how to find standard monomials of an Ideal?

asked 2013-06-07 04:17:14 -0500

Neda
35 ●3 ●7 ●13

Hello Is there any special command for contributing standard monomials of an Ideal I?

answered 2013-06-08 13:44:51 -0500

slelievre
7007 ●1 ●71 ●136 http://carva.org/samue...

Is groebner_basis the command you need?

sage: R.<x,y> = PolynomialRing(QQ, order='lex')
sage: R.ideal(x^2+y^2-1, 16*x^2*y^2-1).groebner_basis()
[x^2 + y^2 - 1, y^4 - y^2 + 1/16]

This example is from section 9.3 of the book Calcul mathématique avec Sage (in French). The link is to a page where you can download or order the book.

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Thank you, but I need to know is there any commands for standard monomial of an ideal i.e. for each ideal I with an special order, the monomials which not exist in <lt(i)> are standard monomials.

Neda ( 2013-06-11 21:39:28 -0500 )edit

By the way Do you know any English book with some good examples for learning and practicing sage? thank you so much

Neda ( 2013-06-11 21:43:08 -0500 )edit

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