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# Modules, single 31
#
# 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("modules31.tst");
# doc/../gap/BasicFunctors.gi:1473-1556
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> CE := Resolution( GP );
<An acyclic cocomplex containing a single morphism of right complexes at degre\
es [ 0 .. 1 ]>
gap> FCE := Hom( CE, L );
<A non-zero acyclic complex containing a single morphism of left cocomplexes a\
t degrees [ 0 .. 1 ]>
gap> BC := HomalgBicomplex( FCE );
<A non-zero bicomplex containing left modules at bidegrees [ 0 .. 1 ]x
[ -1 .. 0 ]>
gap> II_E := SecondSpectralSequenceWithFiltration( BC );
<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 );
<An ascending filtration with degrees [ -1 .. 0 ] and graded parts:
0: <A rank 1 left module presented by 1 relation for 2 generators>
-1: <A non-zero left module presented by 2 relations for 2 generators>
of
<A non-zero left module presented by 4 relations for 4 generators>>
gap> ByASmallerPresentation( filt );
<An ascending filtration with degrees [ -1 .. 0 ] and graded parts:
0: <A rank 1 left module presented by 1 relation for 2 generators>
-1: <A non-zero torsion left module presented by 2 relations
for 2 generators>
of
<A rank 1 left module presented by 3 relations for 4 generators>>
gap> Display( filt );
Degree 0:
Z/< 3 > + Z^(1 x 1)
----------
Degree -1:
Z/< 3 > + Z/< 3 >
gap> Display( ML );
Z/< 3 > + Z/< 3 > + Z/< 3 > + Z^(1 x 1)
#
gap> STOP_TEST("modules31.tst", 1);
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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