265 lines
6.4 KiB
Scilab
265 lines
6.4 KiB
Scilab
#############################################################################
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##
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#W lib.tst Testing libraries of loops G. P. Nagy / P. Vojtechovsky
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##
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#H @(#)$Id: lib.tst, v 3.3.0 2016/10/26 gap Exp $
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##
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#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
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#Y P. Vojtechovsky (University of Denver, USA)
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##
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gap> START_TEST("LOOPS, lib: testing all libraries except Moufang");
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# INTERESTING LOOPS
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gap> DisplayLibraryInfo( "interesting" );
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The library contains a few interesting loops.
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------
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Extent of the library:
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1 loop of order 5
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1 loop of order 6
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1 loop of order 16
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1 loop of order 32
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1 loop of order 96
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true
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# number of orders implemented in the library
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gap> t := Length( LOOPS_interesting_data[ 1 ] );
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5
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# testing loops
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gap> for i in [1..t] do
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> n := LOOPS_interesting_data[ 1 ][ i ];
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> for m in [ 1..LOOPS_interesting_data[ 2 ][ i ] ] do
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> InterestingLoop( n, m );
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> od;
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> od;
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# LEFT/RIGHT BOL LOOPS
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gap> DisplayLibraryInfo( "left Bol" );
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The library contains all nonassociative left Bol loops of order less than 17
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and all nonassociative left Bol loops of order p*q, where p>q>2 are primes.
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------
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Extent of the library:
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6 loops of order 8
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3 loops of order 12
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2038 loops of order 16
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(p-q)/2 loops of order p*q for primes p>q>2 such that q divides p-1
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(p-q+2)/2 loops of order p*q for primes p>q>2 such that q divides p+1
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true
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# number of orders implemented in the library
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gap> t := Length( LOOPS_left_bol_data[ 1 ] );
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3
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# testing loops
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gap> for i in [1..t] do
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> n := LOOPS_left_bol_data[ 1 ][ i ];
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> for m in [ 1..LOOPS_left_bol_data[ 2 ][ i ] ] do
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> LeftBolLoop( n, m );
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> od;
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> od;
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# testing right Bol loop
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gap> RightBolLoop( 8, 1 );
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<right Bol loop 8/1>
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# STEINER LOOPS
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gap> DisplayLibraryInfo( "Steiner" );
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The library contains all nonassociative Steiner loops
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of order less or equal to 16. It also contains the
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associative Steiner loops of order 4 and 8.
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------
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Extent of the library:
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1 loop of order 4
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1 loop of order 8
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1 loop of order 10
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2 loops of order 14
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80 loops of order 16
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true
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# number of orders implemented in the library
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gap> t := Length( LOOPS_steiner_data[ 1 ] );
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5
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# testing loops
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gap> for i in [1..t] do
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> n := LOOPS_steiner_data[ 1 ][ i ];
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> for m in [ 1..LOOPS_steiner_data[ 2 ][ i ] ] do
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> SteinerLoop( n, m );
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> od;
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> od;
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# NILPOTENT LOOPS
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gap> DisplayLibraryInfo( "nilpotent" );
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The library contains all nonassociative nilpotent loops
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of order less than 12.
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------
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Extent of the library:
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2 loops of order 6
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134 loops of order 8
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8 loops of order 9
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1043 loops of order 10
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true
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gap> NilpotentLoop( 10, 1000 );
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<nilpotent loop 10/1000>
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# PAIGE LOOPS
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gap> DisplayLibraryInfo( "Paige" );
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The library contains the smallest nonassociative finite
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simple Moufang loop.
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------
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Extent of the library:
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1 loop of order 120
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true
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gap> PaigeLoop( 2 );
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<Paige loop 120/1>
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# RCC LOOPS
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gap> DisplayLibraryInfo("RCC");
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The library contains all nonassociative RCC loops of order less than 28.
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------
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Extent of the library:
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3 loops of order 6
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19 loops of order 8
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5 loops of order 9
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16 loops of order 10
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155 loops of order 12
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97 loops of order 14
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17 loops of order 15
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6317 loops of order 16
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1901 loops of order 18
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8248 loops of order 20
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119 loops of order 21
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10487 loops of order 22
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471995 loops of order 24
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119 loops of order 25
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151971 loops of order 26
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152701 loops of order 27
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true
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gap> RCCLoop(6,1); RCCLoop(16,6317); RightConjugacyClosedLoop(27,152701);
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<RCC loop 6/1>
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<RCC loop 16/6317>
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<RCC loop 27/152701>
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gap> LCCLoop(6,3); LCCLoop(25,119);
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<LCC loop 6/3>
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<LCC loop 25/119>
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# CC LOOPS
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gap> DisplayLibraryInfo("CC");
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The library contains all nonassociative CC loops of order less than 28
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and all nonassociative CC loops of order p^2 and 2*p for any odd prime p.
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------
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Extent of the library:
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2 loops of order 8
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3 loops of order 12
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28 loops of order 16
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7 loops of order 18
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3 loops of order 20
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1 loop of order 21
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14 loops of order 24
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55 loops of order 27
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3 loops of order p^2 for every odd prime p,
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1 loop of order 2*p for every odd prime p
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true
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gap> CCLoop(25,1); CCLoop(49,2); CCLoop(121,3); CCLoop(14,1);
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<CC loop 25/1>
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<CC loop 49/2>
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<CC loop 121/3>
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<CC loop 14/1>
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gap> CCLoop(16,28); ConjugacyClosedLoop(27,55);
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<CC loop 16/28>
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<CC loop 27/55>
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# SMALL LOOPS
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gap> DisplayLibraryInfo("small");
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The library contains all nonassociative loops of order less than 7.
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------
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Extent of the library:
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5 loops of order 5
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107 loops of order 6
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true
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gap> SmallLoop( 5, 3 ); SmallLoop( 6, 12 );
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<small loop 5/3>
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<small loop 6/12>
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# ITP SMALL LOOPS
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gap> DisplayLibraryInfo("itp small");
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The library contains all nonassociative loops of order less than 7 up to isoto\
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pism.
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------
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Extent of the library:
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1 loop of order 5
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20 loops of order 6
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true
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gap> ItpSmallLoop( 5, 1 ); ItpSmallLoop( 6, 14 );
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<small loop 5/1>
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<small loop 6/42>
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# CODE LOOPS
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gap> DisplayLibraryInfo("code");
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The library contains all nonassociative even code loops
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of order less than 65.
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------
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Extent of the library:
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5 loops of order 16
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16 loops of order 32
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80 loops of order 64
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true
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gap> CodeLoop( 16, 3 );
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<Moufang loop 16/3>
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gap> CodeLoop( 64, 80 );
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<Moufang loop 64/4247>
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# AUTOMORPHIC LOOPS
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gap> DisplayLibraryInfo("automorphic");
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The library contains:
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- all nonassociative automorphic loops of order less than 16,
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- all commutative automorphic loops of order 3, 9, 27, 81,
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- all commutative automorphic loops of order 243 that are central
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extensions of Z_3 by F, where F is not the elem. ab. 3-group.
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Note: Abelian groups are included among the commutative loops.
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------
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Extent of the library:
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1 loop of order 3
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1 loop of order 6
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7 loops of order 8
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2 loops of order 9
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3 loops of order 10
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2 loops of order 12
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5 loops of order 14
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2 loops of order 15
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7 loops of order 27
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72 loops of order 81
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118451 loops of order 243
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true
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gap> AutomorphicLoop(15,2);
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<automorphic loop 15/2>
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gap> AutomorphicLoop(27,1);
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<automorphic loop 27/1>
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gap> AutomorphicLoop(243,100);
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<automorphic loop 243/100>
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gap> STOP_TEST( "lib.tst", 10000000 );
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