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# Modules, single 9
#
# 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("modules09.tst");
# doc/../gap/BasicFunctors.gi:1636-1698
gap> zz := HomalgRingOfIntegers( );
Z
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> Z4 := zz / 4;
Z/( 4 )
gap> Display( Z4 );
<A residue class ring>
gap> M4 := Z4 * M;
<A non-torsion left module presented by 2 relations for 3 generators>
gap> Display( M4 );
[ [ 2, 3, 4 ],
[ 5, 6, 7 ] ]
modulo [ 4 ]
Cokernel of the map
Z/( 4 )^(1x2) --> Z/( 4 )^(1x3),
currently represented by the above matrix
gap> d := Resolution( 2, M4 );
<A right acyclic complex containing 2 morphisms of left modules at degrees
[ 0 .. 2 ]>
gap> dd := Hom( d, Z4 );
<A cocomplex containing 2 morphisms of right modules at degrees [ 0 .. 2 ]>
gap> DD := Resolution( 2, dd );
<A cocomplex containing 2 morphisms of right complexes at degrees [ 0 .. 2 ]>
gap> D := Hom( DD, Z4 );
<A complex containing 2 morphisms of left cocomplexes at degrees [ 0 .. 2 ]>
gap> C := zz * D;
<A "complex" containing 2 morphisms of left cocomplexes at degrees [ 0 .. 2 ]>
gap> LowestDegreeObject( C );
<A "cocomplex" containing 2 morphisms of left modules at degrees [ 0 .. 2 ]>
gap> Display( last );
-------------------------
at cohomology degree: 2
0
------------^------------
(an empty 1 x 0 matrix)
the map is currently represented by the above 1 x 0 matrix
-------------------------
at cohomology degree: 1
Z/< 4 >
------------^------------
[ [ 0 ],
[ 1 ],
[ 2 ],
[ 1 ] ]
the map is currently represented by the above 4 x 1 matrix
-------------------------
at cohomology degree: 0
Z/< 4 > + Z/< 4 > + Z/< 4 > + Z/< 4 >
-------------------------
#
gap> STOP_TEST("modules09.tst", 1);
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
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