Hi Thomas! (sorry, previously I made a wrong guess on your name) On Jul 29, 10:02 am, eggartmumie <eggartmu...@googlemail.com> wrote: > ... > Later I need the coefficients of the Goppa polynomial as linear > combination of monomials.
I don't understand what that means. Please provide explicit examples! Currently I can only jump from assumption to vague interpretation to guess; that makes it very difficult to provide any help. Thus, I think I should ask you more precise questions as well. So far, I thought we are talking about a univariate polynomial, something like sage: R.<x> = QQ[] sage: p = R.random_element() sage: p -x^2 + 4/9*x - 2 Question 1: Is that your setting, or what exactly is the ring you are working with? Concerning coefficients: sage: p.coefficients() [-2, 4/9, -1] A "coefficient" is an element of the base ring (QQ, in my example). I know two conventions for monomials: 1) Some people say that a monomial is a power product of variables, like x^3. 2) Other people say that a monomial is the product of a coefficient with some power product of variables, like 4/9*x (the first sort of people would call this a "term") :/ In either case, I really don't see what it could mean to express "the coefficients as linear combinations of monomials". The best I can come up with are some associations. First association: Get the part of the polynomial that is divisible by a certain monomial sage: p>>1 -x + 4/9 Meaning: p == x*(-x+4/9)+remaining terms not divisible by x. Second association: Start with a multivariate polynomial sage: R.<x,y,z> = GF(3)[] sage: p = R.random_element(6) sage: p -x*y^5 + x^4*y*z + x^2*z^2 - y^2*z sage: p.coefficient(z) x^4*y - y^2 So, here we have a coefficient that, itself, is a linear combination of monomials. Third association: A polynomial ring over a polynomial ring sage: R.<x> = ZZ['t'][] sage: R Univariate Polynomial Ring in x over Univariate Polynomial Ring in t over Integer Ring sage: p = R.random_element() sage: p (-3*t^2 - t - 1)*x^2 + (t^2 - t + 1)*x - 3*t - 2 sage: p.coeffs() [-3*t - 2, t^2 - t + 1, -3*t^2 - t - 1] So, again, each coefficient is a polynomial (but in a different ring). Question 2: Is any of my associations close to what you mean? Otherwise, please provide an example. > In order to be able to once define the Goppa polynomial in a function > I tried to compute the coefficients from the given function goppapolynomial. Question 3: What exactly is the "function" goppapolynomial supposed to do / to be? Is it a function that returns a polynomial? Or is it a polynomial function, itself? Please specify input and output. Is it really just returning X^(N-K) (what are N and K, anyway?)? Cheers, Simon -- 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
