inverse of a polynomial modulo another polynomial
Hi, I'm trying to implement the Baby Step Giant Step algorithm in the group of units of prime fields. I would like to generate the field provided one generator polynomial. But I need to calculate p^(-1) (where p is a polynomial), but can't find a function to do so. This is what I'm doing,
F.<a> = GF(2)[];
R.<b> = PolynomialRing(F)
S.<x> = R.quotient(b^4+b+1)
m = sqrt(S.modulus().degree());
gamma = S.modulus();
alpha = x^3+1;now i need to calculate (alpha)^(-1) modulo gamma
Any help? Better ways to do the same thing?
Thanks!
You should look up the extended gcd algorithm. This is implemented by the xgcd() function in Sage.
Burcin, xgcd doesn't work. It fails with a type error, "cannot coerce nonconstant polynomial".
If you define R over the fraction field of F, or simply over GF(2), then alpha^-1 yields the answer.