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Factorization of multivariate polynomials over complex field

asked 2019-07-04 04:46:51 -0500

swisti10 gravatar image

Is it possible to factorize multivariate polynomials over complex field?

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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 13:07:09 -0500 )edit

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answered 2019-07-15 16:40:26 -0500

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

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.

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Asked: 2019-07-04 04:46:51 -0500

Seen: 23 times

Last updated: Jul 15