loops/data/automorphic.tbl

#############################################################################
##
#W  automorphic.tbl    Automorphic loops         G. P. Nagy / P. Vojtechovsky
##  
#H  @(#)$Id: automorphic.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)
##

#############################################################################
## 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],
#number of nonassociative loops of given order
[1,1,7,2,3,2,5,2,7,72,118451],
#the loops
[
#order 3 (Z_3)
[
"201"
],
#order 6
[
"2045301534540123520143120"
],
#order 8
[ 
"0325476301674521076545670132476102374532016542310",
"0325476301674521076545670312476302174512036542130",
"0325476301674521076545671023476013274523106543201",
"0325476301675421076455671023476013275423106453201",
"0325476301675421076455760123467103274532106542301",
"0325476301675421076455760132467102374523106543201",
"0325476310674520176545761023467013275432106452301"
],
#order 9 (two abelian groups)
[
"204537861534867678012861207201345534",
"204537861534867678120862017012453345"
]
,
#order 10
[
"234067895340178956401289567012395678987601234598740123659834012765923401876512340",
"234067895340178956401289567012395678987603142598720314659842031765914203876531420",
"234067895340178956401289567012395678987602413598730241659813024765941302876524130"
],
#order 12
[
"23450789AB63450189AB67450129AB67850123AB678901234B6789ABA9870123456BA9850123476BA9450123876BA3450129876B234501A9876123450",
"23450789AB63450189AB67450129AB67850123AB678901234B6789ABA9873450126BA9823450176BA9123450876BA0123459876B501234A9876450123"
],
#order 14 
[
"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9801234567DCBA9601234587DCBA5601234987DCB4560123A987DC3456012BA987D2345601CBA9871234560",
"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9804152637DCBA9304152687DCBA6304152987DCB2630415A987DC5263041BA987D1526304CBA9874152630",
"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9805316427DCBA9205316487DCBA4205316987DCB6420531A987DC1642053BA987D3164205CBA9875316420",
"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9802461357DCBA9502461387DCBA3502461987DCB1350246A987DC6135024BA987D4613502CBA9872461350",
"23456089ABCD73456019ABCD78456012ABCD789560123BCD789A601234CD789AB012345D789ABCDCBA9803625147DCBA9403625187DCBA1403625987DCB5140362A987DC2514036BA987D6251403CBA9873625140"
],
#order 15
[
"234068597BDAEC340189675DEBCA401297856ECDAB012375968CAEBD6897ADECB041328975DCABE430215689EABDC102439756CBDEA324107568BECAD21304BDEC0413258976DECA4302187569ABDE1024395687ECAB3241076895CABD2130469758",
"234067895BCDEA340178956CDEAB401289567DEABC012395678EABCD7968ADBEC012348579ECADB340129685DBECA123405796CADBE401236857BECAD23401DBEC0432156789ECAD3210478956ADBE1043295678BECA4321067895CADB2104389567"
],
#order 27 (commutative only, placeholder)
[
]
, 
#order 81 (commutative only, placeholder)
[
]
,
#order 243 (commutative only, placeholder)
[
]
]
];

LOOPS_automorphic_cocycles := [];
LOOPS_automorphic_bases := [];
LOOPS_automorphic_coordinates := [];