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# Modules, single 36
#
# 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("modules36.tst");
# doc/../examples/ExtExt.g:5-82
gap> zz := HomalgRingOfIntegers( );
Z
gap> imat := HomalgMatrix( "[ \
> 262, -33, 75, -40, \
> 682, -86, 196, -104, \
> 1186, -151, 341, -180, \
> -1932, 248, -556, 292, \
> 1018, -127, 293, -156 \
> ]", 5, 4, zz );
<A 5 x 4 matrix over an internal ring>
gap> M := LeftPresentation( imat );
<A left module presented by 5 relations for 4 generators>
gap> N := Hom( zz, M );
<A rank 1 right module on 4 generators satisfying yet unknown relations>
gap> F := InsertObjectInMultiFunctor( Functor_Hom_for_fp_modules, 2, N, "TensorN" );
<The functor TensorN for f.p. modules and their maps over computable rings>
gap> G := LeftDualizingFunctor( zz );;
gap> II_E := GrothendieckSpectralSequence( F, G, M );
<A stable homological spectral sequence with sheets at levels
[ 0 .. 2 ] each consisting of left modules at bidegrees [ -1 .. 0 ]x
[ 0 .. 1 ]>
gap> Display( II_E );
The associated transposed spectral sequence:
a homological spectral sequence at bidegrees
[ [ 0 .. 1 ], [ -1 .. 0 ] ]
---------
Level 0:
* *
* *
---------
Level 1:
* *
. .
---------
Level 2:
s s
. .
Now the spectral sequence of the bicomplex:
a homological spectral sequence at bidegrees
[ [ -1 .. 0 ], [ 0 .. 1 ] ]
---------
Level 0:
* *
* *
---------
Level 1:
* *
. s
---------
Level 2:
s s
. s
gap> filt := FiltrationBySpectralSequence( II_E, 0 );
<An ascending filtration with degrees [ -1 .. 0 ] and graded parts:
0: <A non-torsion left module presented by 3 relations for 4 generators>
-1: <A non-zero left module presented by 21 relations for 8 generators>
of
<A non-zero left module presented by 31 relations for 19 generators>>
gap> ByASmallerPresentation( filt );
<An ascending filtration with degrees [ -1 .. 0 ] and graded parts:
0: <A rank 1 left module presented by 2 relations for 3 generators>
-1: <A non-zero torsion left module presented by 6 relations for 6 generators>
of
<A rank 1 left module presented by 8 relations for 9 generators>>
gap> m := IsomorphismOfFiltration( filt );
<A non-zero isomorphism of left modules>
#
gap> STOP_TEST("modules36.tst", 1);
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
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