Incorrect output of squarefree_decomposition for polynomials over finite fields

[lennartack]

When using squarefree_decomposition on linear polynomials over a finite field, the coefficients are not divided by the unit part, resulting in an incorrect output.

sage: K.<x> = GF(7)[]
sage: (6*x+3).squarefree_decomposition()
(6) * (6*x + 3)
sage: (6*x+3).squarefree_decomposition().expand()
x + 4
sage: K.<x> = GF(5)[]
sage: (2*x).squarefree_decomposition()
(2) * 2*x

CC: @wbhart @mstreng

Component: factorization

Issue created by migration from https://trac.sagemath.org/ticket/20003

[lennartack]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-When using squarefree_decomposition on linear polynomials over a finite field, an incorrect unit part is returned.
+When using squarefree_decomposition on linear polynomials over a finite field, the coefficients are not divided by the unit part, resulting in an incorrect output.
 
 ```
 sage: K.<x> = GF(7)[]

[mstreng]

comment:2

Is this a bug in Flint or does Sage wrap Flint incorrectly in factor_helper?

[lennartack]

comment:3

It seems Flint doesn't return a monic factor in case of a linear input. I attached a patch to "fix" it.

[mkoeppe]

comment:4

Attachment: nmod_poly_linkage.pxi.patch.gz