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.Mon, 15 Jul 2019 23:40:26 +0200Factorization of multivariate polynomials over complex fieldhttps://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/ Is it possible to factorize multivariate polynomials over complex field?Thu, 04 Jul 2019 11:46:51 +0200https://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/Comment by slelievre for <p>Is it possible to factorize multivariate polynomials over complex field?</p>
https://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/?comment=47104#post-id-47104Please give an example of what you would like to input and what output you would hope to get.Mon, 08 Jul 2019 20:07:09 +0200https://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/?comment=47104#post-id-47104Answer by dan_fulea for <p>Is it possible to factorize multivariate polynomials over complex field?</p>
https://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/?answer=47172#post-id-47172Factorization is a process of writing a polynomial to be *equal* to some product of irreducible polynomials. The accent falls on the word *equal*. So we have to perform this operation / this process over an *exact ring*. Best, we take a field as ring of constants. Examples of exact fields are `QQ`, `GF(p)`, for a prime `p`, and it is simple to factorize over such rings. For instance:
sage: R.<x,y,z> = QQ[]
sage: factor(x^3 + y^3 + z^3 - 3*x*y*z)
(x + y + z) * (x^2 - x*y + y^2 - x*z - y*z + z^2)
sage: R.<x,y,z> = PolynomialRing(GF(3))
sage: factor(x^3 + y^3 + z^3)
(x + y + z)^3
But:
sage:
sage: S.<x,y,z> = CC[]
sage: factor(x^3 + y^3 + z^3 - 3*x*y*z)
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
since `CC` is not an exact ring.
Please always insert an example, or share with us the own tries, the answers are then pointed, and targeting a similar situarion.Mon, 15 Jul 2019 23:40:26 +0200https://ask.sagemath.org/question/47061/factorization-of-multivariate-polynomials-over-complex-field/?answer=47172#post-id-47172