# Factorization of multivariate polynomials over complex field

Is it possible to factorize multivariate polynomials over complex field?

Factorization of multivariate polynomials over complex field

Is it possible to factorize multivariate polynomials over complex field?

0

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 11:46:51 +0200 **

Seen: **67 times**

Last updated: **Jul 15 '19**

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