Quelle examplesforhomalg04.tst Sprache: unbekannt

# ExamplesForHomalg, single 4
#
# 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("examplesforhomalg04.tst");

# doc/../examples/TorExt_Grothendieck.g:5-114
gap> Qxyz := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";
Q[x,y,z]
gap> wmat := HomalgMatrix( "[ \
> x*y,  y*z,    z,        0,         0,    \
> x^3*z,x^2*z^2,0,        x*z^2,     -z^2, \
> x^4,  x^3*z,  0,        x^2*z,     -x*z, \
> 0,    0,      x*y,      -y^2,      x^2-1,\
> 0,    0,      x^2*z,    -x*y*z,    y*z,  \
> 0,    0,      x^2*y-x^2,-x*y^2+x*y,y^2-y \
> ]", 6, 5, Qxyz );
<A 6 x 5 matrix over an external ring>
gap> W := LeftPresentation( wmat );
<A left module presented by 6 relations for 5 generators>
gap> F := InsertObjectInMultiFunctor( Functor_TensorProduct_for_fp_modules, 2, W, "TensorW" );
<The functor TensorW for f.p. modules and their maps over computable rings>
gap> G := LeftDualizingFunctor( Qxyz );;
gap> II_E := GrothendieckSpectralSequence( F, G, W );
<A stable cohomological spectral sequence with sheets at levels
[ 0 .. 4 ] each consisting of left modules at bidegrees [ -3 .. 0 ]x
[ 0 .. 3 ]>
gap> Display( II_E );
The associated transposed spectral sequence:

a cohomological spectral sequence at bidegrees
[ [ 0 .. 3 ], [ -3 .. 0 ] ]
---------
Level 0:

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

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

s s s s
. . . .
. . . .
. . . .

Now the spectral sequence of the bicomplex:

a cohomological spectral sequence at bidegrees
[ [ -3 .. 0 ], [ 0 .. 3 ] ]
---------
Level 0:

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

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

* * s s
* * * *
. * * *
. . . *
---------
Level 3:

* s s s
. s s s
. . s *
. . . s
---------
Level 4:

s s s s
. s s s
. . s s
. . . s
gap> filt := FiltrationBySpectralSequence( II_E, 0 );
<A descending filtration with degrees [ -3 .. 0 ] and graded parts:

-3:   <A non-zero cyclic torsion left module presented by yet unknown relations \
for a cyclic generator>
  -2:   <A non-zero left module presented by 17 relations for 6 generators>
  -1:   <A non-zero left module presented by 27 relations for 12 generators>
   0:   <A non-zero left module presented by 13 relations for 10 generators>
of
<A left module presented by yet unknown relations for 49 generators>>
gap> ByASmallerPresentation( filt );
<A descending filtration with degrees [ -3 .. 0 ] and graded parts:

-3:   <A non-zero cyclic torsion left module presented by 3 relations for a cycl\
ic generator>
  -2:   <A non-zero left module presented by 12 relations for 4 generators>
  -1:   <A non-zero left module presented by 21 relations for 8 generators>
   0:   <A non-zero left module presented by 11 relations for 10 generators>
of
<A non-zero left module presented by 27 relations for 14 generators>>
gap> m := IsomorphismOfFiltration( filt );
<A non-zero isomorphism of left modules>

#
gap> STOP_TEST("examplesforhomalg04.tst", 1);

Quelle examplesforhomalg04.tst Sprache: unbekannt

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