#19171: Add a method `divides` to Polynomial
-------------------------------------+-------------------------------------
Reporter: bruno | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: commutative | Resolution:
algebra |
Keywords: polynomial, | Merged in:
division |
Authors: Bruno Grenet | Reviewers: Vincent Delecroix
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/bruno/t19171_divides_poly | ac43c02c86eb8884bc3d7fa4013f78aef1e34803
Dependencies: #16649 | Stopgaps:
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Changes (by bruno):
* status: needs_work => needs_review
Comment:
Replying to [comment:9 vdelecroix]:
> You would better use `coerce_binop` from `sage.structure.element` rather
than a manually handled coercion.
Done.
> Why is this code specific to polynomials?
I tried to explain the reasons in the description: For polynomials over
(say) `ZZ`, the euclidean division is not well defined. The problem occurs
when the leading coefficient is not invertible. There are several ways to
deal with this problem, and different implementations in Sage use
different conventions (see #16649 for pointers on this). As a result,
testing divisibility by invoking `self % p == 0` can lead to
`ArithmeticError` for polynomials: But when this exception is raised, we
know that `self` does not divide `p`.¹ That's why I decided to add this
new method which only differs from the generic one by the fact it catches
the exception.
I could have changed the generic method instead to catch an
`ArithmeticError` and return `False` in such case, but though I am pretty
confident that it makes sense for polynomials, I am much less confident
concerning other rings.
¹ "We know" is maybe a too strong assumption. In #16649, I did changes
that ensure that the assumption holds for all ''current implementations''
of polynomials in Sage. (This was not the case before.) Yet, future
implementations may break this rule. This may imply that we shouldn't
simply rely on `quo_rem` to test divisibility.
--
Ticket URL: <https://trac.sagemath.org/ticket/19171#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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