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reducing ideal wrt another ideal

asked 2011-09-26 14:32:26 -0500

I have two ideals I & J in k[X_1,\cdots,x_n], where k is a field. How do I reduce an ideal I wrt ideal J.

e.g. Singular provides me a command

reduce(I,std(J));

Without moving back and forth to Singular, is it possible to implement this in sage?

Thanks and regards

-- VInay Wagh

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answered 2011-09-30 04:07:19 -0500

mmarco gravatar image

updated 2011-09-30 04:08:08 -0500

You can do the following:

R.ideal([f.reduce(J.groebner_basis()) for f in I.gens()])

That is basically what singular does: reduce the generators of I w.r.t. J.

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answered 2011-10-07 20:32:02 -0500

Thanks marco, It works!

-- VInay

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Asked: 2011-09-26 14:32:26 -0500

Seen: 85 times

Last updated: Oct 07 '11