Use flattening in quo_rem

[videlec]

Using the flattening morphism from #21106 we can divide more polynomials! With the branch applied the following works

sage: R = QQ['a','b']['c','d']
sage: R('(a*b+1)*c + c^2').quo_rem(R('c'))
(c + a*b + 1, 0)

However, will persist a discrepency between QQ['a']['b']['c'] and QQ['a','b','c'] when the division is not exact.

sage: R1 = QQ['a']['b']['c']
sage: R2 = QQ['a','b','c']
sage: R1('a').quo_rem(R1('b'))
Traceback (most recent call last):
...
ArithmeticError: Division non exact (consider coercing
to polynomials over the fraction field)
sage: R2('a').quo_rem(R2('b'))
(0, a)

See this sage-devel thread.

Depends on #21106

CC: @bhutz

Component: algebra

Author: Vincent Delecroix

Branch: a593121

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/21108

[videlec]

Commit: d9afab6

[videlec]

Branch: u/vdelecroix/21108

[videlec]

New commits:

cf97fed	21106: create polynomial ring flattening class
957589f	21106: minor fixes
8c22f75	21106: new version of _call_
570d9ee	21106: added doc tests
f05f7db	21106:cleaning
6e50942	21106: change file mode
19cb171	21106: Python3 compatibility + more cleaning
d7b066d	21108: method flattening_morphism
d9afab6	21108: use flattening in quo_rem

[videlec]

Author: Vincent Delecroix

[bhutz]

Changed branch from u/vdelecroix/21108 to u/bhutz/21108

[bhutz]

Changed branch from u/bhutz/21108 to u/vdelecroix/21108

[bhutz]

comment:4

Looks fine to me. All test pan out.

Note that fixing the quo_rem resolves the issue in #21100. So I've included a commit with that example to test that issue. We can then close that ticket as resolved or whatever is appropriate.

If you're fine with the example, this can be marked positive-review.

[bhutz]

Reviewer: Ben Hutz

[bhutz]

Changed branch from u/vdelecroix/21108 to u/bhutz/21108

[bhutz]

Changed commit from d9afab6 to a593121

[bhutz]

New commits:

a593121

21108: add normalaize_coordinates example

[vbraun]

Changed branch from u/bhutz/21108 to a593121

[xcaruso]

Changed branch from a593121 to u/caruso/a5931218dac6be179f0338df0e3ce8e4793896c1

[xcaruso]

comment:10

Sorry, I made a typo and pushed on this ticket instead of #31108

[xcaruso]

Changed commit from a593121 to none

[xcaruso]

Changed branch from u/caruso/a5931218dac6be179f0338df0e3ce8e4793896c1 to a593121