Thanks for the swift reply! That is a neat function, but I don't think it is what I need. I was being too unclear, so here is an example:
Let R = Q[x], f1 = x^2 + 1 and f2 = x + 3 and g = x4+x3+4x2+x+3. We wish to write g as a polynomial in f1 and f2 over Q; more precisely, we wish to find a q On Apr 5, 1:42 pm, Mike Hansen <mhan...@gmail.com> wrote: > 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
