Quelle linearalgebraforcap03.tst Sprache: unbekannt

# LinearAlgebraForCAP, single 3
#
# 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("linearalgebraforcap03.tst");

# doc/_Chapter_Examples_and_Tests.xml:43-79
gap> alphap := homalg_matrix/vec;;
gap> IsCongruentForMorphisms( alpha, alphap );
true
gap> homalg_matrix := HomalgMatrix( [ [ 1, 1, 0, 0 ],
> [ 0, 1, 0, -1 ],
> [ -1, 0, 2, 1 ] ], 3, 4, Q );;
gap> beta := VectorSpaceMorphism( a, homalg_matrix, b );
<A morphism in Category of matrices over Q>
gap> CokernelObject( alpha );
<A vector space object over Q of dimension 1>
gap> c := CokernelProjection( alpha );;
gap> Display( EntriesOfHomalgMatrixAsListList( UnderlyingMatrix( c ) ) );
[ [ 0 ], [ 1 ], [ -1/2 ], [ 1 ] ]
gap> gamma := UniversalMorphismIntoDirectSum( [ c, c ] );;
gap> Display( EntriesOfHomalgMatrixAsListList( UnderlyingMatrix( gamma ) ) );
[ [ 0, 0 ], [ 1, 1 ], [ -1/2, -1/2 ], [ 1, 1 ] ]
gap> colift := CokernelColift( alpha, gamma );;
gap> IsEqualForMorphisms( PreCompose( c, colift ), gamma );
true
gap> FiberProduct( alpha, beta );
<A vector space object over Q of dimension 2>
gap> F := FiberProduct( alpha, beta );
<A vector space object over Q of dimension 2>
gap> p1 := ProjectionInFactorOfFiberProduct( [ alpha, beta ], 1 );
<A morphism in Category of matrices over Q>
gap> Display( EntriesOfHomalgMatrixAsListList( UnderlyingMatrix( PreCompose( p1, alpha ) ) ) );
[ [ 0, 1, 0, -1 ], [ -1, 0, 2, 1 ] ]
gap> Pushout( alpha, beta );
<A vector space object over Q of dimension 5>
gap> i1 := InjectionOfCofactorOfPushout( [ alpha, beta ], 1 );
<A morphism in Category of matrices over Q>
gap> i2 := InjectionOfCofactorOfPushout( [ alpha, beta ], 2 );
<A morphism in Category of matrices over Q>
gap> u := UniversalMorphismFromDirectSum( [ b, b ], [ i1, i2 ] );
<A morphism in Category of matrices over Q>

#
gap> STOP_TEST("linearalgebraforcap03.tst", 1);

Quelle linearalgebraforcap03.tst Sprache: unbekannt

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