On Tue, Apr 5, 2011 at 1:24 PM, Johan S. R. Nielsen <santaph...@gmail.com> wrote: > Let's say that I have a multivariate polynomial ring R which contains > the polynomials p, f1, ..., fn. I also know that p is in the ideal J = > <f1,..., fn>. Now I wish to write p as a polynomial in the f- > polynomials. How can I do that with Sage?
The main tool for you to use is the lift method. sage: R.<x0,x1,x2,x3> = PolynomialRing(QQ) sage: f = x0^2*x1 + x1^2*x2 + x2^2*x3 + x3^2*x0 sage: (f0, f1, f2, f3) = [f.derivative(v) for v in [x0, x1, x2, x3]] sage: I = R.ideal(f0, f1, f2, f3) sage: p = x0*f0 + x1*f1 + x2*f2 + x3*f3; p 3*x0^2*x1 + 3*x1^2*x2 + 3*x2^2*x3 + 3*x0*x3^2 sage: p in I True sage: p.lift(I) [x0, x1, x2, x3] sage: p.lift(I.gens()) #Also works [x0, x1, x2, x3] Those are the coefficients in front of the f-polynomials used to form p. --Mike -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
