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# Modules, single 25
#
# 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("modules25.tst");
# doc/../gap/BasicFunctors.gi:1049-1093
gap> zz := HomalgRingOfIntegers( );
Z
gap> M := HomalgMatrix( "[ 2, 3, 4, 5, 6, 7 ]", 2, 3, zz );;
gap> M := LeftPresentation( M );
<A non-torsion left module presented by 2 relations for 3 generators>
gap> N := HomalgMatrix( "[ 2, 3, 4, 5, 6, 7, 8, 9 ]", 2, 4, zz );;
gap> N := LeftPresentation( N );
<A non-torsion left module presented by 2 relations for 4 generators>
gap> mat := HomalgMatrix( "[ \
> 1, 0, -3, -6, \
> 0, 1, 6, 11, \
> 1, 0, -3, -6 \
> ]", 3, 4, zz );;
gap> phi := HomalgMap( mat, M, N );;
gap> IsMorphism( phi );
true
gap> phi;
<A homomorphism of left modules>
gap> ker := Kernel( phi );
<A cyclic left module presented by yet unknown relations for a cyclic generato\
r>
gap> Display( ker );
Z/< -3 >
gap> ByASmallerPresentation( last );
<A cyclic torsion left module presented by 1 relation for a cyclic generator>
gap> Display( ker );
Z/< 3 >
gap> iota := KernelEmb( phi );
<A monomorphism of left modules>
gap> Display( iota );
[ [ 0, 1, 2 ] ]
the map is currently represented by the above 1 x 3 matrix
gap> DefectOfExactness( iota, phi );
<A zero left module>
gap> ByASmallerPresentation( iota );
<A non-zero monomorphism of left modules>
gap> Display( iota );
[ [ 1, 0 ] ]
the map is currently represented by the above 1 x 2 matrix
gap> PostInverse( iota );
<A non-zero split epimorphism of left modules>
#
gap> STOP_TEST("modules25.tst", 1);
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
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