Hi,
Here's the code I'm interested in using:
L.<c> = NumberField(x^3 -2*x +5)
G=L.galois_group(names="b")
x = var('x')
eqn = x^3 - 2*x + 5 == 0
a = solve(eqn, x)[0].rhs()
G.1(a)
This gives an error:
TypeError: -1/2*(I*sqrt(3) + 1)*(1/18*sqrt(3)*sqrt(643) - 5/2)^(1/3) +
1/3*(I*sqrt(3) - 1)/(1/18*sqrt(3)*sqrt(643) - 5/2)^(1/3) must be
coercible into Number Field in c with defining polynomial x^3 - 2*x +
5
I don't see why [of course I also tried G.1(L(a)) ]. The roots that
solve finds should be coercible to L; I've tried it with the other
roots as well. I tried to look at this another way, and tried
x = var('x')
eqn = x^3 - 2*x + 5 == 0
a1 = solve(eqn, x)[0].rhs()
b1 = solve(eqn, x)[1].rhs()
c1 = solve(eqn, x)[2].rhs()
(x-a1)*(x-b1)*(x-c1)
The output is not the original cubic. I don't see what I'm doing
wrong. Does solve(eqn, x)[0].rhs() (somehow?) not find a root of the
cubic?
I'm using SAGE 4.3.3 on Ubuntu 10.10.
Thanks,
Zach
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