Implement quo_rem for Polynomial_sparse_generic

[bgrenet]

It is not possible to compute the Euclidean division for generic sparse polynomials.

sage: R.<x>=PolynomialRing(ZZ,sparse=True)
sage: p=R.random_element(10)
sage: q=R.random_element(5)
sage: p//q
---------------------------------------------------------------------------
AttributeError
...
AttributeError: 'Polynomial_generic_sparse' object has no attribute 'quo_rem'

Component: commutative algebra

Keywords: sparse polynomial, quo_rem

Author: Bruno Grenet

Branch/Commit: fb1d21c

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/16544

[bgrenet]

Branch: u/bruno/implement__quo_rem__for__polynomial_sparse_generic_

[bgrenet]

Author: Bruno Grenet

[bgrenet]

Commit: fb1d21c

[bgrenet]

comment:2

I've implemented an Euclidean Division algorithm in the class Polynomial_generic_sparse objects that raises an

ArithmeticError: Nonunit leading coefficient

if the leading coefficient of the divisor is not invertible, as it is done in the class Polynomial_generic_dense. Also, if the divisor is zero, a

ZeroDivisionError: Division by zero polynomial

is raised.

The error in the description of the ticket does not occur anymore:

sage: R.<x>=PolynomialRing(ZZ,sparse=True)
sage: p=R.random_element(10)
sage: q=R.random_element(5)
sage: p//q
---------------------------------------------------------------------------
ArithmeticError
...
ArithmeticError: Nonunit leading coefficient
sage: q += x^6
sage: p//q
x^4 + 4*x^3 - 14*x^2 + 6*x + 61

Needs review!

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:3

I'm somewhat surprised we didn't catch this earlier. LGTM, positive review.

[vbraun]

Changed branch from u/bruno/implement__quo_rem__for__polynomial_sparse_generic_ to fb1d21c