On Thursday, August 22, 2013 4:06:22 PM UTC-4, Santanu wrote:

> How to define  polynomial ring  like Z[x]/(x^10-1) & Z_5[x]/(x^10-1) in 
> Sage? 
>
>
sage: R1.<a> = PolynomialRing(ZZ)
sage: R.<x> = R1.quotient(a^10 - 1)

sage: R2.<b> = PolynomialRing(GF(5))
sage: S.<y> = R2.quotient(b^10 - 1)

Now you can do:

sage: x^12
x^2

sage: y^14 + 7 * y
y^4 + 2*y

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