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LoadPackage( "GradedRingForHomalg", false );
R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0,x1,x2";
S := GradedRing( R );
A := KoszulDualRing( S, "e0,e1,e2" );
LoadPackage( "GradedModules", false );
## the residue class field (i.e. S modulo the maximal homogeneous ideal)
k := HomalgMatrix( Indeterminates( S ), Length( Indeterminates( S ) ), 1, S );
k := LeftPresentationWithDegrees( k );
## the sheaf supported on a point
p := HomalgMatrix( Indeterminates( S ){[ 1 .. Length( Indeterminates( S ) ) - 1 ]}, 1, Length( Indeterminates( S ) ) - 1, S );
p := RightPresentationWithDegrees( p );
## the sheaf supported on a line
l := HomalgMatrix( Indeterminates( S ){[ 1 .. Length( Indeterminates( S ) ) - 2 ]}, 1, Length( Indeterminates( S ) ) - 2, S );
l := RightPresentationWithDegrees( l );
## the twisted line bundle O(a)
O := a -> S^a;
## the cotangent bundle
cotangent := SyzygiesObject( 2, k );
## the canonical bundle
omega := S^(-2-1);
## from [ Decker, Eisenbud ]
M := HomalgMatrix( "[ x0^2, x1^2 ]", 1, 2, S );
M := RightPresentationWithDegrees( M );
m := SubmoduleGeneratedByHomogeneousPart( CastelnuovoMumfordRegularity( M ), M );
N := HomalgMatrix( "[ x0^2, x1^2, x2^2 ]", 1, 3, S );
N := RightPresentationWithDegrees( N );
N2 := SubmoduleGeneratedByHomogeneousPart( 2, M );
tate := TateResolution( cotangent, -5, 5 );
betti := BettiTable( tate );
Assert( 0,
MatrixOfDiagram( betti ) =
[ [ 48, 35, 24, 15, 8, 3, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 3, 8, 15, 24 ] ]
);
Display( betti );
[ Dauer der Verarbeitung: 0.3 Sekunden
(vorverarbeitet)
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