|
# Modules, single 37
#
# 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("modules37.tst");
# doc/../examples/Purity.g:5-94
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> filt := PurityFiltration( M );
<The ascending purity filtration with degrees [ -1 .. 0 ] and graded parts:
0: <A free left module of rank 1 on a free generator>
-1: <A non-zero torsion left module presented by 2 relations for 2 generators>
of
<A non-pure rank 1 left module presented by 2 relations for 3 generators>>
gap> M;
<A non-pure rank 1 left module presented by 2 relations for 3 generators>
gap> II_E := SpectralSequence( filt );
<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 .
. .
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
gap> m := IsomorphismOfFiltration( filt );
<A non-zero isomorphism of left modules>
gap> IsIdenticalObj( Range( m ), M );
true
gap> Source( m );
<A non-torsion left module presented by 2 relations for 3 generators (locked)>
gap> Display( last );
[ [ 0, 2, 0 ],
[ 0, 0, 12 ] ]
Cokernel of the map
Z^(1x2) --> Z^(1x3),
currently represented by the above matrix
gap> Display( filt );
Degree 0:
Z^(1 x 1)
----------
Degree -1:
Z/< 2 > + Z/< 12 >
#
gap> STOP_TEST("modules37.tst", 1);
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
|
