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# GradedModules, single 21
#
# 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("gradedmodules21.tst");
# doc/../examples/Schenck-3.2.g:5-44
gap> Qxyz := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";;
gap> mmat := HomalgMatrix( "[ x, x^3 + y^3 + z^3 ]", 1, 2, Qxyz );
<A 1 x 2 matrix over an external ring>
gap> S := GradedRing( Qxyz );;
gap> M := RightPresentationWithDegrees( mmat, S );
<A graded cyclic right module on a cyclic generator satisfying 2 relations>
gap> Mr := Resolution( M );
<A right acyclic complex containing
2 morphisms of graded right modules at degrees [ 0 .. 2 ]>
gap> bettiM := BettiTable( Mr );
<A Betti diagram of <A right acyclic complex containing
2 morphisms of graded right modules at degrees [ 0 .. 2 ]>>
gap> Display( bettiM );
total: 1 2 1
--------------
0: 1 1 .
1: . . .
2: . 1 1
--------------
degree: 0 1 2
gap> R := GradedRing( CoefficientsRing( S ) * "x,y,z,w" );;
gap> nmat := HomalgMatrix( "[ z^2 - y*w, y*z - x*w, y^2 - x*z ]", 1, 3, R );
<A 1 x 3 matrix over a graded ring>
gap> N := RightPresentationWithDegrees( nmat );
<A graded cyclic right module on a cyclic generator satisfying 3 relations>
gap> Nr := Resolution( N );
<A right acyclic complex containing
2 morphisms of graded right modules at degrees [ 0 .. 2 ]>
gap> bettiN := BettiTable( Nr );
<A Betti diagram of <A right acyclic complex containing
2 morphisms of graded right modules at degrees [ 0 .. 2 ]>>
gap> Display( bettiN );
total: 1 3 2
--------------
0: 1 . .
1: . 3 2
--------------
degree: 0 1 2
#
gap> STOP_TEST("gradedmodules21.tst", 1);
[ Dauer der Verarbeitung: 0.15 Sekunden
(vorverarbeitet)
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