Tower extension not a field

asked 2023-11-20 14:54:32 +0100

anonymous user


I'm trying to take the degree two tower extension of the complex extension of a field.

I'm new to Sage but I expected F4 to be a field rather than a ring. My question is how to I get the field F4 and not the ring?

P = 2^31 - 1
F = GF(P)
K.<x> = PolynomialRing(F)
F2.<i> = F.extension(x^2+1)
K2.<y> = PolynomialRing(F2)
F4.<u> = F2.extension(y^2-2*i-1)
# print(F4.gens()[0].multiplicative_order())


Univariate Quotient Polynomial Ring in u over Finite Field in i of size 2147483647^2 with modulus u^2 + 2147483645*i + 2147483646
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If you evaluate F4.is_field(), it should return True.

John Palmieri gravatar imageJohn Palmieri ( 2023-11-20 18:33:27 +0100 )edit

Thanks, is there a way I to get access to the F4 object as a field in order to call functions like F4.gens()[0].multiplicative_order()?

mildog8 gravatar imagemildog8 ( 2023-11-21 12:23:53 +0100 )edit