f4976545a1
* Add GAP console session mode This is also appropriate for GAP .tst files. Add `analyse_text` methods for `ScilabLexer` and `GAPConsoleLexer` to distinguish Scilab and GAP .tst files * Use explicit name for 'keepends' argument to splitlines
58 lines
1.7 KiB
Scilab
58 lines
1.7 KiB
Scilab
#@local F,M,T
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gap> START_TEST( "magma.tst" );
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#
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gap> M:= MagmaByMultiplicationTable( [ [ 1, 1 ], [ 1, 1 ] ] );;
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gap> IsGeneratorsOfMagmaWithInverses( Elements( M ) );
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false
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# IsAssociative and IsCommutative
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gap> T := [
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> [ 2, 4, 3, 4, 5 ],
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> [ 3, 3, 2, 3, 3 ],
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> [ 5, 5, 5, 4, 4 ],
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> [ 5, 1, 4, 1, 1 ],
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> [ 5, 3, 3, 4, 5 ]
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> ];;
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gap> M := MagmaByMultiplicationTable(T);
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<magma with 5 generators>
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gap> IsAssociative(M) or IsCommutative(M);
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false
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gap> Filtered(Combinations(Elements(M)), x -> Size(x) > 0 and IsAssociative(x));
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[ [ m5 ] ]
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gap> Filtered(Combinations(Elements(M)), x -> Size(x) > 0 and IsCommutative(x));
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[ [ m1 ], [ m1, m5 ], [ m2 ], [ m2, m5 ], [ m3 ], [ m3, m4 ], [ m4 ], [ m5 ] ]
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gap> T := [
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> [ 1, 4, 3, 3, 2 ],
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> [ 4, 2, 4, 4, 2 ],
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> [ 3, 4, 3, 4, 1 ],
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> [ 1, 4, 5, 4, 3 ],
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> [ 2, 2, 3, 5, 3 ]
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> ];;
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gap> M := MagmaByMultiplicationTable(T);
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<magma with 5 generators>
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gap> IsAssociative(M) or IsCommutative(M);
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false
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gap> Filtered(Combinations(Elements(M)), x -> Size(x) > 0 and IsAssociative(x));
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[ [ m1 ], [ m1, m3 ], [ m2 ], [ m2, m4 ], [ m3 ], [ m4 ] ]
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gap> AsSemigroup([Elements(M)[1], Elements(M)[2]]);
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fail
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gap> AsSemigroup([Elements(M)[1], Elements(M)[3]]);
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<semigroup of size 2, with 2 generators>
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gap> Filtered(Combinations(Elements(M)), x -> Size(x) > 0 and IsCommutative(x));
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[ [ m1 ], [ m1, m2 ], [ m1, m2, m3 ], [ m1, m2, m5 ], [ m1, m3 ], [ m1, m5 ],
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[ m2 ], [ m2, m3 ], [ m2, m4 ], [ m2, m5 ], [ m3 ], [ m4 ], [ m5 ] ]
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#
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gap> F := Elements( GL(2,2) );;
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gap> IsAssociative( F );
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true
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gap> IsCommutative( F );
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false
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gap> Number( Combinations( F, 3 ), IsCommutative );
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1
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gap> AsSemigroup( F );
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<semigroup of size 6, with 2 generators>
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#
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gap> STOP_TEST( "magma.tst" );
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