull \hbox (badness 10000) in paragraph at lines 3224--3227 - - [] - -[47] [48] -Chapter 9. - -Underfull \hbox (badness 10000) in paragraph at lines 3361--3362 -[][]\T1/cmtt/m/n/10.95 LOOPS_my_library_data[2][k] \T1/ptm/m/n/10.95 is the num --ber of loops of or-der - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 3383--3386 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 3397--3402 - - [] - -[49 - -] [50] [51] -Underfull \hbox (badness 10000) in paragraph at lines 3588--3591 - - [] - -[52] [53] [54] -Appendix A. - -Underfull \hbox (badness 10000) in paragraph at lines 3788--3833 - - [] - -[55 - -] [56] -Appendix B. - -Underfull \hbox (badness 10000) in paragraph at lines 3842--3962 - - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 3842--3962 -\T1/cmtt/m/n/10.95 ( HasAntiautomorphicInverseProperty, HasAutomorphicInversePr -operty and - [] - - -Underfull \hbox (badness 10000) in paragraph at lines 3842--3962 -\T1/cmtt/m/n/10.95 ( HasAutomorphicInverseProperty, HasAntiautomorphicInversePr -operty and - [] - - -Overfull \hbox (21.33267pt too wide) in paragraph at lines 3842--3962 -\T1/cmtt/m/n/10.95 ( HasInverseProperty, HasLeftInverseProperty and HasAntiauto -morphicInverseProperty - [] - - -Overfull \hbox (26.99104pt too wide) in paragraph at lines 3842--3962 -\T1/cmtt/m/n/10.95 ( HasInverseProperty, 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input line 3986. - ) -Here is how much of TeX's memory you used: - 7134 strings out of 493922 - 107334 string characters out of 3147269 - 214990 words of memory out of 3000000 - 10330 multiletter control sequences out of 15000+200000 - 56657 words of font info for 68 fonts, out of 3000000 for 9000 - 841 hyphenation exceptions out of 8191 - 32i,7n,29p,918b,613s stack positions out of 5000i,500n,10000p,200000b,50000s - -Output written on loops.dvi (66 pages, 548296 bytes). diff --git a/doc/loops.out b/doc/loops.out deleted file mode 100644 index b2946b2..0000000 --- a/doc/loops.out +++ /dev/null @@ -1,83 +0,0 @@ -\BOOKMARK [0][-]{chapter.1}{Introduction}{}% 1 -\BOOKMARK [1][-]{section.1.1}{License}{chapter.1}% 2 -\BOOKMARK [1][-]{section.1.2}{Installation}{chapter.1}% 3 -\BOOKMARK [1][-]{section.1.3}{Documentation}{chapter.1}% 4 -\BOOKMARK [1][-]{section.1.4}{Test Files}{chapter.1}% 5 -\BOOKMARK [1][-]{section.1.5}{Memory Management}{chapter.1}% 6 -\BOOKMARK [1][-]{section.1.6}{Feedback}{chapter.1}% 7 -\BOOKMARK [1][-]{section.1.7}{Acknowledgment}{chapter.1}% 8 -\BOOKMARK [0][-]{chapter.2}{Mathematical Background}{}% 9 -\BOOKMARK [1][-]{section.2.1}{Quasigroups and Loops}{chapter.2}% 10 -\BOOKMARK [1][-]{section.2.2}{Translations}{chapter.2}% 11 -\BOOKMARK [1][-]{section.2.3}{Subquasigroups and Subloops}{chapter.2}% 12 -\BOOKMARK [1][-]{section.2.4}{Nilpotence and Solvability}{chapter.2}% 13 -\BOOKMARK [1][-]{section.2.5}{Associators and Commutators}{chapter.2}% 14 -\BOOKMARK [1][-]{section.2.6}{Homomorphism and Homotopisms}{chapter.2}% 15 -\BOOKMARK [0][-]{chapter.3}{How the Package Works}{}% 16 -\BOOKMARK [1][-]{section.3.1}{Representing Quasigroups}{chapter.3}% 17 -\BOOKMARK [1][-]{section.3.2}{Conversions between magmas, quasigroups, loops and groups}{chapter.3}% 18 -\BOOKMARK [1][-]{section.3.3}{Calculating with Quasigroups}{chapter.3}% 19 -\BOOKMARK [1][-]{section.3.4}{Naming, Viewing and Printing Quasigroups and their Elements}{chapter.3}% 20 -\BOOKMARK [0][-]{chapter.4}{Creating Quasigroups and Loops}{}% 21 -\BOOKMARK [1][-]{section.4.1}{About Cayley Tables}{chapter.4}% 22 -\BOOKMARK [1][-]{section.4.2}{Testing Cayley Tables}{chapter.4}% 23 -\BOOKMARK [1][-]{section.4.3}{Canonical and Normalized Cayley Tables}{chapter.4}% 24 -\BOOKMARK [1][-]{section.4.4}{Creating Quasigroups and Loops From Cayley Tables}{chapter.4}% 25 -\BOOKMARK [1][-]{section.4.5}{Creating Quasigroups and Loops from a File}{chapter.4}% 26 -\BOOKMARK [1][-]{section.4.6}{Creating Quasigroups and Loops From Sections}{chapter.4}% 27 -\BOOKMARK [1][-]{section.4.7}{Creating Quasigroups and Loops From Folders}{chapter.4}% 28 -\BOOKMARK [1][-]{section.4.8}{Creating Quasigroups and Loops By Nuclear Extensions}{chapter.4}% 29 -\BOOKMARK [1][-]{section.4.9}{Random Quasigroups and Loops}{chapter.4}% 30 -\BOOKMARK [1][-]{section.4.10}{Conversions}{chapter.4}% 31 -\BOOKMARK [1][-]{section.4.11}{Products of Quasigroups and Loops}{chapter.4}% 32 -\BOOKMARK [1][-]{section.4.12}{Opposite Quasigroups and Loops}{chapter.4}% 33 -\BOOKMARK [0][-]{chapter.5}{Basic Methods And Attributes}{}% 34 -\BOOKMARK [1][-]{section.5.1}{Basic Attributes}{chapter.5}% 35 -\BOOKMARK [1][-]{section.5.2}{Basic Arithmetic Operations}{chapter.5}% 36 -\BOOKMARK [1][-]{section.5.3}{Powers and Inverses}{chapter.5}% 37 -\BOOKMARK [1][-]{section.5.4}{Associators and Commutators}{chapter.5}% 38 -\BOOKMARK [1][-]{section.5.5}{Generators}{chapter.5}% 39 -\BOOKMARK [0][-]{chapter.6}{Methods Based on Permutation Groups}{}% 40 -\BOOKMARK [1][-]{section.6.1}{Parent of a Quasigroup}{chapter.6}% 41 -\BOOKMARK [1][-]{section.6.2}{Subquasigroups and Subloops}{chapter.6}% 42 -\BOOKMARK [1][-]{section.6.3}{Translations and Sections}{chapter.6}% 43 -\BOOKMARK [1][-]{section.6.4}{Multiplication Groups}{chapter.6}% 44 -\BOOKMARK [1][-]{section.6.5}{Inner Mapping Groups}{chapter.6}% 45 -\BOOKMARK [1][-]{section.6.6}{Nuclei, Commutant, Center, and Associator Subloop}{chapter.6}% 46 -\BOOKMARK [1][-]{section.6.7}{Normal Subloops and Simple Loops}{chapter.6}% 47 -\BOOKMARK [1][-]{section.6.8}{Factor Loops}{chapter.6}% 48 -\BOOKMARK [1][-]{section.6.9}{Nilpotency and Central Series}{chapter.6}% 49 -\BOOKMARK [1][-]{section.6.10}{Solvability, Derived Series and Frattini Subloop}{chapter.6}% 50 -\BOOKMARK [1][-]{section.6.11}{Isomorphisms and Automorphisms}{chapter.6}% 51 -\BOOKMARK [1][-]{section.6.12}{Isotopisms}{chapter.6}% 52 -\BOOKMARK [0][-]{chapter.7}{Testing Properties of Quasigroups and Loops}{}% 53 -\BOOKMARK [1][-]{section.7.1}{Associativity, Commutativity and Generalizations}{chapter.7}% 54 -\BOOKMARK [1][-]{section.7.2}{Inverse Propeties}{chapter.7}% 55 -\BOOKMARK [1][-]{section.7.3}{Some Properties of Quasigroups}{chapter.7}% 56 -\BOOKMARK [1][-]{section.7.4}{Loops of Bol Moufang Type}{chapter.7}% 57 -\BOOKMARK [1][-]{section.7.5}{Power Alternative Loops}{chapter.7}% 58 -\BOOKMARK [1][-]{section.7.6}{Conjugacy Closed Loops and Related Properties}{chapter.7}% 59 -\BOOKMARK [1][-]{section.7.7}{Automorphic Loops}{chapter.7}% 60 -\BOOKMARK [1][-]{section.7.8}{Additonal Varieties of Loops}{chapter.7}% 61 -\BOOKMARK [0][-]{chapter.8}{Specific Methods}{}% 62 -\BOOKMARK [1][-]{section.8.1}{Core Methods for Bol Loops}{chapter.8}% 63 -\BOOKMARK [1][-]{section.8.2}{Moufang Modifications}{chapter.8}% 64 -\BOOKMARK [1][-]{section.8.3}{Triality for Moufang Loops}{chapter.8}% 65 -\BOOKMARK [1][-]{section.8.4}{Realizing Groups as Multiplication Groups of Loops}{chapter.8}% 66 -\BOOKMARK [0][-]{chapter.9}{Libraries of Loops}{}% 67 -\BOOKMARK [1][-]{section.9.1}{A Typical Library}{chapter.9}% 68 -\BOOKMARK [1][-]{section.9.2}{Left Bol Loops and Right Bol Loops}{chapter.9}% 69 -\BOOKMARK [1][-]{section.9.3}{Moufang Loops}{chapter.9}% 70 -\BOOKMARK [1][-]{section.9.4}{Code Loops}{chapter.9}% 71 -\BOOKMARK [1][-]{section.9.5}{Steiner Loops}{chapter.9}% 72 -\BOOKMARK [1][-]{section.9.6}{Conjugacy Closed Loops}{chapter.9}% 73 -\BOOKMARK [1][-]{section.9.7}{Small Loops}{chapter.9}% 74 -\BOOKMARK [1][-]{section.9.8}{Paige Loops}{chapter.9}% 75 -\BOOKMARK [1][-]{section.9.9}{Nilpotent Loops}{chapter.9}% 76 -\BOOKMARK [1][-]{section.9.10}{Automorphic Loops}{chapter.9}% 77 -\BOOKMARK [1][-]{section.9.11}{Interesting Loops}{chapter.9}% 78 -\BOOKMARK [1][-]{section.9.12}{Libraries of Loops Up To Isotopism}{chapter.9}% 79 -\BOOKMARK [0][-]{appendix.A}{Files}{}% 80 -\BOOKMARK [0][-]{appendix.B}{Filters}{}% 81 -\BOOKMARK [0][-]{appendix*.3}{References}{}% 82 -\BOOKMARK [0][-]{section*.4}{Index}{}% 83 diff --git a/doc/loops.pnr b/doc/loops.pnr deleted file mode 100644 index b74a11f..0000000 --- a/doc/loops.pnr +++ /dev/null @@ -1,246 +0,0 @@ -PAGENRS := [ -[ 0, 0, 0 ], 1, -[ 0, 0, 1 ], 2, -[ 0, 0, 2 ], 3, -[ 1, 0, 0 ], 6, -[ 1, 1, 0 ], 6, -[ 1, 2, 0 ], 6, -[ 1, 3, 0 ], 6, -[ 1, 4, 0 ], 7, -[ 1, 5, 0 ], 7, -[ 1, 6, 0 ], 7, -[ 1, 7, 0 ], 7, -[ 2, 0, 0 ], 8, -[ 2, 1, 0 ], 8, -[ 2, 2, 0 ], 8, -[ 2, 3, 0 ], 9, -[ 2, 4, 0 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-\definecolor{fileColor}{rgb}{0.0,0.0,0.554} -\definecolor{urlColor}{rgb}{0.0,0.0,0.554} -\definecolor{promptColor}{rgb}{0.0,0.0,0.589} -\definecolor{brkpromptColor}{rgb}{0.589,0.0,0.0} -\definecolor{gapinputColor}{rgb}{0.589,0.0,0.0} -\definecolor{gapoutputColor}{rgb}{0.0,0.0,0.0} - -%% for a long time these were red and blue by default, -%% now black, but keep variables to overwrite -\definecolor{FuncColor}{rgb}{0.0,0.0,0.0} -%% strange name because of pdflatex bug: -\definecolor{Chapter }{rgb}{0.0,0.0,0.0} -\definecolor{DarkOlive}{rgb}{0.1047,0.2412,0.0064} - - -\usepackage{fancyvrb} - -\usepackage{mathptmx,helvet} -\usepackage[T1]{fontenc} -\usepackage{textcomp} - - -\usepackage[ - pdftex=true, - bookmarks=true, - a4paper=true, - pdftitle={Written with GAPDoc}, - pdfcreator={LaTeX with hyperref package / GAPDoc}, - colorlinks=true, - backref=page, - breaklinks=true, - linkcolor=linkColor, - citecolor=citeColor, - filecolor=fileColor, - urlcolor=urlColor, - pdfpagemode={UseNone}, - ]{hyperref} - -\newcommand{\maintitlesize}{\fontsize{50}{55}\selectfont} - -% write page numbers to a .pnr log file for online help -\newwrite\pagenrlog -\immediate\openout\pagenrlog =\jobname.pnr -\immediate\write\pagenrlog{PAGENRS := [} -\newcommand{\logpage}[1]{\protect\write\pagenrlog{#1, \thepage,}} -%% were never documented, give conflicts with some additional packages - -\newcommand{\GAP}{\textsf{GAP}} - -%% nicer description environments, allows long labels -\usepackage{enumitem} -\setdescription{style=nextline} - -%% depth of toc -\setcounter{tocdepth}{1} - - - - - -%% command for ColorPrompt style examples -\newcommand{\gapprompt}[1]{\color{promptColor}{\bfseries #1}} -\newcommand{\gapbrkprompt}[1]{\color{brkpromptColor}{\bfseries #1}} -\newcommand{\gapinput}[1]{\color{gapinputColor}{#1}} - - -\begin{document} - -\logpage{[ 0, 0, 0 ]} -\begin{titlepage} -\mbox{}\vfill - -\begin{center}{\maintitlesize \textbf{The \textsf{LOOPS} Package\mbox{}}}\\ -\vfill - -\hypersetup{pdftitle=The \textsf{LOOPS} Package} -\markright{\scriptsize \mbox{}\hfill The \textsf{LOOPS} Package \hfill\mbox{}} -{\Huge \textbf{Computing with quasigroups and loops in \textsf{GAP}\mbox{}}}\\ -\vfill - -{\Huge Version 3.3.0\mbox{}}\\[1cm] -\mbox{}\\[2cm] -{\Large \textbf{G{\a'a}bor P. Nagy \mbox{}}}\\ -{\Large \textbf{Petr Vojt{\v e}chovsk{\a'y} \mbox{}}}\\ -\hypersetup{pdfauthor=G{\a'a}bor P. Nagy ; Petr Vojt{\v e}chovsk{\a'y} } -\end{center}\vfill - -\mbox{}\\ -{\mbox{}\\ -\small \noindent \textbf{G{\a'a}bor P. Nagy } Email: \href{mailto://nagyg@math.u-szeged.hu} {\texttt{nagyg@math.u-szeged.hu}}\\ - Address: \begin{minipage}[t]{8cm}\noindent -Department of Mathematics, University of Szeged\end{minipage} -}\\ -{\mbox{}\\ -\small \noindent \textbf{Petr Vojt{\v e}chovsk{\a'y} } Email: \href{mailto://petr@math.du.edu} {\texttt{petr@math.du.edu}}\\ - Address: \begin{minipage}[t]{8cm}\noindent -Department of Mathematics, University of Denver\end{minipage} -}\\ -\end{titlepage} - -\newpage\setcounter{page}{2} -{\small -\section*{Copyright} -\logpage{[ 0, 0, 1 ]} -{\copyright} 2016 G{\a'a}bor P. Nagy and Petr Vojt{\v e}chovsk{\a'y}. \mbox{}}\\[1cm] -\newpage - -\def\contentsname{Contents\logpage{[ 0, 0, 2 ]}} - -\tableofcontents -\newpage - - -\chapter{\textcolor{Chapter }{Introduction}}\label{Chap:Introduction} -\logpage{[ 1, 0, 0 ]} -\hyperdef{L}{X7DFB63A97E67C0A1}{} -{ - \textsf{LOOPS} is a package for \textsf{GAP4} whose purpose is to: -\begin{itemize} -\item provide researchers in nonassociative algebra with a powerful computational -tool concerning finite loops and quasigroups, -\item extend \textsf{GAP} toward the realm of nonassociative structures. -\end{itemize} - \textsf{LOOPS} has been accepted as an official package of \textsf{GAP} in May 2015. -\section{\textcolor{Chapter }{License}}\label{Sec:License} -\logpage{[ 1, 1, 0 ]} -\hyperdef{L}{X861E5DF986F89AE2}{} -{ - \textsf{LOOPS} is free software. You can redistribute it and/or modify it under the terms of -the GNU General Public License version 3 as published by the Free Software -Foundation. } - - -\section{\textcolor{Chapter }{Installation}}\label{Sec:Installation} -\logpage{[ 1, 2, 0 ]} -\hyperdef{L}{X8360C04082558A12}{} -{ - Have \textsf{GAP 4.7} or newer installed on your computer. - -If you do not see the subfolder \texttt{pkg/loops} in the main directory of \textsf{GAP} then download the \textsf{LOOPS} package from the distribution website \href{http://www.math.du.edu/loops} {\texttt{http://www.math.du.edu/loops}} and unpack the downloaded file into the \texttt{pkg} subfolder. - -The package \textsf{LOOPS} can then be loaded to \textsf{GAP} anytime by calling \texttt{LoadPackage("loops");}. - -If you wish to load \textsf{LOOPS} automatically while starting \textsf{GAP}, start \textsf{GAP}, execute the following commands, -\begin{verbatim} - gap> pref := UserPreference( "PackagesToLoad " );; - gap> Add( pref, "loops" );; - gap> SetUserPreference( "PackagesToLoad", pref );; - gap> WriteGapIniFile();; -\end{verbatim} - quit \textsf{GAP} and restart it. } - - -\section{\textcolor{Chapter }{Documentation}}\label{Sec:Documentation} -\logpage{[ 1, 3, 0 ]} -\hyperdef{L}{X7F4F8D6F7CD6B765}{} -{ - The documentation has been prepared with the \textsf{GAPDoc} package and is therefore available in several formats: {\LaTeX}, pdf, ps, html, and as an inline help in \textsf{GAP}. All these formats have been obtained directly from the master XML -documentation file. Consequently, the different formats of the documentation -differ only in their appearance, not in content. - -The preferred format of the documentation is html with MathJax turned on. - -All formats of the documentation can be found in the \texttt{doc} folder of \textsf{LOOPS}. You can also download the documentation from the \textsf{LOOPS} distribution website. - -The inline \textsf{GAP} help is available upon installing \textsf{LOOPS} and can be accessed in the usual way, i.e., upon typing \texttt{?command}, \textsf{GAP} displays the section of the \textsf{LOOPS} manual containing information about \texttt{command}. } - - -\section{\textcolor{Chapter }{Test Files}}\label{Sec:TestFiles} -\logpage{[ 1, 4, 0 ]} -\hyperdef{L}{X801051CC86594630}{} -{ - Test files conforming to \textsf{GAP} standards are provided for \textsf{LOOPS} and can be found in the folder \texttt{tst}. The command \texttt{ReadPackage("loops","tst/testall.g")} runs all tests for \textsf{LOOPS}. } - - -\section{\textcolor{Chapter }{Memory Management}}\label{Sec:MemoryManagement} -\logpage{[ 1, 5, 0 ]} -\hyperdef{L}{X79342B4E7E55FD0F}{} -{ - Some libraries of loops are loaded only upon explicit demand and can occupy a -lot of memory. For instance, the library or RCC loops occupies close to 100 MB -of memory when fully loaded. The command \texttt{LOOPS{\textunderscore}FreeMemory();} will attempt to free memory by unbinding on-demand library data loaded by \textsf{LOOPS}. } - - -\section{\textcolor{Chapter }{Feedback}}\label{Sec:Feedback} -\logpage{[ 1, 6, 0 ]} -\hyperdef{L}{X80D704CC7EBFDF7A}{} -{ - We welcome all comments and suggestions on \textsf{LOOPS}, especially those concerning the future development of the package. You can -contact us by e-mail. } - - -\section{\textcolor{Chapter }{Acknowledgment}}\label{Sec:Acknowledgment} -\logpage{[ 1, 7, 0 ]} -\hyperdef{L}{X811B08C07BD79486}{} -{ - We thank the following people for sending us remarks and comments, and for -suggesting new functionality of the package: Muniru Asiru, Bjoern Assmann, -Andreas Distler, Ale{\v s} Dr{\a'a}pal, Steve Flammia, Kenneth W. Johnson, -Michael K. Kinyon, Alexander Konovalov, Frank L{\"u}beck and Jonathan D.H. -Smith. - -The library of Moufang loops of order 243 was generated from data provided by -Michael C. Slattery and Ashley L. Zenisek. The library of right conjugacy -closed loops of order less than 28 was generated from data provided by -Katharina Artic. The library of commutative automorphic loops of order 27, 81 -and 243 was obtained jointly with Izabella Stuhl. - -G{\a'a}bor P. Nagy was supported by OTKA grants F042959 and T043758, and Petr -Vojt{\v e}chovsk{\a'y} was supported by the 2006 and 2016 University of Denver -PROF grants and the Simons Foundation Collaboration Grant 210176. } - - } - - -\chapter{\textcolor{Chapter }{Mathematical Background}}\label{Chap:MathematicalBackground} -\logpage{[ 2, 0, 0 ]} -\hyperdef{L}{X7EF1B6708069B0C7}{} -{ - We assume that you are familiar with the theory of quasigroups and loops, for -instance with the textbook of Bruck \cite{Br} or Pflugfelder \cite{Pf}. Nevertheless, we did include definitions and results in this manual in order -to unify terminology and improve legibility of the text. Some general concepts -of quasigroups and loops can be found in this chapter. More special concepts -are defined throughout the text as needed. -\section{\textcolor{Chapter }{Quasigroups and Loops}}\label{Sec:QuasigroupsAndLoops} -\logpage{[ 2, 1, 0 ]} -\hyperdef{L}{X80243DE5826583B8}{} -{ - A set with one binary operation (denoted $\cdot$ here) is called \index{groupoid}\emph{groupoid} or \index{magma}\emph{magma}, the latter name being used in \textsf{GAP}. - -An element $1$ of a groupoid $G$ is a \index{neutral element}\emph{neutral element} or an \index{identity!element}\emph{identity element} if $1\cdot x = x\cdot 1 = x$ for every $x$ in $G$. - -Let $G$ be a groupoid with neutral element $1$. Then an element $x^{-1}$ is called a \index{inverse!two-sided}\emph{two-sided inverse} of $x$ in $G$ if $ x\cdot x^{-1} = x^{-1}\cdot x = 1$. - -Recall that \index{group}groups are associative groupoids with an identity element and two-sided -inverses. Groups can be reached in another way from groupoids, namely via -quasigroups and loops. - -A \index{quasigroup}\emph{quasigroup} $Q$ is a groupoid such that the equation $x\cdot y=z$ has a unique solution in $Q$ whenever two of the three elements $x$, $y$, $z$ of $Q$ are specified. Note that multiplication tables of finite quasigroups are -precisely \index{latin square}\emph{latin squares}, i.e., square arrays with symbols arranged so that each symbol occurs in each -row and in each column exactly once. A \index{loop}\emph{loop} $L$ is a quasigroup with a neutral element. - -Groups are clearly loops. Conversely, it is not hard to show that associative -quasigroups are groups. } - - -\section{\textcolor{Chapter }{Translations}}\label{Sec:Translations} -\logpage{[ 2, 2, 0 ]} -\hyperdef{L}{X7EC01B437CC2B2C9}{} -{ - Given an element $x$ of a quasigroup $Q$, we can associative two permutations of $Q$ with it: the \index{translation!left}\emph{left translation} $L_x:Q\to Q$ defined by $y\mapsto x\cdot y$, and the \index{translation!right}\emph{right translation} $R_x:Q\to Q$ defined by $y\mapsto y\cdot x$. - -The binary operation $x\backslash y = L_x^{-1}(y)$ is called the \index{division!left}\emph{left division}, and $x/y = R_y^{-1}(x)$ is called the \index{division!right}\emph{right division}. - -Although it is possible to compose two left (right) translations of a -quasigroup, the resulting permutation is not necessarily a left (right) -translation. The set $\{L_x|x\in Q\}$ is called the \index{section!left}\emph{left section} of $Q$, and $\{R_x|x\in Q\}$ is the \index{section!right}\emph{right section} of $Q$. - -Let $S_Q$ be the symmetric group on $Q$. Then the subgroup ${\rm Mlt}_{\lambda}(Q)=\langle L_x|x\in Q\rangle$ of $S_Q$ generated by all left translations is the \index{multiplication group!left}\emph{left multiplication group} of $Q$. Similarly, ${\rm Mlt}_{\rho}(Q)= \langle R_x|x\in Q\rangle$ is the \index{multiplication group!right}\emph{right multiplication group} of $Q$. The smallest group containing both ${\rm Mlt}_{\lambda}(Q)$ and ${\rm Mlt}_{\rho}(Q)$ is called the \index{multiplication group}\emph{multiplication group} of $Q$ and is denoted by ${\rm Mlt}(Q)$. - -For a loop $Q$, the \index{inner mapping group!left}\emph{left inner mapping group} ${\rm Inn}_{\lambda}(Q)$ is the stabilizer of $1$ in ${\rm Mlt}_{\lambda}(Q)$. The \index{inner mapping group!right}\emph{right inner mapping group} ${\rm Inn}_{\rho}(Q)$ is defined dually. The \index{inner mapping group}\emph{inner mapping group} ${\rm Inn}(Q)$ is the stabilizer of $1$ in $Q$. } - - -\section{\textcolor{Chapter }{Subquasigroups and Subloops}}\label{Sec:SubquasigroupsAndSubloops} -\logpage{[ 2, 3, 0 ]} -\hyperdef{L}{X83EDF04F7952143F}{} -{ - A nonempty subset $S$ of a quasigroup $Q$ is a \index{subquasigroup}\emph{subquasigroup} if it is closed under multiplication and the left and right divisions. In the -finite case, it suffices for $S$ to be closed under multiplication. \index{subloop}\emph{Subloops} are defined analogously when $Q$ is a loop. - -The \index{nucleus!left}\emph{left nucleus} ${\rm Nuc}_{\lambda}(Q)$ of $Q$ consists of all elements $x$ of $Q$ such that $x(yz) = (xy)z$ for every $y$, $z$ in $Q$. The \index{nucleus!middle}\emph{middle nucleus} ${\rm Nuc}_{\mu}(Q)$ and the \index{nucleus!right}\emph{right nucleus} ${\rm Nuc}_{\rho}(Q)$ are defined analogously. The \index{nucleus}\emph{nucleus} ${\rm Nuc}(Q)$ is the intersection of the left, middle and right nuclei. - -The \index{commutant}\emph{commutant} $C(Q)$ of $Q$ consists of all elements $x$ of $Q$ that commute with all elements of $Q$. The \index{center}\emph{center} $Z(Q)$ of $Q$ is the intersection of ${\rm Nuc}(Q)$ with $C(Q)$. - -A subloop $S$ of $Q$ is \index{subloop!normal}\emph{normal} in $Q$ if $f(S)=S$ for every inner mapping $f$ of $Q$. } - - -\section{\textcolor{Chapter }{Nilpotence and Solvability}}\label{Sec:NilpotenceAndSolvability} -\logpage{[ 2, 4, 0 ]} -\hyperdef{L}{X869CBCE381E2C422}{} -{ - For a loop $Q$ define $Z_0(Q) = 1$ and let $Z_{i+1}(Q)$ be the preimage of the center of $Q/Z_i(Q)$ in $Q$. A loop $Q$ is \index{nilpotence class}\index{nilpotent loop}\index{loop!nilpotent}\emph{nilpotent of class} $n$ if $n$ is the least nonnegative integer such that $Z_n(Q)=Q$. In such case $Z_0(Q)\le Z_1(Q)\le \dots \le Z_n(Q)$ is the \emph{upper central series}\index{central series!upper}. - -The \index{derived subloop}\emph{derived subloop} $Q'$ of $Q$ is the least normal subloop of $Q$ such that $Q/Q'$ is a commutative group. Define $Q^{(0)}=Q$ and let $Q^{(i+1)}$ be the derived subloop of $Q^{(i)}$. Then $Q$ is \index{solvability class}\index{solvable loop}\index{loop!solvable}\emph{solvable of class} $n$ if $n$ is the least nonnegative integer such that $Q^{(n)} = 1$. In such a case $Q^{(0)}\ge Q^{(1)}\ge \cdots \ge Q^{(n)}$ is the \emph{derived series}\index{derived series} of $Q$. } - - -\section{\textcolor{Chapter }{Associators and Commutators}}\label{Sec:AssociatorsAndCommutators} -\logpage{[ 2, 5, 0 ]} -\hyperdef{L}{X7E0849977869E53D}{} -{ - Let $Q$ be a quasigroup and let $x$, $y$, $z$ be elements of $Q$. Then the \index{commutator}\emph{commutator} of $x$, $y$ is the unique element $[x,y]$ of $Q$ such that $xy = [x,y](yx)$, and the \index{associator}\emph{associator} of $x$, $y$, $z$ is the unique element $[x,y,z]$ of $Q$ such that $(xy)z = [x,y,z](x(yz))$. - -The \index{associator subloop}\emph{associator subloop} $A(Q)$ of $Q$ is the least normal subloop of $Q$ such that $Q/A(Q)$ is a group. - -It is not hard to see that $A(Q)$ is the least normal subloop of $Q$ containing all commutators, and $Q'$ is the least normal subloop of $Q$ containing all commutators and associators. } - - -\section{\textcolor{Chapter }{Homomorphism and Homotopisms}}\label{Sec:HomomorphismsAndHomotopisms} -\logpage{[ 2, 6, 0 ]} -\hyperdef{L}{X791066ED7DD9F254}{} -{ - Let $K$, $H$ be two quasigroups. Then a map $f:K\to H$ is a \index{homomorphism}\emph{homomorphism} if $f(x)\cdot f(y)=f(x\cdot y)$ for every $x$, $y\in K$. If $f$ is also a bijection, we speak of an \index{isomorphism}\emph{isomorphism}, and the two quasigroups are called isomorphic. - -An ordered triple $(\alpha,\beta,\gamma)$ of maps $\alpha$, $\beta$, $\gamma:K\to H$ is a \index{homotopism}\emph{homotopism} if $\alpha(x)\cdot\beta(y) = \gamma(x\cdot y)$ for every $x$, $y$ in $K$. If the three maps are bijections, then $(\alpha,\beta,\gamma)$ is an \index{isotopism}\emph{isotopism}, and the two quasigroups are isotopic. - -Isotopic groups are necessarily isomorphic, but this is certainly not true for -nonassociative quasigroups or loops. In fact, every quasigroup is isotopic to -a loop. - -Let $(K,\cdot)$, $(K,\circ)$ be two quasigroups defined on the same set $K$. Then an isotopism $(\alpha,\beta,{\rm id}_K)$ is called a \index{isotopism!principal}\emph{principal isotopism}. An important class of principal isotopisms is obtained as follows: Let $(K,\cdot)$ be a quasigroup, and let $f$, $g$ be elements of $K$. Define a new operation $\circ$ on $K$ by $x\circ y = R_g^{-1}(x)\cdot L_f^{-1}(y)$, where $R_g$, $L_f$ are translations. Then $(K,\circ)$ is a quasigroup isotopic to $(K,\cdot)$, in fact a loop with neutral element $f\cdot g$. We call $(K,\circ)$ a \index{loop isotope!principal}\emph{principal loop isotope} of $(K,\cdot)$. } - - } - - -\chapter{\textcolor{Chapter }{How the Package Works}}\label{Chap:HowThePackageWorks} -\logpage{[ 3, 0, 0 ]} -\hyperdef{L}{X7A6DF65E826B8CFF}{} -{ - The package consists of three complementary components: -\begin{itemize} -\item the core algorithms for quasigroup theoretical notions (see Chapters \ref{Chap:CreatingQuasigroupsAndLoops}, \ref{Chap:BasicMethodsAndAttributes}, \ref{Chap:MethodsBasedOnPermutationGroups} and \ref{Chap:TestingPropertiesOfQuasigroupsAndLoops}), -\item algorithms for specific varieties of loops, mostly for Moufang loops (see -Chapter \ref{Chap:SpecificMethods}), -\item the library of small loops (see Chapter \ref{Chap:LibrariesOfLoops}). -\end{itemize} - Although we do not explain the algorithms in detail here, we describe the -general philosophy so that users can anticipate the capabilities and behavior -of \textsf{LOOPS}. -\section{\textcolor{Chapter }{Representing Quasigroups}}\label{Sec:RepresentingQuasigroups} -\logpage{[ 3, 1, 0 ]} -\hyperdef{L}{X86F02BBD87FEA1C6}{} -{ - Since permutation representation in the usual sense is impossible for -nonassociative structures, and since the theory of nonassociative -presentations is not well understood, we resorted to multiplication tables to -represent quasigroups in \textsf{GAP}. (In order to save storage space, we sometimes use one multiplication table -to represent several quasigroups, for instance when a quasigroup is a -subquasigroup of another quasigroup. See Section \ref{Sec:AboutCayleyTables} for more details.) - -Consequently, the package is intended primarily for quasigroups and loops of -small order, say up to 1000. - -The \textsf{GAP} categories \index{IsQuasigroupElement}\texttt{IsQuasigroupElement}, \index{IsLoopElement}\texttt{IsLoopElement}, \index{IsQuasigroup}\texttt{IsQuasigroup} and \index{IsLoop}\texttt{IsLoop} are declared in \textsf{LOOPS} as follows: -\begin{verbatim} - DeclareCategory( "IsQuasigroupElement", IsMultiplicativeElement ); - DeclareRepresentation( "IsQuasigroupElmRep", - IsPositionalObjectRep and IsMultiplicativeElement, [1] ); - DeclareCategory( "IsLoopElement", - IsQuasigroupElement and IsMultiplicativeElementWithInverse ); - DeclareRepresentation( "IsLoopElmRep", - IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] ); - ## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup) - DeclareCategory( "IsLatin", IsObject ); - DeclareCategory( "IsQuasigroup", IsMagma and IsLatin ); - DeclareCategory( "IsLoop", IsQuasigroup and - IsMultiplicativeElementWithInverseCollection); -\end{verbatim} - } - - -\section{\textcolor{Chapter }{Conversions between magmas, quasigroups, loops and groups}}\label{Sec:ConversionsEtc} -\logpage{[ 3, 2, 0 ]} -\hyperdef{L}{X807D76EF81B9D061}{} -{ - Whether an object is considered a magma, quasigroup, loop or group is a matter -of declaration in \textsf{LOOPS}. Loops are automatically quasigroups, and both groups and quasigroups are -automatically magmas. All standard \textsf{GAP} commands for magmas are therefore available for quasigroups and loops. - -In \textsf{GAP}, functions of the type \texttt{AsSomething(\mbox{\texttt{\mdseries\slshape X}})} convert the domain \mbox{\texttt{\mdseries\slshape X}} into \texttt{Something}, if possible, without changing the underlying domain \mbox{\texttt{\mdseries\slshape X}}. For example, if \mbox{\texttt{\mdseries\slshape X}} is declared as magma but is associative and has neutral element and inverses, \texttt{AsGroup(\mbox{\texttt{\mdseries\slshape X}})} returns the corresponding group with the underlying domain \mbox{\texttt{\mdseries\slshape X}}. - -We have opted for a more general kind of conversions in \textsf{LOOPS} (starting with version 2.1.0), using functions of the type \texttt{IntoSomething(\mbox{\texttt{\mdseries\slshape X}})}. The two main features that distinguish \texttt{IntoSomething} from \texttt{AsSomething} are: -\begin{itemize} -\item The function \texttt{IntoSomething(\mbox{\texttt{\mdseries\slshape X}})} does not necessarily return the same domain as \mbox{\texttt{\mdseries\slshape X}}. The reason is that \mbox{\texttt{\mdseries\slshape X}} can be a group, for instance, defined on one of many possible domains, while \texttt{IntoLoop(\mbox{\texttt{\mdseries\slshape X}})} must result in a loop, and hence be defined on a subset of some interval $1$, $\dots$, $n$ (see Section \ref{Sec:ParentOfAQuasigroup}). -\item In some special situations, the function \texttt{IntoSomething(\mbox{\texttt{\mdseries\slshape X}})} allows to convert \mbox{\texttt{\mdseries\slshape X}} into \texttt{Something} even though \mbox{\texttt{\mdseries\slshape X}} does not have all the properties of \texttt{Something}. For instance, every quasigroup is isotopic to a loop, so it makes sense to -allow the conversion \texttt{IntoLoop(\mbox{\texttt{\mdseries\slshape Q}})} even if the quasigroup \mbox{\texttt{\mdseries\slshape Q}} does not posses a neutral element. -\end{itemize} - Details of all conversions in \textsf{LOOPS} can be found in Section \ref{Sec:Conversions}. } - - -\section{\textcolor{Chapter }{Calculating with Quasigroups}}\label{Sec:CalculationWithQuasigroups} -\logpage{[ 3, 3, 0 ]} -\hyperdef{L}{X87E49ED884FA6DC4}{} -{ - Although the quasigroups are ultimately represented by multiplication tables, -the algorithms are efficient because nearly all calculations are delegated to -groups. The connection between quasigroups and groups is facilitated via -translations (see Section \ref{Sec:Translations}), and we illustrate it with a few examples: \\ - - -\textsc{Example:} This example shows how properties of quasigroups can be translated into -properties of translations in a straightforward way. Let $Q$ be a quasigroup. We ask if $Q$ is associative. We can either test if $(xy)z=x(yz)$ for every $x$, $y$, $z$ in $Q$, or we can ask if $L_{xy}=L_xL_y$ for every $x$, $y$ in $Q$. Note that since $L_{xy}$, $L_x$ and $L_y$ are elements of a permutation group, we do not have to refer directly to the -multiplication table once the left translations of $Q$ are known. \\ - - -\textsc{Example:} This example shows how properties of loops can be translated into properties -of translations in a way that requires some theory. A \index{Bol loop!left}\index{loop!left Bol}\emph{left Bol loop} is a loop satisfying $x(y(xz)) = (x(yx))z$. We claim (without proof) that a loop $Q$ is left Bol if and only if $L_xL_yL_x$ is a left translation for every $x$, $y$ in $Q$. \\ - - -\textsc{Example:} This example shows that many properties of loops become purely -group-theoretical once they are expressed in terms of translations. A loop is \index{simple loop}\index{loop!simple}\emph{simple} if it has no nontrivial congruences. It is possible to show that a loop is -simple if and only if its multiplication group is a primitive permutation -group. \\ - - -The main idea of the package is therefore to: -\begin{itemize} -\item calculate the translations and the associated permutation groups when they are -needed, -\item store them as attributes, -\item use them in algorithms as often as possible. -\end{itemize} - } - - -\section{\textcolor{Chapter }{Naming, Viewing and Printing Quasigroups and their Elements}}\label{Sec:NamingEtc} -\logpage{[ 3, 4, 0 ]} -\hyperdef{L}{X7D75C7A6787AF72A}{} -{ - \textsf{GAP} displays information about objects in two modes: the \texttt{View} mode (default, short), and the \texttt{Print} mode (longer). Moreover, when the name of an object is set, the name is always -shown, no matter which display mode is used. - -Only loops contained in the libraries of \textsf{LOOPS} are named. For instance, the loop obtained via \texttt{MoufangLoop(32,4)}, the 4th Moufang loop of order 32, is named "Moufang loop 32/4'' and is shown -as \texttt{{\textless}Moufang loop 32/4{\textgreater}}. - -A generic quasigroup of order $n$ is displayed as \texttt{{\textless}quasigroup of order n{\textgreater}}. Similarly, a loop of order $n$ appears as \texttt{{\textless}loop of order n{\textgreater}}. - -The displayed information of a generic loop is enhanced if more information -about the loop becomes available. For instance, when it is established that a -loop of order 12 has the left alternative property, the loop will be shown as \texttt{{\textless}left alternative loop of order 12{\textgreater}} until a stronger property is obtained. Which property is diplayed is governed -by the filters built into \textsf{LOOPS} (see Appendix \ref{Apx:Filters}). -\subsection{\textcolor{Chapter }{SetQuasigroupElmName and SetLoopElmName}}\logpage{[ 3, 4, 1 ]} -\hyperdef{L}{X7A7EB1B579273D07}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{SetQuasigroupElmName({\mdseries\slshape Q, name})\index{SetQuasigroupElmName@\texttt{SetQuasigroupElmName}} -\label{SetQuasigroupElmName} -}\hfill{\scriptsize (function)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{SetLoopElmName({\mdseries\slshape Q, name})\index{SetLoopElmName@\texttt{SetLoopElmName}} -\label{SetLoopElmName} -}\hfill{\scriptsize (function)}}\\ - - -The above functions change the names of elements of a quasigroup (resp. loop) \mbox{\texttt{\mdseries\slshape Q}} to \mbox{\texttt{\mdseries\slshape name}}. - -By default, elements of a quasigroup appear as \texttt{qi} and elements of a loop appear as \texttt{li} in both display modes, where \texttt{i} is a positive integer. The neutral element of a loop is always indexed by 1.\\ -} - - - -For quasigroups and loops in the \texttt{Print} mode, we display the multiplication table (if it is known), otherwise we -display the elements. \\ - - -In the following example, \texttt{L} is a loop with two elements. -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@L; | - - !gapprompt@gap>| !gapinput@Print( L ); | - - !gapprompt@gap>| !gapinput@Elements( L ); | - [ l1, l2 ] - !gapprompt@gap>| !gapinput@SetLoopElmName( L, "loop_element" );; Elements( L ); | - [ loop_element1, loop_element2 ] -\end{Verbatim} - } - - } - - -\chapter{\textcolor{Chapter }{Creating Quasigroups and Loops}}\label{Chap:CreatingQuasigroupsAndLoops} -\logpage{[ 4, 0, 0 ]} -\hyperdef{L}{X7AA4B9C0877550ED}{} -{ - In this chapter we describe several ways in which quasigroups and loops can be -created in \textsf{LOOPS}. -\section{\textcolor{Chapter }{About Cayley Tables}}\label{Sec:AboutCayleyTables} -\logpage{[ 4, 1, 0 ]} -\hyperdef{L}{X7DE8405B82BC36A9}{} -{ - Let $X=\{x_1,\dots,x_n\}$ be a set and $\cdot$ a binary operation on $X$. Then an $n$ by $n$ array with rows and columns bordered by $x_1$, $\dots$, $x_n$, in this order, is a \index{Cayley table}\emph{Cayley table}, or a \index{multiplication table}\emph{multiplication table} of $\cdot$, if the entry in the row $x_i$ and column $x_j$ is $x_i\cdot x_j$. - -A Cayley table is a \index{quasigroup table}\emph{quasigroup table} if it is a \index{latin square}latin square, i.e., if every entry $x_i$ appears in every column and every row exactly once. - -An unfortunate feature of multiplication tables in practice is that they are -often not bordered, that is, it is up to the reader to figure out what is -meant. Throughout this manual and in \textsf{LOOPS}, we therefore make the following assumption: \emph{All distinct entries in a quasigroup table must be positive integers, say $x_1 < x_2 < \cdots < x_n$, and if no border is specified, we assume that the table is bordered by $x_1$, $\dots$, $x_n$, in this order.} Note that we do not assume that the distinct entries $x_1$, $\dots$, $x_n$ form the interval $1$, $\dots$, $n$. The significance of this observation will become clear in Chapter \ref{Chap:MethodsBasedOnPermutationGroups}. - -Finally, we say that a quasigroup table is a \index{loop table}\emph{loop table} if the first row and the first column are the same, and if the entries in the -first row are ordered in an ascending fashion. } - - -\section{\textcolor{Chapter }{Testing Cayley Tables}}\label{Sec:TestingCayleyTables} -\logpage{[ 4, 2, 0 ]} -\hyperdef{L}{X7827BF877AA87246}{} -{ - -\subsection{\textcolor{Chapter }{IsQuasigroupTable and IsQuasigroupCayleyTable}}\logpage{[ 4, 2, 1 ]} -\hyperdef{L}{X81179355869B9DFE}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsQuasigroupTable({\mdseries\slshape T})\index{IsQuasigroupTable@\texttt{IsQuasigroupTable}} -\label{IsQuasigroupTable} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsQuasigroupCayleyTable({\mdseries\slshape T})\index{IsQuasigroupCayleyTable@\texttt{IsQuasigroupCayleyTable}} -\label{IsQuasigroupCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape T}} is a quasigroup table as defined above, else \texttt{false}. - -} - - -\subsection{\textcolor{Chapter }{IsLoopTable and IsLoopCayleyTable}}\logpage{[ 4, 2, 2 ]} -\hyperdef{L}{X7AAE48507A471069}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLoopTable({\mdseries\slshape T})\index{IsLoopTable@\texttt{IsLoopTable}} -\label{IsLoopTable} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLoopCayleyTable({\mdseries\slshape T})\index{IsLoopCayleyTable@\texttt{IsLoopCayleyTable}} -\label{IsLoopCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape T}} is a loop table as defined above, else \texttt{false}.\\ - - -} - - - -\textsc{Remark:}The package \textsf{GUAVA} also contains operations dealing with latin squares. In particular, \texttt{IsLatinSquare} is declared in \textsf{GUAVA}. } - - -\section{\textcolor{Chapter }{Canonical and Normalized Cayley Tables}}\label{Sec:CanonicalAndNormalizedCayleyTables} -\logpage{[ 4, 3, 0 ]} -\hyperdef{L}{X7BA749CA7DB4EA87}{} -{ - - -\subsection{\textcolor{Chapter }{CanonicalCayleyTable}} -\logpage{[ 4, 3, 1 ]}\nobreak -\hyperdef{L}{X7971CCB87DAFF7B9}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CanonicalCayleyTable({\mdseries\slshape T})\index{CanonicalCayleyTable@\texttt{CanonicalCayleyTable}} -\label{CanonicalCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -Canonical Cayley table constructed from Cayley table \mbox{\texttt{\mdseries\slshape T}} by replacing entries $x_i$ with $i$. - - - -A Cayley table is said to be \index{Cayley table!canonical}\emph{canonical} if it is based on elements $1$, $\dots$, $n$. Although we do not assume that every quasigroup table is canonical, it is -often desirable to present quasigroup tables in canonical way.} - - - -\subsection{\textcolor{Chapter }{CanonicalCopy}} -\logpage{[ 4, 3, 2 ]}\nobreak -\hyperdef{L}{X7B816D887F46E6B7}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CanonicalCopy({\mdseries\slshape Q})\index{CanonicalCopy@\texttt{CanonicalCopy}} -\label{CanonicalCopy} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A canonical copy of the quasigroup or loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -This is a shorthand for \texttt{QuasigroupByCayleyTable(CanonicalCayleyTable(\mbox{\texttt{\mdseries\slshape Q}})} when \mbox{\texttt{\mdseries\slshape Q}} is a declared quasigroup, and \texttt{LoopByCayleyTable(CanonicalCayleyTable(\mbox{\texttt{\mdseries\slshape Q}})} when \mbox{\texttt{\mdseries\slshape Q}} is a loop.} - - - -\subsection{\textcolor{Chapter }{NormalizedQuasigroupTable}} -\logpage{[ 4, 3, 3 ]}\nobreak -\hyperdef{L}{X821A2F9E85FAD8BF}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NormalizedQuasigroupTable({\mdseries\slshape T})\index{NormalizedQuasigroupTable@\texttt{NormalizedQuasigroupTable}} -\label{NormalizedQuasigroupTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A normalized version of the Cayley table \mbox{\texttt{\mdseries\slshape T}}. - - - -A given Cayley table \mbox{\texttt{\mdseries\slshape T}} is normalized in three steps as follows: first, \texttt{CanonicalCayleyTable} is called to rename entries to $1$, $\dots$, $n$, then the columns of \mbox{\texttt{\mdseries\slshape T}} are permuted so that the first row reads $1$, $\dots$, $n$, and finally the rows of \mbox{\texttt{\mdseries\slshape T}} are permuted so that the first column reads $1$, $\dots$, $n$.} - - } - - -\section{\textcolor{Chapter }{Creating Quasigroups and Loops From Cayley Tables}}\label{Sec:CreatingQuasigroupsAndLoopsFromCayleyTables} -\logpage{[ 4, 4, 0 ]} -\hyperdef{L}{X7C2372BB8739C5A2}{} -{ - -\subsection{\textcolor{Chapter }{QuasigroupByCayleyTable and LoopByCayleyTable}}\logpage{[ 4, 4, 1 ]} -\hyperdef{L}{X860135BB85F2DB19}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupByCayleyTable({\mdseries\slshape T})\index{QuasigroupByCayleyTable@\texttt{QuasigroupByCayleyTable}} -\label{QuasigroupByCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByCayleyTable({\mdseries\slshape T})\index{LoopByCayleyTable@\texttt{LoopByCayleyTable}} -\label{LoopByCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The quasigroup (resp. loop) with quasigroup table (resp. loop table) \mbox{\texttt{\mdseries\slshape T}}. - - - -Since \texttt{CanonicalCayleyTable} is called within the above operation, the resulting quasigroup will have -Cayley table with distinct entries $1$, $\dots$, $n$. } - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@ct := CanonicalCayleyTable( [[5,3],[3,5]] ); | - [ [ 2, 1 ], [ 1, 2 ] ] - !gapprompt@gap>| !gapinput@NormalizedQuasigroupTable( ct ); | - [ [ 1, 2 ], [ 2, 1 ] ] - !gapprompt@gap>| !gapinput@LoopByCayleyTable( last ); | - - !gapprompt@gap>| !gapinput@[ IsQuasigroupTable( ct ), IsLoopTable( ct ) ]; | - [ true, false ] -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Creating Quasigroups and Loops from a File}}\label{Sec:CreatingQuasigroupsAndLoopsFromAFile} -\logpage{[ 4, 5, 0 ]} -\hyperdef{L}{X849944F17E2B37F8}{} -{ - Typing a large multiplication table manually is tedious and error-prone. We -have therefore included a general method in \textsf{LOOPS} that reads multiplication tables of quasigroups from a file. - -Instead of writing a separate algorithm for each common format, our algorithm -relies on the user to provide a bit of information about the input file. Here -is an outline of the algorithm, with file named \mbox{\texttt{\mdseries\slshape filename}} and a string \mbox{\texttt{\mdseries\slshape del}} as input (in essence, the characters of \mbox{\texttt{\mdseries\slshape del}} will be ignored while reading the file): -\begin{itemize} -\item read the entire content of \mbox{\texttt{\mdseries\slshape filename}} into a string \mbox{\texttt{\mdseries\slshape s}}, -\item replace all end-of-line characters in \mbox{\texttt{\mdseries\slshape s}} by spaces, -\item replace by spaces all characters of \mbox{\texttt{\mdseries\slshape s}} that appear in \mbox{\texttt{\mdseries\slshape del}}, -\item split \mbox{\texttt{\mdseries\slshape s}} into maximal substrings without spaces, called \emph{chunks} here, -\item let $n$ be the number of distinct chunks, -\item if the number of chunks is not $n^2$, report error, -\item construct the multiplication table by assigning numerical values $1$, $\dots$, $n$ to chunks, depending on their position among distinct chunks. -\end{itemize} - - -The following examples clarify the algorithm and document its versatility. All -examples are of the form $F+D\Longrightarrow T$, meaning that an input file containing $F$ together with the deletion string $D$ produce multiplication table $T$. \\ - - -\textsc{Example:} Data does not have to be arranged into an array of any kind. -\[ \begin{array}{cccc} 0&1&2&1\\ 2&0&2& \\ 0&1& & \end{array}\quad + \quad "" -\quad \Longrightarrow\quad \begin{array}{ccc} 1&2&3\\ 2&3&1\\ 3&1&2 -\end{array} \] - - -\textsc{Example:} Chunks can be any strings. -\[ \begin{array}{cc} {\rm red}&{\rm green}\\ {\rm green}&{\rm red}\\ -\end{array}\quad + \quad "" \quad \Longrightarrow\quad \begin{array}{cc} 1& -2\\ 2& 1 \end{array} \] - - -\textsc{Example:} A typical table produced by \textsf{GAP} is easily parsed by deleting brackets and commas. -\[ [ [0, 1], [1, 0] ] \quad + \quad "[,]" \quad \Longrightarrow\quad -\begin{array}{cc} 1& 2\\ 2& 1 \end{array} \] - - -\textsc{Example:} A typical {\TeX} table with rows separated by lines is also easily converted. Note that we have -to use $\backslash\backslash$ to ensure that every occurrence of $\backslash$ is deleted, since $\backslash\backslash$ represents the character $\backslash$ in \textsf{GAP} -\[ \begin{array}{lll} x\&& y\&&\ z\backslash\backslash\cr y\&& z\&&\ -x\backslash\backslash\cr z\&& x\&&\ y \end{array} \quad + \quad -"\backslash\backslash\&" \quad \Longrightarrow\quad \begin{array}{ccc} -1&2&3\cr 2&3&1\cr 3&1&2 \end{array} \] - -\subsection{\textcolor{Chapter }{QuasigroupFromFile and LoopFromFile}}\logpage{[ 4, 5, 1 ]} -\hyperdef{L}{X81A1DB918057933E}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupFromFile({\mdseries\slshape filename, del})\index{QuasigroupFromFile@\texttt{QuasigroupFromFile}} -\label{QuasigroupFromFile} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopFromFile({\mdseries\slshape filename, del})\index{LoopFromFile@\texttt{LoopFromFile}} -\label{LoopFromFile} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The quasigroup (resp. loop) whose multiplication table data is in file \mbox{\texttt{\mdseries\slshape filename}}, ignoring the characters contained in the string \mbox{\texttt{\mdseries\slshape del}}. - -} - - } - - -\section{\textcolor{Chapter }{Creating Quasigroups and Loops From Sections}}\label{Sec:CreatingQuasigroupsAndLoopsFromSections} -\logpage{[ 4, 6, 0 ]} -\hyperdef{L}{X820E67F88319C38B}{} -{ - - -\subsection{\textcolor{Chapter }{CayleyTableByPerms}} -\logpage{[ 4, 6, 1 ]}\nobreak -\hyperdef{L}{X7F94C8DD7E1A3470}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CayleyTableByPerms({\mdseries\slshape P})\index{CayleyTableByPerms@\texttt{CayleyTableByPerms}} -\label{CayleyTableByPerms} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape P}} is a set of $n$ permutations of an $n$-element set $X$, returns Cayley table $C$ such that $C[i][j] = X[j]^{P[i]}$. - - - - - -The cardinality of the underlying set is determined by the moved points of the -first permutation in \mbox{\texttt{\mdseries\slshape P}}, unless the first permutation is the identity permutation, in which case the -second permutation is used. - -In particular, if \mbox{\texttt{\mdseries\slshape P}} is the left section of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}, \texttt{CayleyTableByPerms(\mbox{\texttt{\mdseries\slshape Q}})} returns the multiplication table of \mbox{\texttt{\mdseries\slshape Q}}. } - - -\subsection{\textcolor{Chapter }{QuasigroupByLeftSection and LoopByLeftSection}}\logpage{[ 4, 6, 2 ]} -\hyperdef{L}{X7EC1EB0D7B8382A1}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupByLeftSection({\mdseries\slshape P})\index{QuasigroupByLeftSection@\texttt{QuasigroupByLeftSection}} -\label{QuasigroupByLeftSection} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByLeftSection({\mdseries\slshape P})\index{LoopByLeftSection@\texttt{LoopByLeftSection}} -\label{LoopByLeftSection} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape P}} is a set of permutations corresponding to the left translations of a -quasigroup (resp. loop), returns the corresponding quasigroup (resp. loop). - - - -The order of permutations in \mbox{\texttt{\mdseries\slshape P}} is important in the quasigroup case, but it is disregarded in the loop case, -since then the order of rows in the corresponding multiplication table is -determined by the presence of the neutral element.} - - -\subsection{\textcolor{Chapter }{QuasigroupByRightSection and LoopByRightSection}}\logpage{[ 4, 6, 3 ]} -\hyperdef{L}{X80B436ED7CC0749E}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupByRightSection({\mdseries\slshape P})\index{QuasigroupByRightSection@\texttt{QuasigroupByRightSection}} -\label{QuasigroupByRightSection} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByRightSection({\mdseries\slshape P})\index{LoopByRightSection@\texttt{LoopByRightSection}} -\label{LoopByRightSection} -}\hfill{\scriptsize (operation)}}\\ - - - These are the dual operations to \texttt{QuasigroupByLeftSection} and \texttt{LoopByLeftSection}.} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@S := Subloop( MoufangLoop( 12, 1 ), [ 3 ] );; | - !gapprompt@gap>| !gapinput@ls := LeftSection( S ); | - [ (), (1,3,5), (1,5,3) ] - !gapprompt@gap>| !gapinput@CayleyTableByPerms( ls ); | - [ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ] - !gapprompt@gap>| !gapinput@CayleyTable( LoopByLeftSection( ls ) ); | - [ [ 1, 2, 3 ], [ 2, 3, 1 ], [ 3, 1, 2 ] ] -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Creating Quasigroups and Loops From Folders}}\label{Sec:CreatingQuasigroupsAndLoopsFromFolders} -\logpage{[ 4, 7, 0 ]} -\hyperdef{L}{X85ABE99E84E5B0E8}{} -{ - Let $G$ be a group, $H$ a subgroup of $G$, and $T$ a right transversal to $H$ in $G$. Let $\tau:G\to T$ be defined by $x\in H\tau(x)$. Then the operation $\circ$ defined on the right cosets $Q = \{Ht|t\in T\}$ by $Hs\circ Ht = H\tau(st)$ turns $Q$ into a quasigroup if and only if $T$ is a right transversal to all conjugates $g^{-1}Hg$ of $H$ in $G$. (In fact, every quasigroup $Q$ can be obtained in this way by letting $G={\rm Mlt}_\rho(Q)$, $H={\rm Inn}_\rho(Q)$ and $T=\{R_x|x\in Q\}$.) - -We call the triple $(G,H,T)$ a \index{folder!quasigroup}\emph{right quasigroup (or loop) folder}. -\subsection{\textcolor{Chapter }{QuasigroupByRightFolder and LoopByRightFolder}}\logpage{[ 4, 7, 1 ]} -\hyperdef{L}{X83168E62861F70AB}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupByRightFolder({\mdseries\slshape G, H, T})\index{QuasigroupByRightFolder@\texttt{QuasigroupByRightFolder}} -\label{QuasigroupByRightFolder} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByRightFolder({\mdseries\slshape G, H, T})\index{LoopByRightFolder@\texttt{LoopByRightFolder}} -\label{LoopByRightFolder} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The quasigroup (resp. loop) from the right folder (\mbox{\texttt{\mdseries\slshape G}}, \mbox{\texttt{\mdseries\slshape H}}, \mbox{\texttt{\mdseries\slshape T}}). - -} - - - -\textsc{Remark:} We do not support the dual operations for left sections since, by default, -actions in \textsf{GAP} act on the right. \\ - - -Here is a simple example in which $T$ is actually the right section of the resulting loop. -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@T := [ (), (1,2)(3,4,5), (1,3,5)(2,4), (1,4,3)(2,5), (1,5,4)(2,3) ];; | - !gapprompt@gap>| !gapinput@G := Group( T );; H := Stabilizer( G, 1 );; | - !gapprompt@gap>| !gapinput@LoopByRightFolder( G, H, T ); | - -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Creating Quasigroups and Loops By Nuclear Extensions}}\label{Sec:CreatingQuasigroupsAndLoopsByNuclearExtensions} -\logpage{[ 4, 8, 0 ]} -\hyperdef{L}{X8759431780AC81A9}{} -{ - Let $K$, $F$ be loops. Then a loop $Q$ is an \index{extension}\emph{extension} of $K$ by $F$ if $K$ is a normal subloop of $Q$ such that $Q/K$ is isomorphic to $F$. An extension $Q$ of $K$ by $F$ is \index{extension!nuclear}\emph{nuclear} if $K$ is an abelian group and $K\le N(Q)$. - -A map $\theta:F\times F\to K$ is a \index{cocycle}\emph{cocycle} if $\theta(1,x) = \theta(x,1) = 1$ for every $x\in F$. - -The following theorem holds for loops $Q$, $F$ and an abelian group $K$: $Q$ is a nuclear extension of $K$ by $F$ if and only if there is a cocycle $\theta:F\times F\to K$ and a homomorphism $\varphi:F\to{\rm Aut}(Q)$ such that $K\times F$ with multiplication $(a,x)(b,y) = (a\varphi_x(b)\theta(x,y),xy)$ is isomorphic to $Q$. - -\subsection{\textcolor{Chapter }{NuclearExtension}} -\logpage{[ 4, 8, 1 ]}\nobreak -\hyperdef{L}{X784733C67AA6B2FA}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NuclearExtension({\mdseries\slshape Q, K})\index{NuclearExtension@\texttt{NuclearExtension}} -\label{NuclearExtension} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } - The data necessary to construct \mbox{\texttt{\mdseries\slshape Q}} as a nuclear extension of the subloop \mbox{\texttt{\mdseries\slshape K}} by \mbox{\texttt{\mdseries\slshape Q}}$/$\mbox{\texttt{\mdseries\slshape K}}, namely $[K, F, \varphi, \theta]$ as above. Note that \mbox{\texttt{\mdseries\slshape K}} must be a commutative subloop of the nucleus of \mbox{\texttt{\mdseries\slshape Q}}. - - - -If $n=|F|$ and $m=|$\mbox{\texttt{\mdseries\slshape K}}$|$, the cocycle $\theta$ is returned as an $n\times n$ array with entries in $\{1,\dots,m\}$, and the homomorphism $\varphi$ is returned as a list of length $n$ of permutations of $\{1,\dots,m\}$.} - - - -\subsection{\textcolor{Chapter }{LoopByExtension}} -\logpage{[ 4, 8, 2 ]}\nobreak -\hyperdef{L}{X79AEE93E7E15B802}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByExtension({\mdseries\slshape K, F, f, t})\index{LoopByExtension@\texttt{LoopByExtension}} -\label{LoopByExtension} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The extension of an abelian group \mbox{\texttt{\mdseries\slshape K}} by a loop \mbox{\texttt{\mdseries\slshape F}}, using action \mbox{\texttt{\mdseries\slshape f}} and cocycle \mbox{\texttt{\mdseries\slshape t}}. The arguments must be formatted as the output of \texttt{NuclearExtension}. - -} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@F := IntoLoop( Group( (1,2) ) ); | - - !gapprompt@gap>| !gapinput@K := DirectProduct( F, F );; | - !gapprompt@gap>| !gapinput@phi := [ (), (2,3) ];; | - !gapprompt@gap>| !gapinput@theta := [ [ 1, 1 ], [ 1, 3 ] ];; | - !gapprompt@gap>| !gapinput@LoopByExtension( K, F, phi, theta ); | - - !gapprompt@gap>| !gapinput@IsAssociative( last ); | - false -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Random Quasigroups and Loops}}\label{Sec:RandomQuasigroupsAndLoops} -\logpage{[ 4, 9, 0 ]} -\hyperdef{L}{X7AE29A1A7AA5C25A}{} -{ - An algorithm is said to select a latin square of order $n$ \emph{at random}\index{latin square!random} if every latin square of order $n$ is returned by the algorithm with the same probability. Selecting a latin -square at random is a nontrivial problem. - -In \cite{JaMa}, Jacobson and Matthews defined a random walk on the space of latin squares -and so-called improper latin squares that visits every latin square with the -same probability. The diameter of the space is no more than $4(n-1)^3$ in the sense that no more than $4(n-1)^3$ properly chosen steps are needed to travel from one latin square of order $n$ to another. - -The Jacobson-Matthews algorithm can be used to generate random quasigroups as -follows: (i) select any latin square of order $n$, for instance the canonical multiplication table of the cyclic group of order $n$, (ii) perform sufficiently many steps of the random walk, stopping at a -proper or improper latin square, (iii) if necessary, perform a few more steps -to end up with a proper latin square. Upon normalizing the resulting latin -square, we obtain a random loop of order $n$. - -By the above result, it suffices to use about $n^3$ steps to arrive at any latin square of order $n$ from the initial latin square. In fact, a smaller number of steps is probably -sufficient. -\subsection{\textcolor{Chapter }{RandomQuasigroup and RandomLoop}}\logpage{[ 4, 9, 1 ]} -\hyperdef{L}{X8271C0F5786B6FA9}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RandomQuasigroup({\mdseries\slshape n[, iter]})\index{RandomQuasigroup@\texttt{RandomQuasigroup}} -\label{RandomQuasigroup} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RandomLoop({\mdseries\slshape n[, iter]})\index{RandomLoop@\texttt{RandomLoop}} -\label{RandomLoop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A random quasigroup (resp. loop) of order \mbox{\texttt{\mdseries\slshape n}} using the Jacobson-Matthews algorithm. If the optional argument \mbox{\texttt{\mdseries\slshape iter}} is omitted, \mbox{\texttt{\mdseries\slshape n}}${}^3$ steps are used. Otherwise \mbox{\texttt{\mdseries\slshape iter}} steps are used. - - - -If \mbox{\texttt{\mdseries\slshape iter}} is small, the Cayley table of the returned quasigroup (resp. loop) will be -close to the canonical Cayley table of the cyclic group of order \mbox{\texttt{\mdseries\slshape n}}.} - - - -\subsection{\textcolor{Chapter }{RandomNilpotentLoop}} -\logpage{[ 4, 9, 2 ]}\nobreak -\hyperdef{L}{X817132C887D3FD3A}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RandomNilpotentLoop({\mdseries\slshape lst})\index{RandomNilpotentLoop@\texttt{RandomNilpotentLoop}} -\label{RandomNilpotentLoop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A random nilpotent loop\index{loop!nilpotent} as follows (see Section \ref{Sec:NilpotencyAndCentralSeries} for more information on nilpotency): \mbox{\texttt{\mdseries\slshape lst}} must be a list of positive integers and/or finite abelian groups. If \texttt{\mbox{\texttt{\mdseries\slshape lst}}=[a1]} and \texttt{a1} is an integer, a random abelian group of order \texttt{a1} is returned, else \texttt{a1} is an abelian group and \texttt{AsLoop(a1)} is returned. If \texttt{\mbox{\texttt{\mdseries\slshape lst}}= [a1,...,am]}, a random central extension of \texttt{RandomNilpotentLoop([a1])} by \texttt{RandomNilpotentLoop([a2,...,am])} is returned. - - - -To determine the nilpotency class $c$ of the resulting loop, assume that \mbox{\texttt{\mdseries\slshape lst}} has length at least 2, contains only integers bigger than 1, and let $m$ be the last entry of \mbox{\texttt{\mdseries\slshape lst}}. If $m>2$ then $c$ is equal to \texttt{Length(\mbox{\texttt{\mdseries\slshape lst}})}, else $c$ is equal to \texttt{Length(\mbox{\texttt{\mdseries\slshape lst}})-1}.} - - } - - -\section{\textcolor{Chapter }{Conversions}}\label{Sec:Conversions} -\logpage{[ 4, 10, 0 ]} -\hyperdef{L}{X7BC2D8877A943D74}{} -{ - \textsf{LOOPS} contains methods that convert between magmas, quasigroups, loops and groups, -provided such conversions are possible. Each of the conversion methods \texttt{IntoQuasigroup}, \texttt{IntoLoop} and \texttt{IntoGroup} returns \texttt{fail} if the requested conversion is not possible. \\ - - -\textsc{Remark:} Up to version 2.0.0 of \textsf{LOOPS}, we supported \texttt{AsQuasigroup}, \texttt{AsLoop} and \texttt{AsGroup} in place of \texttt{IntoQuasigroup}, \texttt{IntoLoop} and \texttt{IntoGroup}, respectively. We have changed the terminology starting with version 2.1.0 in -order to comply with \textsf{GAP} naming rules for \texttt{AsSomething}, as explained in Chapter \ref{Chap:HowThePackageWorks}. Finally, the method \texttt{AsGroup} is a core method of \textsf{GAP} that returns an fp group if its argument is an associative loop. - -\subsection{\textcolor{Chapter }{IntoQuasigroup}} -\logpage{[ 4, 10, 1 ]}\nobreak -\hyperdef{L}{X84575A4B78CC545E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IntoQuasigroup({\mdseries\slshape M})\index{IntoQuasigroup@\texttt{IntoQuasigroup}} -\label{IntoQuasigroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape M}} is a declared magma that happens to be a quasigroup, the corresponding -quasigroup is returned. If \mbox{\texttt{\mdseries\slshape M}} is already declared as a quasigroup, \mbox{\texttt{\mdseries\slshape M}} is returned. - -} - - - -\subsection{\textcolor{Chapter }{PrincipalLoopIsotope}} -\logpage{[ 4, 10, 2 ]}\nobreak -\hyperdef{L}{X79CEA57C850C7070}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{PrincipalLoopIsotope({\mdseries\slshape M, f, g})\index{PrincipalLoopIsotope@\texttt{PrincipalLoopIsotope}} -\label{PrincipalLoopIsotope} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -An isomorphic copy of the principal isotope $($\mbox{\texttt{\mdseries\slshape M}},$\circ)$ via the transposition $(1$,\mbox{\texttt{\mdseries\slshape f}}$\cdot$\mbox{\texttt{\mdseries\slshape g}}$)$. An isomorphic copy is returned rather than $($\mbox{\texttt{\mdseries\slshape M}},$\circ)$ because in \textsf{LOOPS} all loops have to have neutral element labeled as $1$. - - - -Given a quasigroup $M$ and two of its elements $f$, $g$, the principal loop isotope $x\circ y = R_g^{-1}(x)\cdot L_f^{-1}(y)$ turns $(M,\circ)$ into a loop with neutral element $f\cdot g$ (see Section \ref{Sec:HomomorphismsAndHomotopisms}).} - - - -\subsection{\textcolor{Chapter }{IntoLoop}} -\logpage{[ 4, 10, 3 ]}\nobreak -\hyperdef{L}{X7A59C36683118E5A}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IntoLoop({\mdseries\slshape M})\index{IntoLoop@\texttt{IntoLoop}} -\label{IntoLoop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape M}} is a declared magma that happens to be a quasigroup (but not necessarily a -loop!), a loop is returned as follows: If \mbox{\texttt{\mdseries\slshape M}} is already declared as a loop, \mbox{\texttt{\mdseries\slshape M}} is returned. Else, if \mbox{\texttt{\mdseries\slshape M}} possesses a neutral element $e$ and if $f$ is the first element of \mbox{\texttt{\mdseries\slshape M}}, then an isomorphic copy of \mbox{\texttt{\mdseries\slshape M}} via the transposition $(e,f)$ is returned. If \mbox{\texttt{\mdseries\slshape M}} does not posses a neutral element, \texttt{PrincipalLoopIsotope(\mbox{\texttt{\mdseries\slshape M}}, \mbox{\texttt{\mdseries\slshape M.1}}, \mbox{\texttt{\mdseries\slshape M.1}})} is returned.\\ - - -} - - - -\textsc{Remark:} One could obtain a loop from a declared magma \mbox{\texttt{\mdseries\slshape M}} in yet another way, by normalizing the Cayley table of \mbox{\texttt{\mdseries\slshape M}}. The three approaches can result in nonisomorphic loops in general. - -\subsection{\textcolor{Chapter }{IntoGroup}} -\logpage{[ 4, 10, 4 ]}\nobreak -\hyperdef{L}{X7B5C6C64831B866E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IntoGroup({\mdseries\slshape M})\index{IntoGroup@\texttt{IntoGroup}} -\label{IntoGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape M}} is a declared magma that happens to be a group, the corresponding group is -returned as follows: If \mbox{\texttt{\mdseries\slshape M}} is already declared as a group, \mbox{\texttt{\mdseries\slshape M}} is returned, else \texttt{RightMultiplicationGroup(IntoLoop(\mbox{\texttt{\mdseries\slshape M}}))} is returned, which is a permutation group isomorphic to \mbox{\texttt{\mdseries\slshape M}}. - -} - - } - - -\section{\textcolor{Chapter }{Products of Quasigroups and Loops}}\label{Sec:ProductsOfLoops} -\logpage{[ 4, 11, 0 ]} -\hyperdef{L}{X79B7327C79029086}{} -{ - - -\subsection{\textcolor{Chapter }{DirectProduct}} -\logpage{[ 4, 11, 1 ]}\nobreak -\hyperdef{L}{X861BA02C7902A4F4}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{DirectProduct({\mdseries\slshape Q1, ..., Qn})\index{DirectProduct@\texttt{DirectProduct}} -\label{DirectProduct} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -If each \mbox{\texttt{\mdseries\slshape Qi}} is either a declared quasigroup, declared loop or a declared group, the direct -product of \mbox{\texttt{\mdseries\slshape Q1}}, $\dots$, \mbox{\texttt{\mdseries\slshape Qn}} is returned. If every \mbox{\texttt{\mdseries\slshape Qi}} is a declared group, a group is returned; if every \mbox{\texttt{\mdseries\slshape Qi}} is a declared loop, a loop is returned; otherwise a quasigroup is returned. - -} - - } - - -\section{\textcolor{Chapter }{Opposite Quasigroups and Loops}}\label{Sec:OppositeQuasigroupsAndLoops} -\logpage{[ 4, 12, 0 ]} -\hyperdef{L}{X7865FC8D7854C2E3}{} -{ - When $Q$ is a quasigroup with multiplication $\cdot$, the \index{opposite quasigroup}\index{quasigroup!opposite}\emph{opposite quasigroup} of $Q$ is a quasigroup with the same underlying set as $Q$ and with multiplication $*$ defined by $x*y=y\cdot x$. -\subsection{\textcolor{Chapter }{Opposite, OppositeQuasigroup and OppositeLoop}}\logpage{[ 4, 12, 1 ]} -\hyperdef{L}{X87B6AED47EE2BCD3}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Opposite({\mdseries\slshape Q})\index{Opposite@\texttt{Opposite}} -\label{Opposite} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{OppositeQuasigroup({\mdseries\slshape Q})\index{OppositeQuasigroup@\texttt{OppositeQuasigroup}} -\label{OppositeQuasigroup} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{OppositeLoop({\mdseries\slshape Q})\index{OppositeLoop@\texttt{OppositeLoop}} -\label{OppositeLoop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } - The opposite of the quasigroup (resp. loop) \mbox{\texttt{\mdseries\slshape Q}}. Note that if \texttt{OppositeQuasigroup(\mbox{\texttt{\mdseries\slshape Q}})} or \texttt{OppositeLoop(\mbox{\texttt{\mdseries\slshape Q}})} are called, then the returned quasigroup or loop is not stored as an attribute -of \mbox{\texttt{\mdseries\slshape Q}}. - -} - - } - - } - - -\chapter{\textcolor{Chapter }{Basic Methods And Attributes}}\label{Chap:BasicMethodsAndAttributes} -\logpage{[ 5, 0, 0 ]} -\hyperdef{L}{X7B9F619279641FAA}{} -{ - In this chapter we describe the basic core methods and attributes of the \textsf{LOOPS} package. -\section{\textcolor{Chapter }{Basic Attributes}}\label{Sec:BasicAttributes} -\logpage{[ 5, 1, 0 ]} -\hyperdef{L}{X8373A7348161DB23}{} -{ - We associate many attributes with quasigroups in order to speed up -computation. This section lists some basic attributes of quasigroups and -loops. - -\subsection{\textcolor{Chapter }{Elements}} -\logpage{[ 5, 1, 1 ]}\nobreak -\hyperdef{L}{X79B130FC7906FB4C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Elements({\mdseries\slshape Q})\index{Elements@\texttt{Elements}} -\label{Elements} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The list of elements of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - - - -See Section \ref{Sec:NamingEtc} for more information about element labels.} - - - -\subsection{\textcolor{Chapter }{CayleyTable}} -\logpage{[ 5, 1, 2 ]}\nobreak -\hyperdef{L}{X85457FA27DE7114D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CayleyTable({\mdseries\slshape Q})\index{CayleyTable@\texttt{CayleyTable}} -\label{CayleyTable} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The Cayley table of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - - - -See Section \ref{Sec:AboutCayleyTables} for more information about quasigroup Cayley tables.} - - - -\subsection{\textcolor{Chapter }{One}} -\logpage{[ 5, 1, 3 ]}\nobreak -\hyperdef{L}{X8129A6877FFD804B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{One({\mdseries\slshape Q})\index{One@\texttt{One}} -\label{One} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The identity element of a loop \mbox{\texttt{\mdseries\slshape Q}}. - -} - - - -\textsc{Remark:}If you want to know if a quasigroup \mbox{\texttt{\mdseries\slshape Q}} has a neutral element, you can find out with the standard function for magmas \texttt{MultiplicativeNeutralElement(\mbox{\texttt{\mdseries\slshape Q}})}. - -\subsection{\textcolor{Chapter }{Size}} -\logpage{[ 5, 1, 4 ]}\nobreak -\hyperdef{L}{X858ADA3B7A684421}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Size({\mdseries\slshape Q})\index{Size@\texttt{Size}} -\label{Size} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The size of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - -} - - - -\subsection{\textcolor{Chapter }{Exponent}} -\logpage{[ 5, 1, 5 ]}\nobreak -\hyperdef{L}{X7D44470C7DA59C1C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Exponent({\mdseries\slshape Q})\index{Exponent@\texttt{Exponent}} -\label{Exponent} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The exponent of a power associative loop \mbox{\texttt{\mdseries\slshape Q}}. (The method does not test if \mbox{\texttt{\mdseries\slshape Q}} is power associative.) - - - -When \mbox{\texttt{\mdseries\slshape Q}} is a \emph{power associative loop}\index{loop!power associative}\index{power associative loop}, that is, the powers of elements are well-defined in \mbox{\texttt{\mdseries\slshape Q}}, then the \emph{exponent}\index{exponent} of \mbox{\texttt{\mdseries\slshape Q}} is the smallest positive integer divisible by the orders of all elements of \mbox{\texttt{\mdseries\slshape Q}}. } - - } - - -\section{\textcolor{Chapter }{Basic Arithmetic Operations}}\label{Sec:BasicArithemticOperations} -\logpage{[ 5, 2, 0 ]} -\hyperdef{L}{X82F2CA4A848ABD2B}{} -{ - Each quasigroup element in \textsf{GAP} knows to which quasigroup it belongs. It is therefore possible to perform -arithmetic operations with quasigroup elements without referring to the -quasigroup. All elements involved in the calculation must belong to the same -quasigroup. - -Two elements $x$, $y$ of the same quasigroup are multiplied by $x*y$ in \textsf{GAP}. Since multiplication of at least three elements is ambiguous in the -nonassociative case, we parenthesize elements by default from left to right, -i.e., $x*y*z$ means $((x*y)*z)$. Of course, one can specify the order of multiplications by providing -parentheses. -\subsection{\textcolor{Chapter }{LeftDivision and RightDivision}}\logpage{[ 5, 2, 1 ]} -\hyperdef{L}{X7D5956967BCC1834}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftDivision({\mdseries\slshape x, y})\index{LeftDivision@\texttt{LeftDivision}} -\label{LeftDivision} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightDivision({\mdseries\slshape x, y})\index{RightDivision@\texttt{RightDivision}} -\label{RightDivision} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The left division \mbox{\texttt{\mdseries\slshape x}}$\backslash$\mbox{\texttt{\mdseries\slshape y}} (resp. the right division \mbox{\texttt{\mdseries\slshape x}}$/$\mbox{\texttt{\mdseries\slshape y}}) of two elements \mbox{\texttt{\mdseries\slshape x}}, \mbox{\texttt{\mdseries\slshape y}} of the same quasigroup.\\ - - -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftDivision({\mdseries\slshape S, x})\index{LeftDivision@\texttt{LeftDivision}} -\label{LeftDivision} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftDivision({\mdseries\slshape x, S})\index{LeftDivision@\texttt{LeftDivision}} -\label{LeftDivision} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightDivision({\mdseries\slshape S, x})\index{RightDivision@\texttt{RightDivision}} -\label{RightDivision} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightDivision({\mdseries\slshape x, S})\index{RightDivision@\texttt{RightDivision}} -\label{RightDivision} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The list of elements obtained by performing the specified arithmetical -operation elementwise using a list \mbox{\texttt{\mdseries\slshape S}} of elements and an element \mbox{\texttt{\mdseries\slshape x}}.\\ - - -} - - - -\textsc{Remark:} We support $/$ in place of \texttt{RightDivision}. But we do not support $\backslash$ in place of \texttt{LeftDivision}. -\subsection{\textcolor{Chapter }{LeftDivisionCayleyTable and RightDivisionCayleyTable}}\logpage{[ 5, 2, 2 ]} -\hyperdef{L}{X804F67C8796A0EB3}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftDivisionCayleyTable({\mdseries\slshape Q})\index{LeftDivisionCayleyTable@\texttt{LeftDivisionCayleyTable}} -\label{LeftDivisionCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightDivisionCayleyTable({\mdseries\slshape Q})\index{RightDivisionCayleyTable@\texttt{RightDivisionCayleyTable}} -\label{RightDivisionCayleyTable} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The Cayley table of the respective arithmetic operation of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - -} - - } - - -\section{\textcolor{Chapter }{Powers and Inverses}}\label{Sec:PowersAndInverses} -\logpage{[ 5, 3, 0 ]} -\hyperdef{L}{X810850247ADB4EE9}{} -{ - Powers of elements are generally not well-defined in quasigroups. For magmas -and a positive integral exponent, \textsf{GAP} calculates powers in the following way: $x^1=x$, $x^{2k}=(x^k)\cdot(x^k)$ and $x^{2k+1}=(x^{2k})\cdot x$. One can easily see that this returns $x^k$ in about $\log_2(k)$ steps. For \textsf{LOOPS}, we have decided to keep this method, but the user should be aware that the -method is sound only in power associative quasigroups. - -Let $x$ be an element of a loop $Q$ with neutral element $1$. Then the \emph{left inverse}\index{inverse!left} $x^\lambda$ of $x$ is the unique element of $Q$ satisfying $x^\lambda x=1$. Similarly, the \emph{right inverse}\index{inverse!right} $x^\rho$ satisfies $xx^\rho=1$. If $x^\lambda=x^\rho$, we call $x^{-1}=x^\lambda=x^\rho$ the \emph{inverse}\index{inverse} of $x$. -\subsection{\textcolor{Chapter }{LeftInverse, RightInverse and Inverse}}\logpage{[ 5, 3, 1 ]} -\hyperdef{L}{X805781838020CF44}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftInverse({\mdseries\slshape x})\index{LeftInverse@\texttt{LeftInverse}} -\label{LeftInverse} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightInverse({\mdseries\slshape x})\index{RightInverse@\texttt{RightInverse}} -\label{RightInverse} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Inverse({\mdseries\slshape x})\index{Inverse@\texttt{Inverse}} -\label{Inverse} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The left inverse, right inverse and inverse, respectively, of the quasigroup -element \mbox{\texttt{\mdseries\slshape x}}. - -} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@CayleyTable( Q ); | - [ [ 1, 2, 3, 4, 5 ], - [ 2, 1, 4, 5, 3 ], - [ 3, 4, 5, 1, 2 ], - [ 4, 5, 2, 3, 1 ], - [ 5, 3, 1, 2, 4 ] ] - !gapprompt@gap>| !gapinput@elms := Elements( Q ); | - !gapprompt@gap>| !gapinput@[ l1, l2, l3, l4, l5 ]; | - !gapprompt@gap>| !gapinput@[ LeftInverse( elms[3] ), RightInverse( elms[3] ), Inverse( elms[3] ) ]; | - [ l5, l4, fail ] -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Associators and Commutators}}\label{Sec:AssociatorsAndCommutators2} -\logpage{[ 5, 4, 0 ]} -\hyperdef{L}{X7E0849977869E53D}{} -{ - See Section \ref{Sec:AssociatorsAndCommutators} for definitions of associators and commutators. - -\subsection{\textcolor{Chapter }{Associator}} -\logpage{[ 5, 4, 1 ]}\nobreak -\hyperdef{L}{X82B7448879B91F7B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Associator({\mdseries\slshape x, y, z})\index{Associator@\texttt{Associator}} -\label{Associator} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The associator of the elements \mbox{\texttt{\mdseries\slshape x}}, \mbox{\texttt{\mdseries\slshape y}}, \mbox{\texttt{\mdseries\slshape z}} of the same quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{Commutator}} -\logpage{[ 5, 4, 2 ]}\nobreak -\hyperdef{L}{X7D624A9587FB1FE5}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Commutator({\mdseries\slshape x, y})\index{Commutator@\texttt{Commutator}} -\label{Commutator} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The commutator of the elements \mbox{\texttt{\mdseries\slshape x}}, \mbox{\texttt{\mdseries\slshape y}} of the same quasigroup. - -} - - } - - -\section{\textcolor{Chapter }{Generators}}\label{Sec:Generators} -\logpage{[ 5, 5, 0 ]} -\hyperdef{L}{X7BD5B55C802805B4}{} -{ - -\subsection{\textcolor{Chapter }{GeneratorsOfQuasigroup and GeneratorsOfLoop}}\logpage{[ 5, 5, 1 ]} -\hyperdef{L}{X83944A777D161D10}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{GeneratorsOfQuasigroup({\mdseries\slshape Q})\index{GeneratorsOfQuasigroup@\texttt{GeneratorsOfQuasigroup}} -\label{GeneratorsOfQuasigroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{GeneratorsOfLoop({\mdseries\slshape Q})\index{GeneratorsOfLoop@\texttt{GeneratorsOfLoop}} -\label{GeneratorsOfLoop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -A set of generators of a quasigroup (resp. loop) \mbox{\texttt{\mdseries\slshape Q}}. (Both methods are synonyms of \texttt{GeneratorsOfMagma}.) - -} - - - -As usual in \textsf{GAP}, one can refer to the \texttt{i}th generator of a quasigroup \texttt{Q} by \texttt{Q.i}. Note that while it is often the case that \texttt{ Q.i = Elements(Q)[i]}, it is not necessarily so. - -\subsection{\textcolor{Chapter }{GeneratorsSmallest}} -\logpage{[ 5, 5, 2 ]}\nobreak -\hyperdef{L}{X82FD78AF7F80A0E2}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{GeneratorsSmallest({\mdseries\slshape Q})\index{GeneratorsSmallest@\texttt{GeneratorsSmallest}} -\label{GeneratorsSmallest} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -A generating set $\{q_0$, $\dots$, $q_m\}$ of \mbox{\texttt{\mdseries\slshape Q}} such that $Q_0=\emptyset$, $Q_m=$\mbox{\texttt{\mdseries\slshape Q}}, $Q_i=\langle q_1$, $\dots$, $q_i \rangle$, and $q_{i+1}$ is the least element of \mbox{\texttt{\mdseries\slshape Q}}$\setminus Q_i$. - -} - - - -\subsection{\textcolor{Chapter }{SmallGeneratingSet}} -\logpage{[ 5, 5, 3 ]}\nobreak -\hyperdef{L}{X814DBABC878D5232}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{SmallGeneratingSet({\mdseries\slshape Q})\index{SmallGeneratingSet@\texttt{SmallGeneratingSet}} -\label{SmallGeneratingSet} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -A small generating set $\{q_0$, $\dots$, $q_m\}$ of \mbox{\texttt{\mdseries\slshape Q}} obtained as follows: $q_0$ is the least element for which $\langle q_0\rangle$ is largest possible, $q_1$\$ is the least element for which $\langle q_0,q_1$ is largest possible, and so on. - -} - - } - - } - - -\chapter{\textcolor{Chapter }{Methods Based on Permutation Groups}}\label{Chap:MethodsBasedOnPermutationGroups} -\logpage{[ 6, 0, 0 ]} -\hyperdef{L}{X794A04C5854D352B}{} -{ - Most calculations in the \textsf{LOOPS} package are delegated to groups, taking advantage of the various permutations -and permutation groups associated with quasigroups. This chapter explains in -detail how the permutations associated with a quasigroup are calculated, and -it also describes some of the core methods of \textsf{LOOPS} based on permutations. Additional core methods can be found in Chapter \ref{Chap:TestingPropertiesOfQuasigroupsAndLoops}. -\section{\textcolor{Chapter }{Parent of a Quasigroup}}\label{Sec:ParentOfAQuasigroup} -\logpage{[ 6, 1, 0 ]} -\hyperdef{L}{X8731D818827C08F3}{} -{ - Let $Q$ be a quasigroup and $S$ a subquasigroup of $Q$. Since the multiplication in $S$ coincides with the multiplication in $Q$, it is reasonable not to store the multiplication table of $S$. However, the quasigroup $S$ then must know that it is a subquasigroup of $Q$. - -\subsection{\textcolor{Chapter }{Parent}} -\logpage{[ 6, 1, 1 ]}\nobreak -\hyperdef{L}{X7BC856CC7F116BB0}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Parent({\mdseries\slshape Q})\index{Parent@\texttt{Parent}} -\label{Parent} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The parent quasigroup of the quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - - - -When \mbox{\texttt{\mdseries\slshape Q}} is not created as a subquasigroup of another quasigroup, the attribute \texttt{Parent(\mbox{\texttt{\mdseries\slshape Q}})} is set to \mbox{\texttt{\mdseries\slshape Q}}. When \mbox{\texttt{\mdseries\slshape Q}} is created as a subquasigroup of a quasigroup \mbox{\texttt{\mdseries\slshape H}}, we set \texttt{Parent(\mbox{\texttt{\mdseries\slshape Q}})} equal to \texttt{Parent(\mbox{\texttt{\mdseries\slshape H}})}. Thus, in effect, \texttt{Parent(\mbox{\texttt{\mdseries\slshape Q}})} is the largest quasigroup from which \mbox{\texttt{\mdseries\slshape Q}} has been created.} - - - -\subsection{\textcolor{Chapter }{Position}} -\logpage{[ 6, 1, 2 ]}\nobreak -\hyperdef{L}{X79975EC6783B4293}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Position({\mdseries\slshape Q, x})\index{Position@\texttt{Position}} -\label{Position} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The position of \mbox{\texttt{\mdseries\slshape x}} among the elements of \mbox{\texttt{\mdseries\slshape Q}}.\\ - - -} - - - -Let \mbox{\texttt{\mdseries\slshape Q}} be a quasigroup with parent \mbox{\texttt{\mdseries\slshape P}}, where \mbox{\texttt{\mdseries\slshape P}} is some $n$-element quasigroup. Let \mbox{\texttt{\mdseries\slshape x}} be an element of \mbox{\texttt{\mdseries\slshape Q}}. Then \texttt{\mbox{\texttt{\mdseries\slshape x}}![1]} is the position of \mbox{\texttt{\mdseries\slshape x}} among the elements of \mbox{\texttt{\mdseries\slshape P}}, i.e., \texttt{\mbox{\texttt{\mdseries\slshape x}}![1] = Position(Elements(\mbox{\texttt{\mdseries\slshape P}}),\mbox{\texttt{\mdseries\slshape x}})}. - -While referring to elements of \mbox{\texttt{\mdseries\slshape Q}} by their positions, the user should understand whether the positions are meant -among the elements of \mbox{\texttt{\mdseries\slshape Q}}, or among the elements of the parent \mbox{\texttt{\mdseries\slshape P}} of \mbox{\texttt{\mdseries\slshape Q}}. Since it requires no calculation to obtain \texttt{\mbox{\texttt{\mdseries\slshape x}}![1]}, we always use the position of an element in its parent quasigroup in \textsf{LOOPS}. In this way, many attributes of a quasigroup, including its Cayley table, -are permanently tied to its parent. - -It is now clear why we have not insisted that Cayley tables of quasigroups -must have entries covering the entire interval $1$, $\dots$, $n$ for some $n$. - -\subsection{\textcolor{Chapter }{PosInParent}} -\logpage{[ 6, 1, 3 ]}\nobreak -\hyperdef{L}{X832295DE866E44EE}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{PosInParent({\mdseries\slshape S})\index{PosInParent@\texttt{PosInParent}} -\label{PosInParent} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape S}} is a list of quasigroup elements (not necessarily from the same quasigroup), -returns the corresponding list of positions of elements of \mbox{\texttt{\mdseries\slshape S}} in the corresponding parent, i.e., \texttt{PosInParent(\mbox{\texttt{\mdseries\slshape S}})[i] = \mbox{\texttt{\mdseries\slshape S}}[i]![1] = Position(Parent(\mbox{\texttt{\mdseries\slshape S}}[i]),\mbox{\texttt{\mdseries\slshape S}}[i])}.\\ - - -} - - - -Quasigroups with the same parent can be compared as follows. Assume that $A$, $B$ are two quasigroups with common parent $Q$. Let $G_A$, $G_B$ be the canonical generating sets of $A$ and $B$, respectively, obtained by the method \texttt{GeneratorsSmallest} (see Section \ref{Sec:Generators}). Then we define $A| !gapinput@M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.5 ] ); | - - !gapprompt@gap>| !gapinput@[ Parent( S ) = M, Elements( S ), PosInParent( S ) ]; | - [ true, [ l1, l3, l5], [ 1, 3, 5 ] ] - !gapprompt@gap>| !gapinput@HasCayleyTable( S ); | - false - !gapprompt@gap>| !gapinput@SetLoopElmName( S, "s" );; Elements( S ); Elements( M ); | - [ s1, s3, s5 ] - [ s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12 ] - !gapprompt@gap>| !gapinput@CayleyTable( S ); | - [ [ 1, 3, 5 ], [ 3, 5, 1 ], [ 5, 1, 3 ] ] - !gapprompt@gap>| !gapinput@LeftSection( S ); | - [ (), (1,3,5), (1,5,3) ] - !gapprompt@gap>| !gapinput@[ HasCayleyTable( S ), Parent( S ) = M ]; | - [ true, true ] - !gapprompt@gap>| !gapinput@L := LoopByCayleyTable( CayleyTable( S ) );; Elements( L ); | - [ l1, l2, l3 ] - !gapprompt@gap>| !gapinput@[ Parent( L ) = L, IsSubloop( M, S ), IsSubloop( M, L ) ]; | - [ true, true, false ] - !gapprompt@gap>| !gapinput@LeftSection( L ); | - [ (), (1,2,3), (1,3,2) ] -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Multiplication Groups}}\label{Sec:MultiplicationGroups} -\logpage{[ 6, 4, 0 ]} -\hyperdef{L}{X78ED50F578A88046}{} -{ - -\subsection{\textcolor{Chapter }{LeftMutliplicationGroup, RightMultiplicationGroup and MultiplicationGroup}}\logpage{[ 6, 4, 1 ]} -\hyperdef{L}{X87302BE983A5FC61}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftMultiplicationGroup({\mdseries\slshape Q})\index{LeftMultiplicationGroup@\texttt{LeftMultiplicationGroup}} -\label{LeftMultiplicationGroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightMultiplicationGroup({\mdseries\slshape Q})\index{RightMultiplicationGroup@\texttt{RightMultiplicationGroup}} -\label{RightMultiplicationGroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MultiplicationGroup({\mdseries\slshape Q})\index{MultiplicationGroup@\texttt{MultiplicationGroup}} -\label{MultiplicationGroup} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The left multiplication group, right multiplication group, resp. -multiplication group of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - -} - - -\subsection{\textcolor{Chapter }{RelativeLeftMultiplicationGroup, RelativeRightMultiplicationGroup and -RelativeMultiplicationGroup}}\logpage{[ 6, 4, 2 ]} -\hyperdef{L}{X847256B779E1E7E5}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RelativeLeftMultiplicationGroup({\mdseries\slshape Q, S})\index{RelativeLeftMultiplicationGroup@\texttt{RelativeLeftMultiplicationGroup}} -\label{RelativeLeftMultiplicationGroup} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RelativeRightMultiplicationGroup({\mdseries\slshape Q, S})\index{RelativeRightMultiplicationGroup@\texttt{RelativeRightMultiplicationGroup}} -\label{RelativeRightMultiplicationGroup} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RelativeMultiplicationGroup({\mdseries\slshape Q, S})\index{RelativeMultiplicationGroup@\texttt{RelativeMultiplicationGroup}} -\label{RelativeMultiplicationGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The relative left multiplication group, the relative right multiplication -group, resp. the relative multiplication group of a quasigroup \mbox{\texttt{\mdseries\slshape Q}} with respect to a subquasigroup \mbox{\texttt{\mdseries\slshape S}} of \mbox{\texttt{\mdseries\slshape Q}}. - - - -Let $S$ be a subquasigroup of a quasigroup $Q$. Then the \index{multiplication group!relative left}\emph{relative left multiplication group} of $Q$ with respect to $S$ is the group $\langle L(x)|x\in S\rangle$, where $L(x)$ is the left translation by $x$ in $Q$ restricted to $S$. The \index{multiplication group!relative right }\emph{relative right multiplication group} and the \index{multiplication group!relative}\emph{relative multiplication group} are defined analogously.} - - } - - -\section{\textcolor{Chapter }{Inner Mapping Groups}}\label{Sec:InnerMappingGroups} -\logpage{[ 6, 5, 0 ]} -\hyperdef{L}{X8740D61178ACD217}{} -{ - By a result of Bruck, the left inner mapping group of a loop is generated by -all \index{inner mapping!left}\emph{left inner mappings} $L(x,y) = L_{yx}^{-1}L_yL_x$, and the right inner mapping group is generated by all \index{inner mapping!right}\emph{right inner mappings} $R(x,y) = R_{xy}^{-1}R_yR_x$. - -In analogy with group theory, we define the \index{conjugation}\emph{conjugations} or the \index{inner mapping!middle}\emph{middle inner mappings} as $T(x) = L_x^{-1}R_x$. The \index{inner mapping group!middle}\emph{middle inner mapping grroup} is then the group generated by all conjugations. -\subsection{\textcolor{Chapter }{LeftInnerMapping, RightInnerMapping, MiddleInnerMapping}}\logpage{[ 6, 5, 1 ]} -\hyperdef{L}{X7EE1E78C856C6F7C}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftInnerMapping({\mdseries\slshape Q, x, y})\index{LeftInnerMapping@\texttt{LeftInnerMapping}} -\label{LeftInnerMapping} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightInnerMapping({\mdseries\slshape Q, x, y})\index{RightInnerMapping@\texttt{RightInnerMapping}} -\label{RightInnerMapping} -}\hfill{\scriptsize (operation)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MiddleInnerMapping({\mdseries\slshape Q, x})\index{MiddleInnerMapping@\texttt{MiddleInnerMapping}} -\label{MiddleInnerMapping} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The left inner mapping $L($\mbox{\texttt{\mdseries\slshape x}},\mbox{\texttt{\mdseries\slshape y}}$)$, the right inner mapping $R($\mbox{\texttt{\mdseries\slshape x}},\mbox{\texttt{\mdseries\slshape y}}$)$, resp. the middle inner mapping $T($\mbox{\texttt{\mdseries\slshape x}}$)$ of a loop \mbox{\texttt{\mdseries\slshape Q}}. - -} - - -\subsection{\textcolor{Chapter }{LeftInnerMappingGroup, RightInnerMappingGroup, MiddleInnerMappingGroup}}\logpage{[ 6, 5, 2 ]} -\hyperdef{L}{X79CDA09A7D48BF2B}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftInnerMappingGroup({\mdseries\slshape Q})\index{LeftInnerMappingGroup@\texttt{LeftInnerMappingGroup}} -\label{LeftInnerMappingGroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightInnerMappingGroup({\mdseries\slshape Q})\index{RightInnerMappingGroup@\texttt{RightInnerMappingGroup}} -\label{RightInnerMappingGroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MiddleInnerMappingGroup({\mdseries\slshape Q})\index{MiddleInnerMappingGroup@\texttt{MiddleInnerMappingGroup}} -\label{MiddleInnerMappingGroup} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The left inner mapping group, right inner mapping group, resp. middle inner -mapping group of a loop \mbox{\texttt{\mdseries\slshape Q}}. - -} - - - -\subsection{\textcolor{Chapter }{InnerMappingGroup}} -\logpage{[ 6, 5, 3 ]}\nobreak -\hyperdef{L}{X82513A3B7C3A6420}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{InnerMappingGroup({\mdseries\slshape Q})\index{InnerMappingGroup@\texttt{InnerMappingGroup}} -\label{InnerMappingGroup} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The inner mapping group of a loop \mbox{\texttt{\mdseries\slshape Q}}.\\ - - -} - - - -Here is an example for multiplication groups and inner mapping groups: -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@M := MoufangLoop(12,1); | - - !gapprompt@gap>| !gapinput@LeftSection(M)[2]; | - (1,2)(3,4)(5,6)(7,8)(9,12)(10,11) - !gapprompt@gap>| !gapinput@Mlt := MultiplicationGroup(M); Inn := InnerMappingGroup(M); | - - Group([ (4,6)(7,11), (7,11)(8,10), (2,6,4)(7,9,11), (3,5)(9,11), (8,12,10) ]) - !gapprompt@gap>| !gapinput@Size(Inn); | - 216 -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Nuclei, Commutant, Center, and Associator Subloop}}\label{Sec:NucleiEtal} -\logpage{[ 6, 6, 0 ]} -\hyperdef{L}{X7B45C2AF7C2E28AB}{} -{ - See Section \ref{Sec:SubquasigroupsAndSubloops} for the relevant definitions. -\subsection{\textcolor{Chapter }{LeftNucles, MiddleNucleus, and RightNucleus}}\logpage{[ 6, 6, 1 ]} -\hyperdef{L}{X7DF536FC85BBD1D2}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftNucleus({\mdseries\slshape Q})\index{LeftNucleus@\texttt{LeftNucleus}} -\label{LeftNucleus} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MiddleNucleus({\mdseries\slshape Q})\index{MiddleNucleus@\texttt{MiddleNucleus}} -\label{MiddleNucleus} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightNucleus({\mdseries\slshape Q})\index{RightNucleus@\texttt{RightNucleus}} -\label{RightNucleus} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The left nucleus, middle nucleus, resp. right nucleus of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - -} - - -\subsection{\textcolor{Chapter }{Nuc, NucleusOfQuasigroup and NucleusOfLoop}}\logpage{[ 6, 6, 2 ]} -\hyperdef{L}{X84D389677A91C290}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Nuc({\mdseries\slshape Q})\index{Nuc@\texttt{Nuc}} -\label{Nuc} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NucleusOfQuasigroup({\mdseries\slshape Q})\index{NucleusOfQuasigroup@\texttt{NucleusOfQuasigroup}} -\label{NucleusOfQuasigroup} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NucleusOfLoop({\mdseries\slshape Q})\index{NucleusOfLoop@\texttt{NucleusOfLoop}} -\label{NucleusOfLoop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -These synonymous attributes return the nucleus of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - - - -Since all nuclei are subquasigroups of \mbox{\texttt{\mdseries\slshape Q}}, they are returned as subquasigroups (resp. subloops). When \mbox{\texttt{\mdseries\slshape Q}} is a loop then all nuclei are in fact groups, and they are returned as -associative loops. - -\textsc{Remark:} The name \texttt{Nucleus} is a global function of \textsf{GAP} with two variables. We have therefore used \texttt{Nuc} rather than \texttt{Nucleus} for the nucleus. This abbreviation is sometimes used in the literature, too.} - - - -\subsection{\textcolor{Chapter }{Commutant}} -\logpage{[ 6, 6, 3 ]}\nobreak -\hyperdef{L}{X7C8428DE791F3CE1}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Commutant({\mdseries\slshape Q})\index{Commutant@\texttt{Commutant}} -\label{Commutant} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The commutant of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - -} - - - -\subsection{\textcolor{Chapter }{Center}} -\logpage{[ 6, 6, 4 ]}\nobreak -\hyperdef{L}{X7C1FBE7A84DD4873}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Center({\mdseries\slshape Q})\index{Center@\texttt{Center}} -\label{Center} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The center of a quasigroup \mbox{\texttt{\mdseries\slshape Q}}. - - - -If \mbox{\texttt{\mdseries\slshape Q}} is a loop, the center of \mbox{\texttt{\mdseries\slshape Q}} is a subgroup of \mbox{\texttt{\mdseries\slshape Q}} and it is returned as an associative loop.} - - - -\subsection{\textcolor{Chapter }{AssociatorSubloop}} -\logpage{[ 6, 6, 5 ]}\nobreak -\hyperdef{L}{X7F7FDE82780EDD7E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AssociatorSubloop({\mdseries\slshape Q})\index{AssociatorSubloop@\texttt{AssociatorSubloop}} -\label{AssociatorSubloop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The associator subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -We calculate the associator subloop of \mbox{\texttt{\mdseries\slshape Q}} as the smallest normal subloop of \mbox{\texttt{\mdseries\slshape Q}} containing all elements $x\backslash\alpha(x)$, where $x$ is an element of \mbox{\texttt{\mdseries\slshape Q}} and $\alpha$ is a left inner mapping of \mbox{\texttt{\mdseries\slshape Q}}.} - - } - - -\section{\textcolor{Chapter }{Normal Subloops and Simple Loops}}\label{Sec:NormalSubloopsAndSimpleLoops} -\logpage{[ 6, 7, 0 ]} -\hyperdef{L}{X85B650D284FE39F3}{} -{ - - -\subsection{\textcolor{Chapter }{IsNormal}} -\logpage{[ 6, 7, 1 ]}\nobreak -\hyperdef{L}{X838186F9836F678C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsNormal({\mdseries\slshape Q, S})\index{IsNormal@\texttt{IsNormal}} -\label{IsNormal} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape S}} is a normal subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -A subloop $S$ of a loop $Q$ is \emph{normal}\index{subloop!normal}\index{normal subloop} if it is invariant under all inner mappings of $Q$. } - - - -\subsection{\textcolor{Chapter }{NormalClosure}} -\logpage{[ 6, 7, 2 ]}\nobreak -\hyperdef{L}{X7BDEA0A98720D1BB}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NormalClosure({\mdseries\slshape Q, S})\index{NormalClosure@\texttt{NormalClosure}} -\label{NormalClosure} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -The normal closure of a subset \mbox{\texttt{\mdseries\slshape S}} of a loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -For a subset $S$ of a loop $Q$, the \emph{normal closure}\index{normal closure} of $S$ in $Q$ is the smallest normal subloop of $Q$ containing $S$.} - - - -\subsection{\textcolor{Chapter }{IsSimple}} -\logpage{[ 6, 7, 3 ]}\nobreak -\hyperdef{L}{X7D8E63A7824037CC}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsSimple({\mdseries\slshape Q})\index{IsSimple@\texttt{IsSimple}} -\label{IsSimple} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a simple loop. - - - -A loop $Q$ is \emph{simple}\index{simple loop}\index{loop!simple} if $\{1\}$ and $Q$ are the only normal subloops of $Q$.} - - } - - -\section{\textcolor{Chapter }{Factor Loops}}\label{Sec:FactorLoops} -\logpage{[ 6, 8, 0 ]} -\hyperdef{L}{X87F66DB383C29A4A}{} -{ - - -\subsection{\textcolor{Chapter }{FactorLoop}} -\logpage{[ 6, 8, 1 ]}\nobreak -\hyperdef{L}{X83E1953980E2DE2F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{FactorLoop({\mdseries\slshape Q, S})\index{FactorLoop@\texttt{FactorLoop}} -\label{FactorLoop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape S}} is a normal subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}, returns the factor loop \mbox{\texttt{\mdseries\slshape Q}}$/$\mbox{\texttt{\mdseries\slshape S}}. - -} - - - -\subsection{\textcolor{Chapter }{NaturalHomomorphismByNormalSubloop}} -\logpage{[ 6, 8, 2 ]}\nobreak -\hyperdef{L}{X870FCB497AECC730}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NaturalHomomorphismByNormalSubloop({\mdseries\slshape Q, S})\index{NaturalHomomorphismByNormalSubloop@\texttt{NaturalHomomorphismByNormalSubloop}} -\label{NaturalHomomorphismByNormalSubloop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape S}} is a normal subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}, returns the natural projection from \mbox{\texttt{\mdseries\slshape Q}} onto \mbox{\texttt{\mdseries\slshape Q}}$/$\mbox{\texttt{\mdseries\slshape S}}. - -} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@M := MoufangLoop( 12, 1 );; S := Subloop( M, [ M.3 ] ); | - - !gapprompt@gap>| !gapinput@IsNormal( M, S ); | - true - !gapprompt@gap>| !gapinput@F := FactorLoop( M, S ); | - - !gapprompt@gap>| !gapinput@NaturalHomomorphismByNormalSubloop( M, S ); | - MappingByFunction( , , - function( x ) ... end ) -\end{Verbatim} - } - - -\section{\textcolor{Chapter }{Nilpotency and Central Series}}\label{Sec:NilpotencyAndCentralSeries} -\logpage{[ 6, 9, 0 ]} -\hyperdef{L}{X821F40748401D698}{} -{ - See Section \ref{Sec:NilpotenceAndSolvability} for the relevant definitions. - -\subsection{\textcolor{Chapter }{IsNilpotent}} -\logpage{[ 6, 9, 1 ]}\nobreak -\hyperdef{L}{X78A4B93781C96AAE}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsNilpotent({\mdseries\slshape Q})\index{IsNilpotent@\texttt{IsNilpotent}} -\label{IsNilpotent} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a nilpotent loop. - -} - - - -\subsection{\textcolor{Chapter }{NilpotencyClassOfLoop}} -\logpage{[ 6, 9, 2 ]}\nobreak -\hyperdef{L}{X7D5FC62581A99482}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NilpotencyClassOfLoop({\mdseries\slshape Q})\index{NilpotencyClassOfLoop@\texttt{NilpotencyClassOfLoop}} -\label{NilpotencyClassOfLoop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The nilpotency class of a loop \mbox{\texttt{\mdseries\slshape Q}} if \mbox{\texttt{\mdseries\slshape Q}} is nilpotent, \texttt{fail} otherwise. - -} - - - -\subsection{\textcolor{Chapter }{IsStronglyNilpotent}} -\logpage{[ 6, 9, 3 ]}\nobreak -\hyperdef{L}{X7E7C2D117B55F6A0}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsStronglyNilpotent({\mdseries\slshape Q})\index{IsStronglyNilpotent@\texttt{IsStronglyNilpotent}} -\label{IsStronglyNilpotent} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a strongly nilpotent loop. - - - -A loop $Q$ is said to be \emph{strongly nilpotent}\index{strongly nilpotent loop}\index{nilpotent loop!strongly}\index{loop!strongly nilpotent} if its multiplication group is nilpotent.} - - - -\subsection{\textcolor{Chapter }{UpperCentralSeries}} -\logpage{[ 6, 9, 4 ]}\nobreak -\hyperdef{L}{X7ED37AA07BEE79E0}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{UpperCentralSeries({\mdseries\slshape Q})\index{UpperCentralSeries@\texttt{UpperCentralSeries}} -\label{UpperCentralSeries} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape Q}} is a nilpotent loop, returns the upper central series of \mbox{\texttt{\mdseries\slshape Q}}, else returns \texttt{fail}. - -} - - - -\subsection{\textcolor{Chapter }{LowerCentralSeries}} -\logpage{[ 6, 9, 5 ]}\nobreak -\hyperdef{L}{X817BDBC2812992ED}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LowerCentralSeries({\mdseries\slshape Q})\index{LowerCentralSeries@\texttt{LowerCentralSeries}} -\label{LowerCentralSeries} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape Q}} is a nilpotent loop, returns the lower central series of \mbox{\texttt{\mdseries\slshape Q}}, else returns \texttt{fail}. - - - -The \emph{lower central series}\index{central series!lower} for loops is defined analogously to groups.} - - } - - -\section{\textcolor{Chapter }{Solvability, Derived Series and Frattini Subloop}}\label{Sec:SolvabilityEtc} -\logpage{[ 6, 10, 0 ]} -\hyperdef{L}{X83A38A6C7EDBCA63}{} -{ - See Section \ref{Sec:NilpotenceAndSolvability} for definitions of solvability an derived subloop. - -\subsection{\textcolor{Chapter }{IsSolvable}} -\logpage{[ 6, 10, 1 ]}\nobreak -\hyperdef{L}{X79B10B337A3B1C6E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsSolvable({\mdseries\slshape Q})\index{IsSolvable@\texttt{IsSolvable}} -\label{IsSolvable} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a solvable loop. - -} - - - -\subsection{\textcolor{Chapter }{DerivedSubloop}} -\logpage{[ 6, 10, 2 ]}\nobreak -\hyperdef{L}{X7A82DC4680DAD67C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{DerivedSubloop({\mdseries\slshape Q})\index{DerivedSubloop@\texttt{DerivedSubloop}} -\label{DerivedSubloop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The derived subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}. - -} - - - -\subsection{\textcolor{Chapter }{DerivedLength}} -\logpage{[ 6, 10, 3 ]}\nobreak -\hyperdef{L}{X7A9AA1577CEC891F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{DerivedLength({\mdseries\slshape Q})\index{DerivedLength@\texttt{DerivedLength}} -\label{DerivedLength} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -If \mbox{\texttt{\mdseries\slshape Q}} is solvable, returns the derived length of \mbox{\texttt{\mdseries\slshape Q}}, else returns \texttt{fail}. - -} - - -\subsection{\textcolor{Chapter }{FrattiniSubloop and FrattinifactorSize}}\logpage{[ 6, 10, 4 ]} -\hyperdef{L}{X85BD2C517FA7A47E}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{FrattiniSubloop({\mdseries\slshape Q})\index{FrattiniSubloop@\texttt{FrattiniSubloop}} -\label{FrattiniSubloop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The Frattini subloop of \mbox{\texttt{\mdseries\slshape Q}}. The method is implemented only for strongly nilpotent loops. - - - -\emph{Frattini subloop}\index{Frattini subloop} of a loop $Q$ is the intersection of maximal subloops of $Q$.} - - - -\subsection{\textcolor{Chapter }{FrattinifactorSize}} -\logpage{[ 6, 10, 5 ]}\nobreak -\hyperdef{L}{X855286367A2D5A54}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{FrattinifactorSize({\mdseries\slshape Q})\index{FrattinifactorSize@\texttt{FrattinifactorSize}} -\label{FrattinifactorSize} -}\hfill{\scriptsize (attribute)}}\\ -} - - } - - -\section{\textcolor{Chapter }{Isomorphisms and Automorphisms}}\label{Sec:IsomorphismsAndAutomorphisms} -\logpage{[ 6, 11, 0 ]} -\hyperdef{L}{X81F3496578EAA74E}{} -{ - - -\subsection{\textcolor{Chapter }{IsomorphismQuasigroups}} -\logpage{[ 6, 11, 1 ]}\nobreak -\hyperdef{L}{X801067F67E5292F7}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsomorphismQuasigroups({\mdseries\slshape Q, L})\index{IsomorphismQuasigroups@\texttt{IsomorphismQuasigroups}} -\label{IsomorphismQuasigroups} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -An isomorphism from a quasigroup \mbox{\texttt{\mdseries\slshape Q}} to a quasigroup \mbox{\texttt{\mdseries\slshape L}} if the quasigroups are isomorphic, \texttt{fail} otherwise. - - - -If an isomorphism exists, it is returned as a permutation $f$ of $1,\dots,|$\mbox{\texttt{\mdseries\slshape Q}}$|$, where $i^f=j$ means that the $i$th element of \mbox{\texttt{\mdseries\slshape Q}} is mapped onto the $j$th element of \mbox{\texttt{\mdseries\slshape L}}. Note that this convention is used even if the underlying sets of \mbox{\texttt{\mdseries\slshape Q}}, \mbox{\texttt{\mdseries\slshape L}} are not indexed by consecutive integers.} - - - -\subsection{\textcolor{Chapter }{IsomorphismLoops}} -\logpage{[ 6, 11, 2 ]}\nobreak -\hyperdef{L}{X7D7B10D6836FCA9F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsomorphismLoops({\mdseries\slshape Q, L})\index{IsomorphismLoops@\texttt{IsomorphismLoops}} -\label{IsomorphismLoops} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -An isomorphism from a loop \mbox{\texttt{\mdseries\slshape Q}} to a loop \mbox{\texttt{\mdseries\slshape L}} if the loops are isomorphic, \texttt{fail} otherwise, with the same convention as in \texttt{IsomorphismQuasigroups}. - -} - - - -\subsection{\textcolor{Chapter }{QuasigroupsUpToIsomorphism}} -\logpage{[ 6, 11, 3 ]}\nobreak -\hyperdef{L}{X82373C5479574F22}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{QuasigroupsUpToIsomorphism({\mdseries\slshape ls})\index{QuasigroupsUpToIsomorphism@\texttt{QuasigroupsUpToIsomorphism}} -\label{QuasigroupsUpToIsomorphism} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -Given a list \mbox{\texttt{\mdseries\slshape ls}} of quasigroups, returns a sublist of \mbox{\texttt{\mdseries\slshape ls}} consisting of representatives of isomorphism classes of quasigroups from \mbox{\texttt{\mdseries\slshape ls}}. - -} - - - -\subsection{\textcolor{Chapter }{LoopsUpToIsomorphism}} -\logpage{[ 6, 11, 4 ]}\nobreak -\hyperdef{L}{X8308F38283C61B20}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopsUpToIsomorphism({\mdseries\slshape ls})\index{LoopsUpToIsomorphism@\texttt{LoopsUpToIsomorphism}} -\label{LoopsUpToIsomorphism} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -Given a list \mbox{\texttt{\mdseries\slshape ls}} of loops, returns a sublist of \mbox{\texttt{\mdseries\slshape ls}} consisting of representatives of isomorphism classes of loops from \mbox{\texttt{\mdseries\slshape ls}}. - -} - - - -\subsection{\textcolor{Chapter }{AutomorphismGroup}} -\logpage{[ 6, 11, 5 ]}\nobreak -\hyperdef{L}{X87677B0787B4461A}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AutomorphismGroup({\mdseries\slshape Q})\index{AutomorphismGroup@\texttt{AutomorphismGroup}} -\label{AutomorphismGroup} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The automorphism group of a loop or quasigroups \mbox{\texttt{\mdseries\slshape Q}}, with the same convention on permutations as in \texttt{IsomorphismQuasigroups}.\\ - - -} - - - -\textsc{Remark:} Since two isomorphisms differ by an automorphism, all isomorphisms from \mbox{\texttt{\mdseries\slshape Q}} to \mbox{\texttt{\mdseries\slshape L}} can be obtained by a combination of \texttt{IsomorphismLoops(\mbox{\texttt{\mdseries\slshape Q}},\mbox{\texttt{\mdseries\slshape L}})} (or \texttt{IsomorphismQuasigroups(\mbox{\texttt{\mdseries\slshape Q}},\mbox{\texttt{\mdseries\slshape L}})}) and \texttt{AutomorphismGroup(\mbox{\texttt{\mdseries\slshape L}})}. \\ - - -While dealing with Cayley tables, it is often useful to rename or reorder the -elements of the underlying quasigroup without changing the isomorphism type of -the quasigroups. \textsf{LOOPS} contains several functions for this purpose. - -\subsection{\textcolor{Chapter }{IsomorphicCopyByPerm}} -\logpage{[ 6, 11, 6 ]}\nobreak -\hyperdef{L}{X85B3E22679FD8D81}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsomorphicCopyByPerm({\mdseries\slshape Q, f})\index{IsomorphicCopyByPerm@\texttt{IsomorphicCopyByPerm}} -\label{IsomorphicCopyByPerm} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape Q}} is a quasigroup and \mbox{\texttt{\mdseries\slshape f}} is a permutation of $1,\dots,|$\mbox{\texttt{\mdseries\slshape Q}}$|$, returns a quasigroup defined on the same set as \mbox{\texttt{\mdseries\slshape Q}} with multiplication $*$ defined by $x*y = $\mbox{\texttt{\mdseries\slshape f}}$($\mbox{\texttt{\mdseries\slshape f}}${}^{-1}(x)$\mbox{\texttt{\mdseries\slshape f}}${}^{-1}(y))$. When \mbox{\texttt{\mdseries\slshape Q}} is a declared loop, a loop is returned. Consequently, when \mbox{\texttt{\mdseries\slshape Q}} is a declared loop and \mbox{\texttt{\mdseries\slshape f}}$(1) = k\ne 1$, then \mbox{\texttt{\mdseries\slshape f}} is first replaced with \mbox{\texttt{\mdseries\slshape f}}$\circ (1,k)$, to make sure that the resulting Cayley table is normalized. - -} - - - -\subsection{\textcolor{Chapter }{IsomorphicCopyByNormalSubloop}} -\logpage{[ 6, 11, 7 ]}\nobreak -\hyperdef{L}{X8121DE3A78795040}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsomorphicCopyByNormalSubloop({\mdseries\slshape Q, S})\index{IsomorphicCopyByNormalSubloop@\texttt{IsomorphicCopyByNormalSubloop}} -\label{IsomorphicCopyByNormalSubloop} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -When \mbox{\texttt{\mdseries\slshape S}} is a normal subloop of a loop \mbox{\texttt{\mdseries\slshape Q}}, returns an isomorphic copy of \mbox{\texttt{\mdseries\slshape Q}} in which the elements are ordered according to the right cosets of \mbox{\texttt{\mdseries\slshape S}}. In particular, the Cayley table of \mbox{\texttt{\mdseries\slshape S}} will appear in the top left corner of the Cayley table of the resulting loop.\\ - - -} - - - -In order to speed up the search for isomorphisms and automorphisms, we first -calculate some loop invariants preserved under isomorphisms, and then we use -these invariants to partition the loop into blocks of elements preserved under -isomorphisms. The following two operations are used in the search. - -\subsection{\textcolor{Chapter }{Discriminator}} -\logpage{[ 6, 11, 8 ]}\nobreak -\hyperdef{L}{X7D09D8957E4A0973}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{Discriminator({\mdseries\slshape Q})\index{Discriminator@\texttt{Discriminator}} -\label{Discriminator} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A data structure with isomorphism invariants of a loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -See \cite{Vo} or the file \texttt{iso.gi} for more details. The format of the discriminator has been changed from -version 3.2.0 up to accommodate isomorphism searches for quasigroups.} - - - -If two loops have different discriminators, they are not isomorphic. If they -have identical discriminators, they may or may not be isomorphic. - -\subsection{\textcolor{Chapter }{AreEqualDiscriminators}} -\logpage{[ 6, 11, 9 ]}\nobreak -\hyperdef{L}{X812F0DEE7C896E18}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AreEqualDiscriminators({\mdseries\slshape D1, D2})\index{AreEqualDiscriminators@\texttt{AreEqualDiscriminators}} -\label{AreEqualDiscriminators} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape D1}}, \mbox{\texttt{\mdseries\slshape D2}} are equal discriminators for the purposes of isomorphism searches. - -} - - } - - -\section{\textcolor{Chapter }{Isotopisms}}\label{Sec:Isotopism} -\logpage{[ 6, 12, 0 ]} -\hyperdef{L}{X7E996BDD81E594F9}{} -{ - At the moment, \textsf{LOOPS} contains only slow methods for testing if two loops are isotopic. The method -works as follows: It is well known that if a loop $K$ is isotopic to a loop $L$ then there exist a principal loop isotope $P$ of $K$ such that $P$ is isomorphic to $L$. The algorithm first finds all principal isotopes of $K$, then filters them up to isomorphism, and then checks if any of them is -isomorphic to $L$. This is rather slow already for small orders. - -\subsection{\textcolor{Chapter }{IsotopismLoops}} -\logpage{[ 6, 12, 1 ]}\nobreak -\hyperdef{L}{X84C5ADE77F910F63}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsotopismLoops({\mdseries\slshape K, L})\index{IsotopismLoops@\texttt{IsotopismLoops}} -\label{IsotopismLoops} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{fail} if \mbox{\texttt{\mdseries\slshape K}}, \mbox{\texttt{\mdseries\slshape L}} are not isotopic loops, else it returns an isotopism as a triple of bijections -on $1,\dots,|$\mbox{\texttt{\mdseries\slshape K}}$|$. - -} - - - -\subsection{\textcolor{Chapter }{LoopsUpToIsotopism}} -\logpage{[ 6, 12, 2 ]}\nobreak -\hyperdef{L}{X841E540B7A7EF29F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopsUpToIsotopism({\mdseries\slshape ls})\index{LoopsUpToIsotopism@\texttt{LoopsUpToIsotopism}} -\label{LoopsUpToIsotopism} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -Given a list \mbox{\texttt{\mdseries\slshape ls}} of loops, returns a sublist of \mbox{\texttt{\mdseries\slshape ls}} consisting of representatives of isotopism classes of loops from \mbox{\texttt{\mdseries\slshape ls}}. - -} - - } - - } - - -\chapter{\textcolor{Chapter }{Testing Properties of Quasigroups and Loops}}\label{Chap:TestingPropertiesOfQuasigroupsAndLoops} -\logpage{[ 7, 0, 0 ]} -\hyperdef{L}{X7910E575825C713E}{} -{ - Although loops are quasigroups, it is often the case in the literature that a -property of the same name can differ for quasigroups and loops. For instance, -a Steiner loop is not necessarily a Steiner quasigroup. - -To avoid such ambivalences, we often include the noun \texttt{Loop} or \texttt{Quasigroup} as part of the name of the property, e.g., \texttt{IsSteinerQuasigroup} versus \texttt{IsSteinerLoop}. - -On the other hand, some properties coincide for quasigroups and loops and we -therefore do not include \texttt{Loop}, \texttt{Quasigroup} as part of the name of the property, e.g., \texttt{IsCommutative}. -\section{\textcolor{Chapter }{Associativity, Commutativity and Generalizations}}\label{Sec:AssociativityCommutativityAndGeneralizations} -\logpage{[ 7, 1, 0 ]} -\hyperdef{L}{X7960E3FB7A7F0F00}{} -{ - - -\subsection{\textcolor{Chapter }{IsAssociative}} -\logpage{[ 7, 1, 1 ]}\nobreak -\hyperdef{L}{X7C83B5A47FD18FB7}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsAssociative({\mdseries\slshape Q})\index{IsAssociative@\texttt{IsAssociative}} -\label{IsAssociative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an associative quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{IsCommutative}} -\logpage{[ 7, 1, 2 ]}\nobreak -\hyperdef{L}{X830A4A4C795FBC2D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsCommutative({\mdseries\slshape Q})\index{IsCommutative@\texttt{IsCommutative}} -\label{IsCommutative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a commutative quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{IsPowerAssociative}} -\logpage{[ 7, 1, 3 ]}\nobreak -\hyperdef{L}{X7D53EA947F1CDA69}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsPowerAssociative({\mdseries\slshape Q})\index{IsPowerAssociative@\texttt{IsPowerAssociative}} -\label{IsPowerAssociative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a power associative quasigroup. - - - -A quasigroup $Q$ is said to be \emph{power associative}\index{quasigroup!power associative}\index{power associative quasigroup} if every element of $Q$ generates an associative quasigroup, that is, a group.} - - - -\subsection{\textcolor{Chapter }{IsDiassociative}} -\logpage{[ 7, 1, 4 ]}\nobreak -\hyperdef{L}{X872DCA027E1A4A1D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsDiassociative({\mdseries\slshape Q})\index{IsDiassociative@\texttt{IsDiassociative}} -\label{IsDiassociative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a diassociative quasigroup. - - - -A quasigroup $Q$ is said to be \emph{diassociative}\index{quasigroup!diassociative}\index{diassociative quasigroup} if any two elements of $Q$ generate an associative quasigroup, that is, a group. Note that a -diassociative quasigroup is necessarily a loop, but it need not be so declared -in \textsf{LOOPS}.} - - } - - -\section{\textcolor{Chapter }{Inverse Propeties}}\label{Sec:InverseProperties} -\logpage{[ 7, 2, 0 ]} -\hyperdef{L}{X853841C5820BFEA4}{} -{ - For an element $x$ of a loop $Q$, the \emph{left inverse}\index{inverse!left} of $x$ is the element $x^\lambda$ of $Q$ such that $x^\lambda \cdot x = 1$, while the \emph{right inverse}\index{inverse!right} of $x$ is the element $x^\rho$ of $Q$ such that $x\cdot x^\rho = 1$. -\subsection{\textcolor{Chapter }{HasLeftInverseProperty, HasRightInverseProperty and HasInverseProperty}}\logpage{[ 7, 2, 1 ]} -\hyperdef{L}{X85EDD10586596458}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasLeftInverseProperty({\mdseries\slshape Q})\index{HasLeftInverseProperty@\texttt{HasLeftInverseProperty}} -\label{HasLeftInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasRightInverseProperty({\mdseries\slshape Q})\index{HasRightInverseProperty@\texttt{HasRightInverseProperty}} -\label{HasRightInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasInverseProperty({\mdseries\slshape Q})\index{HasInverseProperty@\texttt{HasInverseProperty}} -\label{HasInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if a loop \mbox{\texttt{\mdseries\slshape Q}} has the left inverse property, right inverse property, resp. inverse property. - - - -A loop $Q$ has the \emph{left inverse property}\index{inverse property!left} if $x^\lambda(xy)=y$ for every $x$, $y$ in $Q$. Dually, $Q$ has the \emph{right inverse property}\index{inverse property!right} if $(yx)x^\rho=y$ for every $x$, $y$ in $Q$. If $Q$ has both the left inverse property and the right inverse property, it has the \emph{inverse property}\index{inverse property}.} - - - -\subsection{\textcolor{Chapter }{HasTwosidedInverses}} -\logpage{[ 7, 2, 2 ]}\nobreak -\hyperdef{L}{X86B93E1B7AEA6EDA}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasTwosidedInverses({\mdseries\slshape Q})\index{HasTwosidedInverses@\texttt{HasTwosidedInverses}} -\label{HasTwosidedInverses} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if a loop \mbox{\texttt{\mdseries\slshape Q}} has two-sided inverses. - - - -A loop $Q$ is said to have \emph{two-sided inverses}\index{inverse!two-sided} if $x^\lambda=x^\rho$ for every $x$ in $Q$.} - - - -\subsection{\textcolor{Chapter }{HasWeakInverseProperty}} -\logpage{[ 7, 2, 3 ]}\nobreak -\hyperdef{L}{X793909B780761EA8}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasWeakInverseProperty({\mdseries\slshape Q})\index{HasWeakInverseProperty@\texttt{HasWeakInverseProperty}} -\label{HasWeakInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if a loop \mbox{\texttt{\mdseries\slshape Q}} has the weak inverse property. - - - -A loop $Q$ has the \emph{weak inverse property}\index{inverse property!weak} if $(xy)^\lambda x = y^\lambda$ (equivalently, $x(yx)^\rho = y^\rho$) holds for every $x$, $y$ in $Q$.} - - - -\subsection{\textcolor{Chapter }{HasAutomorphicInverseProperty}} -\logpage{[ 7, 2, 4 ]}\nobreak -\hyperdef{L}{X7F46CE6B7D387158}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasAutomorphicInverseProperty({\mdseries\slshape Q})\index{HasAutomorphicInverseProperty@\texttt{HasAutomorphicInverseProperty}} -\label{HasAutomorphicInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if a loop \mbox{\texttt{\mdseries\slshape Q}} has the automorphic inverse property. - - - -According to \cite{Ar}, a loop $Q$ has the \emph{automorphic inverse property}\index{automorphic inverse property}\index{inverse property!automorphic} if $(xy)^\lambda = x^\lambda y^\lambda$, or, equivalently, $(xy)^\rho = x^\rho y^\rho$ holds for every $x$, $y$ in $Q$.} - - - -\subsection{\textcolor{Chapter }{HasAntiautomorphicInverseProperty}} -\logpage{[ 7, 2, 5 ]}\nobreak -\hyperdef{L}{X8538D4638232DB51}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{HasAntiautomorphicInverseProperty({\mdseries\slshape Q})\index{HasAntiautomorphicInverseProperty@\texttt{HasAntiautomorphicInverseProperty}} -\label{HasAntiautomorphicInverseProperty} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if a loop \mbox{\texttt{\mdseries\slshape Q}} has the antiautomorphic inverse property. - - - -A loop $Q$ has the \emph{antiautomorphic inverse property}\index{antiautomorphic inverse property}\index{inverse property!antiautomorphic} if $(xy)^\lambda=y^\lambda x^\lambda$, or, equivalently, $(xy)^\rho = y^\rho x^\rho$ holds for every $x$, $y$ in $Q$.\\ -} - - - -See Appendix \ref{Apx:Filters} for implications implemented in \textsf{LOOPS} among various inverse properties. } - - -\section{\textcolor{Chapter }{Some Properties of Quasigroups}}\label{Sec:SomePropertiesOfQuasigroups} -\logpage{[ 7, 3, 0 ]} -\hyperdef{L}{X7D8CB6DA828FD744}{} -{ - - -\subsection{\textcolor{Chapter }{IsSemisymmetric}} -\logpage{[ 7, 3, 1 ]}\nobreak -\hyperdef{L}{X834848ED85F9012B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsSemisymmetric({\mdseries\slshape Q})\index{IsSemisymmetric@\texttt{IsSemisymmetric}} -\label{IsSemisymmetric} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a semisymmetric quasigroup. - - - -A quasigroup $Q$ is \emph{semisymmetric}\index{semisymmetric quasigroup}\index{quasigroup!semisymmetric} if $(xy)x=y$, or, equivalently $x(yx)=y$ holds for every $x$, $y$ in $Q$.} - - - -\subsection{\textcolor{Chapter }{IsTotallySymmetric}} -\logpage{[ 7, 3, 2 ]}\nobreak -\hyperdef{L}{X834F809B8060B754}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsTotallySymmetric({\mdseries\slshape Q})\index{IsTotallySymmetric@\texttt{IsTotallySymmetric}} -\label{IsTotallySymmetric} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a totally symmetric quasigroup. - - - -A commutative semisymmetric quasigroup is called \emph{totally symmetric}\index{totally symmetric quasigroup}\index{quasigroup!totally symmetric}. Totally symmetric quasigroups are precisely the quasigroups satisfying $xy=x\backslash y = x/y$.} - - - -\subsection{\textcolor{Chapter }{IsIdempotent}} -\logpage{[ 7, 3, 3 ]}\nobreak -\hyperdef{L}{X7CB5896082D29173}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsIdempotent({\mdseries\slshape Q})\index{IsIdempotent@\texttt{IsIdempotent}} -\label{IsIdempotent} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an idempotent quasigroup. - - - -A quasigroup is \emph{idempotent}\index{idempotent quasigroup}\index{quasigroup!idempotent} if it satisfies $x^2=x$.} - - - -\subsection{\textcolor{Chapter }{IsSteinerQuasigroup}} -\logpage{[ 7, 3, 4 ]}\nobreak -\hyperdef{L}{X83DE7DD77C056C1F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsSteinerQuasigroup({\mdseries\slshape Q})\index{IsSteinerQuasigroup@\texttt{IsSteinerQuasigroup}} -\label{IsSteinerQuasigroup} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a Steiner quasigroup. - - - -A totally symmetric idempotent quasigroup is called a \emph{Steiner quasigroup}\index{Steiner quasigroup}\index{quasigroup!Steiner}.} - - - -\subsection{\textcolor{Chapter }{IsUnipotent}} -\logpage{[ 7, 3, 5 ]}\nobreak -\hyperdef{L}{X7CA3DCA07B6CB9BD}{} -{ - -A quasigroup $Q$ is \emph{unipotent}\index{unipotent quasigroup}\index{quasigroup!unipotent} if it satisfies $x^2=y^2$ for every $x$, $y$ in $Q$.\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsUnipotent({\mdseries\slshape Q})\index{IsUnipotent@\texttt{IsUnipotent}} -\label{IsUnipotent} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a unipotent quasigroup. - -} - - -\subsection{\textcolor{Chapter }{IsLeftDistributive, IsRightDistributive, IsDistributive}}\logpage{[ 7, 3, 6 ]} -\hyperdef{L}{X7B76FD6E878ED4F1}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftDistributive({\mdseries\slshape Q})\index{IsLeftDistributive@\texttt{IsLeftDistributive}} -\label{IsLeftDistributive} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightDistributive({\mdseries\slshape Q})\index{IsRightDistributive@\texttt{IsRightDistributive}} -\label{IsRightDistributive} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsDistributive({\mdseries\slshape Q})\index{IsDistributive@\texttt{IsDistributive}} -\label{IsDistributive} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left distributive quasigroup, resp. a right distributive quasigroup, -resp. a distributive quasigroup. - - - -A quasigroup is \emph{left distributive}\index{quasigroup!left distributive}\index{distributive quasigroup!left} if it satisfies $x(yz) = (xy)(xz)$, \emph{right distributive}\index{quasigroup!right distributive}\index{distributive quasigroup!right} if it satisfies $(xy)z = (xz)(yz)$, and \emph{distributive}\index{quasigroup!distributive}\index{distributive quasigroup} if it is both left distributive and right distributive. - -\textsc{Remark:} In order to be compatible with \textsf{GAP}s terminology, we also support the synonyms \texttt{IsLDistributive} and \texttt{IsRDistributive} of \texttt{IsLeftDistributive} and \texttt{IsRightDistributive}, respectively.} - - -\subsection{\textcolor{Chapter }{IsEntropic and IsMedial}}\logpage{[ 7, 3, 7 ]} -\hyperdef{L}{X7F23D4D97A38D223}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsEntropic({\mdseries\slshape Q})\index{IsEntropic@\texttt{IsEntropic}} -\label{IsEntropic} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsMedial({\mdseries\slshape Q})\index{IsMedial@\texttt{IsMedial}} -\label{IsMedial} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an entropic (aka medial) quasigroup. - - - -A quasigroup is \emph{entropic}\index{entropic quasigroup}\index{quasigroup!entropic} or \emph{medial}\index{medial quasigroup}\index{quasigroup!medial} if it satisfies the identity $(xy)(uv) = (xu)(yv)$.} - - } - - -\section{\textcolor{Chapter }{Loops of Bol Moufang Type}}\label{Sec:LoopsOfBolMoufangType} -\logpage{[ 7, 4, 0 ]} -\hyperdef{L}{X780D907986EBA6C7}{} -{ - Following \cite{Fe} and \cite{PhiVoj}, a variety of loops is said to be of \emph{Bol-Moufang type}\index{loop!of Bol-Moufang type} if it is defined by a single \emph{identity of Bol-Moufang type}\index{identity!of Bol-Moufang type}, i.e., by an identity that contains the same 3 variables on both sides, -exactly one of the variables occurs twice on both sides, and the variables -occur in the same order on both sides. - -It is proved in \cite{PhiVoj} that there are 13 varieties of nonassociative loops of Bol-Moufang type. These -are: -\begin{itemize} -\item \emph{left alternative loops}\index{alternative loop!left}\index{loop!left alternative} defined by $x(xy) = (xx)y$, -\item \emph{right alternative loops}\index{alternative loop!right}\index{loop!right alternative} defined by $x(yy) = (xy)y$, -\item \emph{left nuclear square loops}\index{nuclear square loop!left}\index{loop!left nuclear square} defined by $(xx)(yz) = ((xx)y)z$, -\item \emph{middle nuclear square loops}\index{nuclear square loop!middle}\index{loop!middle nuclear square}defined by $x((yy)z) = (x(yy))z$, -\item \emph{right nuclear square loops}\index{nuclear square loop!right}\index{loop!right nuclear square} defined by $x(y(zz)) = (xy)(zz)$, -\item \emph{flexible loops}\index{flexible loop}\index{loop!flexible} defined by $x(yx) = (xy)x$, -\item \emph{left Bol loops}\index{Bol loop!left}\index{loop!left Bol} defined by $x(y(xz)) = (x(yx))z$, always left alternative, -\item \emph{right Bol loops}\index{Bol loop!right}\index{loop!right Bol} defined by $x((yz)y) = ((xy)z)y$, always right alternative, -\item \emph{LC loops}\index{LC loop}\index{loop!LC} defined by $(xx)(yz) = (x(xy))z$, always left alternative, left nuclear square and middle nuclear square, -\item \emph{RC loops}\index{RC loop}\index{loop!RC} defined by $x((yz)z) = (xy)(zz)$, always right alternative, right nuclear square and middle nuclear square, -\item \emph{Moufang loops}\index{Moufang loop}\index{loop!Moufang} defined by $(xy)(zx) = (x(yz))x$, always flexible, left Bol and right Bol, -\item \emph{C loops}\index{C loop}\index{loop!C} defined by $x(y(yz)) = ((xy)y)z$, always LC and RC, -\item \emph{extra loops}\index{extra loop}\index{loop!extra} defined by $x(y(zx)) = ((xy)z)x$, always Moufang and C. -\end{itemize} - - -Note that although some of the defining identities are not of Bol-Moufang -type, they are equivalent to a Bol-Moufang identity. Moreover, many varieties -of loops of Bol-Moufang type can be defined by one of several equivalent -identities of Bol-Moufang type. - -There are also several varieties related to loops of Bol-Moufang type. A loop -is said to be \emph{alternative}\index{alternative loop}\index{loop!alternative} if it is both left alternative and right alternative. A loop is \emph{nuclear square}\index{nuclear square loop}\index{loop!nuclear square} if it is left nuclear square, middle nuclear square and right nuclear square. - -\subsection{\textcolor{Chapter }{IsExtraLoop}} -\logpage{[ 7, 4, 1 ]}\nobreak -\hyperdef{L}{X7988AFE27D06ACB5}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsExtraLoop({\mdseries\slshape Q})\index{IsExtraLoop@\texttt{IsExtraLoop}} -\label{IsExtraLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an extra loop. - -} - - - -\subsection{\textcolor{Chapter }{IsMoufangLoop}} -\logpage{[ 7, 4, 2 ]}\nobreak -\hyperdef{L}{X7F1C151484C97E61}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsMoufangLoop({\mdseries\slshape Q})\index{IsMoufangLoop@\texttt{IsMoufangLoop}} -\label{IsMoufangLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a Moufang loop. - -} - - - -\subsection{\textcolor{Chapter }{IsCLoop}} -\logpage{[ 7, 4, 3 ]}\nobreak -\hyperdef{L}{X866F04DC7AE54B7C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsCLoop({\mdseries\slshape Q})\index{IsCLoop@\texttt{IsCLoop}} -\label{IsCLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a C loop. - -} - - - -\subsection{\textcolor{Chapter }{IsLeftBolLoop}} -\logpage{[ 7, 4, 4 ]}\nobreak -\hyperdef{L}{X801DAAE8834A1A65}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftBolLoop({\mdseries\slshape Q})\index{IsLeftBolLoop@\texttt{IsLeftBolLoop}} -\label{IsLeftBolLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left Bol loop. - -} - - - -\subsection{\textcolor{Chapter }{IsRightBolLoop}} -\logpage{[ 7, 4, 5 ]}\nobreak -\hyperdef{L}{X79279F9787E72566}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightBolLoop({\mdseries\slshape Q})\index{IsRightBolLoop@\texttt{IsRightBolLoop}} -\label{IsRightBolLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right Bol loop. - -} - - - -\subsection{\textcolor{Chapter }{IsLCLoop}} -\logpage{[ 7, 4, 6 ]}\nobreak -\hyperdef{L}{X789E0A6979697C4C}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLCLoop({\mdseries\slshape Q})\index{IsLCLoop@\texttt{IsLCLoop}} -\label{IsLCLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an LC loop. - -} - - - -\subsection{\textcolor{Chapter }{IsRCLoop}} -\logpage{[ 7, 4, 7 ]}\nobreak -\hyperdef{L}{X7B03CC577802F4AB}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRCLoop({\mdseries\slshape Q})\index{IsRCLoop@\texttt{IsRCLoop}} -\label{IsRCLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an RC loop. - -} - - - -\subsection{\textcolor{Chapter }{IsLeftNuclearSquareLoop}} -\logpage{[ 7, 4, 8 ]}\nobreak -\hyperdef{L}{X819F285887B5EB9E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftNuclearSquareLoop({\mdseries\slshape Q})\index{IsLeftNuclearSquareLoop@\texttt{IsLeftNuclearSquareLoop}} -\label{IsLeftNuclearSquareLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left nuclear square loop. - -} - - - -\subsection{\textcolor{Chapter }{IsMiddleNuclearSquareLoop}} -\logpage{[ 7, 4, 9 ]}\nobreak -\hyperdef{L}{X8474F55681244A8A}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsMiddleNuclearSquareLoop({\mdseries\slshape Q})\index{IsMiddleNuclearSquareLoop@\texttt{IsMiddleNuclearSquareLoop}} -\label{IsMiddleNuclearSquareLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a middle nuclear square loop. - -} - - - -\subsection{\textcolor{Chapter }{IsRightNuclearSquareLoop}} -\logpage{[ 7, 4, 10 ]}\nobreak -\hyperdef{L}{X807B3B21825E3076}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightNuclearSquareLoop({\mdseries\slshape Q})\index{IsRightNuclearSquareLoop@\texttt{IsRightNuclearSquareLoop}} -\label{IsRightNuclearSquareLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right nuclear square loop. - -} - - - -\subsection{\textcolor{Chapter }{IsNuclearSquareLoop}} -\logpage{[ 7, 4, 11 ]}\nobreak -\hyperdef{L}{X796650088213229B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsNuclearSquareLoop({\mdseries\slshape Q})\index{IsNuclearSquareLoop@\texttt{IsNuclearSquareLoop}} -\label{IsNuclearSquareLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a nuclear square loop. - -} - - - -\subsection{\textcolor{Chapter }{IsFlexible}} -\logpage{[ 7, 4, 12 ]}\nobreak -\hyperdef{L}{X7C32851A7AF1C45F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsFlexible({\mdseries\slshape Q})\index{IsFlexible@\texttt{IsFlexible}} -\label{IsFlexible} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a flexible quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{IsLeftAlternative}} -\logpage{[ 7, 4, 13 ]}\nobreak -\hyperdef{L}{X7DF0196786B9CE08}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftAlternative({\mdseries\slshape Q})\index{IsLeftAlternative@\texttt{IsLeftAlternative}} -\label{IsLeftAlternative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left alternative quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{IsRightAlternative}} -\logpage{[ 7, 4, 14 ]}\nobreak -\hyperdef{L}{X8416FAD87F148F5D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightAlternative({\mdseries\slshape Q})\index{IsRightAlternative@\texttt{IsRightAlternative}} -\label{IsRightAlternative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right alternative quasigroup. - -} - - - -\subsection{\textcolor{Chapter }{IsAlternative}} -\logpage{[ 7, 4, 15 ]}\nobreak -\hyperdef{L}{X8379356E82DB5DDA}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsAlternative({\mdseries\slshape Q})\index{IsAlternative@\texttt{IsAlternative}} -\label{IsAlternative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an alternative quasigroup.\\ - - -} - - - -While listing the varieties of loops of Bol-Moufang type, we have also listed -all inclusions among them. These inclusions are built into \textsf{LOOPS} as filters. \\ - - -The following trivial example shows some of the implications and the naming -conventions of \textsf{LOOPS} at work: -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@L := LoopByCayleyTable( [ [ 1, 2 ], [ 2, 1 ] ] ); | - - !gapprompt@gap>| !gapinput@[ IsLeftBolLoop( L ), L ] | - [ true, ] - !gapprompt@gap>| !gapinput@[ HasIsLeftAlternativeLoop( L ), IsLeftAlternativeLoop( L ) ]; | - [ true, true ] - !gapprompt@gap>| !gapinput@[ HasIsRightBolLoop( L ), IsRightBolLoop( L ) ]; | - [ false, true ] - !gapprompt@gap>| !gapinput@L; | - - !gapprompt@gap>| !gapinput@[ IsAssociative( L ), L ]; | - [ true, ] -\end{Verbatim} - - -The analogous terminology for quasigroups of Bol-Moufang type is not standard -yet, and hence is not supported in \textsf{LOOPS} except for the situations explicitly noted above. } - - -\section{\textcolor{Chapter }{Power Alternative Loops}}\label{Sec:PowerAlternativeLoops} -\logpage{[ 7, 5, 0 ]} -\hyperdef{L}{X83A501387E1AC371}{} -{ - A loop is \emph{left power alternative}\index{power alternative loop!left}\index{loop!left power alternative} if it is power associative and satisfies $x^n(x^m y) = x^{n+m}y$ for all elements $x$, $y$ and all integers $m$, $n$. Similarly, a loop is \emph{right power alternative}\index{power alternative loop!right}\index{loop!right power alternative} if it is power associative and satisfies $(x y^n)y^m = xy^{n+m}$ for all elements $x$, $y$ and all integers $m$, $n$. A loop is \emph{power alternative}\index{power alternative loop}\index{loop!power alternative} if it is both left power alternative and right power alternative. - -Left power alternative loops are left alternative and have the left inverse -property. Left Bol loops and LC loops are left power alternative. -\subsection{\textcolor{Chapter }{IsLeftPowerAlternative, IsRightPowerAlternative and IsPowerAlternative}}\logpage{[ 7, 5, 1 ]} -\hyperdef{L}{X875C3DF681B3FAE2}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftPowerAlternative({\mdseries\slshape Q})\index{IsLeftPowerAlternative@\texttt{IsLeftPowerAlternative}} -\label{IsLeftPowerAlternative} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightPowerAlternative({\mdseries\slshape Q})\index{IsRightPowerAlternative@\texttt{IsRightPowerAlternative}} -\label{IsRightPowerAlternative} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsPowerAlternative({\mdseries\slshape Q})\index{IsPowerAlternative@\texttt{IsPowerAlternative}} -\label{IsPowerAlternative} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left power alternative loop, resp. a right power alternative loop, resp. -a power alternative loop. - -} - - } - - -\section{\textcolor{Chapter }{Conjugacy Closed Loops and Related Properties}}\label{Sec:ConjugacyClosedEtc} -\logpage{[ 7, 6, 0 ]} -\hyperdef{L}{X8176B2C47A4629CD}{} -{ - A loop $Q$ is \emph{left conjugacy closed}\index{conjugacy closed loop!left}\index{loop!left conjugacy closed} if the set of left translations of $Q$ is closed under conjugation (by itself). Similarly, a loop $Q$ is \emph{right conjugacy closed}\index{conjugacy closed loop!right}\index{loop!right conjugacy closed} if the set of right translations of $Q$ is closed under conjugation. A loop is \emph{conjugacy closed}\index{conjugacy closed loop}\index{loop!conjugacy closed} if it is both left conjugacy closed and right conjugacy closed. It is common -to refer to these loops as LCC, RCC, and CC loops, respectively. - -The equivalence LCC $+$ RCC $=$ CC is built into \textsf{LOOPS}. - -\subsection{\textcolor{Chapter }{IsLCCLoop}} -\logpage{[ 7, 6, 1 ]}\nobreak -\hyperdef{L}{X784E08CD7B710AF4}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLCCLoop({\mdseries\slshape Q})\index{IsLCCLoop@\texttt{IsLCCLoop}} -\label{IsLCCLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftConjugacyClosedLoop({\mdseries\slshape Q})\index{IsLeftConjugacyClosedLoop@\texttt{IsLeftConjugacyClosedLoop}} -\label{IsLeftConjugacyClosedLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left conjugacy closed loop. - -} - - - -\subsection{\textcolor{Chapter }{IsRCCLoop}} -\logpage{[ 7, 6, 2 ]}\nobreak -\hyperdef{L}{X7B3016B47A1A8213}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRCCLoop({\mdseries\slshape Q})\index{IsRCCLoop@\texttt{IsRCCLoop}} -\label{IsRCCLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightConjugacyClosedLoop({\mdseries\slshape Q})\index{IsRightConjugacyClosedLoop@\texttt{IsRightConjugacyClosedLoop}} -\label{IsRightConjugacyClosedLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right conjugacy closed loop. - -} - - - -\subsection{\textcolor{Chapter }{IsCCLoop}} -\logpage{[ 7, 6, 3 ]}\nobreak -\hyperdef{L}{X878B614479DCB83F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsCCLoop({\mdseries\slshape Q})\index{IsCCLoop@\texttt{IsCCLoop}} -\label{IsCCLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsConjugacyClosedLoop({\mdseries\slshape Q})\index{IsConjugacyClosedLoop@\texttt{IsConjugacyClosedLoop}} -\label{IsConjugacyClosedLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a conjugacy closed loop. - -} - - - -\subsection{\textcolor{Chapter }{IsOsbornLoop}} -\logpage{[ 7, 6, 4 ]}\nobreak -\hyperdef{L}{X8655956878205FC1}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsOsbornLoop({\mdseries\slshape Q})\index{IsOsbornLoop@\texttt{IsOsbornLoop}} -\label{IsOsbornLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an Osborn loop. - - - -A loop is \emph{Osborn}\index{Osborn loop}\index{loop!Osborn} if it satisfies $x(yz\cdot x)=(x^\lambda\backslash y)(zx)$. Both Moufang loops and CC loops are Osborn.} - - } - - -\section{\textcolor{Chapter }{Automorphic Loops}}\label{Sec:AutomorphicLoops} -\logpage{[ 7, 7, 0 ]} -\hyperdef{L}{X793B22EA8643C667}{} -{ - A loop $Q$ whose all left (resp. middle, resp. right) inner mappings are automorphisms of $Q$ is known as a \emph{left automorphic loop}\index{automorphic loop!left}\index{loop!left automorphic} (resp. \emph{middle automorphic loop}\index{automorphic loop!middle}\index{loop!middle automorphic}, resp. \emph{right automorphic loop}\index{automorphic loop!right}\index{loop!right automorphic}). - -A loop $Q$ is an \emph{automorphic loop}\index{automorphic loop}\index{loop!automorphic} if all inner mappings of $Q$ are automorphisms of $Q$. - -Automorphic loops are also known as \emph{A loops}, and similar terminology exists for left, right and middle automorphic loops. - -The following results hold for automorphic loops: -\begin{itemize} -\item automorphic loops are power associative \cite{BrPa} -\item in an automorphic loop $Q$ we have ${\rm Nuc}(Q) = {\rm Nuc}_{\lambda}(Q) = {\rm Nuc}_{\rho}(Q)\le {\rm -Nuc}_{\mu}(Q)$ and all nuclei are normal \cite{BrPa} -\item a loop that is left automorphic and right automorphic satisfies the -anti-automorphic inverse property and is automorphic \cite{JoKiNaVo} -\item diassociative automorphic loops are Moufang \cite{KiKuPh} -\item automorphic loops of odd order are solvable \cite{KiKuPhVo} -\item finite commutative automorphic loops are solvable \cite{GrKiNa} -\item commutative automorphic loops of order $p$, $2p$, $4p$, $p^2$, $2p^2$, $4p^2$ ($p$ an odd prime) are abelian groups \cite{VoQRS} -\item commutative automorphic loops of odd prime power order are centrally nilpotent \cite{JeKiVo} -\item for any prime $p$, there are $7$ commutative automorphic loops of order $p^3$ up to isomorphism \cite{BaGrVo} -\end{itemize} - See the built-in filters and the survey \cite{VoQRS} for additional properties of automorphic loops. - -\subsection{\textcolor{Chapter }{IsLeftAutomorphicLoop}} -\logpage{[ 7, 7, 1 ]}\nobreak -\hyperdef{L}{X7F063914804659F1}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftAutomorphicLoop({\mdseries\slshape Q})\index{IsLeftAutomorphicLoop@\texttt{IsLeftAutomorphicLoop}} -\label{IsLeftAutomorphicLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftALoop({\mdseries\slshape Q})\index{IsLeftALoop@\texttt{IsLeftALoop}} -\label{IsLeftALoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left automorphic loop. - -} - - - -\subsection{\textcolor{Chapter }{IsMiddleAutomorphicLoop}} -\logpage{[ 7, 7, 2 ]}\nobreak -\hyperdef{L}{X7DFE830584A769E5}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsMiddleAutomorphicLoop({\mdseries\slshape Q})\index{IsMiddleAutomorphicLoop@\texttt{IsMiddleAutomorphicLoop}} -\label{IsMiddleAutomorphicLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsMiddleALoop({\mdseries\slshape Q})\index{IsMiddleALoop@\texttt{IsMiddleALoop}} -\label{IsMiddleALoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a middle automorphic loop. - -} - - - -\subsection{\textcolor{Chapter }{IsRightAutomorphicLoop}} -\logpage{[ 7, 7, 3 ]}\nobreak -\hyperdef{L}{X7EA9165A87F99E35}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightAutomorphicLoop({\mdseries\slshape Q})\index{IsRightAutomorphicLoop@\texttt{IsRightAutomorphicLoop}} -\label{IsRightAutomorphicLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightALoop({\mdseries\slshape Q})\index{IsRightALoop@\texttt{IsRightALoop}} -\label{IsRightALoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right automorphic loop. - -} - - - -\subsection{\textcolor{Chapter }{IsAutomorphicLoop}} -\logpage{[ 7, 7, 4 ]}\nobreak -\hyperdef{L}{X7899603184CF13FD}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsAutomorphicLoop({\mdseries\slshape Q})\index{IsAutomorphicLoop@\texttt{IsAutomorphicLoop}} -\label{IsAutomorphicLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsALoop({\mdseries\slshape Q})\index{IsALoop@\texttt{IsALoop}} -\label{IsALoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is an automorphic loop. - -} - - - -\textsc{Remark:} Be careful not to confuse \texttt{IsALoop} and \texttt{IsLoop}. } - - -\section{\textcolor{Chapter }{Additonal Varieties of Loops}}\label{Sec:AdditionalVarietiesOfLoops} -\logpage{[ 7, 8, 0 ]} -\hyperdef{L}{X846F363879BAB349}{} -{ - - -\subsection{\textcolor{Chapter }{IsCodeLoop}} -\logpage{[ 7, 8, 1 ]}\nobreak -\hyperdef{L}{X790FA1188087D5C1}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsCodeLoop({\mdseries\slshape Q})\index{IsCodeLoop@\texttt{IsCodeLoop}} -\label{IsCodeLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a code loop. - - - -A \emph{code loop}\index{code loop}\index{loop!code} is a Moufang 2-loop with a Frattini subloop of order 1 or 2. Code loops are -extra and conjugacy closed.} - - - -\subsection{\textcolor{Chapter }{IsSteinerLoop}} -\logpage{[ 7, 8, 2 ]}\nobreak -\hyperdef{L}{X793600C9801F4F62}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsSteinerLoop({\mdseries\slshape Q})\index{IsSteinerLoop@\texttt{IsSteinerLoop}} -\label{IsSteinerLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a Steiner loop. - - - -A \emph{Steiner loop}\index{Steiner loop}\index{loop!Steiner} is an inverse property loop of exponent 2. Steiner loops are commutative.} - - -\subsection{\textcolor{Chapter }{IsLeftBruckLoop and IsLeftKLoop}}\logpage{[ 7, 8, 3 ]} -\hyperdef{L}{X85F1BD4280E44F5B}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftBruckLoop({\mdseries\slshape Q})\index{IsLeftBruckLoop@\texttt{IsLeftBruckLoop}} -\label{IsLeftBruckLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsLeftKLoop({\mdseries\slshape Q})\index{IsLeftKLoop@\texttt{IsLeftKLoop}} -\label{IsLeftKLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a left Bruck loop (aka left K loop). - - - -A left Bol loop with the automorphic inverse property is known as a \emph{left Bruck loop}\index{Bruck loop!left}\index{loop!left Bruck} or a \emph{left K loop}\index{K loop!left}\index{loop!left K}.} - - -\subsection{\textcolor{Chapter }{IsRightBruckLoop and IsRightKLoop}}\logpage{[ 7, 8, 4 ]} -\hyperdef{L}{X857B373E7B4E0519}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightBruckLoop({\mdseries\slshape Q})\index{IsRightBruckLoop@\texttt{IsRightBruckLoop}} -\label{IsRightBruckLoop} -}\hfill{\scriptsize (property)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsRightKLoop({\mdseries\slshape Q})\index{IsRightKLoop@\texttt{IsRightKLoop}} -\label{IsRightKLoop} -}\hfill{\scriptsize (property)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if \mbox{\texttt{\mdseries\slshape Q}} is a right Bruck loop (aka right K loop). - - - -A right Bol loop with the automorphic inverse property is known as a \emph{right Bruck loop}\index{Bruck loop!right}\index{loop!right Bruck} or a \emph{right K loop}\index{K loop!right}\index{loop!right K}.} - - } - - } - - -\chapter{\textcolor{Chapter }{Specific Methods}}\label{Chap:SpecificMethods} -\logpage{[ 8, 0, 0 ]} -\hyperdef{L}{X85AFC9C47FD3C03F}{} -{ - This chapter describes methods of \textsf{LOOPS} that apply to specific classes of loops, mostly Bol and Moufang loops. -\section{\textcolor{Chapter }{Core Methods for Bol Loops}}\label{Sec:CoreMethodsForBolLoops} -\logpage{[ 8, 1, 0 ]} -\hyperdef{L}{X7990F2F880E717EE}{} -{ - -\subsection{\textcolor{Chapter }{AssociatedLeftBruckLoop and AssociatedRightBruckLoop}}\logpage{[ 8, 1, 1 ]} -\hyperdef{L}{X8664CA927DD73DBE}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AssociatedLeftBruckLoop({\mdseries\slshape Q})\index{AssociatedLeftBruckLoop@\texttt{AssociatedLeftBruckLoop}} -\label{AssociatedLeftBruckLoop} -}\hfill{\scriptsize (attribute)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AssociatedRightBruckLoop({\mdseries\slshape Q})\index{AssociatedRightBruckLoop@\texttt{AssociatedRightBruckLoop}} -\label{AssociatedRightBruckLoop} -}\hfill{\scriptsize (attribute)}}\\ -\textbf{\indent Returns:\ } -The left (resp. right) Bruck loop associated with a uniquely 2-divisible left -(resp. right) Bol loop \mbox{\texttt{\mdseries\slshape Q}}. - - - -Let $Q$ be a left Bol loop\index{loop!left Bol}\index{Bol loop!left} such that the mapping $x\mapsto x^2$ is a permutation of $Q$. Define a new operation $*$ on $Q$ by $x*y =(x(y^2x))^{1/2}$. Then $(Q,*)$ is a left Bruck loop, called the \emph{associated left Bruck loop}\index{Bruck loop!associated left}\index{loop!associated left Bruck}. (In fact, Bruck used the isomorphic operation $x*y = x^{1/2}(yx^{1/2})$ instead. Our approach is more natural in the sense that the left Bruck loop -associated with a left Bruck loop is identical to the original loop.) -Associated right Bruck loops are defined dually.} - - - -\subsection{\textcolor{Chapter }{IsExactGroupFactorization}} -\logpage{[ 8, 1, 2 ]}\nobreak -\hyperdef{L}{X82FC16F386CE11F1}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{IsExactGroupFactorization({\mdseries\slshape G, H1, H2})\index{IsExactGroupFactorization@\texttt{IsExactGroupFactorization}} -\label{IsExactGroupFactorization} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -\texttt{true} if (\mbox{\texttt{\mdseries\slshape G}}, \mbox{\texttt{\mdseries\slshape H1}}, \mbox{\texttt{\mdseries\slshape H2}}) is an exact group factorization. - - - -Many right Bol loops can be constructed from exact group factorizations. The -triple $(G,H_1,H_2)$ is an \emph{exact group factorization}\index{exact group factorization} if $H_1$, $H_2$ are subgroups of $G$ such that $H_1H_2=G$ and $H_1\cap H_2=1$.} - - - -\subsection{\textcolor{Chapter }{RightBolLoopByExactGroupFactorization}} -\logpage{[ 8, 1, 3 ]}\nobreak -\hyperdef{L}{X7DCA64807F899127}{} -{ - -If $(G,H_1,H_2)$ is an exact group factorization then $(G\times G, H_1\times H_2, T)$ with $T=\{(x,x^{-1})| x\in G\}$ is a loop folder that gives rise to a right Bol loop.\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightBolLoopByExactGroupFactorization({\mdseries\slshape arg})\index{RightBolLoopByExactGroupFactorization@\texttt{Right}\-\texttt{Bol}\-\texttt{Loop}\-\texttt{By}\-\texttt{Exact}\-\texttt{Group}\-\texttt{Factorization}} -\label{RightBolLoopByExactGroupFactorization} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The right Bol loop constructed from an exact group factorization. The argument \mbox{\texttt{\mdseries\slshape arg}} can either be an exact group factorization \texttt{[G,H1,H2]}, or the tuple \texttt{[G,H]}, where \texttt{H} is a regular subgroup of \texttt{G}. We also allow \mbox{\texttt{\mdseries\slshape arg}} to be separate entries rather than a list of entries. - -} - - } - - -\section{\textcolor{Chapter }{Moufang Modifications}}\label{Sec:MoufangModifications} -\logpage{[ 8, 2, 0 ]} -\hyperdef{L}{X819F82737C2A860D}{} -{ - Dr{\a'a}pal \cite{DrapalCD} described two prominent families of extensions of Moufang loops. It turns out -that these extensions suffice to obtain all nonassociative Moufang loops of -order at most 64 if one starts with so-called Chein loops. We call the two -constructions \emph{Moufang modifications}\index{modification!Moufang}. The library of Moufang loops included in \textsf{LOOPS} is based on Moufang modifications. See \cite{DrVo} for details. - -\subsection{\textcolor{Chapter }{LoopByCyclicModification}} -\logpage{[ 8, 2, 1 ]}\nobreak -\hyperdef{L}{X7B3165C083709831}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByCyclicModification({\mdseries\slshape Q, S, a, h})\index{LoopByCyclicModification@\texttt{LoopByCyclicModification}} -\label{LoopByCyclicModification} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The cyclic modification of a Moufang loop \mbox{\texttt{\mdseries\slshape Q}} obtained from \mbox{\texttt{\mdseries\slshape S}}, \mbox{\texttt{\mdseries\slshape a}}$=\alpha$ and \mbox{\texttt{\mdseries\slshape h}} described below. - - - -Assume that $Q$ is a Moufang loop with a normal subloop $S$ such that $Q/S$ is a cyclic group of order $2m$. Let $h\in S\cap Z(L)$. Let $\alpha$ be a generator of $Q/S$ and write $Q = \bigcup_{i\in M} \alpha^i$, where $M=\{-m+1$, $\dots$, $m\}$. Let $\sigma:\mathbb{Z}\to M$ be defined by $\sigma(i)=0$ if $i\in M$, $\sigma(i)=1$ if $i>m$, and $\sigma(i)=-1$ if $i<-m+1$. Introduce a new multiplication $*$ on $Q$ by $x*y = xyh^{\sigma(i+j)}$, where $x\in \alpha^i$, $y\in\alpha^j$, $i\in M$ and $j\in M$. Then $(Q,*)$ is a Moufang loop, a \emph{cyclic modification}\index{modification!cyclic} of $Q$.} - - - -\subsection{\textcolor{Chapter }{LoopByDihedralModification}} -\logpage{[ 8, 2, 2 ]}\nobreak -\hyperdef{L}{X7D7717C587BC2D1E}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopByDihedralModification({\mdseries\slshape Q, S, e, f, h})\index{LoopByDihedralModification@\texttt{LoopByDihedralModification}} -\label{LoopByDihedralModification} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The dihedral modification of a Moufang loop \mbox{\texttt{\mdseries\slshape Q}} obtained from \mbox{\texttt{\mdseries\slshape S}}, \mbox{\texttt{\mdseries\slshape e}}, \mbox{\texttt{\mdseries\slshape f}} and \mbox{\texttt{\mdseries\slshape h}} as described below. - - - -Let $Q$ be a Moufang loop with a normal subloop $S$ such that $Q/S$ is a dihedral group of order $4m$, with $m\ge 1$. Let $M$ and $\sigma$ be defined as in the cyclic case. Let $\beta$, $\gamma$ be two involutions of $Q/S$ such that $\alpha=\beta\gamma$ generates a cyclic subgroup of $Q/S$ of order $2m$. Let $e\in\beta$ and $f\in\gamma$ be arbitrary. Then $Q$ can be written as a disjoint union $Q=\bigcup_{i\in M}(\alpha^i\cup e\alpha^i)$, and also $Q=\bigcup_{i\in M}(\alpha^i\cup \alpha^if)$. Let $G_0=\bigcup_{i\in M}\alpha^i$, and $G_1=L\setminus G_0$. Let $h\in S\cap N(L)\cap Z(G_0)$. Introduce a new multiplication $*$ on $Q$ by $x*y = xyh^{(-1)^r\sigma(i+j)}$, where $x\in\alpha^i\cup e\alpha^i$, $y\in\alpha^j\cup \alpha^jf$, $i\in M$, $j\in M$, $y\in G_r$ and $r\in\{0,1\}$. Then $(Q,*)$ is a Moufang loop, a \emph{dihedral modification}\index{modification!dihedral} of $Q$.} - - - -\subsection{\textcolor{Chapter }{LoopMG2}} -\logpage{[ 8, 2, 3 ]}\nobreak -\hyperdef{L}{X7CC6CDB786E9BBA0}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LoopMG2({\mdseries\slshape G})\index{LoopMG2@\texttt{LoopMG2}} -\label{LoopMG2} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The Chein loop constructed from a group \mbox{\texttt{\mdseries\slshape G}}. - - - -Let $G$ be a group. Let $\overline{G}=\{\overline{g}|g\in G\}$ be a disjoint copy of elements of $G$. Define multiplication $*$ on $Q=G\cup \overline{G}$ by $g*h = gh$, $g*\overline{h}=\overline{hg}$, $\overline{g}*h = \overline{gh^{-1}}$ and $\overline{g}*\overline{h}=h^{-1}g$, where $g$, $h\in G$. Then $(Q,*)=M(G,2)$ is a so-called \emph{Chein loop}\index{Chein loop}\index{loop!Chein}, which is always a Moufang loop, and it is associative if and only if $G$ is commutative.} - - } - - -\section{\textcolor{Chapter }{Triality for Moufang Loops}}\label{Sec:TrialityForMoufangLoops} -\logpage{[ 8, 3, 0 ]} -\hyperdef{L}{X83E73A767D79FAFD}{} -{ - Let $G$ be a group and $\sigma$, $\rho$ be automorphisms of $G$ satisfying $\sigma^2 = \rho^3 = (\sigma \rho)^2 = 1$. Below we write automorphisms as exponents and $[g,\sigma]$ for $g^{-1}g^\sigma$. We say that the triple $(G,\rho,\sigma)$ is a \emph{group with triality}\index{group with triality} if $[g, \sigma] [g,\sigma]^\rho [g,\sigma]^{\rho^2} =1$ holds for all $g \in G$. It is known that one can associate a group with triality $(G,\rho,\sigma)$ in a canonical way with a Moufang loop $Q$. See \cite{NaVo2003} for more details. - -For any Moufang loop $Q$, we can calculate the triality group as a permutation group acting on $3|Q|$ points. If the multiplication group of $Q$ is polycyclic, then we can also represent the triality group as a pc group. In -both cases, the automorphisms $\sigma$ and $\rho$ are in the same family as the elements of $G$. - -\subsection{\textcolor{Chapter }{TrialityPermGroup}} -\logpage{[ 8, 3, 1 ]}\nobreak -\hyperdef{L}{X7DB4DE647F6F56F0}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{TrialityPermGroup({\mdseries\slshape Q})\index{TrialityPermGroup@\texttt{TrialityPermGroup}} -\label{TrialityPermGroup} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -A record with components \texttt{G}, \texttt{rho}, \texttt{sigma}, where \texttt{G} is the canonical group with triality associated with a Moufang loop \mbox{\texttt{\mdseries\slshape Q}}, and \texttt{rho}, \texttt{sigma} are the corresponding triality automorphisms. - -} - - - -\subsection{\textcolor{Chapter }{TrialityPcGroup}} -\logpage{[ 8, 3, 2 ]}\nobreak -\hyperdef{L}{X82CC977085DFDFE8}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{TrialityPcGroup({\mdseries\slshape Q})\index{TrialityPcGroup@\texttt{TrialityPcGroup}} -\label{TrialityPcGroup} -}\hfill{\scriptsize (function)}}\\ - - -This is a variation of \texttt{TrialityPermGroup} in which \texttt{G} is returned as a pc group.} - - } - - -\section{\textcolor{Chapter }{Realizing Groups as Multiplication Groups of Loops}}\label{Sec:RealizingGroupsEtc} -\logpage{[ 8, 4, 0 ]} -\hyperdef{L}{X841ED66B8084AA73}{} -{ - It is difficult to determine which groups can occur as multiplication groups -of loops. - -The following operations search for loops whose multiplication groups are -contained within a specified transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. In all these operations, one can speed up the search by increasing the -optional argument \mbox{\texttt{\mdseries\slshape depth}}, the price being a much higher memory consumption. The argument \mbox{\texttt{\mdseries\slshape depth}} is optimally chosen if in the permutation group \mbox{\texttt{\mdseries\slshape G}} there are not many permutations fixing \mbox{\texttt{\mdseries\slshape depth}} elements. It is safe to omit the argument or set it equal to 2. - -The optional argument \mbox{\texttt{\mdseries\slshape infolevel}} determines the amount of information displayed during the search. With \texttt{\mbox{\texttt{\mdseries\slshape infolevel}}=0}, no information is provided. With \texttt{\mbox{\texttt{\mdseries\slshape infolevel}}=1}, you get some information on timing and hits. With \texttt{\mbox{\texttt{\mdseries\slshape infolevel}}=2}, the results are printed as well. - -\subsection{\textcolor{Chapter }{AllLoopTablesInGroup}} -\logpage{[ 8, 4, 1 ]}\nobreak -\hyperdef{L}{X804F40087DD1225D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AllLoopTablesInGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{AllLoopTablesInGroup@\texttt{AllLoopTablesInGroup}} -\label{AllLoopTablesInGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -All Cayley tables of loops whose multiplication group is contained in the -transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - - -\subsection{\textcolor{Chapter }{AllProperLoopTablesInGroup}} -\logpage{[ 8, 4, 2 ]}\nobreak -\hyperdef{L}{X7854C8E382DC8E8B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AllProperLoopTablesInGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{AllProperLoopTablesInGroup@\texttt{AllProperLoopTablesInGroup}} -\label{AllProperLoopTablesInGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -All Cayley tables of nonassociative loops whose multiplication group is -contained in the transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - - -\subsection{\textcolor{Chapter }{OneLoopTableInGroup}} -\logpage{[ 8, 4, 3 ]}\nobreak -\hyperdef{L}{X7BFFC66A824BA6AA}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{OneLoopTableInGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{OneLoopTableInGroup@\texttt{OneLoopTableInGroup}} -\label{OneLoopTableInGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A Cayley table of a loop whose multiplication group is contained in the -transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - - -\subsection{\textcolor{Chapter }{OneProperLoopTableInGroup}} -\logpage{[ 8, 4, 4 ]}\nobreak -\hyperdef{L}{X84C5A76585B335FF}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{OneProperLoopTableInGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{OneProperLoopTableInGroup@\texttt{OneProperLoopTableInGroup}} -\label{OneProperLoopTableInGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A Cayley table of a nonassociative loop whose multiplication group is -contained in the transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - - -\subsection{\textcolor{Chapter }{AllLoopsWithMltGroup}} -\logpage{[ 8, 4, 5 ]}\nobreak -\hyperdef{L}{X7E5F1C2879358EEF}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AllLoopsWithMltGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{AllLoopsWithMltGroup@\texttt{AllLoopsWithMltGroup}} -\label{AllLoopsWithMltGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -A list of all loops (given as sections) whose multiplication group is equal to -the transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - - -\subsection{\textcolor{Chapter }{OneLoopWithMltGroup}} -\logpage{[ 8, 4, 6 ]}\nobreak -\hyperdef{L}{X8266DE05824226E6}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{OneLoopWithMltGroup({\mdseries\slshape G[, depth[, infolevel]]})\index{OneLoopWithMltGroup@\texttt{OneLoopWithMltGroup}} -\label{OneLoopWithMltGroup} -}\hfill{\scriptsize (operation)}}\\ -\textbf{\indent Returns:\ } -One loop (given as a section) whose multiplication group is equal to the -transitive permutation group \mbox{\texttt{\mdseries\slshape G}}. - -} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@g:=PGL(3,3); | - Group([ (6,7)(8,11)(9,13)(10,12), (1,2,5,7,13,3,8,6,10,9,12,4,11) ]) - !gapprompt@gap>| !gapinput@a:=AllLoopTablesInGroup(g,3,0);; Size(a); | - 56 - !gapprompt@gap>| !gapinput@a:=AllLoopsWithMltGroup(g,3,0);; Size(a); | - 52 -\end{Verbatim} - } - - } - - -\chapter{\textcolor{Chapter }{Libraries of Loops}}\label{Chap:LibrariesOfLoops} -\logpage{[ 9, 0, 0 ]} -\hyperdef{L}{X7BF3EE6E7953560D}{} -{ - Libraries of small loops form an integral part of \textsf{LOOPS}. The loops are stored in libraries up to isomorphism and, sometimes, up to -isotopism. -\section{\textcolor{Chapter }{A Typical Library}}\label{Sec:ATypicalLibrary} -\logpage{[ 9, 1, 0 ]} -\hyperdef{L}{X874DFEAA79B3377C}{} -{ - A library named \emph{my Library} is stored in file \texttt{data/mylibrary.tbl}, and the corresponding data structure is named \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data}. For example, when the library is called \emph{left Bol}, the corresponding data file is called \texttt{data/leftbol.tbl} and the corresponding data structure is named \texttt{LOOPS{\textunderscore}left{\textunderscore}bol{\textunderscore}data}. - -In most cases, the array \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data} consists of three lists: -\begin{itemize} -\item \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[1]} is a list of orders for which there is at least one loop in the library, -\item \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[2][k]} is the number of loops of order \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[1][k]} in the library, -\item \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[3][k][s]} contains data necessary to produce the \texttt{s}th loop of order \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[1][k]} in the library. -\end{itemize} - The format of \texttt{LOOPS{\textunderscore}my{\textunderscore}library{\textunderscore}data[3]} depends heavily on the particular library and is not standardized in any way. -The data is often coded to save space. - -\subsection{\textcolor{Chapter }{LibraryLoop}} -\logpage{[ 9, 1, 1 ]}\nobreak -\hyperdef{L}{X849865D6786EEF9B}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LibraryLoop({\mdseries\slshape libname, n, m})\index{LibraryLoop@\texttt{LibraryLoop}} -\label{LibraryLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th loop of order \mbox{\texttt{\mdseries\slshape n}} from the library named \mbox{\texttt{\mdseries\slshape libname}}. - -} - - - -\subsection{\textcolor{Chapter }{MyLibraryLoop}} -\logpage{[ 9, 1, 2 ]}\nobreak -\hyperdef{L}{X78C4B8757902D49F}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MyLibraryLoop({\mdseries\slshape n, m})\index{MyLibraryLoop@\texttt{MyLibraryLoop}} -\label{MyLibraryLoop} -}\hfill{\scriptsize (function)}}\\ - - -This is a template function that retrieves the \mbox{\texttt{\mdseries\slshape m}}th loop of order \mbox{\texttt{\mdseries\slshape n}} from the library named \emph{my library}.} - - - -For example, the \mbox{\texttt{\mdseries\slshape m}}th left Bol loop of order \mbox{\texttt{\mdseries\slshape n}} is obtained via \texttt{LeftBolLoop(\mbox{\texttt{\mdseries\slshape n}},\mbox{\texttt{\mdseries\slshape m}})} or via \texttt{LibraryLoop("left Bol",\mbox{\texttt{\mdseries\slshape n}},\mbox{\texttt{\mdseries\slshape m}})}. - -\subsection{\textcolor{Chapter }{DisplayLibraryInfo}} -\logpage{[ 9, 1, 3 ]}\nobreak -\hyperdef{L}{X7A64372E81E713B4}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{DisplayLibraryInfo({\mdseries\slshape libname})\index{DisplayLibraryInfo@\texttt{DisplayLibraryInfo}} -\label{DisplayLibraryInfo} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -Brief information about the loops contained in the library named \mbox{\texttt{\mdseries\slshape libname}}.\\ - - -} - - - -We are now going to describe the individual libraries. } - - -\section{\textcolor{Chapter }{Left Bol Loops and Right Bol Loops}}\label{Sec:LeftBolLoopsEtc} -\logpage{[ 9, 2, 0 ]} -\hyperdef{L}{X7DF21BD685FBF258}{} -{ - The library named \emph{left Bol} contains all nonassociative left Bol loops of order less than 17, including -Moufang loops, as well as all left Bol loops of order $pq$ for primes $p>q>2$. There are 6 such loops of order 8, 1 of order 12, 2 of order 15, 2038 of -order 16, and $(p+q-4)/2$ of order $pq$. - -The classification of left Bol loops of order 16 was first accomplished by -Moorhouse \cite{Mo}. Our library was generated independently and it agrees with Moorhouse's -results. The left Bol loops of order $pq$ were classified in \cite{KiNaVo2015}. - -\subsection{\textcolor{Chapter }{LeftBolLoop}} -\logpage{[ 9, 2, 1 ]}\nobreak -\hyperdef{L}{X7EE99F647C537994}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftBolLoop({\mdseries\slshape n, m})\index{LeftBolLoop@\texttt{LeftBolLoop}} -\label{LeftBolLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th left Bol loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - - -\subsection{\textcolor{Chapter }{RightBolLoop}} -\logpage{[ 9, 2, 2 ]}\nobreak -\hyperdef{L}{X8774304282654C58}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightBolLoop({\mdseries\slshape n, m})\index{RightBolLoop@\texttt{RightBolLoop}} -\label{RightBolLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th right Bol loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - - -\textsc{Remark:} Only left Bol loops are stored in the library. Right Bol loops are retrieved -by calling \texttt{Opposite} on left Bol loops. } - - -\section{\textcolor{Chapter }{Moufang Loops}}\label{Sec:MoufangLoops} -\logpage{[ 9, 3, 0 ]} -\hyperdef{L}{X7953702D84E60AF4}{} -{ - The library named \emph{Moufang} contains all nonassociative Moufang loops of order $n\le 64$ and $n\in\{81,243\}$. - -\subsection{\textcolor{Chapter }{MoufangLoop}} -\logpage{[ 9, 3, 1 ]}\nobreak -\hyperdef{L}{X81E82098822543EE}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{MoufangLoop({\mdseries\slshape n, m})\index{MoufangLoop@\texttt{MoufangLoop}} -\label{MoufangLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th Moufang loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - - -For $n\le 63$, our catalog numbers coincide with those of Goodaire et al. \cite{Go}. The classification of Moufang loops of order 64 and 81 was carried out in \cite{NaVo2007}. The classification of Moufang loops of order 243 was carried out by Slattery -and Zenisek \cite{SlZe2011}. - -The extent of the library is summarized below: -\[ \begin{array}{r|rrrrrrrrrrrrrrrrrr} -order&12&16&20&24&28&32&36&40&42&44&48&52&54&56&60&64&81&243\cr loops&1 &5 &1 -&5 &1 &71&4 &5 &1 &1 &51&1 &2 &4 &5 &4262& 5 &72 \end{array} \] - - -The \emph{octonion loop}\index{octonion loop}\index{loop!octonion} of order 16 (i.e., the multiplication loop of the basis elements in the -8-dimensional standard real octonion algebra) can be obtained as \texttt{MoufangLoop(16,3)}. } - - -\section{\textcolor{Chapter }{Code Loops}}\label{Sec:CodeLoops} -\logpage{[ 9, 4, 0 ]} -\hyperdef{L}{X7BCA6BCB847F79DC}{} -{ - The library named \emph{code} contains all nonassociative code loops of order less than 65. There are 5 such -loops of order 16, 16 of order 32, and 80 of order 64, all Moufang. The -library merely points to the corresponding Moufang loops. See \cite{NaVo2007} for a classification of small code loops. - -\subsection{\textcolor{Chapter }{CodeLoop}} -\logpage{[ 9, 4, 1 ]}\nobreak -\hyperdef{L}{X7DB4D3B27BB4D7EE}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CodeLoop({\mdseries\slshape n, m})\index{CodeLoop@\texttt{CodeLoop}} -\label{CodeLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th code loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Steiner Loops}}\label{Sec:SteinerLoops} -\logpage{[ 9, 5, 0 ]} -\hyperdef{L}{X84E941EE7846D3EE}{} -{ - Here is how the libary named \emph{Steiner} is described within \textsf{LOOPS}: -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@DisplayLibraryInfo( "Steiner" ); | - The library contains all nonassociative Steiner loops of order less or equal to 16. - It also contains the associative Steiner loops of order 4 and 8. - ------ - Extent of the library: - 1 loop of order 4 - 1 loop of order 8 - 1 loop of order 10 - 2 loops of order 14 - 80 loops of order 16 - true -\end{Verbatim} - - -Our labeling of Steiner loops of order 16 coincides with the labeling of -Steiner triple systems of order 15 in \cite{CoRo}. - -\subsection{\textcolor{Chapter }{SteinerLoop}} -\logpage{[ 9, 5, 1 ]}\nobreak -\hyperdef{L}{X87C235457E859AF4}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{SteinerLoop({\mdseries\slshape n, m})\index{SteinerLoop@\texttt{SteinerLoop}} -\label{SteinerLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th Steiner loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Conjugacy Closed Loops}}\label{Sec:ConjugacyClosedLoops} -\logpage{[ 9, 6, 0 ]} -\hyperdef{L}{X867E5F0783FEB8B5}{} -{ - The library named \emph{RCC} contains all nonassocitive right conjugacy closed loops of order $n\le 27$ up to isomorphism. The data for the library was generated by Katharina Artic \cite{Artic} who can also provide additional data for all right conjugacy closed loops of -order $n\le 31$. - -Let $Q$ be a right conjugacy closed loop, $G$ its right multiplication group and $T$ its right section. Then $\langle T\rangle = G$ is a transitive group, and $T$ is a union of conjugacy classes of $G$. Every right conjugacy closed loop of order $n$ can therefore be represented as a union of certain conjugacy classes of a -transitive group of degree $n$. This is how right conjugacy closed loops of order less than $28$ are represented in \textsf{LOOPS}. The following table summarizes the number of right conjugacy closed loops of -a given order up to isomorphism: -\[ \begin{array}{r|rrrrrrrrrrrrrrrr} order &6& 8&9&10& 12&14&15& 16& 18& 20&\cr -loops &3&19&5&16&155&97& 17&6317&1901&8248&\cr \hline order &21& 22& 24& 25& -26& 27\cr loops &119&10487&471995& 119&151971&152701 \end{array} \] - -\subsection{\textcolor{Chapter }{RCCLoop and RightConjugacyClosedLoop}}\logpage{[ 9, 6, 1 ]} -\hyperdef{L}{X806B2DE67990E42F}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RCCLoop({\mdseries\slshape n, m})\index{RCCLoop@\texttt{RCCLoop}} -\label{RCCLoop} -}\hfill{\scriptsize (function)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{RightConjugacyClosedLoop({\mdseries\slshape n, m})\index{RightConjugacyClosedLoop@\texttt{RightConjugacyClosedLoop}} -\label{RightConjugacyClosedLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th right conjugacy closed loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - -\subsection{\textcolor{Chapter }{LCCLoop and LeftConjugacyClosedLoop}}\logpage{[ 9, 6, 2 ]} -\hyperdef{L}{X80AB8B107D55FB19}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LCCLoop({\mdseries\slshape n, m})\index{LCCLoop@\texttt{LCCLoop}} -\label{LCCLoop} -}\hfill{\scriptsize (function)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{LeftConjugacyClosedLoop({\mdseries\slshape n, m})\index{LeftConjugacyClosedLoop@\texttt{LeftConjugacyClosedLoop}} -\label{LeftConjugacyClosedLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th left conjugacy closed loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - - - -\textsc{Remark:} Only the right conjugacy closed loops are stored in the library. Left -conjugacy closed loops are obtained from right conjugacy closed loops via \texttt{Opposite}.\\ -} - - - -The library named \emph{CC} contains all nonassociative conjugacy closed loops of order $n\le 27$ and also of orders $2p$ and $p^2$ for all primes $p$. - -By results of Kunen \cite{Kun}, for every odd prime $p$ there are precisely 3 nonassociative conjugacy closed loops of order $p^2$. Cs{\"o}rg{\H o} and Dr{\a'a}pal \cite{CsDr} described these 3 loops by multiplicative formulas on $\mathbb{Z}_{p^2}$ and $\mathbb{Z}_p \times \mathbb{Z}_p$ as follows: -\begin{itemize} -\item Case $m = 1$:Let $k$ be the smallest positive integer relatively prime to $p$ and such that $k$ is a square modulo $p$ (i.e., $k=1$). Define multiplication on $\mathbb{Z}_{p^2}$ by $x\cdot y = x + y + kpx^2y$. -\item Case $m = 2$: Let $k$ be the smallest positive integer relatively prime to $p$ and such that $k$ is not a square modulo $p$. Define multiplication on $\mathbb{Z}_{p^2}$ by $x\cdot y = x + y + kpx^2y$. -\item Case $m = 3$: Define multiplication on $\mathbb{Z}_p \times \mathbb{Z}_p$ by $(x,a)(y,b) = (x+y, a+b+x^2y )$. -\end{itemize} - - -Moreover, Wilson \cite{Wi} constructed a nonassociative conjugacy closed loop of order $2p$ for every odd prime $p$, and Kunen \cite{Kun} showed that there are no other nonassociative conjugacy closed oops of this -order. Here is the relevant multiplication formula on $\mathbb{Z}_2 \times \mathbb{Z}_p$: $(0,m)(0,n) = ( 0, m + n )$, $(0,m)(1,n) = ( 1, -m + n )$, $(1,m)(0,n) = ( 1, m + n)$, $(1,m)(1,n) = ( 0, 1 - m + n )$. -\subsection{\textcolor{Chapter }{CCLoop and ConjugacyClosedLoop}}\logpage{[ 9, 6, 3 ]} -\hyperdef{L}{X798BC601843E8916}{} -{ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{CCLoop({\mdseries\slshape n, m})\index{CCLoop@\texttt{CCLoop}} -\label{CCLoop} -}\hfill{\scriptsize (function)}}\\ -\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{ConjugacyClosedLoop({\mdseries\slshape n, m})\index{ConjugacyClosedLoop@\texttt{ConjugacyClosedLoop}} -\label{ConjugacyClosedLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th conjugacy closed loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Small Loops}}\label{Sec:SmallLoops} -\logpage{[ 9, 7, 0 ]} -\hyperdef{L}{X7E3A8F2C790F2CA1}{} -{ - The library named \emph{small} contains all nonassociative loops of order 5 and 6. There are 5 and 107 such -loops, respectively. - -\subsection{\textcolor{Chapter }{SmallLoop}} -\logpage{[ 9, 7, 1 ]}\nobreak -\hyperdef{L}{X7C6EE23E84CD87D3}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{SmallLoop({\mdseries\slshape n, m})\index{SmallLoop@\texttt{SmallLoop}} -\label{SmallLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Paige Loops}}\label{Sec:PaigeLoops} -\logpage{[ 9, 8, 0 ]} -\hyperdef{L}{X8135C8FD8714C606}{} -{ - \emph{Paige loops}\index{Paige loop}\index{loop!Paige} are nonassociative finite simple Moufang loops. By \cite{Li}, there is precisely one Paige loop for every finite field. - -The library named \emph{Paige} contains the smallest nonassociative simple Moufang loop. - -\subsection{\textcolor{Chapter }{PaigeLoop}} -\logpage{[ 9, 8, 1 ]}\nobreak -\hyperdef{L}{X7FCF4D6B7AD66D74}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{PaigeLoop({\mdseries\slshape q})\index{PaigeLoop@\texttt{PaigeLoop}} -\label{PaigeLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The Paige loop constructed over the finite field of order \mbox{\texttt{\mdseries\slshape q}}. Only the case \texttt{\mbox{\texttt{\mdseries\slshape q}}=2} is implemented. - -} - - } - - -\section{\textcolor{Chapter }{Nilpotent Loops}}\label{Sec:NilpotentLoops} -\logpage{[ 9, 9, 0 ]} -\hyperdef{L}{X86695C577A4D1784}{} -{ - The library named \emph{nilpotent} contains all nonassociative nilpotent loops of order less than 12 up to -isomorphism. There are 2 nonassociative nilpotent loops of order 6, 134 of -order 8, 8 of order 9 and 1043 of order 10. - -See \cite{DaVo} for more on enumeration of nilpotent loops. For instance, there are 2623755 -nilpotent loops of order 12, and 123794003928541545927226368 nilpotent loops -of order 22. - -\subsection{\textcolor{Chapter }{NilpotentLoop}} -\logpage{[ 9, 9, 1 ]}\nobreak -\hyperdef{L}{X7A9C960D86E2AD28}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{NilpotentLoop({\mdseries\slshape n, m})\index{NilpotentLoop@\texttt{NilpotentLoop}} -\label{NilpotentLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th nilpotent loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Automorphic Loops}}\label{Sec:AutomorphicLoops} -\logpage{[ 9, 10, 0 ]} -\hyperdef{L}{X793B22EA8643C667}{} -{ - The library named \emph{automorphic} contains all nonassociative automorphic loops of order less than 16 up to -isomorphism (there is 1 such loop of order 6, 7 of order 8, 3 of order 10, 2 -of order 12, 5 of order 14, and 2 of order 15), all commutative automorphic -loops of order 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops, -respectively, including abelian groups), and commutative automorphic loops $Q$ of order 243 possessing a central subloop $S$ of order 3 such that $Q/S$ is not the elementary abelian group of order 81 (there are 118451 such loops). - -\subsection{\textcolor{Chapter }{AutomorphicLoop}} -\logpage{[ 9, 10, 1 ]}\nobreak -\hyperdef{L}{X784FFA9E7FDA9F43}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{AutomorphicLoop({\mdseries\slshape n, m})\index{AutomorphicLoop@\texttt{AutomorphicLoop}} -\label{AutomorphicLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th automorphic loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Interesting Loops}}\label{Sec:InterestingLoops} -\logpage{[ 9, 11, 0 ]} -\hyperdef{L}{X843BD73F788049F7}{} -{ - The library named \emph{interesting} contains some loops that are illustrative in the theory of loops. At this -point, the library contains a nonassociative loop of order 5, a nonassociative -nilpotent loop of order 6, a non-Moufang left Bol loop of order 16, the loop -of sedenions\index{sedenion loop}\index{loop!sedenion} of order 32 (sedenions generalize octonions), and the unique nonassociative -simple right Bol loop of order 96 and exponent 2. - -\subsection{\textcolor{Chapter }{InterestingLoop}} -\logpage{[ 9, 11, 1 ]}\nobreak -\hyperdef{L}{X87F24AD3811910D3}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{InterestingLoop({\mdseries\slshape n, m})\index{InterestingLoop@\texttt{InterestingLoop}} -\label{InterestingLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th interesting loop of order \mbox{\texttt{\mdseries\slshape n}} in the library. - -} - - } - - -\section{\textcolor{Chapter }{Libraries of Loops Up To Isotopism}}\label{Sec:LibrariesOfLoopsUpToIsotopism} -\logpage{[ 9, 12, 0 ]} -\hyperdef{L}{X864839227D5C0A90}{} -{ - For the library named \emph{small} we also provide the corresponding library of loops up to isotopism. In -general, given a library named \emph{libname}, the corresponding library of loops up to isotopism is named \emph{itp lib}, and the loops can be retrieved by the template \texttt{ItpLibLoop(n,m)}. - -\subsection{\textcolor{Chapter }{ItpSmallLoop}} -\logpage{[ 9, 12, 1 ]}\nobreak -\hyperdef{L}{X850C4C01817A098D}{} -{\noindent\textcolor{FuncColor}{$\triangleright$\ \ \texttt{ItpSmallLoop({\mdseries\slshape n, m})\index{ItpSmallLoop@\texttt{ItpSmallLoop}} -\label{ItpSmallLoop} -}\hfill{\scriptsize (function)}}\\ -\textbf{\indent Returns:\ } -The \mbox{\texttt{\mdseries\slshape m}}th small loop of order \mbox{\texttt{\mdseries\slshape n}} up to isotopism in the library. - -} - - -\begin{Verbatim}[commandchars=!@|,fontsize=\small,frame=single,label=Example] - !gapprompt@gap>| !gapinput@SmallLoop( 6, 14 ); | - - !gapprompt@gap>| !gapinput@ItpSmallLoop( 6, 14 ); | - - !gapprompt@gap>| !gapinput@LibraryLoop( "itp small", 6, 14 ); | - -\end{Verbatim} - - -Note that loops up to isotopism form a subset of the corresponding library of -loops up to isomorphism. For instance, the above example shows that the 14th -small loop of order 6 up to isotopism is in fact the 42nd small loop of order -6 up to isomorphism. } - - } - - - -\appendix - - -\chapter{\textcolor{Chapter }{Files}}\label{Apx:Files} -\logpage{[ "A", 0, 0 ]} -\hyperdef{L}{X7BC4571A79FFB7D0}{} -{ - Below is a list of all relevant files forming the \textsf{LOOPS} package. Some technical files are not included. A typical user will not need -to know any of this information. All paths are relative to the \texttt{pkg/loops} folder. \\ -\\ -\texttt{../README.loops} (installation and usage instructions) \\ -\texttt{init.g} (declarations) \\ -\texttt{PackageInfo.g} (loading info for GAP 4.4) \\ -\texttt{read.g} (implementations) \\ -\texttt{data/automorphic.tbl} (library of automorphic loops) \\ -\texttt{data/automorphic/*.*} (addition files for the library of automorphic loops) \\ -\texttt{data/cc.tbl} (library of conjugacy closed loops) \\ -\texttt{data/code.tbl} (library of code loops) \\ -\texttt{data/interesting.tbl} (library of interesting loops) \\ -\texttt{data/itp{\textunderscore}small.tbl} (library of small loops up to isotopism) \\ -\texttt{data/leftbol.tbl} (library of left Bol loops) \\ -\texttt{data/moufang.tbl} (library of Moufang loops) \\ -\texttt{data/nilpotent.tbl} (library of small nilpotent loops) \\ -\texttt{data/rcc.tbl} (library of right conjugacy closed loops) \\ -\texttt{data/rcc/*.*} (additional files for the library of right conjugacy closed loops) \\ -\texttt{data/paige.tbl} (library of Paige loops) \\ -\texttt{data/small.tbl} (library of small loops) \\ -\texttt{data/steiner.tbl} (library of Steiner loops) \\ -\texttt{doc/*.*} (all documentation files) \\ -\texttt{doc/loops.xml} (the main documentation file for GAPDoc) \\ -\texttt{doc/loops.bib} (the main bibliography file for documentation) \\ -\texttt{gap/banner.g} (banner of LOOPS) \\ -\texttt{gap/bol{\textunderscore}core{\textunderscore}methods.gd .gi} (core methods for Bol loops) \\ -\texttt{gap/classes.gd .gi} (properties of quasigroups and loops) \\ -\texttt{gap/convert.gd .gi} (methods for data conversion and compression) \\ -\texttt{gap/core{\textunderscore}methods.gd .gi} (core methods for quasigroups and loops) \\ -\texttt{gap/elements.gd .gi} (elements and basic arithmetic operations) \\ -\texttt{gap/examples.gd .gi} (methods for libraries of loops) \\ -\texttt{gap/extensions.gd .gi} (methods for extensions of loops) \\ -\texttt{gap/iso.gd .gi} (methods for isomorphisms and isotopisms of loops) \\ -\texttt{gap/memory.gd .gi} (memory management) \\ -\texttt{gap/mlt{\textunderscore}search.gd .gi} (realizing groups as multiplication groups of loops) \\ -\texttt{gap/moufang{\textunderscore}modifications.gd .gi} (methods for Moufang modifications) \\ -\texttt{gap/moufang{\textunderscore}triality.gd .gi} (methods for triality of Moufang loops) \\ -\texttt{gap/quasigroups.gd .gi} (representing, creating and displaying quasigroups) \\ -\texttt{gap/random.gd .gi} (random quasigroups and loops) \\ -\texttt{tst/bol.tst} (test file for Bol loops) \\ -\texttt{tst/core{\textunderscore}methods.tst} (test file for core methods) \\ -\texttt{tst/iso.tst} (test file for isomorphisms and automorphisms) \\ -\texttt{tst/lib.tst} (test file for libraries of loops, except Moufang loops) \\ -\texttt{tst/nilpot.tst} (test file for nilpotency and triality) \\ -\texttt{tst/testall.g} (batch for all tets files) } - - -\chapter{\textcolor{Chapter }{Filters}}\label{Apx:Filters} -\logpage{[ "B", 0, 0 ]} -\hyperdef{L}{X84EFA4C07D4277BB}{} -{ - Many implications among properties of loops are built directly into \textsf{LOOPS}. A sizeable portion of these properties are of trivial character or are based -on definitions (e.g., alternative loops $=$ left alternative loops $+$ right alternative loops). The remaining implications are theorems. - -All filters of \textsf{LOOPS} are summarized below, using the \textsf{GAP} convention that the property on the left is implied by the property -(properties) on the right. \\ -\\ - \texttt{( IsExtraLoop, IsAssociative and IsLoop )} \\ -\texttt{( IsExtraLoop, IsCodeLoop )} \\ -\texttt{( IsCCLoop, IsCodeLoop )} \\ -\texttt{( HasTwosidedInverses, IsPowerAssociative and IsLoop )} \\ -\texttt{( IsPowerAlternative, IsDiassociative )} \\ -\texttt{( IsFlexible, IsDiassociative )} \\ -\texttt{( HasAntiautomorphicInverseProperty, HasAutomorphicInverseProperty and -IsCommutative )} \\ -\texttt{( HasAutomorphicInverseProperty, HasAntiautomorphicInverseProperty and -IsCommutative )} \\ -\texttt{( HasLeftInverseProperty, HasInverseProperty )} \\ -\texttt{( HasRightInverseProperty, HasInverseProperty )} \\ -\texttt{( HasWeakInverseProperty, HasInverseProperty )} \\ -\texttt{( HasAntiautomorphicInverseProperty, HasInverseProperty )} \\ -\texttt{( HasTwosidedInverses, HasAntiautomorphicInverseProperty )} \\ -\texttt{( HasInverseProperty, HasLeftInverseProperty and IsCommutative )} \\ -\texttt{( HasInverseProperty, HasRightInverseProperty and IsCommutative )} \\ -\texttt{( HasInverseProperty, HasLeftInverseProperty and HasRightInverseProperty )} \\ -\texttt{( HasInverseProperty, HasLeftInverseProperty and HasWeakInverseProperty )} \\ -\texttt{( HasInverseProperty, HasRightInverseProperty and HasWeakInverseProperty )} \\ -\texttt{( HasInverseProperty, HasLeftInverseProperty and -HasAntiautomorphicInverseProperty )} \\ -\texttt{( HasInverseProperty, HasRightInverseProperty and -HasAntiautomorphicInverseProperty )} \\ -\texttt{( HasInverseProperty, HasWeakInverseProperty and -HasAntiautomorphicInverseProperty )} \\ -\texttt{( HasTwosidedInverses, HasLeftInverseProperty )} \\ -\texttt{( HasTwosidedInverses, HasRightInverseProperty )} \\ -\texttt{( HasTwosidedInverses, IsFlexible and IsLoop )} \\ -\texttt{( IsMoufangLoop, IsExtraLoop )} \\ -\texttt{( IsCLoop, IsExtraLoop )} \\ -\texttt{( IsExtraLoop, IsMoufangLoop and IsLeftNuclearSquareLoop )} \\ -\texttt{( IsExtraLoop, IsMoufangLoop and IsMiddleNuclearSquareLoop )} \\ -\texttt{( IsExtraLoop, IsMoufangLoop and IsRightNuclearSquareLoop )} \\ -\texttt{( IsLeftBolLoop, IsMoufangLoop )} \\ -\texttt{( IsRightBolLoop, IsMoufangLoop )} \\ -\texttt{( IsDiassociative, IsMoufangLoop )} \\ -\texttt{( IsMoufangLoop, IsLeftBolLoop and IsRightBolLoop )} \\ -\texttt{( IsLCLoop, IsCLoop )} \\ -\texttt{( IsRCLoop, IsCLoop )} \\ -\texttt{( IsDiassociative, IsCLoop and IsFlexible)} \\ -\texttt{( IsCLoop, IsLCLoop and IsRCLoop )} \\ -\texttt{( IsRightBolLoop, IsLeftBolLoop and IsCommutative )} \\ -\texttt{( IsLeftPowerAlternative, IsLeftBolLoop )} \\ -\texttt{( IsLeftBolLoop, IsRightBolLoop and IsCommutative )} \\ -\texttt{( IsRightPowerAlternative, IsRightBolLoop )} \\ -\texttt{( IsLeftPowerAlternative, IsLCLoop )} \\ -\texttt{( IsLeftNuclearSquareLoop, IsLCLoop )} \\ -\texttt{( IsMiddleNuclearSquareLoop, IsLCLoop )} \\ -\texttt{( IsRCLoop, IsLCLoop and IsCommutative )} \\ -\texttt{( IsRightPowerAlternative, IsRCLoop )} \\ -\texttt{( IsRightNuclearSquareLoop, IsRCLoop )} \\ -\texttt{( IsMiddleNuclearSquareLoop, IsRCLoop )} \\ -\texttt{( IsLCLoop, IsRCLoop and IsCommutative )} \\ -\texttt{( IsRightNuclearSquareLoop, IsLeftNuclearSquareLoop and IsCommutative )} \\ -\texttt{( IsLeftNuclearSquareLoop, IsRightNuclearSquareLoop and IsCommutative )} \\ -\texttt{( IsLeftNuclearSquareLoop, IsNuclearSquareLoop )} \\ -\texttt{( IsRightNuclearSquareLoop, IsNuclearSquareLoop )} \\ -\texttt{( IsMiddleNuclearSquareLoop, IsNuclearSquareLoop )} \\ -\texttt{( IsNuclearSquareLoop, IsLeftNuclearSquareLoop and IsRightNuclearSquareLoop} \\ -\texttt{ and IsMiddleNuclearSquareLoop )} \\ -\texttt{( IsFlexible, IsCommutative )} \\ -\texttt{( IsRightAlternative, IsLeftAlternative and IsCommutative )} \\ -\texttt{( IsLeftAlternative, IsRightAlternative and IsCommutative )} \\ -\texttt{( IsLeftAlternative, IsAlternative )} \\ -\texttt{( IsRightAlternative, IsAlternative )} \\ -\texttt{( IsAlternative, IsLeftAlternative and IsRightAlternative )} \\ -\texttt{( IsLeftAlternative, IsLeftPowerAlternative )} \\ -\texttt{( HasLeftInverseProperty, IsLeftPowerAlternative )} \\ -\texttt{( IsPowerAssociative, IsLeftPowerAlternative )} \\ -\texttt{( IsRightAlternative, IsRightPowerAlternative )} \\ -\texttt{( HasRightInverseProperty, IsRightPowerAlternative )} \\ -\texttt{( IsPowerAssociative, IsRightPowerAlternative )} \\ -\texttt{( IsLeftPowerAlternative, IsPowerAlternative )} \\ -\texttt{( IsRightPowerAlternative, IsPowerAlternative )} \\ -\texttt{( IsAssociative, IsLCCLoop and IsCommutative )} \\ -\texttt{( IsExtraLoop, IsLCCLoop and IsMoufangLoop )} \\ -\texttt{( IsAssociative, IsRCCLoop and IsCommutative )} \\ -\texttt{( IsExtraLoop, IsRCCLoop and IsMoufangLoop )} \\ -\texttt{( IsLCCLoop, IsCCLoop )} \\ -\texttt{( IsRCCLoop, IsCCLoop )} \\ -\texttt{( IsCCLoop, IsLCCLoop and IsRCCLoop )} \\ -\texttt{( IsOsbornLoop, IsMoufangLoop )} \\ -\texttt{( IsOsbornLoop, IsCCLoop )} \\ -\texttt{( HasAutomorphicInverseProperty, IsLeftBruckLoop )} \\ -\texttt{( IsLeftBolLoop, IsLeftBruckLoop )} \\ -\texttt{( IsRightBruckLoop, IsLeftBruckLoop and IsCommutative )} \\ -\texttt{( IsLeftBruckLoop, IsLeftBolLoop and HasAutomorphicInverseProperty )} \\ -\texttt{( HasAutomorphicInverseProperty, IsRightBruckLoop )} \\ -\texttt{( IsRightBolLoop, IsRightBruckLoop )} \\ -\texttt{( IsLeftBruckLoop, IsRightBruckLoop and IsCommutative )} \\ -\texttt{( IsRightBruckLoop, IsRightBolLoop and HasAutomorphicInverseProperty )} \\ -\texttt{( IsCommutative, IsSteinerLoop )} \\ -\texttt{( IsCLoop, IsSteinerLoop )} \\ -\texttt{( IsLeftAutomorphicLoop, IsAutomorphicLoop )} \\ -\texttt{( IsRightAutomorphicLoop, IsAutomorphicLoop )} \\ -\texttt{( IsMiddleAutomorphicLoop, IsAutomorphicLoop )} \\ -\texttt{( IsMiddleAutomorphicLoop, IsCommutative )} \\ -\texttt{( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsCommutative )} \\ -\texttt{( IsAutomorphicLoop, IsRightAutomorphicLoop and IsCommutative )} \\ -\texttt{( IsLeftAutomorphicLoop, IsRightAutomorphicLoop and -HasAntiautomorphicInverseProperty )} \\ -\texttt{( IsRightAutomorphicLoop, IsLeftAutomorphicLoop and -HasAntiautomorphicInverseProperty )} \\ -\texttt{( IsFlexible, IsMiddleAutomorphicLoop )} \\ -\texttt{( HasAntiautomorphicInverseProperty, IsFlexible and IsLeftAutomorphicLoop )} \\ -\texttt{( HasAntiautomorphicInverseProperty, IsFlexible and IsRightAutomorphicLoop )} \\ -\texttt{( IsMoufangLoop, IsAutomorphicLoop and IsLeftAlternative )} \\ -\texttt{( IsMoufangLoop, IsAutomorphicLoop and IsRightAlternative )} \\ -\texttt{( IsMoufangLoop, IsAutomorphicLoop and HasLeftInverseProperty )} \\ -\texttt{( IsMoufangLoop, IsAutomorphicLoop and HasRightInverseProperty )} \\ -\texttt{( IsMoufangLoop, IsAutomorphicLoop and HasWeakInverseProperty )} \\ -\texttt{( IsLeftAutomorphicLoop, IsLeftBruckLoop )} \\ -\texttt{( IsLeftAutomorphicLoop, IsLCCLoop )} \\ -\texttt{( IsRightAutomorphicLoop, IsRightBruckLoop )} \\ -\texttt{( IsRightAutomorphicLoop, IsRCCLoop )} \\ -\texttt{( IsAutomorphicLoop, IsCommutative and IsMoufangLoop )} } - -\def\bibname{References\logpage{[ "Bib", 0, 0 ]} -\hyperdef{L}{X7A6F98FD85F02BFE}{} -} - -\bibliographystyle{alpha} -\bibliography{loops_bib.xml} - -\addcontentsline{toc}{chapter}{References} - -\def\indexname{Index\logpage{[ "Ind", 0, 0 ]} -\hyperdef{L}{X83A0356F839C696F}{} -} - -\cleardoublepage -\phantomsection -\addcontentsline{toc}{chapter}{Index} - - -\printindex - -\newpage -\immediate\write\pagenrlog{["End"], \arabic{page}];} -\immediate\closeout\pagenrlog -\end{document} diff --git a/doc/loops.toc b/doc/loops.toc deleted file mode 100644 index 32bc3b0..0000000 --- a/doc/loops.toc +++ /dev/null @@ -1,241 +0,0 @@ -\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Introduction}}{6}{chapter.1} -\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }License}}{6}{section.1.1} -\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Installation}}{6}{section.1.2} -\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Documentation}}{6}{section.1.3} -\contentsline {section}{\numberline {1.4}\leavevmode {\color {Chapter }Test Files}}{7}{section.1.4} -\contentsline {section}{\numberline {1.5}\leavevmode {\color {Chapter }Memory Management}}{7}{section.1.5} -\contentsline {section}{\numberline {1.6}\leavevmode {\color {Chapter }Feedback}}{7}{section.1.6} -\contentsline {section}{\numberline {1.7}\leavevmode {\color {Chapter }Acknowledgment}}{7}{section.1.7} -\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Mathematical Background}}{8}{chapter.2} -\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Quasigroups and Loops}}{8}{section.2.1} -\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Translations}}{8}{section.2.2} -\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Subquasigroups and Subloops}}{9}{section.2.3} -\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter }Nilpotence and Solvability}}{9}{section.2.4} -\contentsline {section}{\numberline {2.5}\leavevmode {\color {Chapter }Associators and Commutators}}{9}{section.2.5} -\contentsline {section}{\numberline {2.6}\leavevmode {\color {Chapter }Homomorphism and Homotopisms}}{9}{section.2.6} -\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }How the Package Works}}{11}{chapter.3} -\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Representing Quasigroups}}{11}{section.3.1} -\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Conversions between magmas, quasigroups, loops and groups}}{12}{section.3.2} -\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Calculating with Quasigroups}}{12}{section.3.3} -\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter }Naming, Viewing and Printing Quasigroups and their Elements}}{13}{section.3.4} -\contentsline {subsection}{\numberline {3.4.1}\leavevmode {\color {Chapter }SetQuasigroupElmName and SetLoopElmName}}{13}{subsection.3.4.1} -\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Creating Quasigroups and Loops}}{14}{chapter.4} -\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }About Cayley Tables}}{14}{section.4.1} -\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Testing Cayley Tables}}{14}{section.4.2} -\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }IsQuasigroupTable and IsQuasigroupCayleyTable}}{14}{subsection.4.2.1} -\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }IsLoopTable and IsLoopCayleyTable}}{14}{subsection.4.2.2} -\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }Canonical and Normalized Cayley Tables}}{15}{section.4.3} -\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }CanonicalCayleyTable}}{15}{subsection.4.3.1} -\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }CanonicalCopy}}{15}{subsection.4.3.2} -\contentsline {subsection}{\numberline {4.3.3}\leavevmode {\color {Chapter }NormalizedQuasigroupTable}}{15}{subsection.4.3.3} -\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter }Creating Quasigroups and Loops From Cayley Tables}}{15}{section.4.4} -\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }QuasigroupByCayleyTable and LoopByCayleyTable}}{15}{subsection.4.4.1} -\contentsline {section}{\numberline {4.5}\leavevmode {\color {Chapter }Creating Quasigroups and Loops from a File}}{16}{section.4.5} -\contentsline {subsection}{\numberline {4.5.1}\leavevmode {\color {Chapter }QuasigroupFromFile and LoopFromFile}}{17}{subsection.4.5.1} -\contentsline {section}{\numberline {4.6}\leavevmode {\color {Chapter }Creating Quasigroups and Loops From Sections}}{17}{section.4.6} -\contentsline {subsection}{\numberline {4.6.1}\leavevmode {\color {Chapter }CayleyTableByPerms}}{17}{subsection.4.6.1} -\contentsline {subsection}{\numberline {4.6.2}\leavevmode {\color {Chapter }QuasigroupByLeftSection and LoopByLeftSection}}{17}{subsection.4.6.2} -\contentsline {subsection}{\numberline {4.6.3}\leavevmode {\color {Chapter }QuasigroupByRightSection and LoopByRightSection}}{17}{subsection.4.6.3} -\contentsline {section}{\numberline {4.7}\leavevmode {\color {Chapter }Creating Quasigroups and Loops From Folders}}{18}{section.4.7} -\contentsline {subsection}{\numberline {4.7.1}\leavevmode {\color {Chapter }QuasigroupByRightFolder and LoopByRightFolder}}{18}{subsection.4.7.1} -\contentsline {section}{\numberline {4.8}\leavevmode {\color {Chapter }Creating Quasigroups and Loops By Nuclear Extensions}}{18}{section.4.8} -\contentsline {subsection}{\numberline {4.8.1}\leavevmode {\color {Chapter }NuclearExtension}}{18}{subsection.4.8.1} -\contentsline {subsection}{\numberline {4.8.2}\leavevmode {\color {Chapter }LoopByExtension}}{18}{subsection.4.8.2} -\contentsline {section}{\numberline {4.9}\leavevmode {\color {Chapter }Random Quasigroups and Loops}}{19}{section.4.9} -\contentsline {subsection}{\numberline {4.9.1}\leavevmode {\color {Chapter }RandomQuasigroup and RandomLoop}}{19}{subsection.4.9.1} -\contentsline {subsection}{\numberline {4.9.2}\leavevmode {\color {Chapter }RandomNilpotentLoop}}{19}{subsection.4.9.2} -\contentsline {section}{\numberline {4.10}\leavevmode {\color {Chapter }Conversions}}{20}{section.4.10} -\contentsline {subsection}{\numberline {4.10.1}\leavevmode {\color {Chapter }IntoQuasigroup}}{20}{subsection.4.10.1} -\contentsline {subsection}{\numberline {4.10.2}\leavevmode {\color {Chapter }PrincipalLoopIsotope}}{20}{subsection.4.10.2} -\contentsline {subsection}{\numberline {4.10.3}\leavevmode 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{Chapter }Nuclei, Commutant, Center, and Associator Subloop}}{30}{section.6.6} -\contentsline {subsection}{\numberline {6.6.1}\leavevmode {\color {Chapter }LeftNucles, MiddleNucleus, and RightNucleus}}{30}{subsection.6.6.1} -\contentsline {subsection}{\numberline {6.6.2}\leavevmode {\color {Chapter }Nuc, NucleusOfQuasigroup and NucleusOfLoop}}{31}{subsection.6.6.2} -\contentsline {subsection}{\numberline {6.6.3}\leavevmode {\color {Chapter }Commutant}}{31}{subsection.6.6.3} -\contentsline {subsection}{\numberline {6.6.4}\leavevmode {\color {Chapter }Center}}{31}{subsection.6.6.4} -\contentsline {subsection}{\numberline {6.6.5}\leavevmode {\color {Chapter }AssociatorSubloop}}{31}{subsection.6.6.5} -\contentsline {section}{\numberline {6.7}\leavevmode {\color {Chapter }Normal Subloops and Simple Loops}}{31}{section.6.7} -\contentsline {subsection}{\numberline {6.7.1}\leavevmode {\color {Chapter }IsNormal}}{31}{subsection.6.7.1} -\contentsline {subsection}{\numberline {6.7.2}\leavevmode 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-\contentsline {section}{\numberline {6.11}\leavevmode {\color {Chapter }Isomorphisms and Automorphisms}}{33}{section.6.11} -\contentsline {subsection}{\numberline {6.11.1}\leavevmode {\color {Chapter }IsomorphismQuasigroups}}{33}{subsection.6.11.1} -\contentsline {subsection}{\numberline {6.11.2}\leavevmode {\color {Chapter }IsomorphismLoops}}{34}{subsection.6.11.2} -\contentsline {subsection}{\numberline {6.11.3}\leavevmode {\color {Chapter }QuasigroupsUpToIsomorphism}}{34}{subsection.6.11.3} -\contentsline {subsection}{\numberline {6.11.4}\leavevmode {\color {Chapter }LoopsUpToIsomorphism}}{34}{subsection.6.11.4} -\contentsline {subsection}{\numberline {6.11.5}\leavevmode {\color {Chapter }AutomorphismGroup}}{34}{subsection.6.11.5} -\contentsline {subsection}{\numberline {6.11.6}\leavevmode {\color {Chapter }IsomorphicCopyByPerm}}{34}{subsection.6.11.6} -\contentsline {subsection}{\numberline {6.11.7}\leavevmode {\color {Chapter 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}IsAssociative}}{36}{subsection.7.1.1} -\contentsline {subsection}{\numberline {7.1.2}\leavevmode {\color {Chapter }IsCommutative}}{36}{subsection.7.1.2} -\contentsline {subsection}{\numberline {7.1.3}\leavevmode {\color {Chapter }IsPowerAssociative}}{36}{subsection.7.1.3} -\contentsline {subsection}{\numberline {7.1.4}\leavevmode {\color {Chapter }IsDiassociative}}{36}{subsection.7.1.4} -\contentsline {section}{\numberline {7.2}\leavevmode {\color {Chapter }Inverse Propeties}}{37}{section.7.2} -\contentsline {subsection}{\numberline {7.2.1}\leavevmode {\color {Chapter }HasLeftInverseProperty, HasRightInverseProperty and HasInverseProperty}}{37}{subsection.7.2.1} -\contentsline {subsection}{\numberline {7.2.2}\leavevmode {\color {Chapter }HasTwosidedInverses}}{37}{subsection.7.2.2} -\contentsline {subsection}{\numberline {7.2.3}\leavevmode {\color {Chapter }HasWeakInverseProperty}}{37}{subsection.7.2.3} -\contentsline {subsection}{\numberline {7.2.4}\leavevmode {\color {Chapter 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IsRightDistributive, IsDistributive}}{38}{subsection.7.3.6} -\contentsline {subsection}{\numberline {7.3.7}\leavevmode {\color {Chapter }IsEntropic and IsMedial}}{39}{subsection.7.3.7} -\contentsline {section}{\numberline {7.4}\leavevmode {\color {Chapter }Loops of Bol Moufang Type}}{39}{section.7.4} -\contentsline {subsection}{\numberline {7.4.1}\leavevmode {\color {Chapter }IsExtraLoop}}{40}{subsection.7.4.1} -\contentsline {subsection}{\numberline {7.4.2}\leavevmode {\color {Chapter }IsMoufangLoop}}{40}{subsection.7.4.2} -\contentsline {subsection}{\numberline {7.4.3}\leavevmode {\color {Chapter }IsCLoop}}{40}{subsection.7.4.3} -\contentsline {subsection}{\numberline {7.4.4}\leavevmode {\color {Chapter }IsLeftBolLoop}}{40}{subsection.7.4.4} -\contentsline {subsection}{\numberline {7.4.5}\leavevmode {\color {Chapter }IsRightBolLoop}}{40}{subsection.7.4.5} -\contentsline {subsection}{\numberline {7.4.6}\leavevmode {\color {Chapter }IsLCLoop}}{40}{subsection.7.4.6} -\contentsline {subsection}{\numberline {7.4.7}\leavevmode {\color {Chapter }IsRCLoop}}{40}{subsection.7.4.7} -\contentsline {subsection}{\numberline {7.4.8}\leavevmode {\color {Chapter }IsLeftNuclearSquareLoop}}{40}{subsection.7.4.8} -\contentsline {subsection}{\numberline {7.4.9}\leavevmode {\color {Chapter }IsMiddleNuclearSquareLoop}}{40}{subsection.7.4.9} -\contentsline {subsection}{\numberline {7.4.10}\leavevmode {\color {Chapter }IsRightNuclearSquareLoop}}{40}{subsection.7.4.10} -\contentsline {subsection}{\numberline {7.4.11}\leavevmode {\color {Chapter }IsNuclearSquareLoop}}{41}{subsection.7.4.11} -\contentsline {subsection}{\numberline {7.4.12}\leavevmode {\color {Chapter }IsFlexible}}{41}{subsection.7.4.12} -\contentsline {subsection}{\numberline {7.4.13}\leavevmode {\color {Chapter }IsLeftAlternative}}{41}{subsection.7.4.13} -\contentsline {subsection}{\numberline {7.4.14}\leavevmode {\color {Chapter }IsRightAlternative}}{41}{subsection.7.4.14} -\contentsline {subsection}{\numberline {7.4.15}\leavevmode {\color {Chapter }IsAlternative}}{41}{subsection.7.4.15} -\contentsline {section}{\numberline {7.5}\leavevmode {\color {Chapter }Power Alternative Loops}}{42}{section.7.5} -\contentsline {subsection}{\numberline {7.5.1}\leavevmode {\color {Chapter }IsLeftPowerAlternative, IsRightPowerAlternative and IsPowerAlternative}}{42}{subsection.7.5.1} -\contentsline {section}{\numberline {7.6}\leavevmode {\color {Chapter }Conjugacy Closed Loops and Related Properties}}{42}{section.7.6} -\contentsline {subsection}{\numberline {7.6.1}\leavevmode {\color {Chapter }IsLCCLoop}}{42}{subsection.7.6.1} -\contentsline {subsection}{\numberline {7.6.2}\leavevmode {\color {Chapter }IsRCCLoop}}{42}{subsection.7.6.2} -\contentsline {subsection}{\numberline {7.6.3}\leavevmode {\color {Chapter }IsCCLoop}}{42}{subsection.7.6.3} -\contentsline {subsection}{\numberline {7.6.4}\leavevmode {\color {Chapter }IsOsbornLoop}}{42}{subsection.7.6.4} -\contentsline {section}{\numberline {7.7}\leavevmode {\color {Chapter }Automorphic Loops}}{43}{section.7.7} -\contentsline {subsection}{\numberline {7.7.1}\leavevmode {\color {Chapter }IsLeftAutomorphicLoop}}{43}{subsection.7.7.1} -\contentsline {subsection}{\numberline {7.7.2}\leavevmode {\color {Chapter }IsMiddleAutomorphicLoop}}{43}{subsection.7.7.2} -\contentsline {subsection}{\numberline {7.7.3}\leavevmode {\color {Chapter }IsRightAutomorphicLoop}}{44}{subsection.7.7.3} -\contentsline {subsection}{\numberline {7.7.4}\leavevmode {\color {Chapter }IsAutomorphicLoop}}{44}{subsection.7.7.4} -\contentsline {section}{\numberline {7.8}\leavevmode {\color {Chapter }Additonal Varieties of Loops}}{44}{section.7.8} -\contentsline {subsection}{\numberline {7.8.1}\leavevmode {\color {Chapter }IsCodeLoop}}{44}{subsection.7.8.1} -\contentsline {subsection}{\numberline {7.8.2}\leavevmode {\color {Chapter }IsSteinerLoop}}{44}{subsection.7.8.2} -\contentsline {subsection}{\numberline {7.8.3}\leavevmode {\color {Chapter }IsLeftBruckLoop and IsLeftKLoop}}{44}{subsection.7.8.3} -\contentsline {subsection}{\numberline {7.8.4}\leavevmode {\color {Chapter }IsRightBruckLoop and IsRightKLoop}}{44}{subsection.7.8.4} -\contentsline {chapter}{\numberline {8}\leavevmode {\color {Chapter }Specific Methods}}{45}{chapter.8} -\contentsline {section}{\numberline {8.1}\leavevmode {\color {Chapter }Core Methods for Bol Loops}}{45}{section.8.1} -\contentsline {subsection}{\numberline {8.1.1}\leavevmode {\color {Chapter }AssociatedLeftBruckLoop and AssociatedRightBruckLoop}}{45}{subsection.8.1.1} -\contentsline {subsection}{\numberline {8.1.2}\leavevmode {\color {Chapter }IsExactGroupFactorization}}{45}{subsection.8.1.2} -\contentsline {subsection}{\numberline {8.1.3}\leavevmode {\color {Chapter }RightBolLoopByExactGroupFactorization}}{45}{subsection.8.1.3} -\contentsline {section}{\numberline {8.2}\leavevmode {\color {Chapter }Moufang Modifications}}{46}{section.8.2} -\contentsline {subsection}{\numberline {8.2.1}\leavevmode {\color {Chapter }LoopByCyclicModification}}{46}{subsection.8.2.1} -\contentsline {subsection}{\numberline {8.2.2}\leavevmode {\color {Chapter }LoopByDihedralModification}}{46}{subsection.8.2.2} -\contentsline {subsection}{\numberline {8.2.3}\leavevmode {\color {Chapter }LoopMG2}}{46}{subsection.8.2.3} -\contentsline {section}{\numberline {8.3}\leavevmode {\color {Chapter }Triality for Moufang Loops}}{46}{section.8.3} -\contentsline {subsection}{\numberline {8.3.1}\leavevmode {\color {Chapter }TrialityPermGroup}}{47}{subsection.8.3.1} -\contentsline {subsection}{\numberline {8.3.2}\leavevmode {\color {Chapter }TrialityPcGroup}}{47}{subsection.8.3.2} -\contentsline {section}{\numberline {8.4}\leavevmode {\color {Chapter }Realizing Groups as Multiplication Groups of Loops}}{47}{section.8.4} -\contentsline {subsection}{\numberline {8.4.1}\leavevmode {\color {Chapter }AllLoopTablesInGroup}}{47}{subsection.8.4.1} -\contentsline {subsection}{\numberline {8.4.2}\leavevmode {\color {Chapter }AllProperLoopTablesInGroup}}{47}{subsection.8.4.2} -\contentsline {subsection}{\numberline {8.4.3}\leavevmode {\color {Chapter }OneLoopTableInGroup}}{47}{subsection.8.4.3} -\contentsline {subsection}{\numberline {8.4.4}\leavevmode {\color {Chapter }OneProperLoopTableInGroup}}{48}{subsection.8.4.4} -\contentsline {subsection}{\numberline {8.4.5}\leavevmode {\color {Chapter }AllLoopsWithMltGroup}}{48}{subsection.8.4.5} -\contentsline {subsection}{\numberline {8.4.6}\leavevmode {\color {Chapter }OneLoopWithMltGroup}}{48}{subsection.8.4.6} -\contentsline {chapter}{\numberline {9}\leavevmode {\color {Chapter }Libraries of Loops}}{49}{chapter.9} -\contentsline {section}{\numberline {9.1}\leavevmode {\color {Chapter }A Typical Library}}{49}{section.9.1} -\contentsline {subsection}{\numberline {9.1.1}\leavevmode {\color {Chapter }LibraryLoop}}{49}{subsection.9.1.1} -\contentsline {subsection}{\numberline {9.1.2}\leavevmode {\color {Chapter }MyLibraryLoop}}{49}{subsection.9.1.2} -\contentsline {subsection}{\numberline {9.1.3}\leavevmode {\color {Chapter }DisplayLibraryInfo}}{50}{subsection.9.1.3} -\contentsline {section}{\numberline {9.2}\leavevmode {\color {Chapter }Left Bol Loops and Right Bol Loops}}{50}{section.9.2} -\contentsline {subsection}{\numberline {9.2.1}\leavevmode {\color {Chapter }LeftBolLoop}}{50}{subsection.9.2.1} -\contentsline {subsection}{\numberline {9.2.2}\leavevmode {\color {Chapter }RightBolLoop}}{50}{subsection.9.2.2} -\contentsline {section}{\numberline {9.3}\leavevmode {\color {Chapter }Moufang Loops}}{50}{section.9.3} -\contentsline {subsection}{\numberline {9.3.1}\leavevmode {\color {Chapter }MoufangLoop}}{50}{subsection.9.3.1} -\contentsline {section}{\numberline {9.4}\leavevmode {\color {Chapter }Code Loops}}{51}{section.9.4} -\contentsline {subsection}{\numberline {9.4.1}\leavevmode {\color {Chapter }CodeLoop}}{51}{subsection.9.4.1} -\contentsline {section}{\numberline {9.5}\leavevmode {\color {Chapter }Steiner Loops}}{51}{section.9.5} -\contentsline {subsection}{\numberline {9.5.1}\leavevmode {\color {Chapter }SteinerLoop}}{51}{subsection.9.5.1} -\contentsline {section}{\numberline {9.6}\leavevmode {\color {Chapter }Conjugacy Closed Loops}}{51}{section.9.6} -\contentsline {subsection}{\numberline {9.6.1}\leavevmode {\color {Chapter }RCCLoop and RightConjugacyClosedLoop}}{52}{subsection.9.6.1} -\contentsline {subsection}{\numberline {9.6.2}\leavevmode {\color {Chapter }LCCLoop and LeftConjugacyClosedLoop}}{52}{subsection.9.6.2} -\contentsline {subsection}{\numberline {9.6.3}\leavevmode {\color {Chapter }CCLoop and ConjugacyClosedLoop}}{52}{subsection.9.6.3} -\contentsline {section}{\numberline {9.7}\leavevmode {\color {Chapter }Small Loops}}{52}{section.9.7} -\contentsline {subsection}{\numberline {9.7.1}\leavevmode {\color {Chapter }SmallLoop}}{53}{subsection.9.7.1} -\contentsline {section}{\numberline {9.8}\leavevmode {\color {Chapter }Paige Loops}}{53}{section.9.8} -\contentsline {subsection}{\numberline {9.8.1}\leavevmode {\color {Chapter }PaigeLoop}}{53}{subsection.9.8.1} -\contentsline {section}{\numberline {9.9}\leavevmode {\color {Chapter }Nilpotent Loops}}{53}{section.9.9} -\contentsline {subsection}{\numberline {9.9.1}\leavevmode {\color {Chapter }NilpotentLoop}}{53}{subsection.9.9.1} -\contentsline {section}{\numberline {9.10}\leavevmode {\color {Chapter }Automorphic Loops}}{53}{section.9.10} -\contentsline {subsection}{\numberline {9.10.1}\leavevmode {\color {Chapter }AutomorphicLoop}}{53}{subsection.9.10.1} -\contentsline {section}{\numberline {9.11}\leavevmode {\color {Chapter }Interesting Loops}}{54}{section.9.11} -\contentsline {subsection}{\numberline {9.11.1}\leavevmode {\color {Chapter }InterestingLoop}}{54}{subsection.9.11.1} -\contentsline {section}{\numberline {9.12}\leavevmode {\color {Chapter }Libraries of Loops Up To Isotopism}}{54}{section.9.12} -\contentsline {subsection}{\numberline {9.12.1}\leavevmode {\color {Chapter }ItpSmallLoop}}{54}{subsection.9.12.1} -\contentsline {chapter}{\numberline {A}\leavevmode {\color {Chapter }Files}}{55}{appendix.A} -\contentsline {chapter}{\numberline {B}\leavevmode {\color {Chapter }Filters}}{57}{appendix.B} -\contentsline {chapter}{References}{61}{appendix*.3} -\contentsline {chapter}{Index}{62}{section*.4} diff --git a/doc/loops.xml b/doc/loops.xml index eee5a20..e953d25 100644 --- a/doc/loops.xml +++ b/doc/loops.xml @@ -6,7 +6,8 @@ - + +

Left Bruck Loops and Right Bruck Loops + +The emmerging library named left Bruck contains all left Bruck loops of orders 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops, respectively). + +

For an odd prime p, left Bruck loops of order p^k are centrally nilpotent and hence central extensions of the cyclic group of order p by a left Bruck loop of order p^{k-1}. It is known that left Bruck loops of order p and p^2 are abelian groups; we have included them in the library because of the iterative nature of the construction of nilpotent loops. + + + +The mth left Bruck loop of order n in the library. + + + + +The mth right Bruck loop of order n in the library. + + +

+
Moufang Loops @@ -2072,7 +2103,7 @@ The following table summarizes the number of right conjugacy closed loops of a g Remark: Only the right conjugacy closed loops are stored in the library. Left conjugacy closed loops are obtained from right conjugacy closed loops via Opposite.
-

The library named CC contains all nonassociative conjugacy closed loops of order n\le 27 and also of orders 2p and p^2 for all primes p. +

The library named CC contains all CC loops of order 2\le 2^k\le 64, 3\le 3^k\le 81, 5\le 5^k\le 125, 7\le 7^k\le 343, all nonassociative CC loops of order less than 28, and all nonassociative CC loops of order p^2 and 2p for any odd prime p.

By results of Kunen , for every odd prime p there are precisely 3 nonassociative conjugacy closed loops of order p^2. Csörgő and Drápal described these 3 loops by multiplicative formulas on \mathbb{Z}_{p^2} and \mathbb{Z}_p \times \mathbb{Z}_p as follows: @@ -2141,7 +2172,9 @@ are 2623755 nilpotent loops of order 12, and 123794003928541545927226368 nilpote

Automorphic Loops -The library named automorphic contains all nonassociative automorphic loops of order less than 16 up to isomorphism (there is 1 such loop of order 6, 7 of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15), all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops, respectively, including abelian groups), and commutative automorphic loops Q of order 243 possessing a central subloop S of order 3 such that Q/S is not the elementary abelian group of order 81 (there are 118451 such loops). +The library named automorphic contains all nonassociative automorphic loops of order less than 16 up to isomorphism (there is 1 such loop of order 6, 7 of order 8, 3 of order 10, 2 of order 12, 5 of order 14, and 2 of order 15) and all commutative automorphic loops of order 3, 9, 27 and 81 (there are 1, 2, 7 and 72 such loops). + +

It turns out that commutative automorphic loops of order 3, 9, 27 and 81 (but not 243) are in one-to-on correspondence with left Bruck loops of the respective orders, see , . Only the left Bruck loops are stored in the library. @@ -2343,9 +2376,6 @@ Many implications among properties of loops are built directly into LOO
( IsLeftAutomorphicLoop, IsAutomorphicLoop )
( IsRightAutomorphicLoop, IsAutomorphicLoop )
( IsMiddleAutomorphicLoop, IsAutomorphicLoop ) -
( IsMiddleAutomorphicLoop, IsCommutative ) -
( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsCommutative ) -
( IsAutomorphicLoop, IsRightAutomorphicLoop and IsCommutative )
( IsLeftAutomorphicLoop, IsRightAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsRightAutomorphicLoop, IsLeftAutomorphicLoop and HasAntiautomorphicInverseProperty )
( IsFlexible, IsMiddleAutomorphicLoop ) @@ -2356,11 +2386,15 @@ Many implications among properties of loops are built directly into LOO
( IsMoufangLoop, IsAutomorphicLoop and HasLeftInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasRightInverseProperty )
( IsMoufangLoop, IsAutomorphicLoop and HasWeakInverseProperty ) +
( IsMiddleAutomorphicLoop, IsCommutative )
( IsLeftAutomorphicLoop, IsLeftBruckLoop )
( IsLeftAutomorphicLoop, IsLCCLoop )
( IsRightAutomorphicLoop, IsRightBruckLoop )
( IsRightAutomorphicLoop, IsRCCLoop )
( IsAutomorphicLoop, IsCommutative and IsMoufangLoop ) +
( IsAutomorphicLoop, IsLeftAutomorphicLoop and IsMiddleAutomorphicLoop ) +
( IsAutomorphicLoop, IsRightAutomorphicLoop and IsMiddleAutomorphicLoop ) +
( IsAutomorphicLoop, IsAssociative ) @@ -2368,4 +2402,4 @@ Many implications among properties of loops are built directly into LOO - \ No newline at end of file + diff --git a/doc/loops_bib.xml b/doc/loops_bib.xml deleted file mode 100644 index cb0ec01..0000000 --- a/doc/loops_bib.xml +++ /dev/null @@ -1,559 +0,0 @@ - - - - - - KatharinaArtic - - On conjugacy closed loops and conjugacy closed loop folders - RWTH Aachen University - 2015 - -

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- - Michael K.Kinyon - KennethKunen - J. D.Phillips - PetrVojtěchovský - - The structure of automorphic loops - Trans. Amer. Math. Soc. - 2016 - 368 - 12 - 8901–8927 - 0002-9947 - 3551593 - 20N05 - http://dx.doi.org/10.1090/tran/6622 - TAMTAM - 10.1090/tran/6622 - Transactions of the American Mathematical - Society -
-
- - Michael K.Kinyon - Gábor P.Nagy - PetrVojtěchovský - - Bol loops and Bruck loops of order <M>pq</M> - - 2015 - preprint -
-
- - KennethKunen - - The structure of conjugacy closed loops - Trans. Amer. Math. Soc. - 2000 - 352 - 6 - 2889–2911 - 0002-9947 - 1615991 (2000j:20132) - 20N05 (03C05) - Edgar G. Goodaire - http://dx.doi.org/10.1090/S0002-9947-00-02350-3 - TAMTAM - 10.1090/S0002-9947-00-02350-3 - Transactions of the American Mathematical - Society -
-
- - Martin W.Liebeck - - The classification of finite simple <C>M</C>oufang loops - Math. Proc. Cambridge Philos. Soc. - 1987 - 102 - 1 - 33–47 - 0305-0041 - 886433 (88g:20146) - 20N05 - Karl H. Robinson - http://dx.doi.org/10.1017/S0305004100067025 - MPCPCO - 10.1017/S0305004100067025 - Mathematical Proceedings of the Cambridge - Philosophical - Society -
- - - G. EricMoorhouse - - Bol loops of small order - http://www.uwyo.edu/moorhouse/pub/bol/ - -
- - Gábor P.Nagy - - A class of simple proper <C>B</C>ol loops - Manuscripta Math. - 2008 - 127 - 1 - 81–88 - 0025-2611 - 2429915 (2009g:20149) - 20N05 - Ramiro Carrillo-Catalán - http://dx.doi.org/10.1007/s00229-008-0188-5 - MSMHB2 - 10.1007/s00229-008-0188-5 - Manuscripta Mathematica -
-
- - Gábor P.Nagy - PetrVojtěchovský - - Octonions, simple <C>M</C>oufang loops and triality - Quasigroups Related Systems - 2003 - 10 - 65–94 - 1561-2848 - 1998692 (2004f:20118) - 20N05 (17A75) - Orin Chein - Quasigroups and Related Systems -
-
- - Gábor P.Nagy - PetrVojtěchovský - - The <C>M</C>oufang loops of order 64 and 81 - J. Symbolic Comput. - 2007 - 42 - 9 - 871–883 - 0747-7171 - 2355056 (2009d:20155) - 20N05 (20D15) - Chris A. Rowley - http://dx.doi.org/10.1016/j.jsc.2007.06.004 - 10.1016/j.jsc.2007.06.004 - Journal of Symbolic Computation -
- - - Hala O.Pflugfelder - - Quasigroups and loops: introduction - Heldermann Verlag - 1990 - 7 - Sigma Series in Pure Mathematics -
Berlin
- 3-88538-007-2 - 1125767 (93g:20132) - 20N05 (20-01) - D. A. Robinson - viii+147 -
-
- - J. D.Phillips - PetrVojtěchovský - - The varieties of loops of <C>B</C>ol-<C>M</C>oufang type - Algebra Universalis - 2005 - 54 - 3 - 259–271 - 0002-5240 - 2219409 (2007b:20147) - 20N05 - A. Schleiermacher - http://dx.doi.org/10.1007/s00012-005-1941-1 - AGUVA3 - 10.1007/s00012-005-1941-1 - Algebra Universalis -
-
- - M.Slattery - A.Zenisek - - Moufang loops of order 243 - Commentationes Mathematicae Universitatis Carolinae - 2012 - 53 - 3 - 423–428 -
-
- - PetrVojtěchovský - - Toward the classification of <C>M</C>oufang loops of order 64 - European J. Combin. - 2006 - 27 - 3 - 444–460 - 0195-6698 - 2206479 (2006k:20136) - 20N05 - Orin Chein - http://dx.doi.org/10.1016/j.ejc.2004.10.003 - 10.1016/j.ejc.2004.10.003 - European Journal of Combinatorics -
-
- - PetrVojtÄ›chovský - - Three lectures on automorphic loops - Quasigroups Related Systems - 2015 - 23 - 1 - 129–163 - 1561-2848 - 3353114 - 20N05 - Ãgota Figula - Quasigroups and Related Systems -
-
- - Robert L.Wilson Jr. - - Quasidirect products of quasigroups - Comm. Algebra - 1975 - 3 - 9 - 835–850 - 0092-7872 - 0376937 (51 #13112) - 20N05 - D. A. Robinson - Communications in Algebra -
- diff --git a/doc/loops_bib.xml.bib b/doc/loops_bib.xml.bib deleted file mode 100644 index 8f8cb0a..0000000 --- a/doc/loops_bib.xml.bib +++ /dev/null @@ -1,496 +0,0 @@ - - - - -@phdthesis{ Artic, - author = {Artic, K.}, - title = {On conjugacy closed loops and conjugacy closed loop - folders}, - school = {RWTH Aachen University}, - year = {2015}, - printedkey = {Art15} -} -@article{ Ar, - author = {Artzy, R.}, - title = {On automorphic-inverse properties in loops}, - journal = {Proc. Amer. Math. Soc.}, - volume = {10}, - year = {1959}, - pages = {588{\textendash}591}, - fjournal = {Proceedings of the American Mathematical Society}, - issn = {0002-9939}, - mrclass = {20.00}, - mrnumber = {0107674 (21 \#6397)}, - mrreviewer = {H. Minc}, - printedkey = {Art59} -} -@article{ BaGrVo, - author = {De Barros, D. A. S. and Grishkov, A. and Vojt{\v - e}chovsk{\a'y}, P.}, - title = {Commutative automorphic loops of order {$p^3$}}, - journal = {J. Algebra Appl.}, - volume = {11}, - number = {5}, - year = {2012}, - pages = {1250100, 15}, - fjournal = {Journal of Algebra and its Applications}, - issn = {0219-4988}, - mrclass = {20N05 (20G40)}, - mrnumber = {2983192}, - mrreviewer = {{\a'A}gota Figula}, - url = {http://dx.doi.org/10.1142/S0219498812501009}, - doi = {10.1142/S0219498812501009}, - printedkey = {BGV12} -} -@book{ Br, - author = {Bruck, R. H.}, - title = {A survey of binary systems}, - publisher = {Springer Verlag}, - series = {Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue - Folge, Heft 20. Reihe: Gruppentheorie}, - address = {Berlin}, - year = {1958}, - pages = {viii+185}, - mrclass = {20.00}, - mrnumber = {0093552 (20 \#76)}, - mrreviewer = {L. J. Paige}, - printedkey = {Bru58} -} -@article{ BrPa, - author = {Bruck, R. H. and Paige, L. J.}, - title = {Loops whose inner mappings are automorphisms}, - journal = {Ann. of Math. (2)}, - volume = {63}, - year = {1956}, - pages = {308{\textendash}323}, - fjournal = {Annals of Mathematics. Second Series}, - issn = {0003-486X}, - mrclass = {20.0X}, - mrnumber = {0076779}, - mrreviewer = {R. Moufang}, - printedkey = {BP56} -} -@book{ ChPfSm, - editor = {Chein, O. and Pflugfelder, H. O. and Smith, J. D. H.}, - title = {Quasigroups and loops: theory and applications}, - publisher = {Heldermann Verlag}, - series = {Sigma Series in Pure Mathematics}, - volume = {8}, - address = {Berlin}, - year = {1990}, - pages = {xii+568}, - isbn = {3-88538-008-0}, - mrclass = {20N05 (20-06)}, - mrnumber = {1125806 (93g:20133)}, - mrreviewer = {D. A. Robinson}, - printedkey = {CPS90} -} -@book{ CoRo, - author = {Colbourn, C. J. and Rosa, A.}, - title = {Triple systems}, - publisher = {The Clarendon Press Oxford University Press}, - series = {Oxford Mathematical Monographs}, - address = {New York}, - year = {1999}, - pages = {xvi+560}, - isbn = {0-19-853576-7}, - mrclass = {05B07 (05-02)}, - mrnumber = {1843379 (2002h:05024)}, - mrreviewer = {Elizabeth J. Billington}, - printedkey = {CR99} -} -@article{ CsDr, - author = {Cs{\"o}rg{\H o}, P. and Dr{\a'a}pal, A.}, - title = {Left conjugacy closed loops of nilpotency class two}, - journal = {Results Math.}, - volume = {47}, - number = {3-4}, - year = {2005}, - pages = {242{\textendash}265}, - fjournal = {Results in Mathematics. Resultate der Mathematik}, - issn = {1422-6383}, - mrclass = {20N05}, - mrnumber = {2153496 (2006b:20095)}, - mrreviewer = {Huberta Lausch}, - printedkey = {CD05} -} -@article{ DaVo, - author = {Daly, D. and Vojt{\v e}chovsk{\a'y}, P.}, - title = {Enumeration of nilpotent loops via cohomology}, - journal = {J. Algebra}, - volume = {322}, - number = {11}, - year = {2009}, - pages = {4080{\textendash}4098}, - coden = {JALGA4}, - fjournal = {Journal of Algebra}, - issn = {0021-8693}, - mrclass = {20N05 (20J99)}, - mrnumber = {2556139 (2011e:20098)}, - mrreviewer = {Yu. M. Movsisyan}, - url = {http://dx.doi.org/10.1016/j.jalgebra.2009.03.042}, - doi = {10.1016/j.jalgebra.2009.03.042}, - printedkey = {DV09} -} -@article{ DrapalCD, - author = {Dr{\a'a}pal, A.}, - title = {Cyclic and dihedral constructions of even order}, - journal = {Comment. Math. Univ. Carolin.}, - volume = {44}, - number = {4}, - year = {2003}, - pages = {593{\textendash}614}, - coden = {}, - fjournal = {Commentationes Mathematicae Universitatis Carolinae}, - issn = {}, - mrclass = {20D60 (05B15)}, - mrnumber = {MR2062876 (2005d:20038)}, - mrreviewer = {Thomas Michael Keller}, - url = {}, - doi = {}, - printedkey = {Dr{\a'a}03} -} -@article{ DrVo, - author = {Dr{\a'a}pal, A. and Vojt{\v e}chovsk{\a'y}, P.}, - title = {Moufang loops that share associator and three quarters - of their multiplication tables}, - journal = {Rocky Mountain J. Math.}, - volume = {36}, - number = {2}, - year = {2006}, - pages = {425{\textendash}455}, - coden = {RMJMAE}, - fjournal = {The Rocky Mountain Journal of Mathematics}, - issn = {0035-7596}, - mrclass = {20N05 (05B15)}, - mrnumber = {2234814 (2007d:20114)}, - mrreviewer = {Orin Chein}, - url = {http://dx.doi.org/10.1216/rmjm/1181069461}, - doi = {10.1216/rmjm/1181069461}, - printedkey = {DV06} -} -@article{ Fe, - author = {Fenyves, F.}, - title = {Extra loops. {II}. {O}n loops with identities of - {B}ol-{M}oufang type}, - journal = {Publ. Math. Debrecen}, - volume = {16}, - year = {1969}, - pages = {187{\textendash}192}, - fjournal = {Publicationes Mathematicae Debrecen}, - issn = {0033-3883}, - mrclass = {20.95}, - mrnumber = {0262409 (41 \#7017)}, - mrreviewer = {D. A. Robinson}, - printedkey = {Fen69} -} -@book{ Go, - author = {Goodaire, E. G. and May, S. and Raman, M.}, - title = {The {M}oufang loops of order less than 64}, - publisher = {Nova Science Publishers Inc.}, - address = {Commack, NY}, - year = {1999}, - pages = {xviii+287}, - isbn = {1-56072-659-8}, - mrclass = {20N05}, - mrnumber = {1689624 (2000a:20147)}, - printedkey = {GMR99} -} -@article{ GrKiNa, - author = {Grishkov, A. and Kinyon, M. and Nagy, G. P.}, - title = {Solvability of commutative automorphic loops}, - journal = {Proc. Amer. Math. Soc.}, - volume = {142}, - number = {9}, - year = {2014}, - pages = {3029{\textendash}3037}, - fjournal = {Proceedings of the American Mathematical Society}, - issn = {0002-9939}, - mrclass = {20N05 (17B99)}, - mrnumber = {3223359}, - mrreviewer = {J. D. Phillips}, - url = {http://dx.doi.org/10.1090/S0002-9939-2014-12053-3}, - doi = {10.1090/S0002-9939-2014-12053-3}, - printedkey = {GKN14} -} -@article{ JaMa, - author = {Jacobson, M. T. and Matthews, P.}, - title = {Generating uniformly distributed random {L}atin - squares}, - journal = {J. Combin. Des.}, - volume = {4}, - number = {6}, - year = {1996}, - pages = {405{\textendash}437}, - fjournal = {Journal of Combinatorial Designs}, - issn = {1063-8539}, - mrclass = {05B15 (60J10)}, - mrnumber = {1410617 (98b:05021)}, - mrreviewer = {Lars D{\o}vling Andersen}, - url = {http://dx.doi.org/10.1002/(SICI)1520-6610(1996)4:6{\textless}405::AID-JCD3{\textgreater}3.0.CO;2-J}, - doi = {10.1002/(SICI)1520-6610(1996)4:6{\textless}405::AID-JCD3{\textgreater}3.0.CO;2-J}, - printedkey = {JM96} -} -@article{ JeKiVo, - author = {Jedli{\v c}ka, P. and Kinyon, M. and Vojt{\v - e}chovsk{\a'y}, P.}, - title = {Nilpotency in automorphic loops of prime power order}, - journal = {J. Algebra}, - volume = {350}, - year = {2012}, - pages = {64{\textendash}76}, - coden = {JALGA4}, - fjournal = {Journal of Algebra}, - issn = {0021-8693}, - mrclass = {20N05}, - mrnumber = {2859875}, - mrreviewer = {Mohammad Shahryari}, - url = {http://dx.doi.org/10.1016/j.jalgebra.2011.09.034}, - doi = {10.1016/j.jalgebra.2011.09.034}, - printedkey = {JKV12} -} -@article{ JoKiNaVo, - author = {Johnson, K. W. and Kinyon, M. K. and Nagy, G. P. and - Vojt{\v e}chovsk{\a'y}, P.}, - title = {Searching for small simple automorphic loops}, - journal = {LMS J. Comput. Math.}, - volume = {14}, - year = {2011}, - pages = {200{\textendash}213}, - fjournal = {LMS Journal of Computation and Mathematics}, - issn = {1461-1570}, - mrclass = {20N05 (20B15 20B40)}, - mrnumber = {2831230}, - mrreviewer = {Tuval S. Foguel}, - url = {http://dx.doi.org/10.1112/S1461157010000173}, - doi = {10.1112/S1461157010000173}, - printedkey = {JKNV11} -} -@article{ KiKuPh, - author = {Kinyon, M. K. and Kunen, K. and Phillips, J. D.}, - title = {Every diassociative {$A$}-loop is {M}oufang}, - journal = {Proc. Amer. Math. Soc.}, - volume = {130}, - number = {3}, - year = {2002}, - pages = {619{\textendash}624}, - coden = {PAMYAR}, - fjournal = {Proceedings of the American Mathematical Society}, - issn = {0002-9939}, - mrclass = {20N05 (68T15)}, - mrnumber = {1866009 (2002k:20124)}, - mrreviewer = {Orin Chein}, - url = {http://dx.doi.org/10.1090/S0002-9939-01-06090-7}, - doi = {10.1090/S0002-9939-01-06090-7}, - printedkey = {KKP02} -} -@article{ KiKuPhVo, - author = {Kinyon, M. K. and Kunen, K. and Phillips, J. D. and - Vojt{\v e}chovsk{\a'y}, P.}, - title = {The structure of automorphic loops}, - journal = {Trans. Amer. Math. Soc.}, - volume = {368}, - number = {12}, - year = {2016}, - pages = {8901{\textendash}8927}, - coden = {TAMTAM}, - fjournal = {Transactions of the American Mathematical Society}, - issn = {0002-9947}, - mrclass = {20N05}, - mrnumber = {3551593}, - url = {http://dx.doi.org/10.1090/tran/6622}, - doi = {10.1090/tran/6622}, - printedkey = {KKPV16} -} -@article{ KiNaVo2015, - author = {Kinyon, M. K. and Nagy, G. P. and Vojt{\v - e}chovsk{\a'y}, P.}, - title = {Bol loops and Bruck loops of order $pq$}, - journal = {}, - year = {2015}, - note = {preprint}, - printedkey = {KNV15} -} -@article{ Kun, - author = {Kunen, K.}, - title = {The structure of conjugacy closed loops}, - journal = {Trans. Amer. Math. Soc.}, - volume = {352}, - number = {6}, - year = {2000}, - pages = {2889{\textendash}2911}, - coden = {TAMTAM}, - fjournal = {Transactions of the American Mathematical Society}, - issn = {0002-9947}, - mrclass = {20N05 (03C05)}, - mrnumber = {1615991 (2000j:20132)}, - mrreviewer = {Edgar G. Goodaire}, - url = {http://dx.doi.org/10.1090/S0002-9947-00-02350-3}, - doi = {10.1090/S0002-9947-00-02350-3}, - printedkey = {Kun00} -} -@article{ Li, - author = {Liebeck, M. W.}, - title = {The classification of finite simple {M}oufang loops}, - journal = {Math. Proc. Cambridge Philos. Soc.}, - volume = {102}, - number = {1}, - year = {1987}, - pages = {33{\textendash}47}, - coden = {MPCPCO}, - fjournal = {Mathematical Proceedings of the Cambridge - Philosophical Society}, - issn = {0305-0041}, - mrclass = {20N05}, - mrnumber = {886433 (88g:20146)}, - mrreviewer = {Karl H. Robinson}, - url = {http://dx.doi.org/10.1017/S0305004100067025}, - doi = {10.1017/S0305004100067025}, - printedkey = {Lie87} -} -@unpublished{ Mo, - author = {Moorhouse, G. E.}, - title = {Bol loops of small order}, - note = {http://www.uwyo.edu/moorhouse/pub/bol/}, - printedkey = {Moo} -} -@article{ Na, - author = {Nagy, G. P.}, - title = {A class of simple proper {B}ol loops}, - journal = {Manuscripta Math.}, - volume = {127}, - number = {1}, - year = {2008}, - pages = {81{\textendash}88}, - coden = {MSMHB2}, - fjournal = {Manuscripta Mathematica}, - issn = {0025-2611}, - mrclass = {20N05}, - mrnumber = {2429915 (2009g:20149)}, - mrreviewer = {Ramiro Carrillo-Catal{\a'a}n}, - url = {http://dx.doi.org/10.1007/s00229-008-0188-5}, - doi = {10.1007/s00229-008-0188-5}, - printedkey = {Nag08} -} -@article{ NaVo2003, - author = {Nagy, G. P. and Vojt{\v e}chovsk{\a'y}, P.}, - title = {Octonions, simple {M}oufang loops and triality}, - journal = {Quasigroups Related Systems}, - volume = {10}, - year = {2003}, - pages = {65{\textendash}94}, - fjournal = {Quasigroups and Related Systems}, - issn = {1561-2848}, - mrclass = {20N05 (17A75)}, - mrnumber = {1998692 (2004f:20118)}, - mrreviewer = {Orin Chein}, - printedkey = {NV03} -} -@article{ NaVo2007, - author = {Nagy, G. P. and Vojt{\v e}chovsk{\a'y}, P.}, - title = {The {M}oufang loops of order 64 and 81}, - journal = {J. Symbolic Comput.}, - volume = {42}, - number = {9}, - year = {2007}, - pages = {871{\textendash}883}, - fjournal = {Journal of Symbolic Computation}, - issn = {0747-7171}, - mrclass = {20N05 (20D15)}, - mrnumber = {2355056 (2009d:20155)}, - mrreviewer = {Chris A. Rowley}, - url = {http://dx.doi.org/10.1016/j.jsc.2007.06.004}, - doi = {10.1016/j.jsc.2007.06.004}, - printedkey = {NV07} -} -@book{ Pf, - author = {Pflugfelder, H. O.}, - title = {Quasigroups and loops: introduction}, - publisher = {Heldermann Verlag}, - series = {Sigma Series in Pure Mathematics}, - volume = {7}, - address = {Berlin}, - year = {1990}, - pages = {viii+147}, - isbn = {3-88538-007-2}, - mrclass = {20N05 (20-01)}, - mrnumber = {1125767 (93g:20132)}, - mrreviewer = {D. A. Robinson}, - printedkey = {Pfl90} -} -@article{ PhiVoj, - author = {Phillips, J. D. and Vojt{\v e}chovsk{\a'y}, P.}, - title = {The varieties of loops of {B}ol-{M}oufang type}, - journal = {Algebra Universalis}, - volume = {54}, - number = {3}, - year = {2005}, - pages = {259{\textendash}271}, - coden = {AGUVA3}, - fjournal = {Algebra Universalis}, - issn = {0002-5240}, - mrclass = {20N05}, - mrnumber = {2219409 (2007b:20147)}, - mrreviewer = {A. Schleiermacher}, - url = {http://dx.doi.org/10.1007/s00012-005-1941-1}, - doi = {10.1007/s00012-005-1941-1}, - printedkey = {PV05} -} -@article{ SlZe2011, - author = {Slattery, M. and Zenisek, A.}, - title = {Moufang loops of order 243}, - journal = {Commentationes Mathematicae Universitatis Carolinae}, - volume = {53}, - number = {3}, - year = {2012}, - pages = {423{\textendash}428}, - printedkey = {SZ12} -} -@article{ Vo, - author = {Vojt{\v e}chovsk{\a'y}, P.}, - title = {Toward the classification of {M}oufang loops of order - 64}, - journal = {European J. Combin.}, - volume = {27}, - number = {3}, - year = {2006}, - pages = {444{\textendash}460}, - fjournal = {European Journal of Combinatorics}, - issn = {0195-6698}, - mrclass = {20N05}, - mrnumber = {2206479 (2006k:20136)}, - mrreviewer = {Orin Chein}, - url = {http://dx.doi.org/10.1016/j.ejc.2004.10.003}, - doi = {10.1016/j.ejc.2004.10.003}, - printedkey = {Voj06} -} -@article{ VoQRS, - author = {Vojt{\v e}chovsk{\a'y}, P.}, - title = {Three lectures on automorphic loops}, - journal = {Quasigroups Related Systems}, - volume = {23}, - number = {1}, - year = {2015}, - pages = {129{\textendash}163}, - fjournal = {Quasigroups and Related Systems}, - issn = {1561-2848}, - mrclass = {20N05}, - mrnumber = {3353114}, - mrreviewer = {{\a'A}gota Figula}, - printedkey = {Voj15} -} -@article{ Wi, - author = {Wilson Jr., R. L.}, - title = {Quasidirect products of quasigroups}, - journal = {Comm. Algebra}, - volume = {3}, - number = {9}, - year = {1975}, - pages = {835{\textendash}850}, - fjournal = {Communications in Algebra}, - issn = {0092-7872}, - mrclass = {20N05}, - mrnumber = {0376937 (51 \#13112)}, - mrreviewer = {D. A. 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(cite.NaVo2007)] ->> endobj -1933 0 obj << -/Names [(cite.Pf) 483 0 R (cite.PhiVoj) 891 0 R (cite.SlZe2011) 1083 0 R (cite.Vo) 829 0 R (cite.VoQRS) 971 0 R (cite.Wi) 1116 0 R] -/Limits [(cite.Pf) (cite.Wi)] ->> endobj -1934 0 obj << -/Names [(page.1) 339 0 R (page.10) 496 0 R (page.11) 507 0 R (page.12) 516 0 R (page.13) 524 0 R (page.14) 533 0 R] -/Limits [(page.1) (page.14)] ->> endobj -1935 0 obj << -/Names [(page.15) 544 0 R (page.16) 558 0 R (page.17) 563 0 R (page.18) 576 0 R (page.19) 590 0 R (page.2) 349 0 R] -/Limits [(page.15) (page.2)] ->> endobj -1936 0 obj << -/Names [(page.20) 603 0 R (page.21) 616 0 R (page.22) 628 0 R (page.23) 642 0 R (page.24) 655 0 R (page.25) 668 0 R] -/Limits [(page.20) (page.25)] ->> endobj -1937 0 obj << -/Names [(page.26) 678 0 R (page.27) 689 0 R (page.28) 703 0 R (page.29) 718 0 R (page.3) 390 0 R (page.30) 729 0 R] -/Limits [(page.26) (page.30)] ->> endobj -1938 0 obj << -/Names [(page.31) 742 0 R (page.32) 761 0 R (page.33) 780 0 R (page.34) 802 0 R (page.35) 819 0 R (page.36) 833 0 R] -/Limits [(page.31) (page.36)] ->> endobj -1939 0 obj << -/Names [(page.37) 849 0 R (page.38) 866 0 R (page.39) 886 0 R (page.4) 438 0 R (page.40) 895 0 R (page.41) 919 0 R] -/Limits [(page.37) (page.41)] ->> endobj -1940 0 obj << -/Names [(page.42) 933 0 R (page.43) 959 0 R (page.44) 977 0 R (page.45) 996 0 R (page.46) 1009 0 R (page.47) 1026 0 R] -/Limits [(page.42) (page.47)] ->> endobj -1941 0 obj << -/Names [(page.48) 1041 0 R (page.49) 1051 0 R (page.5) 448 0 R (page.50) 1068 0 R (page.51) 1089 0 R (page.52) 1106 0 R] -/Limits [(page.48) (page.52)] ->> endobj -1942 0 obj << -/Names [(page.53) 1122 0 R (page.54) 1138 0 R (page.55) 1148 0 R (page.56) 1154 0 R (page.57) 1158 0 R (page.58) 1163 0 R] -/Limits [(page.53) (page.58)] ->> endobj -1943 0 obj << -/Names [(page.59) 1167 0 R (page.6) 453 0 R (page.60) 1186 0 R (page.61) 1207 0 R (page.62) 1286 0 R (page.63) 1381 0 R] -/Limits [(page.59) (page.63)] ->> endobj -1944 0 obj << -/Names [(page.64) 1480 0 R (page.65) 1574 0 R (page.66) 1652 0 R (page.7) 463 0 R (page.8) 474 0 R (page.9) 487 0 R] -/Limits [(page.64) (page.9)] ->> endobj -1945 0 obj << -/Names [(section*.1) 352 0 R (section*.4) 330 0 R (section.1.1) 6 0 R (section.1.2) 10 0 R (section.1.3) 14 0 R (section.1.4) 18 0 R] -/Limits [(section*.1) (section.1.4)] ->> endobj -1946 0 obj << -/Names [(section.1.5) 22 0 R (section.1.6) 26 0 R (section.1.7) 30 0 R (section.2.1) 38 0 R (section.2.2) 42 0 R (section.2.3) 46 0 R] -/Limits [(section.1.5) (section.2.3)] ->> endobj -1947 0 obj << -/Names [(section.2.4) 50 0 R (section.2.5) 54 0 R (section.2.6) 58 0 R (section.3.1) 66 0 R (section.3.2) 70 0 R (section.3.3) 74 0 R] -/Limits [(section.2.4) (section.3.3)] ->> endobj -1948 0 obj << -/Names [(section.3.4) 78 0 R (section.4.1) 86 0 R (section.4.10) 122 0 R (section.4.11) 126 0 R (section.4.12) 130 0 R (section.4.2) 90 0 R] -/Limits [(section.3.4) (section.4.2)] ->> endobj -1949 0 obj << -/Names [(section.4.3) 94 0 R (section.4.4) 98 0 R (section.4.5) 102 0 R (section.4.6) 106 0 R (section.4.7) 110 0 R (section.4.8) 114 0 R] -/Limits [(section.4.3) (section.4.8)] ->> endobj -1950 0 obj << -/Names [(section.4.9) 118 0 R (section.5.1) 138 0 R (section.5.2) 142 0 R (section.5.3) 146 0 R (section.5.4) 150 0 R (section.5.5) 154 0 R] -/Limits [(section.4.9) (section.5.5)] ->> endobj -1951 0 obj << -/Names [(section.6.1) 162 0 R (section.6.10) 198 0 R (section.6.11) 202 0 R (section.6.12) 206 0 R (section.6.2) 166 0 R (section.6.3) 170 0 R] -/Limits [(section.6.1) (section.6.3)] ->> endobj -1952 0 obj << -/Names [(section.6.4) 174 0 R (section.6.5) 178 0 R (section.6.6) 182 0 R (section.6.7) 186 0 R (section.6.8) 190 0 R (section.6.9) 194 0 R] -/Limits [(section.6.4) (section.6.9)] ->> endobj -1953 0 obj << -/Names [(section.7.1) 214 0 R (section.7.2) 218 0 R (section.7.3) 222 0 R (section.7.4) 226 0 R (section.7.5) 230 0 R (section.7.6) 234 0 R] -/Limits [(section.7.1) (section.7.6)] ->> endobj -1954 0 obj << -/Names [(section.7.7) 238 0 R (section.7.8) 242 0 R (section.8.1) 250 0 R (section.8.2) 254 0 R (section.8.3) 258 0 R (section.8.4) 262 0 R] -/Limits [(section.7.7) (section.8.4)] ->> endobj -1955 0 obj << -/Names [(section.9.1) 270 0 R (section.9.10) 306 0 R (section.9.11) 310 0 R (section.9.12) 314 0 R (section.9.2) 274 0 R (section.9.3) 278 0 R] -/Limits [(section.9.1) (section.9.3)] ->> endobj -1956 0 obj << -/Names [(section.9.4) 282 0 R (section.9.5) 286 0 R (section.9.6) 290 0 R (section.9.7) 294 0 R (section.9.8) 298 0 R (section.9.9) 302 0 R] -/Limits [(section.9.4) (section.9.9)] ->> endobj -1957 0 obj << -/Names [(subsection.3.4.1) 526 0 R (subsection.4.10.1) 605 0 R (subsection.4.10.2) 607 0 R (subsection.4.10.3) 609 0 R (subsection.4.10.4) 611 0 R (subsection.4.11.1) 618 0 R] -/Limits [(subsection.3.4.1) (subsection.4.11.1)] ->> endobj -1958 0 obj << -/Names [(subsection.4.12.1) 621 0 R (subsection.4.2.1) 537 0 R (subsection.4.2.2) 539 0 R (subsection.4.3.1) 546 0 R (subsection.4.3.2) 548 0 R (subsection.4.3.3) 550 0 R] -/Limits [(subsection.4.12.1) (subsection.4.3.3)] ->> endobj -1959 0 obj << -/Names [(subsection.4.4.1) 553 0 R (subsection.4.5.1) 564 0 R (subsection.4.6.1) 567 0 R (subsection.4.6.2) 569 0 R (subsection.4.6.3) 571 0 R (subsection.4.7.1) 578 0 R] -/Limits [(subsection.4.4.1) (subsection.4.7.1)] ->> endobj -1960 0 obj << -/Names [(subsection.4.8.1) 581 0 R (subsection.4.8.2) 583 0 R (subsection.4.9.1) 592 0 R (subsection.4.9.2) 594 0 R (subsection.5.1.1) 631 0 R (subsection.5.1.2) 633 0 R] -/Limits [(subsection.4.8.1) (subsection.5.1.2)] ->> endobj -1961 0 obj << -/Names [(subsection.5.1.3) 635 0 R (subsection.5.1.4) 637 0 R (subsection.5.1.5) 643 0 R (subsection.5.2.1) 646 0 R (subsection.5.2.2) 648 0 R (subsection.5.3.1) 656 0 R] -/Limits [(subsection.5.1.3) (subsection.5.3.1)] ->> endobj -1962 0 obj << -/Names [(subsection.5.4.1) 658 0 R (subsection.5.4.2) 660 0 R (subsection.5.5.1) 663 0 R (subsection.5.5.2) 669 0 R (subsection.5.5.3) 671 0 R (subsection.6.1.1) 681 0 R] -/Limits [(subsection.5.4.1) (subsection.6.1.1)] ->> endobj -1963 0 obj << -/Names [(subsection.6.1.2) 683 0 R (subsection.6.1.3) 690 0 R (subsection.6.10.1) 786 0 R (subsection.6.10.2) 788 0 R (subsection.6.10.3) 790 0 R (subsection.6.10.4) 792 0 R] -/Limits [(subsection.6.1.2) (subsection.6.10.4)] ->> endobj -1964 0 obj << -/Names [(subsection.6.10.5) 794 0 R (subsection.6.11.1) 797 0 R (subsection.6.11.2) 803 0 R (subsection.6.11.3) 805 0 R (subsection.6.11.4) 807 0 R (subsection.6.11.5) 809 0 R] -/Limits [(subsection.6.10.5) (subsection.6.11.5)] ->> endobj -1965 0 obj << -/Names [(subsection.6.11.6) 811 0 R (subsection.6.11.7) 813 0 R (subsection.6.11.8) 820 0 R (subsection.6.11.9) 822 0 R (subsection.6.12.1) 825 0 R (subsection.6.12.2) 827 0 R] -/Limits [(subsection.6.11.6) (subsection.6.12.2)] ->> endobj -1966 0 obj << -/Names [(subsection.6.2.1) 692 0 R (subsection.6.2.2) 694 0 R (subsection.6.2.3) 696 0 R (subsection.6.2.4) 698 0 R (subsection.6.2.5) 704 0 R (subsection.6.2.6) 706 0 R] -/Limits [(subsection.6.2.1) (subsection.6.2.6)] ->> endobj -1967 0 obj << -/Names [(subsection.6.2.7) 708 0 R (subsection.6.3.1) 711 0 R (subsection.6.3.2) 713 0 R (subsection.6.4.1) 720 0 R (subsection.6.4.2) 722 0 R (subsection.6.5.1) 730 0 R] -/Limits [(subsection.6.2.7) (subsection.6.5.1)] ->> endobj -1968 0 obj << -/Names [(subsection.6.5.2) 732 0 R (subsection.6.5.3) 734 0 R (subsection.6.6.1) 737 0 R (subsection.6.6.2) 743 0 R (subsection.6.6.3) 745 0 R (subsection.6.6.4) 747 0 R] -/Limits [(subsection.6.5.2) (subsection.6.6.4)] ->> endobj -1969 0 obj << -/Names [(subsection.6.6.5) 749 0 R (subsection.6.7.1) 752 0 R (subsection.6.7.2) 754 0 R (subsection.6.7.3) 762 0 R (subsection.6.8.1) 765 0 R (subsection.6.8.2) 767 0 R] -/Limits [(subsection.6.6.5) (subsection.6.8.2)] ->> endobj -1970 0 obj << -/Names [(subsection.6.9.1) 770 0 R (subsection.6.9.2) 772 0 R (subsection.6.9.3) 774 0 R (subsection.6.9.4) 781 0 R (subsection.6.9.5) 783 0 R (subsection.7.1.1) 836 0 R] -/Limits [(subsection.6.9.1) (subsection.7.1.1)] ->> endobj -1971 0 obj << -/Names [(subsection.7.1.2) 838 0 R (subsection.7.1.3) 840 0 R (subsection.7.1.4) 842 0 R (subsection.7.2.1) 851 0 R (subsection.7.2.2) 853 0 R (subsection.7.2.3) 855 0 R] -/Limits [(subsection.7.1.2) (subsection.7.2.3)] ->> endobj -1972 0 obj << -/Names [(subsection.7.2.4) 857 0 R (subsection.7.2.5) 859 0 R (subsection.7.3.1) 868 0 R (subsection.7.3.2) 870 0 R (subsection.7.3.3) 872 0 R (subsection.7.3.4) 874 0 R] -/Limits [(subsection.7.2.4) (subsection.7.3.4)] ->> endobj -1973 0 obj << -/Names [(subsection.7.3.5) 876 0 R (subsection.7.3.6) 878 0 R (subsection.7.3.7) 887 0 R (subsection.7.4.1) 896 0 R (subsection.7.4.10) 914 0 R (subsection.7.4.11) 920 0 R] -/Limits [(subsection.7.3.5) (subsection.7.4.11)] ->> endobj -1974 0 obj << -/Names [(subsection.7.4.12) 922 0 R (subsection.7.4.13) 924 0 R (subsection.7.4.14) 926 0 R (subsection.7.4.15) 928 0 R (subsection.7.4.2) 898 0 R (subsection.7.4.3) 900 0 R] -/Limits [(subsection.7.4.12) (subsection.7.4.3)] ->> endobj -1975 0 obj << -/Names [(subsection.7.4.4) 902 0 R (subsection.7.4.5) 904 0 R (subsection.7.4.6) 906 0 R (subsection.7.4.7) 908 0 R (subsection.7.4.8) 910 0 R (subsection.7.4.9) 912 0 R] -/Limits [(subsection.7.4.4) (subsection.7.4.9)] ->> endobj -1976 0 obj << -/Names [(subsection.7.5.1) 935 0 R (subsection.7.6.1) 938 0 R (subsection.7.6.2) 940 0 R (subsection.7.6.3) 942 0 R (subsection.7.6.4) 944 0 R (subsection.7.7.1) 961 0 R] -/Limits [(subsection.7.5.1) (subsection.7.7.1)] ->> endobj -1977 0 obj << -/Names [(subsection.7.7.2) 963 0 R (subsection.7.7.3) 978 0 R (subsection.7.7.4) 980 0 R (subsection.7.8.1) 983 0 R (subsection.7.8.2) 985 0 R (subsection.7.8.3) 987 0 R] -/Limits [(subsection.7.7.2) (subsection.7.8.3)] ->> endobj -1978 0 obj << -/Names [(subsection.7.8.4) 989 0 R (subsection.8.1.1) 999 0 R (subsection.8.1.2) 1001 0 R (subsection.8.1.3) 1003 0 R (subsection.8.2.1) 1011 0 R (subsection.8.2.2) 1015 0 R] -/Limits [(subsection.7.8.4) (subsection.8.2.2)] ->> endobj -1979 0 obj << -/Names [(subsection.8.2.3) 1017 0 R (subsection.8.3.1) 1027 0 R (subsection.8.3.2) 1029 0 R (subsection.8.4.1) 1032 0 R (subsection.8.4.2) 1034 0 R (subsection.8.4.3) 1036 0 R] -/Limits [(subsection.8.2.3) (subsection.8.4.3)] ->> endobj -1980 0 obj << -/Names [(subsection.8.4.4) 1042 0 R (subsection.8.4.5) 1044 0 R (subsection.8.4.6) 1046 0 R (subsection.9.1.1) 1054 0 R (subsection.9.1.2) 1056 0 R (subsection.9.1.3) 1069 0 R] -/Limits [(subsection.8.4.4) (subsection.9.1.3)] ->> endobj -1981 0 obj << -/Names [(subsection.9.10.1) 1131 0 R (subsection.9.11.1) 1140 0 R (subsection.9.12.1) 1143 0 R (subsection.9.2.1) 1072 0 R (subsection.9.2.2) 1074 0 R (subsection.9.3.1) 1077 0 R] -/Limits [(subsection.9.10.1) (subsection.9.3.1)] ->> endobj -1982 0 obj << -/Names [(subsection.9.4.1) 1091 0 R (subsection.9.5.1) 1094 0 R (subsection.9.6.1) 1107 0 R (subsection.9.6.2) 1109 0 R (subsection.9.6.3) 1111 0 R (subsection.9.7.1) 1123 0 R] -/Limits [(subsection.9.4.1) (subsection.9.7.1)] ->> endobj -1983 0 obj << -/Names [(subsection.9.8.1) 1126 0 R (subsection.9.9.1) 1129 0 R] -/Limits [(subsection.9.8.1) (subsection.9.9.1)] ->> endobj -1984 0 obj << -/Kids [1887 0 R 1888 0 R 1889 0 R 1890 0 R 1891 0 R 1892 0 R] -/Limits [(Doc-Start) (L.X79CDA09A7D48BF2B)] ->> endobj -1985 0 obj << -/Kids [1893 0 R 1894 0 R 1895 0 R 1896 0 R 1897 0 R 1898 0 R] -/Limits [(L.X79CEA57C850C7070) (L.X7C8428DE791F3CE1)] ->> endobj -1986 0 obj << -/Kids [1899 0 R 1900 0 R 1901 0 R 1902 0 R 1903 0 R 1904 0 R] -/Limits [(L.X7CA3DCA07B6CB9BD) (L.X7EE99F647C537994)] ->> endobj -1987 0 obj << -/Kids [1905 0 R 1906 0 R 1907 0 R 1908 0 R 1909 0 R 1910 0 R] -/Limits [(L.X7EF1B6708069B0C7) (L.X81A1DB918057933E)] ->> endobj -1988 0 obj << -/Kids [1911 0 R 1912 0 R 1913 0 R 1914 0 R 1915 0 R 1916 0 R] -/Limits [(L.X81E82098822543EE) (L.X841E540B7A7EF29F)] ->> endobj -1989 0 obj << -/Kids [1917 0 R 1918 0 R 1919 0 R 1920 0 R 1921 0 R 1922 0 R] -/Limits [(L.X841ED66B8084AA73) (L.X8664CA927DD73DBE)] ->> endobj -1990 0 obj << -/Kids [1923 0 R 1924 0 R 1925 0 R 1926 0 R 1927 0 R 1928 0 R] -/Limits [(L.X86695C577A4D1784) (chapter.9)] ->> endobj -1991 0 obj << -/Kids [1929 0 R 1930 0 R 1931 0 R 1932 0 R 1933 0 R 1934 0 R] -/Limits [(cite.Ar) (page.14)] ->> endobj -1992 0 obj << -/Kids [1935 0 R 1936 0 R 1937 0 R 1938 0 R 1939 0 R 1940 0 R] -/Limits [(page.15) (page.47)] ->> endobj -1993 0 obj << -/Kids [1941 0 R 1942 0 R 1943 0 R 1944 0 R 1945 0 R 1946 0 R] -/Limits [(page.48) (section.2.3)] ->> endobj -1994 0 obj << -/Kids [1947 0 R 1948 0 R 1949 0 R 1950 0 R 1951 0 R 1952 0 R] -/Limits [(section.2.4) (section.6.9)] ->> endobj -1995 0 obj << -/Kids [1953 0 R 1954 0 R 1955 0 R 1956 0 R 1957 0 R 1958 0 R] -/Limits [(section.7.1) (subsection.4.3.3)] ->> endobj -1996 0 obj << -/Kids [1959 0 R 1960 0 R 1961 0 R 1962 0 R 1963 0 R 1964 0 R] -/Limits [(subsection.4.4.1) (subsection.6.11.5)] ->> endobj -1997 0 obj << -/Kids [1965 0 R 1966 0 R 1967 0 R 1968 0 R 1969 0 R 1970 0 R] -/Limits [(subsection.6.11.6) (subsection.7.1.1)] ->> endobj -1998 0 obj << -/Kids [1971 0 R 1972 0 R 1973 0 R 1974 0 R 1975 0 R 1976 0 R] -/Limits [(subsection.7.1.2) (subsection.7.7.1)] ->> endobj -1999 0 obj << -/Kids [1977 0 R 1978 0 R 1979 0 R 1980 0 R 1981 0 R 1982 0 R] -/Limits [(subsection.7.7.2) (subsection.9.7.1)] ->> endobj -2000 0 obj << -/Kids [1983 0 R] -/Limits [(subsection.9.8.1) (subsection.9.9.1)] ->> endobj -2001 0 obj << -/Kids [1984 0 R 1985 0 R 1986 0 R 1987 0 R 1988 0 R 1989 0 R] -/Limits [(Doc-Start) (L.X8664CA927DD73DBE)] ->> endobj -2002 0 obj << -/Kids [1990 0 R 1991 0 R 1992 0 R 1993 0 R 1994 0 R 1995 0 R] -/Limits [(L.X86695C577A4D1784) (subsection.4.3.3)] ->> endobj -2003 0 obj << -/Kids [1996 0 R 1997 0 R 1998 0 R 1999 0 R 2000 0 R] -/Limits [(subsection.4.4.1) (subsection.9.9.1)] ->> endobj -2004 0 obj << -/Kids [2001 0 R 2002 0 R 2003 0 R] +>> +endobj +1963 0 obj +<< +/Names [(cite.Pf) 488 0 R (cite.PhiVoj) 904 0 R (cite.SlZe2011) 1110 0 R (cite.StuhlVojtechovsky) 1167 0 R (cite.Vo) 836 0 R (cite.VoQRS) 984 0 R] +/Limits [(cite.Pf) (cite.VoQRS)] +>> +endobj +1964 0 obj +<< +/Names [(cite.Wi) 1148 0 R (page.1) 343 0 R (page.10) 501 0 R (page.11) 512 0 R (page.12) 521 0 R (page.13) 529 0 R] +/Limits [(cite.Wi) (page.13)] +>> +endobj +1965 0 obj +<< +/Names [(page.14) 538 0 R (page.15) 549 0 R (page.16) 563 0 R (page.17) 568 0 R (page.18) 581 0 R (page.19) 595 0 R] +/Limits [(page.14) (page.19)] +>> +endobj +1966 0 obj +<< +/Names [(page.2) 353 0 R (page.20) 608 0 R (page.21) 621 0 R (page.22) 633 0 R (page.23) 647 0 R (page.24) 660 0 R] +/Limits [(page.2) (page.24)] +>> +endobj +1967 0 obj +<< +/Names [(page.25) 673 0 R (page.26) 683 0 R (page.27) 694 0 R (page.28) 708 0 R (page.29) 723 0 R (page.3) 394 0 R] +/Limits [(page.25) (page.3)] +>> +endobj +1968 0 obj +<< +/Names [(page.30) 734 0 R (page.31) 747 0 R (page.32) 766 0 R (page.33) 785 0 R (page.34) 807 0 R (page.35) 824 0 R] +/Limits [(page.30) (page.35)] +>> +endobj +1969 0 obj +<< +/Names [(page.36) 840 0 R (page.37) 846 0 R (page.38) 863 0 R (page.39) 879 0 R (page.4) 442 0 R (page.40) 899 0 R] +/Limits [(page.36) (page.40)] +>> +endobj +1970 0 obj +<< +/Names [(page.41) 908 0 R (page.42) 932 0 R (page.43) 946 0 R (page.44) 973 0 R (page.45) 990 0 R (page.46) 1009 0 R] +/Limits [(page.41) (page.46)] +>> +endobj +1971 0 obj +<< +/Names [(page.47) 1022 0 R (page.48) 1039 0 R (page.49) 1054 0 R (page.5) 453 0 R (page.50) 1065 0 R (page.51) 1077 0 R] +/Limits [(page.47) (page.51)] +>> +endobj +1972 0 obj +<< +/Names [(page.52) 1100 0 R (page.53) 1120 0 R (page.54) 1136 0 R (page.55) 1156 0 R (page.56) 1171 0 R (page.57) 1176 0 R] +/Limits [(page.52) (page.57)] +>> +endobj +1973 0 obj +<< +/Names [(page.58) 1180 0 R (page.59) 1185 0 R (page.6) 458 0 R (page.60) 1189 0 R (page.61) 1208 0 R (page.62) 1232 0 R] +/Limits [(page.58) (page.62)] +>> +endobj +1974 0 obj +<< +/Names [(page.63) 1310 0 R (page.64) 1405 0 R (page.65) 1504 0 R (page.66) 1598 0 R (page.67) 1680 0 R (page.7) 468 0 R] +/Limits [(page.63) (page.7)] +>> +endobj +1975 0 obj +<< +/Names [(page.8) 479 0 R (page.9) 492 0 R (section*.1) 356 0 R (section*.4) 334 0 R (section.1.1) 6 0 R (section.1.2) 10 0 R] +/Limits [(page.8) (section.1.2)] +>> +endobj +1976 0 obj +<< +/Names [(section.1.3) 14 0 R (section.1.4) 18 0 R (section.1.5) 22 0 R (section.1.6) 26 0 R (section.1.7) 30 0 R (section.2.1) 38 0 R] +/Limits [(section.1.3) (section.2.1)] +>> +endobj +1977 0 obj +<< +/Names [(section.2.2) 42 0 R (section.2.3) 46 0 R (section.2.4) 50 0 R (section.2.5) 54 0 R (section.2.6) 58 0 R (section.3.1) 66 0 R] +/Limits [(section.2.2) (section.3.1)] +>> +endobj +1978 0 obj +<< +/Names [(section.3.2) 70 0 R (section.3.3) 74 0 R (section.3.4) 78 0 R (section.4.1) 86 0 R (section.4.10) 122 0 R (section.4.11) 126 0 R] +/Limits [(section.3.2) (section.4.11)] +>> +endobj +1979 0 obj +<< +/Names [(section.4.12) 130 0 R (section.4.2) 90 0 R (section.4.3) 94 0 R (section.4.4) 98 0 R (section.4.5) 102 0 R (section.4.6) 106 0 R] +/Limits [(section.4.12) (section.4.6)] +>> +endobj +1980 0 obj +<< +/Names [(section.4.7) 110 0 R (section.4.8) 114 0 R (section.4.9) 118 0 R (section.5.1) 138 0 R (section.5.2) 142 0 R (section.5.3) 146 0 R] +/Limits [(section.4.7) (section.5.3)] +>> +endobj +1981 0 obj +<< +/Names [(section.5.4) 150 0 R (section.5.5) 154 0 R (section.6.1) 162 0 R (section.6.10) 198 0 R (section.6.11) 202 0 R (section.6.12) 206 0 R] +/Limits [(section.5.4) (section.6.12)] +>> +endobj +1982 0 obj +<< +/Names [(section.6.2) 166 0 R (section.6.3) 170 0 R (section.6.4) 174 0 R (section.6.5) 178 0 R (section.6.6) 182 0 R (section.6.7) 186 0 R] +/Limits [(section.6.2) (section.6.7)] +>> +endobj +1983 0 obj +<< +/Names [(section.6.8) 190 0 R (section.6.9) 194 0 R (section.7.1) 214 0 R (section.7.2) 218 0 R (section.7.3) 222 0 R (section.7.4) 226 0 R] +/Limits [(section.6.8) (section.7.4)] +>> +endobj +1984 0 obj +<< +/Names [(section.7.5) 230 0 R (section.7.6) 234 0 R (section.7.7) 238 0 R (section.7.8) 242 0 R (section.8.1) 250 0 R (section.8.2) 254 0 R] +/Limits [(section.7.5) (section.8.2)] +>> +endobj +1985 0 obj +<< +/Names [(section.8.3) 258 0 R (section.8.4) 262 0 R (section.9.1) 270 0 R (section.9.10) 306 0 R (section.9.11) 310 0 R (section.9.12) 314 0 R] +/Limits [(section.8.3) (section.9.12)] +>> +endobj +1986 0 obj +<< +/Names [(section.9.13) 318 0 R (section.9.2) 274 0 R (section.9.3) 278 0 R (section.9.4) 282 0 R (section.9.5) 286 0 R (section.9.6) 290 0 R] +/Limits [(section.9.13) (section.9.6)] +>> +endobj +1987 0 obj +<< +/Names [(section.9.7) 294 0 R (section.9.8) 298 0 R (section.9.9) 302 0 R (subsection.3.4.1) 531 0 R (subsection.4.10.1) 610 0 R (subsection.4.10.2) 612 0 R] +/Limits [(section.9.7) (subsection.4.10.2)] +>> +endobj +1988 0 obj +<< +/Names [(subsection.4.10.3) 614 0 R (subsection.4.10.4) 616 0 R (subsection.4.11.1) 623 0 R (subsection.4.12.1) 626 0 R (subsection.4.2.1) 542 0 R (subsection.4.2.2) 544 0 R] +/Limits [(subsection.4.10.3) (subsection.4.2.2)] +>> +endobj +1989 0 obj +<< +/Names [(subsection.4.3.1) 551 0 R (subsection.4.3.2) 553 0 R (subsection.4.3.3) 555 0 R (subsection.4.4.1) 558 0 R (subsection.4.5.1) 569 0 R (subsection.4.6.1) 572 0 R] +/Limits [(subsection.4.3.1) (subsection.4.6.1)] +>> +endobj +1990 0 obj +<< +/Names [(subsection.4.6.2) 574 0 R (subsection.4.6.3) 576 0 R (subsection.4.7.1) 583 0 R (subsection.4.8.1) 586 0 R (subsection.4.8.2) 588 0 R (subsection.4.9.1) 597 0 R] +/Limits [(subsection.4.6.2) (subsection.4.9.1)] +>> +endobj +1991 0 obj +<< +/Names [(subsection.4.9.2) 599 0 R (subsection.5.1.1) 636 0 R (subsection.5.1.2) 638 0 R (subsection.5.1.3) 640 0 R (subsection.5.1.4) 642 0 R (subsection.5.1.5) 648 0 R] +/Limits [(subsection.4.9.2) (subsection.5.1.5)] +>> +endobj +1992 0 obj +<< +/Names [(subsection.5.2.1) 651 0 R (subsection.5.2.2) 653 0 R (subsection.5.3.1) 661 0 R (subsection.5.4.1) 663 0 R (subsection.5.4.2) 665 0 R (subsection.5.5.1) 668 0 R] +/Limits [(subsection.5.2.1) (subsection.5.5.1)] +>> +endobj +1993 0 obj +<< +/Names [(subsection.5.5.2) 674 0 R (subsection.5.5.3) 676 0 R (subsection.6.1.1) 686 0 R (subsection.6.1.2) 688 0 R (subsection.6.1.3) 695 0 R (subsection.6.10.1) 791 0 R] +/Limits [(subsection.5.5.2) (subsection.6.10.1)] +>> +endobj +1994 0 obj +<< +/Names [(subsection.6.10.2) 793 0 R (subsection.6.10.3) 795 0 R (subsection.6.10.4) 797 0 R (subsection.6.10.5) 799 0 R (subsection.6.11.1) 802 0 R (subsection.6.11.10) 829 0 R] +/Limits [(subsection.6.10.2) (subsection.6.11.10)] +>> +endobj +1995 0 obj +<< +/Names [(subsection.6.11.11) 831 0 R (subsection.6.11.2) 808 0 R (subsection.6.11.3) 810 0 R (subsection.6.11.4) 812 0 R (subsection.6.11.5) 814 0 R (subsection.6.11.6) 816 0 R] +/Limits [(subsection.6.11.11) (subsection.6.11.6)] +>> +endobj +1996 0 obj +<< +/Names [(subsection.6.11.7) 818 0 R (subsection.6.11.8) 825 0 R (subsection.6.11.9) 827 0 R (subsection.6.12.1) 834 0 R (subsection.6.12.2) 841 0 R (subsection.6.2.1) 697 0 R] +/Limits [(subsection.6.11.7) (subsection.6.2.1)] +>> +endobj +1997 0 obj +<< +/Names [(subsection.6.2.2) 699 0 R (subsection.6.2.3) 701 0 R (subsection.6.2.4) 703 0 R (subsection.6.2.5) 709 0 R (subsection.6.2.6) 711 0 R (subsection.6.2.7) 713 0 R] +/Limits [(subsection.6.2.2) (subsection.6.2.7)] +>> +endobj +1998 0 obj +<< +/Names [(subsection.6.3.1) 716 0 R (subsection.6.3.2) 718 0 R (subsection.6.4.1) 725 0 R (subsection.6.4.2) 727 0 R (subsection.6.5.1) 735 0 R (subsection.6.5.2) 737 0 R] +/Limits [(subsection.6.3.1) (subsection.6.5.2)] +>> +endobj +1999 0 obj +<< +/Names [(subsection.6.5.3) 739 0 R (subsection.6.6.1) 742 0 R (subsection.6.6.2) 748 0 R (subsection.6.6.3) 750 0 R (subsection.6.6.4) 752 0 R (subsection.6.6.5) 754 0 R] +/Limits [(subsection.6.5.3) (subsection.6.6.5)] +>> +endobj +2000 0 obj +<< +/Names [(subsection.6.7.1) 757 0 R (subsection.6.7.2) 759 0 R (subsection.6.7.3) 767 0 R (subsection.6.8.1) 770 0 R (subsection.6.8.2) 772 0 R (subsection.6.9.1) 775 0 R] +/Limits [(subsection.6.7.1) (subsection.6.9.1)] +>> +endobj +2001 0 obj +<< +/Names [(subsection.6.9.2) 777 0 R (subsection.6.9.3) 779 0 R (subsection.6.9.4) 786 0 R (subsection.6.9.5) 788 0 R (subsection.7.1.1) 849 0 R (subsection.7.1.2) 851 0 R] +/Limits [(subsection.6.9.2) (subsection.7.1.2)] +>> +endobj +2002 0 obj +<< +/Names [(subsection.7.1.3) 853 0 R (subsection.7.1.4) 855 0 R (subsection.7.2.1) 865 0 R (subsection.7.2.2) 867 0 R (subsection.7.2.3) 869 0 R (subsection.7.2.4) 871 0 R] +/Limits [(subsection.7.1.3) (subsection.7.2.4)] +>> +endobj +2003 0 obj +<< +/Names [(subsection.7.2.5) 873 0 R (subsection.7.3.1) 881 0 R (subsection.7.3.2) 883 0 R (subsection.7.3.3) 885 0 R (subsection.7.3.4) 887 0 R (subsection.7.3.5) 889 0 R] +/Limits [(subsection.7.2.5) (subsection.7.3.5)] +>> +endobj +2004 0 obj +<< +/Names [(subsection.7.3.6) 891 0 R 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Thu Oct 27 11:38:34 2016 -%%Pages: 66 +%%CreationDate: Fri Oct 27 17:20:37 2017 +%%Pages: 67 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: Times-Bold Helvetica-Bold Times-Roman Helvetica-Oblique @@ -12,7 +12,7 @@ %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe loops.dvi %DVIPSParameters: dpi=600 -%DVIPSSource: TeX output 2016.10.27:1138 +%DVIPSSource: TeX output 2017.10.27:1110 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S @@ -62,149 +62,149 @@ B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p %%EndProcSet %%BeginProcSet: 8r.enc 0 0 -% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 -% -% @@psencodingfile@{ -% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, -% W. Schmidt, P. Lehman", -% version = "2.0", -% date = "27nov06", -% filename = "8r.enc", -% email = "tex-fonts@@tug.org", -% docstring = "This is the encoding vector for Type1 and TrueType -% fonts to be used with TeX. This file is part of the -% PSNFSS bundle, version 9" -% @} -% -% The idea is to have all the characters normally included in Type 1 fonts -% available for typesetting. This is effectively the characters in Adobe -% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, -% MacRoman, and some extra characters from Lucida. -% -% Character code assignments were made as follows: -% -% (1) the Windows ANSI characters are almost all in their Windows ANSI -% positions, because some Windows users cannot easily reencode the -% fonts, and it makes no difference on other systems. The only Windows -% ANSI characters not available are those that make no sense for -% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen -% (173). quotesingle and grave are moved just because it's such an -% irritation not having them in TeX positions. -% -% (2) Remaining characters are assigned arbitrarily to the lower part -% of the range, avoiding 0, 10 and 13 in case we meet dumb software. -% -% (3) Y&Y Lucida Bright includes some extra text characters; in the -% hopes that other PostScript fonts, perhaps created for public -% consumption, will include them, they are included starting at 0x12. -% These are /dotlessj /ff /ffi /ffl. -% -% (4) hyphen appears twice for compatibility with both ASCII and Windows. -% -% (5) /Euro was assigned to 128, as in Windows ANSI -% -% (6) Missing characters from MacRoman encoding incorporated as follows: -% -% PostScript MacRoman TeXBase1 -% -------------- -------------- -------------- -% /notequal 173 0x16 -% /infinity 176 0x17 -% /lessequal 178 0x18 -% /greaterequal 179 0x19 -% /partialdiff 182 0x1A -% /summation 183 0x1B -% /product 184 0x1C -% /pi 185 0x1D -% /integral 186 0x81 -% /Omega 189 0x8D -% /radical 195 0x8E -% /approxequal 197 0x8F -% /Delta 198 0x9D -% /lozenge 215 0x9E -% -/TeXBase1Encoding [ -% 0x00 - /.notdef /dotaccent /fi /fl - /fraction /hungarumlaut /Lslash /lslash - /ogonek /ring /.notdef /breve - /minus /.notdef /Zcaron /zcaron -% 0x10 - /caron /dotlessi /dotlessj /ff - /ffi /ffl /notequal /infinity - /lessequal /greaterequal /partialdiff /summation - /product /pi /grave /quotesingle -% 0x20 - /space /exclam /quotedbl /numbersign - /dollar /percent /ampersand /quoteright - /parenleft /parenright /asterisk /plus - /comma /hyphen /period /slash -% 0x30 - /zero /one /two /three - /four /five /six /seven - /eight /nine /colon /semicolon - /less /equal /greater /question -% 0x40 - /at /A /B /C - /D /E /F /G - /H /I /J /K - /L /M /N /O -% 0x50 - /P /Q /R /S - /T /U /V /W - /X /Y /Z /bracketleft - /backslash /bracketright /asciicircum /underscore -% 0x60 - /quoteleft /a /b /c - /d /e /f /g - /h /i /j /k - /l /m /n /o -% 0x70 - /p /q /r /s - /t /u /v /w - /x /y /z /braceleft - /bar /braceright /asciitilde /.notdef -% 0x80 - /Euro /integral /quotesinglbase /florin - /quotedblbase /ellipsis /dagger /daggerdbl - /circumflex /perthousand /Scaron /guilsinglleft - /OE /Omega /radical /approxequal -% 0x90 - /.notdef /.notdef /.notdef /quotedblleft - /quotedblright /bullet /endash /emdash - /tilde /trademark /scaron /guilsinglright - /oe /Delta /lozenge /Ydieresis -% 0xA0 - /.notdef /exclamdown /cent /sterling - /currency /yen /brokenbar /section - /dieresis /copyright /ordfeminine /guillemotleft - /logicalnot /hyphen /registered /macron -% 0xB0 - /degree /plusminus /twosuperior /threesuperior - /acute /mu /paragraph /periodcentered - /cedilla /onesuperior /ordmasculine /guillemotright - /onequarter /onehalf /threequarters /questiondown -% 0xC0 - /Agrave /Aacute /Acircumflex /Atilde - /Adieresis /Aring /AE /Ccedilla - /Egrave /Eacute /Ecircumflex /Edieresis - /Igrave /Iacute /Icircumflex /Idieresis -% 0xD0 - /Eth /Ntilde /Ograve /Oacute - /Ocircumflex /Otilde /Odieresis /multiply - /Oslash /Ugrave /Uacute /Ucircumflex - /Udieresis /Yacute /Thorn /germandbls -% 0xE0 - /agrave /aacute /acircumflex /atilde - /adieresis /aring /ae /ccedilla - /egrave /eacute /ecircumflex /edieresis - /igrave /iacute /icircumflex /idieresis -% 0xF0 - /eth /ntilde /ograve /oacute - /ocircumflex /otilde /odieresis /divide - /oslash /ugrave /uacute /ucircumflex - /udieresis /yacute /thorn /ydieresis -] def - +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. 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The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% These are /dotlessj /ff /ffi /ffl. +% +% (4) hyphen appears twice for compatibility with both ASCII and Windows. +% +% (5) /Euro was assigned to 128, as in Windows ANSI +% +% (6) Missing characters from MacRoman encoding incorporated as follows: +% +% PostScript MacRoman TeXBase1 +% -------------- -------------- -------------- +% /notequal 173 0x16 +% /infinity 176 0x17 +% 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"smallloop", + [ "\033[2XSmallLoop\033[102X", "9.8-1", [ 9, 8, 1 ], 254, 54, "smallloop", "X7C6EE23E84CD87D3" ], - [ "Paige loop", "9.8", [ 9, 8, 0 ], 235, 53, "paige loop", + [ "Paige loop", "9.9", [ 9, 9, 0 ], 259, 54, "paige loop", "X8135C8FD8714C606" ], - [ "loop Paige", "9.8", [ 9, 8, 0 ], 235, 53, "loop paige", + [ "loop Paige", "9.9", [ 9, 9, 0 ], 259, 54, "loop paige", "X8135C8FD8714C606" ], - [ "\033[2XPaigeLoop\033[102X", "9.8-1", [ 9, 8, 1 ], 244, 53, "paigeloop", + [ "\033[2XPaigeLoop\033[102X", "9.9-1", [ 9, 9, 1 ], 268, 54, "paigeloop", "X7FCF4D6B7AD66D74" ], - [ "\033[2XNilpotentLoop\033[102X", "9.9-1", [ 9, 9, 1 ], 261, 53, + [ "\033[2XNilpotentLoop\033[102X", "9.10-1", [ 9, 10, 1 ], 285, 54, "nilpotentloop", "X7A9C960D86E2AD28" ], - [ "\033[2XAutomorphicLoop\033[102X", "9.10-1", [ 9, 10, 1 ], 278, 53, + [ "\033[2XAutomorphicLoop\033[102X", "9.11-1", [ 9, 11, 1 ], 304, 55, "automorphicloop", "X784FFA9E7FDA9F43" ], - [ "sedenion loop", "9.11", [ 9, 11, 0 ], 283, 54, "sedenion loop", + [ "sedenion loop", "9.12", [ 9, 12, 0 ], 309, 55, "sedenion loop", "X843BD73F788049F7" ], - [ "loop sedenion", "9.11", [ 9, 11, 0 ], 283, 54, "loop sedenion", + [ "loop sedenion", "9.12", [ 9, 12, 0 ], 309, 55, "loop sedenion", "X843BD73F788049F7" ], - [ "\033[2XInterestingLoop\033[102X", "9.11-1", [ 9, 11, 1 ], 293, 54, + [ "\033[2XInterestingLoop\033[102X", "9.12-1", [ 9, 12, 1 ], 319, 55, "interestingloop", "X87F24AD3811910D3" ], - [ "\033[2XItpSmallLoop\033[102X", "9.12-1", [ 9, 12, 1 ], 306, 54, + [ "\033[2XItpSmallLoop\033[102X", "9.13-1", [ 9, 13, 1 ], 332, 55, "itpsmallloop", "X850C4C01817A098D" ] ] ); diff --git a/etc/gapdoc.txt b/etc/gapdoc.txt index 96aff9a..02ad7dc 100644 --- a/etc/gapdoc.txt +++ b/etc/gapdoc.txt @@ -22,7 +22,7 @@ chooser.html When files are ready, run the following in GAP: # path to files, change as needed -path := Directory("c:/cygwin64/opt/gap4r7/pkg/loops/doc");; +path := Directory("c:/cygwin64/opt/gap4r8/pkg/loops/doc");; main := "loops.xml";; files := [];; bookname := "loops";; @@ -52,7 +52,7 @@ GAPDoc2HTMLPrintHTMLFiles(h, path); # h := GAPDoc2HTML(r, path );; # GAPDoc2HTMLPrintHTMLFiles(h, path); -# now produce .ps, .dvi from .tex, -# and copy loops.* as manual.* for extensions pdf, ps, dvi +# now produce .ps from .tex +# and copy loops.* as manual.* for extensions pdf, ps # delete auxiliary files diff --git a/gap/banner.g b/gap/banner.g index f06a46b..eb20859 100644 --- a/gap/banner.g +++ b/gap/banner.g @@ -2,7 +2,7 @@ ## #A banner.g loops G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: banner.g, v 3.3.0 2016/09/21 gap Exp $ +#H @(#)$Id: banner.g, v 3.4.0 2017/10/27 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -12,7 +12,7 @@ if not QUIET and BANNER then Print( " ______________________________________________________\n", " LOOPS: Computing with quasigroups and loops in GAP \n", -" version 3.3.0 \n", +" version 3.4.0 \n", " Gabor P. Nagy & Petr Vojtechovsky \n", " nagyg@math.u-szeged.hu petr@math.du.edu \n", " ------------------------------------------------------\n", diff --git a/gap/classes.gi b/gap/classes.gi index ad90f74..7a42fc0 100644 --- a/gap/classes.gi +++ b/gap/classes.gi @@ -2,7 +2,7 @@ ## #W classes.gi Testing properties/varieties [loops] ## -#H @(#)$Id: classes.gi, v 3.3.0 2016/10/26 gap Exp $ +#H @(#)$Id: classes.gi, v 3.4.0 2017/10/26 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -887,16 +887,14 @@ end); InstallMethod( IsALoop, "for loop", [ IsLoop ], function( Q ) - return IsLeftALoop(Q) and IsRightALoop(Q) and IsMiddleALoop(Q); + return IsRightALoop(Q) and IsMiddleALoop(Q); + # Theorem: rigth A-loop + middle A-loop implies left A-loop end); # implies InstallTrueMethod( IsLeftALoop, IsALoop ); InstallTrueMethod( IsRightALoop, IsALoop ); InstallTrueMethod( IsMiddleALoop, IsALoop ); -InstallTrueMethod( IsMiddleALoop, IsCommutative ); -InstallTrueMethod( IsALoop, IsLeftALoop and IsCommutative ); -InstallTrueMethod( IsALoop, IsRightALoop and IsCommutative ); InstallTrueMethod( IsLeftALoop, IsRightALoop and HasAntiautomorphicInverseProperty ); InstallTrueMethod( IsRightALoop, IsLeftALoop and HasAntiautomorphicInverseProperty ); InstallTrueMethod( IsFlexible, IsMiddleALoop ); @@ -909,8 +907,12 @@ InstallTrueMethod( IsMoufangLoop, IsALoop and HasRightInverseProperty ); InstallTrueMethod( IsMoufangLoop, IsALoop and HasWeakInverseProperty ); # is implied by +InstallTrueMethod( IsMiddleALoop, IsCommutative ); InstallTrueMethod( IsLeftALoop, IsLeftBruckLoop ); InstallTrueMethod( IsLeftALoop, IsLCCLoop ); InstallTrueMethod( IsRightALoop, IsRightBruckLoop ); InstallTrueMethod( IsRightALoop, IsRCCLoop ); InstallTrueMethod( IsALoop, IsCommutative and IsMoufangLoop ); +InstallTrueMethod( IsALoop, IsLeftALoop and IsMiddleALoop ); +InstallTrueMethod( IsALoop, IsRightALoop and IsMiddleALoop ); +InstallTrueMethod( IsALoop, IsAssociative ); diff --git a/gap/examples.gd b/gap/examples.gd index 4347138..35e6645 100644 --- a/gap/examples.gd +++ b/gap/examples.gd @@ -2,7 +2,7 @@ ## #W examples.gd Examples [loops] ## -#H @(#)$Id: examples.gd, v 3.1.0 2015/09/23 gap Exp $ +#H @(#)$Id: examples.gd, v 3.4.0 2015/09/23 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -36,6 +36,8 @@ DeclareGlobalFunction( "SmallLoop" ); DeclareGlobalFunction( "InterestingLoop" ); DeclareGlobalFunction( "NilpotentLoop" ); DeclareGlobalFunction( "AutomorphicLoop" ); +DeclareGlobalFunction( "LeftBruckLoop" ); +DeclareGlobalFunction( "RightBruckLoop" ); # up to isotopism @@ -52,3 +54,4 @@ DeclareGlobalFunction( "LOOPS_ActivateRCCLoop" ); DeclareGlobalFunction( "LOOPS_ActivateCCLoop" ); DeclareGlobalFunction( "LOOPS_ActivateNilpotentLoop" ); DeclareGlobalFunction( "LOOPS_ActivateAutomorphicLoop" ); +DeclareGlobalFunction( "LOOPS_ActivateRightBruckLoop" ); diff --git a/gap/examples.gi b/gap/examples.gi index b05ad83..1dc2dc2 100644 --- a/gap/examples.gi +++ b/gap/examples.gi @@ -2,7 +2,7 @@ ## #W examples.gi Examples [loops] ## -#H @(#)$Id: examples.gi, v 3.3.0 2016/10/19 gap Exp $ +#H @(#)$Id: examples.gi, v 3.4.0 2017/10/23 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -32,6 +32,7 @@ ReadPackage("loops", "data/small.tbl"); # small loops ReadPackage("loops", "data/interesting.tbl"); # interesting loops ReadPackage("loops", "data/nilpotent.tbl"); # nilpotent loops ReadPackage("loops", "data/automorphic.tbl"); # automorphic loops +ReadPackage("loops", "data/rightbruck.tbl"); # right Bruck loops # up to isotopism ReadPackage("loops", "data/itp_small.tbl"); # small loops up to isotopism @@ -60,6 +61,7 @@ function( name ) elif name = "interesting" then return LOOPS_interesting_data; elif name = "nilpotent" then return LOOPS_nilpotent_data; elif name = "automorphic" then return LOOPS_automorphic_data; + elif name = "right Bruck" then return LOOPS_right_bruck_data; #up to isotopism elif name = "itp small" then return LOOPS_itp_small_data; fi; @@ -74,11 +76,8 @@ end); InstallGlobalFunction( DisplayLibraryInfo, function( name ) local s, lib, k; # up to isomorphism - if name = "left Bol" then - s := "The library contains all nonassociative left Bol loops of order less than 17\nand all nonassociative left Bol loops of order p*q, where p>q>2 are primes."; - elif name = "right Bol" then - s := "The library contains all nonassociative right Bol loops of order less than 17\nand all nonassociative left Bol loops of order p*q, where p>q>2 are primes."; - name := "left Bol"; # using dual data + if name = "left Bol" or name = "right Bol" then + s := Concatenation( "The library contains all nonassociative ", name, " loops of order less than 17\nand all nonassociative ", name, " loops of order p*q, where p>q>2 are primes." ); elif name = "Moufang" then s := "The library contains all nonassociative Moufang loops \nof order less than 65, and all nonassociative Moufang \nloops of order 81 and 243."; elif name = "Paige" then @@ -88,12 +87,9 @@ InstallGlobalFunction( DisplayLibraryInfo, function( name ) elif name = "Steiner" then s := "The library contains all nonassociative Steiner loops \nof order less or equal to 16. It also contains the \nassociative Steiner loops of order 4 and 8."; elif name = "CC" then - s := "The library contains all nonassociative CC loops of order less than 28 \nand all nonassociative CC loops of order p^2 and 2*p for any odd prime p."; - elif name = "RCC" then - s := "The library contains all nonassociative RCC loops of order less than 28."; - elif name = "LCC" then - s := "The library contains all nonassociative LCC loops of order less than 28."; - name := "RCC"; # using dual data + s := "The library contains all CC loops of order\n2<=2^k<=64, 3<=3^k<=81, 5<=5^k<=125, 7<=7^k<=343,\nall nonassociative CC loops of order less than 28,\nand all nonassociative CC loops of order p^2 and 2*p for any odd prime p."; + elif name = "RCC" or name = "LCC" then + s := Concatenation( "The library contains all nonassociative ", name, " loops of order less than 28." ); elif name = "small" then s := "The library contains all nonassociative loops of order less than 7."; elif name = "interesting" then @@ -103,23 +99,27 @@ InstallGlobalFunction( DisplayLibraryInfo, function( name ) elif name = "automorphic" then s := "The library contains:\n"; s := Concatenation(s," - all nonassociative automorphic loops of order less than 16,\n"); - s := Concatenation(s," - all commutative automorphic loops of order 3, 9, 27, 81,\n"); - s := Concatenation(s," - all commutative automorphic loops of order 243 that are central\n"); - s := Concatenation(s," extensions of Z_3 by F, where F is not the elem. ab. 3-group.\n"); - s := Concatenation(s,"Note: Abelian groups are included among the commutative loops."); + s := Concatenation(s," - all commutative automorphic loops of order 3, 9, 27, 81."); + elif name = "left Bruck" or name = "right Bruck" then + s := Concatenation( "The library contains all ", name, " loops of orders 3, 9, 27 and 81." ); # up to isotopism elif name = "itp small" then s := "The library contains all nonassociative loops of order less than 7 up to isotopism."; else Info( InfoWarning, 1, Concatenation( "The admissible names for loop libraries are: \n", - "[ \"left Bol\", \"right Bol\", \"Moufang\", \"Paige\", \"code\", \"Steiner\", \"CC\", \"RCC\", \"LCC\", \"small\", \"itp small\", \"interesting\", \"nilpotent\", \"automorphic\" ]." + "\"automorphic\", \"CC\", \"code\", \"interesting\", \"itp small\", \"LCC\", \"left Bol\", \"left Bruck\", \"Moufang\", \"nilpotent\", \"Paige\", \"right Bol\", \"right Bruck\", \"RCC\", \"small\", \"Steiner\"." ) ); return fail; fi; s := Concatenation( s, "\n------\nExtent of the library:" ); + # renaming for data access + if name = "right Bol" then name := "left Bol"; fi; + if name = "LCC" then name := "RCC"; fi; + if name = "left Bruck" then name := "right Bruck"; fi; + lib := LOOPS_LibraryByName( name ); for k in [1..Length( lib[ 1 ] ) ] do if lib[ 2 ][ k ] = 1 then @@ -128,12 +128,12 @@ InstallGlobalFunction( DisplayLibraryInfo, function( name ) s := Concatenation( s, "\n ", String( lib[ 2 ][ k ] ), " loops of order ", String( lib[ 1 ][ k ] ) ); fi; od; - if name = "left Bol" or name = "right Bol" then + if name = "left Bol" then s := Concatenation( s, "\n (p-q)/2 loops of order p*q for primes p>q>2 such that q divides p-1"); s := Concatenation( s, "\n (p-q+2)/2 loops of order p*q for primes p>q>2 such that q divides p+1" ); fi; if name = "CC" then - s := Concatenation( s, "\n 3 loops of order p^2 for every odd prime p,\n 1 loop of order 2*p for every odd prime p" ); + s := Concatenation( s, "\n 3 loops of order p^2 for every prime p>7,\n 1 loop of order 2*p for every odd prime p" ); fi; s := Concatenation( s, "\n" ); Print( s ); @@ -436,7 +436,48 @@ end); InstallGlobalFunction( LOOPS_ActivateCCLoop, function( n, pos_n, m, case ) - local T, x, y, k, a, b, p; + local powers, p, i, k, F, basis, coords, coc, T, a, b, x, y; + powers := [ ,[4,8,16,32,64],[9,27,81],,[25,125],,[49,343]]; + if n in Union( powers ) then # use cocycles + # determine p and position of n in database + p := Filtered([2,3,5,7], x -> n in powers[x])[1]; + pos_n := Position( powers[p], n ); + if not IsBound( LOOPS_cc_cocycles[p] ) then + # data not read yet, activate once + ReadPackage( "loops", Concatenation( "data/cc/cc_cocycles_", String(p), ".tbl" ) ); + # decode cocycles and separate coordinates from a long string + for i in [1..Length(powers[p])] do + LOOPS_cc_cocycles[ p ][ i ] := List( LOOPS_cc_cocycles[ p ][ i ], + c -> LOOPS_DecodeCocycle( [ p^i, c[1], c[2] ], [0..p-1] ) + ); + LOOPS_cc_coordinates[ p ][ i ] := List( LOOPS_cc_coordinates[ p ][ i ], + c -> SplitString( c, " " ) + ); + od; + fi; + # data is now read + # determine position of loop in the database + k := 1; + while m > Length( LOOPS_cc_coordinates[ p ][ pos_n ][ k ] ) do + m := m - Length( LOOPS_cc_coordinates[ p ][ pos_n ][ k ] ); + k := k + 1; + od; + # factor loop + F := CCLoop( n/p, LOOPS_cc_used_factors[ p ][ pos_n ][ k ] ); + # basis + basis := List( LOOPS_cc_bases[ p ][ pos_n ][ k ], + i -> LOOPS_cc_cocycles[ p ][ pos_n ][ i ] + ); + # coordinates + coords := LOOPS_cc_coordinates[ p ][ pos_n ][ k ][ m ]; + coords := LOOPS_ConvertBase( coords, 91, p, Length( basis ) ); + coords := List( coords, LOOPS_CharToDigit ); + # cocycle + coc := (coords*basis) mod p; + coc := List( coc, i -> i+1 ); + # return extension of Z_p by F using cocycle and trivial action + return LoopByExtension( CCLoop(p,1), F, List([1..n/p], i -> () ), coc ); + fi; if case=false then # use library of RCC loops, must recalculate pos_n return LOOPS_ActivateRCCLoop( n, Position(LOOPS_rcc_data[ 1 ], n), LOOPS_cc_data[ 3 ][ pos_n ][ m ] ); @@ -543,39 +584,52 @@ end); InstallGlobalFunction( LOOPS_ActivateAutomorphicLoop, function( n, m ) - local i, pos_n, factor_id, F, dim, coords, basis, coc; - if IsEmpty( LOOPS_automorphic_cocycles ) then # only read on demand - ReadPackage( "loops", "data/automorphic/automorphic_cocycles.tbl"); - # decode cocycles - for i in [1..3] do - LOOPS_automorphic_cocycles[ i ] := List( LOOPS_automorphic_cocycles[ i ], - c -> LOOPS_DecodeCocycle( [ 3^(i+2), true, c ], [0,1,2] ) - ); - od; - # separate coordinates (from a long string ) - for i in [1..3] do - LOOPS_automorphic_coordinates[ i ] := SplitString( LOOPS_automorphic_coordinates[ i ], " " ); - od; - fi; + # returns the associated Gamma loop (which here always happens to be automorphic) + # improve later + local P, L, s, Ls, ct, i, j, pos, f; + P := LeftBruckLoop( n, m ); + L := LeftMultiplicationGroup( P );; + s := List(Elements(L), x -> x^2 );; + Ls := List([1..n], i -> LeftTranslation( P, Elements(P)[i] ) );; + ct := List([1..n],i->0*[1..n]);; + for i in [1..n] do for j in [1..n] do + pos := Position( s, Ls[i]*Ls[j]*Ls[i]^(-1)*Ls[j]^(-1) ); + f := Elements(L)[pos]; + ct[i][j] := 1^(f*Ls[j]*Ls[i]); + od; od; + return LoopByCayleyTable(ct); +end); + +############################################################################# +## +#F LOOPS_ActivateRightBruckLoop( n, m ) +## +## Activates a right Bruck loop from the library. + +InstallGlobalFunction( LOOPS_ActivateRightBruckLoop, +function( n, m ) + local pos_n, factor_id, F, basis, coords, coc; # factor loop - pos_n := Position( [27,81,243], n ); - factor_id := LOOPS_CharToDigit( LOOPS_automorphic_coordinates[ pos_n ][ m ][ 1 ] ); - F := AutomorphicLoop( n/3, factor_id ); + pos_n := Position( [27,81], n ); + factor_id := LOOPS_CharToDigit( LOOPS_right_bruck_coordinates[ pos_n ][ m ][ 1 ] ); + F := RightBruckLoop( n/3, factor_id ); + # basis (only decode cocycles at first usage) + if IsString( LOOPS_right_bruck_cocycles[ pos_n ][ 1 ][ 3 ] ) then # not converted yet + LOOPS_right_bruck_cocycles[ pos_n ] := List( LOOPS_right_bruck_cocycles[ pos_n ], + coc -> LOOPS_DecodeCocycle( coc, [0,1,2] ) + ); + fi; + basis := LOOPS_right_bruck_cocycles[ pos_n ]; # coordinates determining the cocycle - dim := Length( LOOPS_automorphic_bases[ pos_n ][ factor_id ] ); - coords := LOOPS_automorphic_coordinates[ pos_n ][ m ]; + coords := LOOPS_right_bruck_coordinates[ pos_n ][ m ]; coords := coords{[2..Length(coords)]}; # remove the character that determines factor id - coords := LOOPS_ConvertBase( coords, 91, 3, dim ); + coords := LOOPS_ConvertBase( coords, 91, 3, Length( basis ) ); coords := List( coords, LOOPS_CharToDigit ); - # basis - basis := List( LOOPS_automorphic_bases[ pos_n ][ factor_id ], - i -> LOOPS_automorphic_cocycles[ pos_n ][ i ] - ); # calculate cocycle coc := (coords*basis) mod 3; - coc := List( coc, i -> i+1 ); + coc := coc + 1; # return extension of Z_3 by F using cocycle and trivial action - return LoopByExtension( AutomorphicLoop(3,1), F, List([1..n/3], i -> () ), coc ); + return LoopByExtension( RightBruckLoop(3,1), F, List([1..n/3], i -> () ), coc ); end); ############################################################################# @@ -593,13 +647,7 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) local lib, implemented_orders, NOL, loop, pos_n, p, q, divs, PG, m_inv, root, half, case, g, h; # selecting data library - if name = "right Bol" then # using dual data - lib := LOOPS_LibraryByName( "left Bol" ); - elif name = "LCC" then # using dual data - lib := LOOPS_LibraryByName( "RCC" ); - else - lib := LOOPS_LibraryByName( name ); - fi; + lib := LOOPS_LibraryByName( name ); # extent of the library implemented_orders := lib[ 1 ]; @@ -614,7 +662,7 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) # parameters for handling systematic cases, such as CCLoop( p^2, 1 ) pos_n := fail; case := false; - if name="left Bol" or name="right Bol" then + if name="left Bol" then divs := DivisorsInt( n ); if Length( divs ) = 4 and not IsInt( divs[3]/divs[2] ) then # case n = p*q q := divs[ 2 ]; @@ -633,13 +681,13 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) fi; if name="CC" then divs := DivisorsInt( n ); - if Length( divs ) = 3 then # case p^2 + if Length( divs ) = 3 and divs[ 2 ] > 7 then # case p^2, p>7 p := divs[ 2 ]; case := [p,"p^2"]; if not m in [1..3] then Error("LOOPS: There are only 3 nonassociative CC-loops of order p^2 for an odd prime p."); fi; - elif Length( divs ) = 4 and not IsInt( divs[3]/divs[2] ) then # p*q + elif Length( divs ) = 4 and not IsInt( divs[3]/divs[2] ) and not n=21 then # p*q p := divs[ 3 ]; case := [p,"2*p"]; if not divs[2] = 2 then @@ -670,9 +718,6 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) if name = "left Bol" then loop := LOOPS_ActivateLeftBolLoop( pos_n, m, case ); SetIsLeftBolLoop( loop, true ); - elif name = "right Bol" then - loop := OppositeLoop( LOOPS_ActivateLeftBolLoop( pos_n, m, case ) ); - SetIsRightBolLoop( loop, true ); elif name = "Moufang" then # renaming loops so that they agree with Goodaire's classification PG := List([1..243], i->()); @@ -701,14 +746,15 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) loop := LOOPS_ActivateSteinerLoop( n, pos_n, m ); SetIsSteinerLoop( loop, true ); elif name = "CC" then - loop := LOOPS_ActivateCCLoop( n, pos_n, m, case ); + if n in [2,3,5,7] then # use Cayley table for canonical cyclic group + loop := LoopByCayleyTable( LOOPS_DecodeCayleyTable( lib[ 3 ][ pos_n ][ m ] ) ); + else + loop := LOOPS_ActivateCCLoop( n, pos_n, m, case ); + fi; SetIsCCLoop( loop, true ); elif name = "RCC" then loop := LOOPS_ActivateRCCLoop( n, pos_n, m ); SetIsRCCLoop( loop, true ); - elif name = "LCC" then - loop := OppositeLoop( LOOPS_ActivateRCCLoop( n, pos_n, m ) ); - SetIsLCCLoop( loop, true ); elif name = "small" then loop := LoopByCayleyTable( LOOPS_DecodeCayleyTable( lib[ 3 ][ pos_n ][ m ] ) ); elif name = "interesting" then @@ -725,12 +771,19 @@ InstallGlobalFunction( LibraryLoop, function( name, n, m ) elif name = "nilpotent" then loop := LOOPS_ActivateNilpotentLoop( lib[ 3 ][ pos_n ][ m ] ); elif name = "automorphic" then - if not n in [27,81,243] then # use Cayley table + if not n in [3, 9, 27, 81] then # use Cayley table loop := LoopByCayleyTable( LOOPS_DecodeCayleyTable( lib[ 3 ][ pos_n ][ m ] ) ); - else # use cocycles - loop := LOOPS_ActivateAutomorphicLoop( n, m ); + else # use associated left Bruck loop + loop := LOOPS_ActivateAutomorphicLoop( n, m ); fi; SetIsAutomorphicLoop( loop, true ); + elif name = "right Bruck" then + if not n in [27,81] then # use Cayley table + loop := LoopByCayleyTable( LOOPS_DecodeCayleyTable( lib[ 3 ][ pos_n ][ m ] ) ); + else # use cocycles + loop := LOOPS_ActivateRightBruckLoop( n, m ); + fi; + SetIsRightBruckLoop( loop, true ); # up to isotopism elif name = "itp small" then return LibraryLoop( "small", n, lib[ 3 ][ pos_n ][ m ] ); @@ -762,6 +815,8 @@ end); #F InterestingLoop( n, m ) #F NilpotentLoop( n, m ) #F AutomorphicLoop( n, m ) +#F LeftBruckLoop( n, m ) +#F RightBruckLoop( n, m ) #F ItpSmallLoop( n, m ) ## @@ -770,7 +825,11 @@ InstallGlobalFunction( LeftBolLoop, function( n, m ) end); InstallGlobalFunction( RightBolLoop, function( n, m ) - return LibraryLoop( "right Bol", n, m ); + local loop; + loop := Opposite( LeftBolLoop( n, m ) ); + SetIsRightBolLoop( loop, true ); + SetName( loop, Concatenation( "" ) ); + return loop; end); InstallGlobalFunction( MoufangLoop, function( n, m ) @@ -808,11 +867,15 @@ InstallGlobalFunction( RightConjugacyClosedLoop, function( n, m ) end); InstallGlobalFunction( LCCLoop, function( n, m ) - return LibraryLoop( "LCC", n, m ); + local loop; + loop := Opposite( RCCLoop( n, m ) ); + SetIsLCCLoop( loop, true ); + SetName( loop, Concatenation( "" ) ); + return loop; end); InstallGlobalFunction( LeftConjugacyClosedLoop, function( n, m ) - return LibraryLoop( "LCC", n, m ); + return LCCLoop( n, m ); end); InstallGlobalFunction( SmallLoop, function( n, m ) @@ -831,6 +894,18 @@ InstallGlobalFunction( AutomorphicLoop, function( n, m ) return LibraryLoop( "automorphic", n, m ); end); +InstallGlobalFunction( RightBruckLoop, function( n, m ) + return LibraryLoop( "right Bruck", n, m ); +end); + +InstallGlobalFunction( LeftBruckLoop, function( n, m ) + local loop; + loop := Opposite( RightBruckLoop( n, m ) ); + SetIsLeftBruckLoop( loop, true ); + SetName( loop, Concatenation( "" ) ); + return loop; +end); + InstallGlobalFunction( ItpSmallLoop, function( n, m ) return LibraryLoop( "itp small", n, m ); end); diff --git a/gap/iso.gd b/gap/iso.gd index cb1ec61..e9f88dc 100644 --- a/gap/iso.gd +++ b/gap/iso.gd @@ -2,7 +2,7 @@ ## #W iso.gd Isomorphisms and isotopisms [loops] ## -#H @(#)$Id: iso.gd, v 3.2.0 2015/06/12 gap Exp $ +#H @(#)$Id: iso.gd, v 3.4.0 2016/12/13 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -23,6 +23,8 @@ DeclareOperation( "IsomorphismQuasigroups", [ IsQuasigroup, IsQuasigroup ] ); DeclareOperation( "IsomorphismLoops", [ IsLoop, IsLoop ] ); DeclareOperation( "QuasigroupsUpToIsomorphism", [ IsList ] ); DeclareOperation( "LoopsUpToIsomorphism", [ IsList ] ); +DeclareOperation( "QuasigroupIsomorph", [ IsQuasigroup, IsPerm ] ); +DeclareOperation( "LoopIsomorph", [ IsLoop, IsPerm ] ); DeclareOperation( "IsomorphicCopyByPerm", [ IsQuasigroup, IsPerm ] ); DeclareOperation( "IsomorphicCopyByNormalSubloop", [ IsLoop, IsLoop ] ); diff --git a/gap/iso.gi b/gap/iso.gi index 4c6a856..6f0cd63 100644 --- a/gap/iso.gi +++ b/gap/iso.gi @@ -2,7 +2,7 @@ ## #W iso.gi Isomorphisms and isotopisms [loops] ## -#H @(#)$Id: iso.gi, v 3.3.0 2016/10/26 gap Exp $ +#H @(#)$Id: iso.gi, v 3.4.0 2017/08/24 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -466,30 +466,54 @@ end); ############################################################################# ## -#O IsomorphicCopyByPerm( Q, p ) +#O QuasigroupIsomorph( Q, p ) ## ## If is a quasigroup of order n and

a permutation of [1..n], returns ## the quasigroup (Q,*) such that p(xy) = p(x)*p(y). -## If is a loop, p is first composed with (1,1^p) to make sure -## that the neutral element of (Q,*) remains 1. -InstallMethod( IsomorphicCopyByPerm, "for a quasigroup and permutation", +InstallMethod( QuasigroupIsomorph, "for a quasigroup and permutation", [ IsQuasigroup, IsPerm ], function( Q, p ) local ctQ, ct, inv_p; ctQ := CanonicalCayleyTable( CayleyTable( Q ) ); - # if Q is a loop and 1^p > 1, must normalize - if (IsLoop( Q ) and (not 1^p = 1)) then - p := p * (1, 1^p ); - fi; inv_p := Inverse( p ); ct := List([1..Size(Q)], i-> List([1..Size(Q)], j -> ( ctQ[ i^inv_p ][ j^inv_p ] )^p ) ); - if IsLoop( Q ) then return LoopByCayleyTable( ct ); fi; return QuasigroupByCayleyTable( ct ); end); +############################################################################# +## +#O LoopIsomorph( Q, p ) +## +## If is a loop of order n and

a permutation of [1..n] such that +## p(1)=1, returns the loop (Q,*) such that p(xy)=p(x)*p(y). +## If p(1)=c<>1, then the quasigroup (Q,*) is converted into loop +## via the isomorphism (1,c). + +InstallMethod( LoopIsomorph, "for a loop and permutation", + [ IsLoop, IsPerm ], +function( Q, p ) + return IntoLoop( QuasigroupIsomorph( Q, p ) ); +end); + +############################################################################# +## +#O IsomorphicCopyByPerm( Q, p ) +## +## Calls LoopIsomorph( Q, p ) if is a loop, +## else QuasigroupIsotope( Q, p ). + +InstallMethod( IsomorphicCopyByPerm, "for a quasigroup and permutation", + [ IsQuasigroup, IsPerm ], +function( Q, p ) + if IsLoop( Q ) then + return LoopIsomorph( Q, p ); + fi; + return QuasigroupIsomorph( Q, p ); +end); + ############################################################################# ## #O IsomorphicCopyByNormalSubloop( L, S ) @@ -594,15 +618,13 @@ end); ## ## If L1, L2 are isotopic loops, returns true, else fail. -# (MATH) First we calculate all principal loop isotopes of L1 of the form -# PrincipalLoopIsotope(L1, f, g), where f, g, are elements of L1. -# Then we filter these up to isomorphism. If L2 is isotopic to L1, then -# L2 is isomorphic to one of these principal isotopes. +# (MATH) We check for isomorphism of L2 against all principal +# isotopes of L1. InstallMethod( IsotopismLoops, "for two loops", [ IsLoop, IsLoop ], function( L1, L2 ) - local istps, fg, f, g, L, phi, pos, alpha, beta, gamma, p; + local f, g, L, phi, alpha, beta, gamma, p; # make all loops canonical to be able to calculate isotopisms if not L1 = Parent( L1 ) then L1 := LoopByCayleyTable( CayleyTable( L1 ) ); fi; @@ -619,20 +641,11 @@ function( L1, L2 ) if not Size(InnerMappingGroup(L1)) = Size(InnerMappingGroup(L2)) then return fail; fi; # now trying to construct an isotopism - istps := []; - fg := []; for f in L1 do for g in L1 do - Add(istps, PrincipalLoopIsotope( L1, f, g )); - Add(fg, [ f, g ] ); - od; od; - for L in LoopsUpToIsomorphism( istps ) do + L := PrincipalLoopIsotope( L1, f, g ); phi := IsomorphismLoops( L, L2 ); if not phi = fail then # must reconstruct the isotopism (alpha, beta, gamma) - # first figure out what f and g were - pos := Position( istps, L ); - f := fg[ pos ][ 1 ]; - g := fg[ pos ][ 2 ]; alpha := RightTranslation( L1, g ); beta := LeftTranslation( L1, f ); # we also applied an isomorphism (1,f*g) inside PrincipalLoopIsotope @@ -649,7 +662,7 @@ function( L1, L2 ) gamma := gamma * phi; return [ alpha, beta, gamma ]; fi; - od; + od; od; return fail; end); diff --git a/gap/memory.gi b/gap/memory.gi index 88280ba..6380f92 100644 --- a/gap/memory.gi +++ b/gap/memory.gi @@ -2,7 +2,7 @@ ## #W memory.gi Memory management [loops] ## -#H @(#)$Id: memory.gi, v 3.3.0 2016/10/20 gap Exp $ +#H @(#)$Id: memory.gi, v 3.4.0 2016/11/4 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -21,9 +21,14 @@ InstallGlobalFunction( LOOPS_FreeMemory, function( ) LOOPS_rcc_transitive_groups := []; LOOPS_rcc_sections := List( [1..Length(LOOPS_rcc_data[1])], i-> [] ); LOOPS_rcc_conjugacy_classes := [ [], [] ]; - # automorphic loops - LOOPS_automorphic_cocycles := []; - LOOPS_automorphic_coordinates := []; + # cc loops + LOOPS_cc_used_factors := []; + LOOPS_cc_cocycles := []; + LOOPS_cc_bases := []; + LOOPS_cc_coordinates := []; + # right Bruck loops + LOOPS_right_bruck_cocycles := []; + LOOPS_right_bruck_coordinates := []; GASMAN("collect"); return GasmanStatistics().full.deadkb; end); diff --git a/gap/quasigroups.gd b/gap/quasigroups.gd index e11cc6f..a6358d2 100644 --- a/gap/quasigroups.gd +++ b/gap/quasigroups.gd @@ -2,7 +2,7 @@ ## #W quasigroups.gd Representing, creating and displaying quasigroups [loops] ## -#H @(#)$Id: quasigroups.gd, v 3.2.0 2016/05/02 gap Exp $ +#H @(#)$Id: quasigroups.gd, v 3.4.0 2017/10/17 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -24,10 +24,10 @@ DeclareRepresentation( "IsLoopElmRep", IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] ); ## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup) -DeclareCategory( "IsLatin", IsObject ); +DeclareCategory( "IsLatinMagma", IsObject ); ## quasigroup -DeclareCategory( "IsQuasigroup", IsMagma and IsLatin ); +DeclareCategory( "IsQuasigroup", IsMagma and IsLatinMagma ); ## loop DeclareCategory( "IsLoop", IsQuasigroup and IsMultiplicativeElementWithInverseCollection); diff --git a/gap/quasigroups.gi b/gap/quasigroups.gi index 5a7627e..653c561 100644 --- a/gap/quasigroups.gi +++ b/gap/quasigroups.gi @@ -789,32 +789,34 @@ end ); InstallMethod( ViewObj, "for loop", [ IsLoop ], function( L ) - if HasIsAssociative( L ) and IsAssociative( L ) then - Print( ""); - elif HasIsExtraLoop( L ) and IsExtraLoop( L ) then - Print( ""); - elif HasIsMoufangLoop( L ) and IsMoufangLoop( L ) then - Print( ""); - elif HasIsCLoop( L ) and IsCLoop( L ) then - Print( ""); - elif HasIsLeftBolLoop( L ) and IsLeftBolLoop( L ) then - Print( ""); - elif HasIsRightBolLoop( L ) and IsRightBolLoop( L ) then - Print( ""); - elif HasIsLCLoop( L ) and IsLCLoop( L ) then - Print( ""); - elif HasIsRCLoop( L ) and IsRCLoop( L ) then - Print( ""); + local PrintMe; + + PrintMe := function( name, L ) + Print( "<", name, " loop of order ", Size( L ), ">"); + + end; + if HasIsAssociative( L ) and IsAssociative( L ) then PrintMe( "associative", L ); + elif HasIsExtraLoop( L ) and IsExtraLoop( L ) then PrintMe( "extra", L ); + elif HasIsMoufangLoop( L ) and IsMoufangLoop( L ) then PrintMe( "Moufang", L ); + elif HasIsCLoop( L ) and IsCLoop( L ) then PrintMe( "C", L ); + elif HasIsLeftBruckLoop( L ) and IsLeftBruckLoop( L ) then PrintMe( "left Bruck", L ); + elif HasIsRightBruckLoop( L ) and IsRightBruckLoop( L ) then PrintMe( "right Bruck", L ); + elif HasIsLeftBolLoop( L ) and IsLeftBolLoop( L ) then PrintMe( "left Bol", L ); + elif HasIsRightBolLoop( L ) and IsRightBolLoop( L ) then PrintMe( "right Bol", L ); + elif HasIsAutomorphicLoop( L ) and IsAutomorphicLoop( L ) then PrintMe( "automorphic", L ); + elif HasIsLeftAutomorphicLoop( L ) and IsLeftAutomorphicLoop( L ) then PrintMe( "left automorphic", L ); + elif HasIsRightAutomorphicLoop( L ) and IsRightAutomorphicLoop( L ) then PrintMe( "right automorphic", L ); + elif HasIsLCLoop( L ) and IsLCLoop( L ) then PrintMe( "LC", L ); + elif HasIsRCLoop( L ) and IsRCLoop( L ) then PrintMe( "RC", L ); elif HasIsLeftAlternative( L ) and IsLeftAlternative( L ) then if HasIsRightAlternative( L ) and IsRightAlternative( L ) then - Print( ""); - else - Print( ""); + PrintMe("alternative", L ); + else + PrintMe("left alternative", L ); fi; - elif HasIsRightAlternative( L ) and IsRightAlternative( L ) then - Print( ""); - elif HasIsFlexible( L ) and IsFlexible( L ) then - Print( ""); + elif HasIsRightAlternative( L ) and IsRightAlternative( L ) then PrintMe( "right alternative", L ); + elif HasIsCommutative( L ) and IsCommutative( L ) then PrintMe( "commutative", L ); + elif HasIsFlexible( L ) and IsFlexible( L ) then PrintMe( "flexible", L); else # MORE ?? Print( "" ); diff --git a/tst/bol.tst b/tst/bol.tst index 06e2ea3..d978bba 100644 --- a/tst/bol.tst +++ b/tst/bol.tst @@ -19,7 +19,7 @@ gap> IsomorphismLoops(B,LeftBolLoop(15,1)); gap> Q := RightBolLoop(15,1);; gap> AssociatedRightBruckLoop( Q ); - + # TESTING EXACT GROUP FACTORIZATIONS diff --git a/tst/core_methods.tst b/tst/core_methods.tst index 1c5d535..0aaebad 100644 --- a/tst/core_methods.tst +++ b/tst/core_methods.tst @@ -2,7 +2,7 @@ ## #W core_methods.tst Testing core methods G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: core_methods.tst, v 3.3.0 2016/10/26 gap Exp $ +#H @(#)$Id: core_methods.tst, v 3.4.0 2017/10/26 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) diff --git a/tst/iso.tst b/tst/iso.tst index 2c19824..aba115b 100644 --- a/tst/iso.tst +++ b/tst/iso.tst @@ -2,7 +2,7 @@ ## #W iso.tst Testing isomorphisms G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: iso.tst, v 3.2.0 2016/06/02 gap Exp $ +#H @(#)$Id: iso.tst, v 3.4.0 2017/10/26 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -34,6 +34,11 @@ Group([ (1,2,3), (1,3,2) ]) gap> Q := DirectProduct( MoufangLoop( 32, 5 ) );; gap> Qp := IsomorphicCopyByPerm( Q, (2,3,4)(17,20) );; +gap> Qq := LoopIsomorph( Q, (2,3,4)(17,20) );; +gap> Qp = Qq; +false +gap> CayleyTable( Qp ) = CayleyTable( Qq ); +true gap> IsomorphismLoops( Q, Qp ); (2,3,4)(18,23)(19,25)(21,27)(22,28)(24,30)(26,31)(29,32) gap> LoopsUpToIsomorphism( [Q,Qp] ); diff --git a/tst/lib.tst b/tst/lib.tst index 507d992..1161891 100644 --- a/tst/lib.tst +++ b/tst/lib.tst @@ -2,7 +2,7 @@ ## #W lib.tst Testing libraries of loops G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: lib.tst, v 3.3.0 2016/10/26 gap Exp $ +#H @(#)$Id: lib.tst, v 3.4.0 2017/10/26 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) @@ -156,19 +156,34 @@ gap> LCCLoop(6,3); LCCLoop(25,119); # CC LOOPS gap> DisplayLibraryInfo("CC"); -The library contains all nonassociative CC loops of order less than 28 +The library contains all CC loops of order +2<=2^k<=64, 3<=3^k<=81, 5<=5^k<=125, 7<=7^k<=343, +all nonassociative CC loops of order less than 28, and all nonassociative CC loops of order p^2 and 2*p for any odd prime p. ------ Extent of the library: - 2 loops of order 8 + 1 loop of order 2 + 1 loop of order 3 + 2 loops of order 4 + 1 loop of order 5 + 1 loop of order 7 + 7 loops of order 8 + 5 loops of order 9 3 loops of order 12 - 28 loops of order 16 + 42 loops of order 16 7 loops of order 18 3 loops of order 20 1 loop of order 21 14 loops of order 24 - 55 loops of order 27 - 3 loops of order p^2 for every odd prime p, + 5 loops of order 25 + 60 loops of order 27 + 437 loops of order 32 + 5 loops of order 49 + 14854 loops of order 64 + 5406 loops of order 81 + 84 loops of order 125 + 122 loops of order 343 + 3 loops of order p^2 for every prime p>7, 1 loop of order 2*p for every odd prime p true @@ -233,10 +248,7 @@ gap> CodeLoop( 64, 80 ); gap> DisplayLibraryInfo("automorphic"); The library contains: - all nonassociative automorphic loops of order less than 16, - - all commutative automorphic loops of order 3, 9, 27, 81, - - all commutative automorphic loops of order 243 that are central - extensions of Z_3 by F, where F is not the elem. ab. 3-group. -Note: Abelian groups are included among the commutative loops. + - all commutative automorphic loops of order 3, 9, 27, 81. ------ Extent of the library: 1 loop of order 3 @@ -249,7 +261,6 @@ Extent of the library: 2 loops of order 15 7 loops of order 27 72 loops of order 81 - 118451 loops of order 243 true gap> AutomorphicLoop(15,2); @@ -258,7 +269,24 @@ gap> AutomorphicLoop(15,2); gap> AutomorphicLoop(27,1); -gap> AutomorphicLoop(243,100); - +gap> AutomorphicLoop(81,10); + + +# RIGHT BRUCK LOOPS + +gap> DisplayLibraryInfo("right Bruck"); +The library contains all right Bruck loops of orders 3, 9, 27 and 81. +------ +Extent of the library: + 1 loop of order 3 + 2 loops of order 9 + 7 loops of order 27 + 72 loops of order 81 +true + +gap> RightBruckLoop(81,3); + + + gap> STOP_TEST( "lib.tst", 10000000 ); diff --git a/tst/testall.g b/tst/testall.g index 30b2de5..2c38ba4 100644 --- a/tst/testall.g +++ b/tst/testall.g @@ -2,15 +2,15 @@ ## #W testall.g Testing LOOPS G. P. Nagy / P. Vojtechovsky ## -#H @(#)$Id: testall.g, v 3.0.0 2015/06/15 gap Exp $ +#H @(#)$Id: testall.g, v 3.4.0 2017/10/26 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) ## dirs := DirectoriesPackageLibrary( "loops", "tst" ); -ReadTest( Filename( dirs, "core_methods.tst" ) ); -ReadTest( Filename( dirs, "nilpot.tst" ) ); -ReadTest( Filename( dirs, "iso.tst" ) ); -ReadTest( Filename( dirs, "lib.tst" ) ); -ReadTest( Filename( dirs, "bol.tst" ) ); +Test( Filename( dirs, "core_methods.tst" ), rec( compareFunction := "uptowhitespace" ) ); +Test( Filename( dirs, "nilpot.tst" ), rec( compareFunction := "uptowhitespace" ) ); +Test( Filename( dirs, "iso.tst" ), rec( compareFunction := "uptowhitespace" ) ); +Test( Filename( dirs, "lib.tst" ), rec( compareFunction := "uptowhitespace" ) ); +Test( Filename( dirs, "bol.tst" ), rec( compareFunction := "uptowhitespace" ) );