This is being cc'd to sage-devel, since no reason not to. It's me
and Robert Bradshaw working on reworking the algebraic number
theory code in Sage (we've done a lot now).
On 9/17/07, Robert Bradshaw <[EMAIL PROTECTED]> wrote:
>
> BTW, I've been working on quadratic number field elements...
That's a good idea.
I have been working on grant proposals all day long.
I'm going to switch gears and work on the ANT package
soon. I'll probably work only on getting all the doctests
not in the number_field directory to pass, since much
was broken by my changes.
I also want to make ZZ[a,b,c]
work, if a,b,c are algebraic integers.
It would also be really neat to have a function that can
compute the minimal polynomial of a symbolic element:
sage: a = sqrt(2)
sage: a.minpoly()
x^2 - 2
sage: a = 5^(1/3)
sage: a.minpoly()
x^3 - 5
One possibility would be to numerically approximate a,
use pari's algdep to get a candidate minpoly f, then
do bool(f(a) == 0). If it works, we're golden. If not,
we give up. Since bool(f(a) == 0) errors on the side of
caution, this would probably be fine.
With that, we could do
ZZ[sqrt(2), 5^(1/7), sqrt(7)]
and it would work. Thoughts?
-- William
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