Modular reduction in Galois fields
I want to compute x^6 mod x^5+x^2+1 in the Galois Field GF(2^5). Does anyone know how to do this in SAGE?
I want to compute x^6 mod x^5+x^2+1 in the Galois Field GF(2^5). Does anyone know how to do this in SAGE?
First, define k
to be the field GF(2^5), whose generator is named a
:
sage: k.<a> = FiniteField(2^5); k
Finite Field in a of size 2^5
Alternatively :
sage: k = GF(2^5, 'a'); k
Finite Field in a of size 2^5
Then, define the polynomial ring k[x]
:
sage: R.<x> = PolynomialRing(k); R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5
Alternatively:
sage: R = k['x']; R
Univariate Polynomial Ring in x over Finite Field in a of size 2^5
Then, do your computation in R:
sage: P = R(x^6)
sage: P.mod(x^5+x^2+1)
x^3 + x
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Asked: 2013-04-28 07:04:04 +0200
Seen: 1,097 times
Last updated: Apr 28 '13
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