It seems you should be able to represent multiplication by y as a matrix equation, which you might have luck inverting.
On Wed, May 28, 2008 at 5:27 PM, vpv <[EMAIL PROTECTED]> wrote: > > Hello, > > I am trying to solve the following equation for y in SAGE: > > x*y = 1 (mod z^8+z^4+z^3+z+1) > > where > > x = x0+x1*z^1+x2*z^2+x3*z^3+x4*z^4+x5*z^5+x6*z^6+x7*z^7 > y = ? > > x0,...,x7 are elements of GF(2). I do not know their values. I am > searching for y in parametric form i.e. as a polynomial of z of degree > 7 with coefficients - some functions of x0,...,x7. > > I define in SAGE: > > P.<x0,x1,x2,x3,x4,x5,x6,x7> = BooleanPolynomialRing(8, order='lex') > Z.<z> = PolynomialRing(P) > > I try to do the following in SAGE > > y = inverse_mod(x0+x1*z^1+x2*z^2+x3*z^3+x4*z^4+x5*z^5+x6*z^6+x7*z^7, > z^8+z^4+z^3+z+1) > > but it does not work. > > Alternatively, I try to define a ring of univariate polynomials of z > with coeffients in P, every element of which is reduced (mod > z^8+z^4+z^3+z+1), but I am not able to get the right syntax to do this > in SAGE. > > Any help is appreciated. > > Thanks! > > > > --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
