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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346LoadPackage( "GradedRingForHomalg" );
##
R := HomalgFieldOfRationalsInDefaultCAS( ) * "a,b,c";
param := Length( Indeterminates( R ) );
##
RR := R * "x0,x1,x2";
S := GradedRing( RR );
n := Length( Indeterminates( S ) ) - param - 1;
weights := Concatenation(
ListWithIdenticalEntries( param, 0 ),
ListWithIdenticalEntries( n + 1, 1 )
);
SetWeightsOfIndeterminates( S, weights );
##
A := KoszulDualRing( S, "e0,e1,e2" );
A!.ByASmallerPresentation := true;
LoadPackage( "GradedModules" );
##
m := HomalgMatrix( "[\
-c,0,-b,0,-c,0,0,0,0,0,0,0,a,0,0,0,0,0,0,0,0,-x2,0,-x1,0,-x2,0,0,0,0,0,0,0,x0,0,0,0,0,0,0,0,0, \
b,-c,0,0,0,0,-c,0,0,0,0,0,0,0,0,a,0,0,0,0,0,x1,-x2,0,0,0,0,-x2,0,0,0,0,0,0,0,0,x0,0,0,0,0,0, \
0,b,0,0,0,0,0,0,-c,0,0,0,0,0,0,0,0,0,a,0,0,0,x1,0,0,0,0,0,0,-x2,0,0,0,0,0,0,0,0,0,x0,0,0, \
0,0,a,-c,0,0,0,0,0,-b,0,-c,0,0,0,0,0,0,0,0,0,0,0,x0,-x2,0,0,0,0,0,-x1,0,-x2,0,0,0,0,0,0,0,0,0, \
0,0,0,b,a,-c,0,0,0,0,0,0,0,0,-c,0,0,0,0,0,0,0,0,0,x1,x0,-x2,0,0,0,0,0,0,0,0,-x2,0,0,0,0,0,0, \
0,0,0,0,0,b,a,-c,0,0,0,0,0,0,0,0,0,-c,0,0,0,0,0,0,0,0,x1,x0,-x2,0,0,0,0,0,0,0,0,0,-x2,0,0,0, \
0,0,0,0,0,0,0,b,a,0,0,0,0,0,0,0,0,0,0,0,-c,0,0,0,0,0,0,0,x1,x0,0,0,0,0,0,0,0,0,0,0,0,-x2, \
0,0,0,0,0,0,0,0,0,a,-c,0,b,0,0,c,0,0,0,0,0,0,0,0,0,0,0,0,0,0,x0,-x2,0,x1,0,0,x2,0,0,0,0,0, \
0,0,0,0,0,0,0,0,0,0,b,a,0,-c,0,0,0,0,c,0,0,0,0,0,0,0,0,0,0,0,0,x1,x0,0,-x2,0,0,0,0,x2,0,0, \
0,0,0,0,0,0,0,0,0,0,0,0,c,b,a,0,-c,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,x2,x1,x0,0,-x2,0,0,0,0, \
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,c,b,a,0,-c,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,x2,x1,x0,0,-x2,0, \
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,c,b,a,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,x2,x1,x0 \
]", 12, 42, S ); ##
M := RightPresentationWithDegrees( m );
phi := RelativeRepresentationMapOfKoszulId( M );
N := Kernel( phi );
##
d := 4;
##
fN := Resolution( 2*d, N );
##
sfN := A^(-d) * Shift( fN, d-1 );
Rpi := DegreeZeroSubcomplex( sfN, R );