Quote:
> Let S be the polynomial ring of n- variables, J be a homogenous ideal generated by homogenous elements f_1,..,f_m.
>Consider the quotient ring S/J of S modulo J. Can one find a basis of the graded piece of (S/J)_i of given degree i by exploiting commands of SINGULAR? If so, what are the appropriate SINGULAR commands?
There are two commands you can use: kbase and jet.
We recommend to use kbase with the second argument, for example
Code:
ring r=32003,(x,y,z),ds;
ideal i=x2,y3,xyz;
kbase(std(i),2);
==> _[1]=z2
==> _[2]=yz
==> _[3]=xz
==> _[4]=y2
==> _[5]=xy
More information you can find in the documentation.
kbase:
http://www.singular.uni-kl.de/Manual/3-0-0/sing_218.htmjet:
http://www.singular.uni-kl.de/Manual/3-0-0/sing_217.htmHave fun,
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