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# Modules, single 13
#
# 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("modules13.tst");
# doc/../gap/HomalgModule.gi:1582-1613
gap> zz := HomalgRingOfIntegers( );;
gap> M := HomalgMatrix( "[ \
> 2, 3, 4, \
> 5, 6, 7 \
> ]", 2, 3, zz );
<A 2 x 3 matrix over an internal ring>
gap> M := LeftPresentation( M );
<A non-torsion left module presented by 2 relations for 3 generators>
gap> Display( M );
[ [ 2, 3, 4 ],
[ 5, 6, 7 ] ]
Cokernel of the map
Z^(1x2) --> Z^(1x3),
currently represented by the above matrix
gap> ByASmallerPresentation( M );
<A rank 1 left module presented by 1 relation for 2 generators>
gap> Display( last );
Z/< 3 > + Z^(1 x 1)
gap> SetsOfGenerators( M );
<A set containing 2 sets of generators of a homalg module>
gap> SetsOfRelations( M );
<A set containing 2 sets of relations of a homalg module>
gap> M;
<A rank 1 left module presented by 1 relation for 2 generators>
gap> SetPositionOfTheDefaultPresentation( M, 1 );
gap> M;
<A rank 1 left module presented by 2 relations for 3 generators>
#
gap> STOP_TEST("modules13.tst", 1);
[ Dauer der Verarbeitung: 0.20 Sekunden
(vorverarbeitet)
]
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