ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 21 Nov 2023 12:23:53 +0100Tower extension not a fieldhttps://ask.sagemath.org/question/74394/tower-extension-not-a-field/ 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)
print((y^2-2*i-1).is_irreducible())
# print(F4.gens()[0].multiplicative_order())
output:
Univariate Quotient Polynomial Ring in u over Finite Field in i of size 2147483647^2 with modulus u^2 + 2147483645*i + 2147483646
TrueMon, 20 Nov 2023 14:54:32 +0100https://ask.sagemath.org/question/74394/tower-extension-not-a-field/Comment by mildog8 for <p>I'm trying to take the degree two tower extension of the complex extension of a field.</p>
<p>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>
<pre><code>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)
print((y^2-2*i-1).is_irreducible())
# print(F4.gens()[0].multiplicative_order())
</code></pre>
<p>output:</p>
<pre><code>Univariate Quotient Polynomial Ring in u over Finite Field in i of size 2147483647^2 with modulus u^2 + 2147483645*i + 2147483646
True
</code></pre>
https://ask.sagemath.org/question/74394/tower-extension-not-a-field/?comment=74422#post-id-74422Thanks, 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()?Tue, 21 Nov 2023 12:23:53 +0100https://ask.sagemath.org/question/74394/tower-extension-not-a-field/?comment=74422#post-id-74422Comment by John Palmieri for <p>I'm trying to take the degree two tower extension of the complex extension of a field.</p>
<p>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>
<pre><code>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)
print((y^2-2*i-1).is_irreducible())
# print(F4.gens()[0].multiplicative_order())
</code></pre>
<p>output:</p>
<pre><code>Univariate Quotient Polynomial Ring in u over Finite Field in i of size 2147483647^2 with modulus u^2 + 2147483645*i + 2147483646
True
</code></pre>
https://ask.sagemath.org/question/74394/tower-extension-not-a-field/?comment=74400#post-id-74400If you evaluate `F4.is_field()`, it should return `True`.Mon, 20 Nov 2023 18:33:27 +0100https://ask.sagemath.org/question/74394/tower-extension-not-a-field/?comment=74400#post-id-74400