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Quelle modules29.tst
Sprache: unbekannt
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# Modules, single 29
#
# 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("modules29.tst");
# doc/../gap/BasicFunctors.gi:1306-1386
gap> dM := Resolution( M );
<A non-zero right acyclic complex containing a single morphism of left modules\
at degrees [ 0 .. 1 ]>
gap> hMM := Hom( dM, dM );
<A non-zero acyclic cocomplex containing a single morphism of right complexes \
at degrees [ 0 .. 1 ]>
gap> BMM := HomalgBicomplex( hMM );
<A non-zero bicocomplex containing right modules at bidegrees [ 0 .. 1 ]x
[ -1 .. 0 ]>
gap> II_E := SecondSpectralSequenceWithFiltration( BMM );
<A stable cohomological spectral sequence with sheets at levels
[ 0 .. 2 ] each consisting of right 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 );
<A descending filtration with degrees [ -1 .. 0 ] and graded parts:
-1: <A non-zero cyclic torsion right module on a cyclic generator satisfying
yet unknown relations>
0: <A rank 1 right module on 3 generators satisfying 2 relations>
of
<A right module on 4 generators satisfying yet unknown relations>>
gap> ByASmallerPresentation( filt );
<A descending filtration with degrees [ -1 .. 0 ] and graded parts:
-1: <A non-zero cyclic torsion right module on a cyclic generator satisfying 1\
relation>
0: <A rank 1 right module on 2 generators satisfying 1 relation>
of
<A rank 1 right module on 3 generators satisfying 2 relations>>
gap> Display( filt );
Degree -1:
Z/< 3 >
----------
Degree 0:
Z/< 3 > + Z^(1 x 1)
gap> Display( homMM );
Z/< 3 > + Z/< 3 > + Z^(1 x 1)
#
gap> STOP_TEST("modules29.tst", 1);
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
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2026-03-28
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