Hello Martin,
> How to set the ring for szy computation in homalg in gap systemZZ :=
> HomalgRing();
> H := HomalgMatrix("[1,x^2+y, x*y-y*z, 0, 0 \
> 0, x*z-y, z-x, 0, 0 \
> 0, 0, 0, x^2+y, x*y-y*z \
> 1, 0, 0, x*z-y, z-x]", 4, 5, ZZ);Regards,Martin
There was a line missing in my previous email.
Best regards,
Mohamed
gap> LoadPackage( "GradedRingForHomalg" );
true
gap> ZZ := HomalgRingOfIntegersInSingular( );
Z
gap> R := ZZ * "x,y,z";
Z[x,y,z]
gap> H := HomalgMatrix("[1,x^2+y, x*y-y*z, 0, 0, \
> 0, x*z-y, z-x, 0, 0, \
> 0, 0, 0, x^2+y, x*y-y*z, \
> 1, 0, 0, x*z-y, z-x]", 4, 5, R);
<A 4 x 5 matrix over an external ring>
gap> SyzygiesOfColumns( H );
<A non-zero right regular 5 x 1 matrix over an external ring>
gap> Display( last );
x^2*y*z-x*y*z^2+x^3-x*y^2-x^2*z+y^2*z+x*y-y*z,
-x+z,
-x*z+y,
-x*y+y*z,
x^2+y
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