Add a method `divides` to Polynomial

[bgrenet]

The generic method divides that can be found in src/sage/structure/element.pyx uses quo_rem (via %) to test if an element divides another one: return (x % self) == 0.

For polynomials, depending on the implementations, the method quo_rem may raise an error if the divisor is not monic (see #16649 for more on this).

This ticket aims at implementing a method divides for the class Polynomial, so that it catches the errors in quo_rem to return False when it is needed.

Example of a problematic behavior:

sage: R.<x> = PolynomialRing(ZZ, implementation="FLINT")
sage: p = 2*x + 1
sage: q = R.random_element(10)
sage: p.divides(q)
False
sage: R.<x> = PolynomialRing(ZZ, implementation="NTL")
sage: p = R(p)
sage: q = R(q)
sage: p.divides(q)
Traceback (most recent call last):
...
ArithmeticError: division not exact in Z[x] (consider coercing to Q[x] first)

Depends on #16649
Depends on #25277

Component: commutative algebra

Keywords: polynomial, division

Author: Bruno Grenet

Branch/Commit: 94c0390

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/19171

[bgrenet]

Dependencies: 16649

[bgrenet]

Changed dependencies from 16649 to #16649

[bgrenet]

Branch: u/bruno/t19171_divides_poly

[bgrenet]

New commits:

98b7ca1	Rebased on 6.9beta1
6d0da24	One last zero_element removed + correct one doctest
dbfb518	Remove useless colons
331c713	#19171: New method divides

[bgrenet]

Commit: 331c713

[sagetrac-git]

Changed commit from 331c713 to 27040e0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

27040e0

#19171: New method divides