Cleanup in rings.arith and rings.integer

[videlec]

In this ticket, we:

• implement the two functions prime_part_m and binomial directly as methods of Sage integers and get rid of the late_import in sage.rings.integer
• simplify the import logic in rings.arith
• replace in arith prod([x for x in hum]) by prod(x for x in hum)
• remove some useless comments in arith
• deprecate powermodm_ui
• remove 1 from the output of prime_powers() (consistent with faster is_prime #16878)
• remove the method lcm from Rational

Depends on #16878

Component: basic arithmetic

Author: Vincent Delecroix

Branch/Commit: d7e1e37

Reviewer: Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/17852

[videlec]

Commit: 613ae23

[videlec]

Branch: u/vdelecroix/17852

[videlec]

New commits:

613ae23

trac #17852: cleanup arith.py and integer.pyx

[jdemeyer]

comment:2

Conflicts with #17819

[jdemeyer]

comment:3

I suggest you revert all changes to Integer.divisors

[videlec]

comment:4

Replying to @jdemeyer:

I suggest you revert all changes to Integer.divisors

there is none...

EDIT: there are... I messed up my develop branch!

[sagetrac-git]

Changed commit from 613ae23 to 7dcce3a

[sagetrac-git]

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

7dcce3a

trac #17852: cleanup in arith.py and integer.pyx

[videlec]

comment:6

No conflicts anymore...

[jdemeyer]

comment:8

I don't like this:

cdef mpz_t g = <mpz_t> mm.value

Just use mm.value instead of g.