Ask Your Question

Factorization of multivariate polynomials over complex field

asked 2019-07-04 11:46:51 +0200

swisti10 gravatar image

Is it possible to factorize multivariate polynomials over complex field?

edit retag flag offensive close merge delete



Please give an example of what you would like to input and what output you would hope to get.

slelievre gravatar imageslelievre ( 2019-07-08 20:07:09 +0200 )edit

1 Answer

Sort by ยป oldest newest most voted

answered 2019-07-15 23:40:26 +0200

dan_fulea gravatar image

Factorization 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


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.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools


Asked: 2019-07-04 11:46:51 +0200

Seen: 145 times

Last updated: Jul 15 '19