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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.
