Hi there,
I am working with the following absolute field extension of a quadratic field.
d = # some integer
K.(a) = NumberField(x^2-d)
R.<x> = PolynomialRing(K)
g = x^2 + x + 1
KL.(b) = K.extension(g)
f = KL.absolute_polynomial()
L.(c) = NumberField(f)
I need to keep track of the element b inside L
and I don't know how. Any help is much appreciated.
Use the absolute_field method instead:
sage: L.<c> = KL.absolute_field()
sage: f = L.defining_polynomial()
sage: from_L, to_L = L.structure()
sage: to_L(b)
2/11*c^3 + 3/11*c^2 + 2/11*c - 5/11
(The output is for the choice of d = 2.)
You also get the morphism in the other direction, which can be handy:
sage: from_L(c)
b - a
(Again, the output is for the choice of d = 2.)
Asked: 2022-02-21 00:26:17 +0100
Seen: 179 times
Last updated: Feb 22 '22
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