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## <#GAPDoc Label="DE-Code">
## <Subsection Label="DE-Code">
## <Heading>DE-Code</Heading>
## <Example><![CDATA[
## gap> R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0,x1,x2";;
## gap> S := GradedRing( R );;
## gap> mat := HomalgMatrix( "[ x0^2, x1^2 ]", 1, 2, S );
## <A 1 x 2 matrix over a graded ring>
## gap> M := RightPresentationWithDegrees( mat, S );
## <A graded cyclic right module on a cyclic generator satisfying 2 relations>
## gap> d := Resolution( M );
## <A right acyclic complex containing
## 2 morphisms of graded right modules at degrees [ 0 .. 2 ]>
## gap> betti := BettiTable( d );
## <A Betti diagram of <A right acyclic complex containing
## 2 morphisms of graded right modules at degrees [ 0 .. 2 ]>>
## gap> Display( betti );
## total: 1 2 1
## --------------
## 0: 1 . .
## 1: . 2 .
## 2: . . 1
## --------------
## degree: 0 1 2
## gap> m := SubmoduleGeneratedByHomogeneousPart( 2, M );
## <A graded torsion right submodule given by 4 generators>
## gap> d2 := Resolution( m );
## <A right acyclic complex containing
## 2 morphisms of graded right modules at degrees [ 0 .. 2 ]>
## gap> betti2 := BettiTable( d2 );
## <A Betti diagram of <A right acyclic complex containing
## 2 morphisms of graded right modules at degrees [ 0 .. 2 ]>>
## gap> Display( betti2 );
## 2: 4 8 4
## --------------
## degree: 0 1 2
## ]]></Example>
## </Subsection>
## <#/GAPDoc>
LoadPackage( "GradedModules", false );
R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0,x1,x2";
S := GradedRing( R );
mat := HomalgMatrix( "[ x0^2, x1^2 ]", 1, 2, S );
M := RightPresentationWithDegrees( mat, S );
d := Resolution( M );
betti := BettiTable( d );
Display( betti );
m := SubmoduleGeneratedByHomogeneousPart( 2, M );
d2 := Resolution( m );
betti2 := BettiTable( d2 );
Display( betti2 );
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