Uniformize truncated multiplication for polynomials

[videlec]

The operation _mul_trunc on polynomials is currently only implemented in specialized classes with custom declaration. We define a global one in Polynomial with signature

class Polynomial:
    cpdef Polynomial _mul_trunc_(self, Polynomial right, long n)

(and deprecate the former _mul_trunc).

We also add specialized implentation for integer polynomials (relying on fmpz_poly_mullow) and rational polynomials (relying on fmpq_poly_mullow).

Such method would be really helpful for multiplication of power series.

Component: algebra

Author: Vincent Delecroix

Branch/Commit: 063516e

Reviewer: Mario Pernici

Issue created by migration from https://trac.sagemath.org/ticket/18420

[videlec]

Branch: u/vdelecroix/18420

[videlec]

New commits:

446b952

Trac 18420: `_mul_trunc_` for all polynomials

[videlec]

Commit: 446b952

[sagetrac-git]

Changed commit from 446b952 to 4e96421

[sagetrac-git]

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

4e96421

Trac 18420: `_mul_trunc_` for all polynomials

[sagetrac-git]

Changed commit from 4e96421 to b73a840

[sagetrac-git]

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

b73a840

Trac 18420: `_mul_trunc_` for all polynomials

[videlec]

comment:5

rebased on 6-7.rc0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

12d6361

Trac #18420: fix declaration im polynomial_template.pxi

[sagetrac-git]

Changed commit from b73a840 to 12d6361

[sagetrac-pernici]

comment:8

Polynomial._mul_trunc_ doctest example should have _mul_trunc_, not _mul_trunc

[sagetrac-git]

Changed commit from 12d6361 to febe298

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

febe298

Trac #18420: _mul_trunc -> `_mul_trunc_` in doctest

[sagetrac-pernici]

comment:10

Why did you add the comment in
cpdef ModuleElement _rmul_(self, RingElement c) # ??!?

[videlec]

comment:12

Because this has nothing to do in sage/rings/polynomial/polynomial_modn_dense_ntl.pxd. Moreover, it seems to be never used.

It is a good idea to introduce special rule for multiplication by constants. But this should be done globally. I will make the comment clearer.

Vincent

[videlec]

comment:13

All right, I can just get rid of the declaration in the pxd file and everything is fine. Let me do it.

[sagetrac-git]

Changed commit from febe298 to 063516e

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

063516e

Trac #18420: remove redundant declaration of `_lmul_`, _rmul_

[videlec]

Reviewer: Mario Pernici

[vbraun]

Changed branch from u/vdelecroix/18420 to 063516e