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# Modules, single 23
#
# 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("modules23.tst");
# doc/../gap/BasicFunctors.gi:931-977
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> coker := Cokernel( phi );
<A left module presented by 5 relations for 4 generators>
gap> ByASmallerPresentation( coker );
<A rank 1 left module presented by 1 relation for 2 generators>
gap> Display( coker );
Z/< 8 > + Z^(1 x 1)
gap> nu := CokernelEpi( phi );
<An epimorphism of left modules>
gap> Display( nu );
[ [ -5, 0 ],
[ -6, 1 ],
[ 1, -2 ],
[ 0, 1 ] ]
the map is currently represented by the above 4 x 2 matrix
gap> DefectOfExactness( phi, nu );
<A zero left module>
gap> ByASmallerPresentation( nu );
<A non-zero epimorphism of left modules>
gap> Display( nu );
[ [ 2, 0 ],
[ 1, -2 ],
[ 0, 1 ] ]
the map is currently represented by the above 3 x 2 matrix
gap> PreInverse( nu );
false
#
gap> STOP_TEST("modules23.tst", 1);
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
]
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