Fix some corner and special cases concerning localization of integral domains

[soehms]

The aime of this ticket is to fix the following issues:

sage: L = ZZ.localization(5)
sage: o = L(0)
sage: o.is_unit()
Traceback (most recent call last)
...
RecursionError: maximum recursion depth exceeded while calling a Python object

sage: R = ZZ.localization(5)
sage: S = R.localization(~5)
Traceback (most recent call last)
...
TypeError: no conversion of this rational to integer

sage: Lau.<u, v> = LaurentPolynomialRing(ZZ)
sage: LauL = Lau.localization(u+1)
sage: LauL(~u)
Traceback (most recent call last)
...
NotImplementedError:

In addition a method factor is added.

CC: @tscrim

Component: commutative algebra

Keywords: integral domain localization

Author: Sebastian Oehms

Branch/Commit: fc1865a

Reviewer: Travis Scrimshaw, Samuel Lelièvre

Issue created by migration from https://trac.sagemath.org/ticket/33463

[soehms]

Branch: u/soehms/fix_corner_cases_localization_33463

[soehms]

Commit: ff2e83e

[soehms]

Author: Sebastian Oehms

[soehms]

New commits:

ff2e83e

33463: initial version

[tscrim]

comment:3

Can you also add this to the docstring (copied from the polynomial factorization):

   Return the factorization of this polynomial.

   INPUT:

   - ``proof`` -- ignored

and a proof=None default argument (for compatibility, although not every factor() implementation seems to support it)?

Addendum: You can also leave off the INPUT: too if you want since it is ignored.

[slel]

comment:4

Please capitalise and use double colon here:

-        check that :trac:`33463` is fixed:
+        Check that :trac:`33463` is fixed::

[sagetrac-git]

Changed commit from ff2e83e to 5df7f55

[sagetrac-git]

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

5df7f55

33464: add kw proof to factor and style fixes

[soehms]

comment:6

Replying to @tscrim:

Can you also add this to the docstring (copied from the polynomial factorization):

   Return the factorization of this polynomial.

   INPUT:

   - ``proof`` -- ignored

and a proof=None default argument (for compatibility, although not every factor() implementation seems to support it)?

Addendum: You can also leave off the INPUT: too if you want since it is ignored.

Yes, you are right, Travis! But, I think instead of ignoring it it could by useful to pass the keyword to the factor method over the base ring in case it is given explicitely.

[soehms]

comment:7

Replying to @slel:

Please capitalise and use double colon here:

-        check that :trac:`33463` is fixed:
+        Check that :trac:`33463` is fixed::

Thanks for this hint, as well, Samuel!

[tscrim]

comment:8

That is fine with me, but factor() still needs a one-line description. Also, one other tweak:

-        - ``proof`` -- optional (default ``None``). If given it is passed
-          to the corresponding method of the numerator of ``self``.
+        - ``proof`` -- (optional) if given it is passed to the
+          corresponding method of the numerator of ``self``

[sagetrac-git]

Changed commit from 5df7f55 to ceeeebc

[sagetrac-git]

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

ceeeebc

33463: add missing description of meth factor

[sagetrac-git]

Changed commit from ceeeebc to d48dc28

[sagetrac-git]

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

d48dc28

33463: once again

[soehms]

comment:11

Replying to @tscrim:

That is fine with me, but factor() still needs a one-line description. Also, one other tweak:

Sorry!

[tscrim]

comment:12

Thanks (although I would normally put the optional in parentheses). I am okay with the current branch. Samuel?

[sagetrac-git]

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

fc1865a

33463: another one

[sagetrac-git]

Changed commit from d48dc28 to fc1865a

[soehms]

comment:14

Replying to @tscrim:

although I would normally put the optional in parentheses

Of course! Sorry again (that was not a good day).

[tscrim]

Reviewer: Travis Scrimshaw, Samuel Lelièvre

[tscrim]

comment:15

No problem. Thank you for the fixes.

I am going to set this to a positive review since the patchbot is (morally) green. Samuel, if you have other changes you want, feel free to revert.

[slel]

comment:16

I wish one could change the display of the variables in the localisation.

Something like:

sage: P.<X, Y> = QQ[]
sage: L.<x, y> = P.localization(X - Y)

where the generators would display as X, Y in P
and as x, y in L.

That could be another ticket.

One could remove a pair of parentheses here:

-        fac = [(P(f), e) for (f, e) in F]
+        fac = [(P(f), e) for f, e in F]

but leaving them is fine too and even emphasizes
the transformation.

The shorter name extra_units might shorten
some lines with respect to additional_units.

One could split this line:

-            additional_units = [au for au in additional_units if ~au not in base_ring._additional_units]  # :trac:`33463`
+            additional_units = [u for u in additional_units
+                                if ~u not in base_ring._additional_units]

These are all minor points. No need to revert positive review.

[soehms]

comment:17

That could be another ticket.

I have opened #33482

[vbraun]

Changed branch from u/soehms/fix_corner_cases_localization_33463 to fc1865a