|
# GradedModules, single 19
#
# 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("gradedmodules19.tst");
# doc/../examples/DE-2.2.g:4-44
gap> R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0,x1,x2";;
gap> S := GradedRing( R );;
gap> mat := HomalgMatrix( "[ x0^2, x1^2, x2^2 ]", 1, 3, S );
<A 1 x 3 matrix over a graded ring>
gap> M := RightPresentationWithDegrees( mat, S );
<A graded cyclic right module on a cyclic generator satisfying 3 relations>
gap> M := RightPresentationWithDegrees( mat );
<A graded cyclic right module on a cyclic generator satisfying 3 relations>
gap> d := Resolution( M );
<A right acyclic complex containing
3 morphisms of graded right modules at degrees [ 0 .. 3 ]>
gap> betti := BettiTable( d );
<A Betti diagram of <A right acyclic complex containing
3 morphisms of graded right modules at degrees [ 0 .. 3 ]>>
gap> Display( betti );
total: 1 3 3 1
----------------
0: 1 . . .
1: . 3 . .
2: . . 3 .
3: . . . 1
----------------
degree: 0 1 2 3
gap> ## we are still below the Castelnuovo-Mumford regularity, which is 3:
gap> M2 := SubmoduleGeneratedByHomogeneousPart( 2, M );
<A graded torsion right submodule given by 3 generators>
gap> d2 := Resolution( M2 );
<A right acyclic complex containing
3 morphisms of graded right modules at degrees [ 0 .. 3 ]>
gap> betti2 := BettiTable( d2 );
<A Betti diagram of <A right acyclic complex containing
3 morphisms of graded right modules at degrees [ 0 .. 3 ]>>
gap> Display( betti2 );
total: 3 8 6 1
----------------
2: 3 8 6 .
3: . . . 1
----------------
degree: 0 1 2 3
#
gap> STOP_TEST("gradedmodules19.tst", 1);
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
]
|
