Make it possible to revert category initialisation

[simon-king-jena]

I am introdicing a method sage.structure.parent.Parent._unset_category() that changes the class into the "category-free" base class and resets the ._category cdef attribute to None.

In this way, it is possible to redo a wrong initialisation or refinement of category.

The idea for creating this method arose in #15229: It is possible to do R = IntegerModRing(15, category=Fields()), and then R will believe that it is a field, and will actually be initialised in a sub-category of Fields(). With the new method, it would be possible to revert the wrong category initialisation and re-initialise it correctly.

Disclaimer:

• I do not think that we should automatically apply this method, e.g., if R.is_field(proof=True) finds out that the modulus actually isn't prime. Its use should be reserved to expert users.
• It is certainly impossible to erase all bad consequences of an originally wrong choice of a category. E.g., if one wrongly initialises/refines some ring R in the category of integral domains, then one can construct the fraction field, and after R._unset_category() the wrong fraction field would still exist, and would still be accessible from R. Hence, unsetting the category may help to cope with some mistakes, but it can of course not be a global eraser.

Component: categories

Keywords: category initialisation, sd53

Author: Simon King

Branch/Commit: u/SimonKing/ticket/15234 @ 4f77364

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/15234

[simon-king-jena]

Branch: u/SimonKing/ticket/15234

[simon-king-jena]

Author: Simon King

[vbraun]

New commits:

4f77364

A method to unset category initialisation

[vbraun]

Commit: 4f77364

[vbraun]

Reviewer: Volker Braun