On 29 Jul., 01:20, Nils Bruin <[email protected]> wrote: > On Jul 28, 1:58 pm, Simon King <[email protected]> wrote:> Anyway. > While differential rings are certainly nice algebraic > > structures, I feel uncomfortable to think of a derivation as some > > calculus stuff. > > The theory of Kaehler differentials does a pretty good job providing > differential calculus with sound algebraic footing and it is > intentional that the terminology mixes derivation and differentials. > One would really only need to prove a few universality properties at > the start of an introductory calculus course to have it make perfect > mathematical sense (but not necessarily to the students) without > having to introduce any epsilons or deltas. > > The term "Goppa polynomial" leads me to suspect that the OP had coding > theoretic and hence probably quite algebraic intentions, so he/she > probably is better off looking at polynomial rings rather than > "symbolic expressions".
yes, I am working on Goppa codes and trying to implement the McEliece PKCS in SAGE -- allthough a newbie. In doing so I stumbled upon different problems very many of which had to do with coercing data types. So I tried to define a Goppa polynomial as polynomial over some field in some indeterminant as Simon helped me to do. Later I need the coefficients of the Goppa polynomial as linear combination of monomials. 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. For me it was quite natural to use formal differentiation to do so. In my opinion differentiation is not necessarily bound to calculus. Formal differentiation (see Forney's algorithm to compute the error values of a generalized Reed-Solomon codes) or formal (infinite) power series do play their role in coding theory. I in vain tried two related things: first, to coerce the polynomial to be a polynomial over the field and in the indeterminant passed as parameters (and not of type 'sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX' ), second to compute the coefficients of the polynomial given by the function goppapolynomial e.g. as a product where I expected formal differentiation would work. As a newbie I was not aware of some other way. At my university, there is no one to ask (I am the one pointing out SAGE to others). Sorry to have mixed up several issues and sorry for my clumsy explanations, Thomas EM -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
