On Mar 10, 2010, at 10:15 AM, John H Palmieri wrote:
On Mar 10, 3:23 am, slabbe <[email protected]> wrote:
Hi,
A friend of mine wants to factorize symbolicly x^2 - 2 :
sage: p = x^2 - 2
sage: p.factor()
x^2 - 2
Apparently p.roots() gives almost what he wants :
sage: p.roots()
[(-sqrt(2), 1), (sqrt(2), 1)]
Or
sage: p.roots(multiplicities=False)
[-sqrt(2), sqrt(2)]
So, I just proposed him to do :
sage: Factorization([(x-r,m) for r,m in p.roots()])
(x - sqrt(2)) * (x + sqrt(2))
Do any of you have a better solution?
How about:
sage: S.<y> = PolynomialRing(QQ[sqrt(2)])
sage: p = y^2 - 2
sage: p.factor()
(y - sqrt2) * (y + sqrt2)
(I don't know why it says "sqrt2" instead of "sqrt(2)".)
That is because this is a number field, and generator names are
supposed to be atomic.
- Robert
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