#19171: Add a method `divides` to Polynomial
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Reporter: bruno | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: basic arithmetic | Keywords: polynomial, division
Merged in: | Authors: Bruno Grenet
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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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:**
{{{#!python
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)
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/19171>
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