Hi:
I am trying to "define" a variable to be an element of GF(2). In
particular, suppose that I create GF(2^4) the following way:
K=GF(2)
S.<x> = K['x']
QR=S.quotient(1+x+x^4,'a')
a=FR.gen()
Now I am trying to compute the following:
(gamma0 + gamma1*a + gamma2*a^2 + gamma3*a^3)*(beta0 + beta1*a +
beta2*a^2 + beta3*a^3)
where gamma0,...,gamma3 and beta0,...,beta3 are symbols in GF(2).
Essentially I want sage to multiply sage to multiply the two
polynomials and then substitute the higher powers of a^i for their
representation in the quotient ring.
Said in different words, I would like to represent two symbolic
elements of GF(2^4) explicitly (in their GF(2) constituents) and have
sage compute what product of the two elements looks like.
I tried defining gamma0,...gamma3,beta0,..,beta3 as regular vars
(gamma0 = var('gamma0')) but I get a typeerror:
TypeError: unsupported operand parent(s) for '*': 'Symbolic Ring' and
'Univariate Quotient Polynomial Ring in a over Finite Field of size 2
with modulus x^4 + x + 1'
not defining them also does not work.
Any ideas?
Thanks!!
Luis
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