# Convolution Polynomial Ring

How to define polynomial ring like Z[x]/(x^10-1) & Z_5[x]/(x^10-1) in Sage?

Following does not give gcd. I want to implement NTRU public key cryptosystem in Sage. Hence I need this.

N=7

p=3

R2.** = PolynomialRing(GF(p))**

S.<x> = R2.quotient(b^N - 1)

f=x^6-x^4+x^3+x^2-1

g=x^6+x^4-x^2-x

print gcd(f,g),xgcd(f,g)

Traceback (click to the left of this block for traceback)

...

TypeError: unable to find gcd*emphasized text*