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LoadPackage( "RingsForHomalg" );
Qxyz := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";
wmat := HomalgMatrix( "[ \
x*y, y*z, z, 0, 0, \
x^3*z,x^2*z^2,0, x*z^2, -z^2, \
x^4, x^3*z, 0, x^2*z, -x*z, \
0, 0, x*y, -y^2, x^2-1,\
0, 0, x^2*z, -x*y*z, y*z, \
0, 0, x^2*y-x^2,-x*y^2+x*y,y^2-y \
]", 6, 5, Qxyz );
LoadPackage( "Modules" );
W := LeftPresentation( wmat );
## the module is isomorphic to LeftPresentation of the multiple extension:
## x,z,1,0, 0, 0,0, 0, 0, 0,
## 0,0,y,-z,0, 0,0, 0, 0, 0,
## 0,0,x,0, -z,1,0, 0, 0, 0,
## 0,0,0,x, -y,0,1, 0, 0, 0,
## 0,0,0,0, 0, y,-z,0, 0, 0,
## 0,0,0,0, 0, x,0, -z, 0, -1,
## 0,0,0,0, 0, 0,x, -y, -1, 0,
## 0,0,0,0, 0, 0,-y,x^2-1,0, 0,
## 0,0,0,0, 0, 0,0, 0, z, 0,
## 0,0,0,0, 0, 0,0, 0, y-1,0,
## 0,0,0,0, 0, 0,0, 0, 0, z,
## 0,0,0,0, 0, 0,0, 0, 0, y,
## 0,0,0,0, 0, 0,0, 0, 0, x
BasisOfModule( W );
syz := SyzygiesGenerators( W );
Y := Hom( Qxyz, W );
iota := TorsionObjectEmb( W );
pi := TorsionFreeFactorEpi( W );
C := HomalgComplex( pi, 0 );
Add( C, iota );
T := TorsionObject( W );
F := TorsionFreeFactor( W );
O := HomalgCocomplex( iota, -1 );
Add( O, pi );
SetAsOriginalPresentation( W );
wmor := HomalgMatrix( "[ \
x^2+y-z,x*z-z, 0, z, -z, \
x-1, x+y-1, -y, -1, 0, \
x^3+y, x^2*z+y,x^2+y^2+y,-x*y+x*z+y,x*y-z,\
x, x, x, y^2+x, 1, \
0, 0, -x*y, y^2, 1 \
]", 5, 5, Qxyz );
phi := HomalgMap( wmor, W, W );
[ Dauer der Verarbeitung: 0.11 Sekunden
(vorverarbeitet)
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