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# LinearAlgebraForCAP, single 19
#
# 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("linearalgebraforcap19.tst");
# doc/_Chapter_Examples_and_Tests.xml:829-854
gap> Q := HomalgFieldOfRationals();;
gap> vec := MatrixCategory( Q );;
gap> V := MatrixCategoryObject( vec, 2 );
<A vector space object over Q of dimension 2>
gap> W := MatrixCategoryObject( vec, 3 );
<A vector space object over Q of dimension 3>
gap> alpha := VectorSpaceMorphism( V, [ [ 1, 1, 1 ], [ -1, -1, -1 ] ], W );
<A morphism in Category of matrices over Q>
gap> k := KernelObject( alpha );
<A vector space object over Q of dimension 1>
gap> k_emb := KernelEmbedding( alpha );
<A split monomorphism in Category of matrices over Q>
gap> IsEqualForObjects( Source( k_emb ), k );
true
gap> V := MatrixCategoryObject( vec, 2 );
<A vector space object over Q of dimension 2>
gap> W := MatrixCategoryObject( vec, 3 );
<A vector space object over Q of dimension 3>
gap> beta := VectorSpaceMorphism( V, [ [ 1, 1, 1 ], [ -1, -1, -1 ] ], W );
<A morphism in Category of matrices over Q>
gap> k_emb := KernelEmbedding( beta );
<A split monomorphism in Category of matrices over Q>
gap> IsIdenticalObj( Source( k_emb ), KernelObject( beta ) );
true
#
gap> STOP_TEST("linearalgebraforcap19.tst", 1);
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