# smallantimagmas, chapter 1
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("smallantimagmas01.tst");
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:17-24
gap> IsAntiassociative(OneSmallGroup(16));
false
gap> IsAntiassociative(OneSmallAntimagma(2));
true
gap> IsAntiassociative(OneSmallAntimagma(3));
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:59-62
gap> List(AllSmallAntimagmas(3), M -> IsLeftDistributive(M) );
[ true, false, false, false, false, false, false, false, false, true ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:77-80
gap> List(AllSmallAntimagmas(3), M -> IsRightDistributive(M) );
[ false, false, false, false, true, false, false, false, true, false ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:95-107
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> Display( MultiplicationTable(M) );
[ [ 2, 1 ],
[ 2, 1 ] ]
gap> IsRightCancellative(M);
false
gap> IsLeftCancellative(M);
true
gap> List(AllSmallAntimagmas(2), M -> IsLeftCancellative(M));
[ true, false ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:122-125
gap> List(AllSmallAntimagmas(2), M -> IsRightCancellative(M));
[ false, true ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:140-143
gap> List(AllSmallAntimagmas(2), M -> IsCancellative(M));
[ false, false ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:158-164
gap> Display( MultiplicationTable( SmallAntimagma(2, 2) ) );
[ [ 2, 2 ],
[ 1, 1 ] ]
gap> IsLeftFPFInducted( SmallAntimagma(2, 2) );
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:179-185
gap> Display( MultiplicationTable( SmallAntimagma(2, 1) ) );
[ [ 2, 1 ],
[ 2, 1 ] ]
gap> IsRightFPFInducted( SmallAntimagma(2, 1) );
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:200-209
gap> M := SmallAntimagma(2, 2);
<magma with 2 generators>
gap> IsLeftFPFInducted(M);
true
gap> IsRightFPFInducted(M);
false
gap> IsRightDerangementInducted(M);
false
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:224-233
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> IsLeftFPFInducted(M);
false
gap> IsRightFPFInducted(M);
true
gap> IsRightDerangementInducted(M);
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:248-249
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:264-265
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:284-295
gap> OneSmallAntimagma(2);
<magma with 2 generators>
gap> AssociativityIndex(OneSmallAntimagma(2));
0
gap> OneSmallGroup(4);
<pc group of size 4 with 2 generators>
gap> AssociativityIndex(OneSmallGroup(4));
64
gap> AssociativityIndex(OneSmallGroup(4)) = 4 ^ 3;
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:308-316
gap> List(AllSmallAntimagmas(3), M -> DiagonalOfMultiplicationTable((M)));
[ [ 2, 1, 1 ], [ 2, 1, 1 ],
[ 2, 3, 2 ], [ 2, 1, 1 ],
[ 2, 1, 1 ], [ 2, 1, 2 ],
[ 2, 3, 2 ], [ 2, 1, 2 ],
[ 2, 3, 1 ], [ 2, 3, 1 ]
]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:329-331
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:344-345
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:358-365
gap> List(AllSmallAntimagmas(2), M -> List(M, m -> m * m) );
[ [ m2, m1 ], [ m2, m1 ] ]
gap> List(AllSmallAntimagmas(2), M -> SquaresIndex(M ));
[ 2, 2 ]
gap> List(AllSmallAntimagmas(3), M -> SquaresIndex(M ));
[ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:378-385
gap> IsAntiassociative(OneSmallGroup(16));
false
gap> IsAntiassociative(OneSmallAntimagma(2));
true
gap> IsAntiassociative(OneSmallAntimagma(3));
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:436-441
gap> AllSmallAntimagmas(2);
[ <magma with 2 generators>, <magma with 2 generators> ]
gap> List(AllSmallAntimagmas(2), M -> AllSubmagmas(M));
[ [ <magma with 1 generator> ], [ <magma with 1 generator> ] ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:462-475
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> N := SmallAntimagma(2, 2);
<magma with 2 generators>
gap> T := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
<magma with 2 generators>
gap> IsMagmaIsomorphic(M, M);
true
gap> IsMagmaIsomorphic(M, T);
true
gap> IsMagmaIsomorphic(M, N);
false
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:488-501
gap> N := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> N := SmallAntimagma(2, 2);
<magma with 2 generators>
gap> IsMagmaAntiisomorphic(M, M);
false
gap> IsMagmaAntiisomorphic(M, N);
true
gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
true
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:514-529
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> IsMagmaAntiisomorphic(M, TransposedMagma(M));
true
gap> IsMagmaIsomorphic(M, TransposedMagma(TransposedMagma(M)));
true
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> Display(MultiplicationTable(M));
[ [ 2, 1 ],
[ 2, 1 ] ]
gap> Display(MultiplicationTable(TransposedMagma(M)));
[ [ 2, 2 ],
[ 1, 1 ] ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:558-568
gap> AllSmallAntimagmas(2);
[ <magma with 2 generators>, <magma with 2 generators> ]
gap> AllSmallAntimagmas(3);
[
<magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
<magma with 3 generators>, <magma with 3 generators>, <magma with 3 generators>,
<magma with 3 generators>, <magma with 3 generators>,
<magma with 3 generators>, <magma with 3 generators>
]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:581-588
gap> NrSmallAntimagmas(2);
2
gap> NrSmallAntimagmas(3);
10
gap> NrSmallAntimagmas(4);
17780
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:601-606
gap> SmallAntimagma(2, 1);
<magma with 2 generators>
gap> SmallAntimagma(4, 5);
<magma with 4 generators>
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:619-625
gap> OneSmallAntimagma(2);
<magma with 2 generators>
gap> OneSmallAntimagma(3);
<magma with 3 generators>
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:638-641
gap> ReallyAllSmallAntimagmas(2);
[ <magma with 2 generators>, <magma with 2 generators> ]
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:654-657
gap> ReallyNrSmallAntimagmas(3);
52
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:676-683
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> N := MagmaByMultiplicationTable([ [2, 1], [2, 1] ]);
<magma with 2 generators>
gap> MagmaIsomorphism(M, N);
<general mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
# doc/_Chapter_smallantimagmas_automatic_generated_documentation.xml:696-703
gap> M := SmallAntimagma(2, 1);
<magma with 2 generators>
gap> N := SmallAntimagma(2, 2);
<magma with 2 generators>
gap> MagmaAntiisomorphism(M, N);
<mapping: Domain([ m1, m2 ]) -> Domain([ m1, m2 ]) >
#
gap> STOP_TEST("smallantimagmas01.tst", 1);
