Standardize modulo operator % on real numbers (step 1)

[videlec]

For any subset of the real numbers we change the modulo operator to be

x%y is the unique x' between [0,y) of the form x + ny with n integer

The main reason for the shift are the following incoherences

sage: 5 % 3
2
sage: 5. % 3.
-1.00000000000000

and

sage: 2/5 % 3
1
sage: 2./5. % 3.
0.400000000000000

The change mainly affects QQ and RR. This ticket concentrates on QQ. For other numbers see #21747.

The specifications for the transition period are as follows:

• both // and % with rational arguments will return rationals
• there will be a deprecation warning with (p/q) % (r/s) when p/q or r/s is not an exact integer
• there will be a deprecation warning with (p/q) // (r/s) when the result is not an exact integer

See this sage-devel thread and also #15260

CC: @sagetrac-tmonteil

Component: basic arithmetic

Author: Vincent Delecroix

Branch/Commit: u/vdelecroix/21745 @ 39f4053

Issue created by migration from https://trac.sagemath.org/ticket/21745

[videlec]

Dependencies: #21746

[videlec]

Author: Vincent Delecroix

[videlec]

Branch: u/vdelecroix/21745

[sagetrac-git]

Commit: 710eee2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

624c322	21745: fix integer mod ring initialization with rationals
cc204ef	21745: fix doctests in integer.pyx
0e57304	21745: use / instead of // in one place
5735ee1	21745: include real_mod_floordiv in the documentation
7e1a281	21745: fix bernoulli mod p tests
6435af1	21745: fix pari ffelt initialization
f62f8bf	21745: fix doctests in ideal.py and integer_ring.pyx
f70825b	21745: doctest finite field initialization
05657ad	21745: fix quadratic form of ideals
710eee2	21745: fix some french book examples

[sagetrac-git]

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

71f5d59

21745: fix a UTF8 character

[sagetrac-git]

Changed commit from 710eee2 to 71f5d59

[sagetrac-git]

Changed commit from 71f5d59 to 1bbc03c

[sagetrac-git]

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

1bbc03c

21745: better documentation in real_mod_floordiv.py

[sagetrac-git]

Changed commit from 1bbc03c to 8517922

[sagetrac-git]

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

8517922

21745: better documentation in real_mod_floordiv.py

[sagetrac-git]

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

c977095	21745: fix quadratic_forms
84a8937	21745: fix in root system
6912371	21745: two fixes in graphs/

[sagetrac-git]

Changed commit from 8517922 to 6912371

[sagetrac-git]

Changed commit from 6912371 to 2bd9c73

[sagetrac-git]

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

2bd9c73

21745: make floordiv returns a rational

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

9decbae	21745: doctest finite field initialization
25a335e	21745: fix quadratic form of ideals
ad9f818	21745: fix some french book examples
f2ceaf1	21745: fix a UTF8 character
2d78c1d	21745: better documentation in real_mod_floordiv.py
5b720f4	21745: fix quadratic_forms
c45b553	21745: fix in root system
6e16f4d	21745: two fixes in graphs/
7aa12c5	21745: make floordiv returns a rational
39f4053	21745: fix projective_morphism.py

[sagetrac-git]

Changed commit from 2bd9c73 to 39f4053

[videlec]

Changed dependencies from #21746 to none

[videlec]

comment:15

rebased on 7.5.beta6

[cheuberg]

comment:16

failing doctests (see patchbot)