Quelle modules39.tst Sprache: unbekannt

# Modules, single 39
#
# 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("modules39.tst");

# doc/../examples/TorExt.g:5-93
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> P := Resolution( M );
<A non-zero right acyclic complex containing a single morphism of left modules\
at degrees [ 0 .. 1 ]>
gap> GP := Hom( P );
<A non-zero acyclic cocomplex containing a single morphism of right modules at\
degrees [ 0 .. 1 ]>
gap> FGP := GP * P;
<A non-zero acyclic cocomplex containing a single morphism of left complexes a\
t degrees [ 0 .. 1 ]>
gap> BC := HomalgBicomplex( FGP );
<A non-zero bicocomplex containing left modules at bidegrees [ 0 .. 1 ]x
[ -1 .. 0 ]>
gap> p_degrees := ObjectDegreesOfBicomplex( BC )[1];
[ 0, 1 ]
gap> II_E := SecondSpectralSequenceWithFiltration( BC, p_degrees );
<A stable cohomological 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 cohomological spectral sequence at bidegrees
[ [ 0 .. 1 ], [ -1 .. 0 ] ]
---------
Level 0:

* *
* *
---------
Level 1:

* *
. .
---------
Level 2:

s s
. .

Now the spectral sequence of the bicomplex:

a cohomological spectral sequence at bidegrees
[ [ -1 .. 0 ], [ 0 .. 1 ] ]
---------
Level 0:

* *
* *
---------
Level 1:

* *
* *
---------
Level 2:

s s
. s
gap> filt := FiltrationBySpectralSequence( II_E, 0 );
<A descending filtration with degrees [ -1 .. 0 ] and graded parts:

-1:   <A non-zero torsion left module presented by yet unknown relations for
     4 generators>
   0:   <A rank 1 left module presented by 3 relations for 4 generators>
of
<A left module presented by yet unknown relations for 13 generators>>
gap> ByASmallerPresentation( filt );
<A descending filtration with degrees [ -1 .. 0 ] and graded parts:
  -1:   <A non-zero torsion left module presented by 4 relations
              for 4 generators>
   0:   <A rank 1 left module presented by 2 relations for 3 generators>
of
<A rank 1 left module presented by 6 relations for 7 generators>>
gap> m := IsomorphismOfFiltration( filt );
<A non-zero isomorphism of left modules>

#
gap> STOP_TEST("modules39.tst", 1);

Quelle modules39.tst Sprache: unbekannt

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