some issues with factorization.py

[williamstein]

Various people worked on factorization.py and unfortunately ignored some implicit
assumptions in what that code is supposed to do. In particular, this function

    def base_ring(self):
        if len(self) > 0:
            return self[0][0].parent()
        else:
            return self.unit().parent()

assumes that (1) ever element has the same parent, and (2) the parent is a ring.
Neither assumption need be satisfied.

This is_commutative function then relies on base_ring working.
Here's an example of this leading to wrong answers:

sage: R.<x,y> = FreeAlgebra(QQ,2)
sage: Factorization([(3,1), (x,2), (y,3), (x,1), (y,2)])
3 * x^3 * y^5

Proposal: Simply call Sequence on the list of bases in the factorization
to get a new list where the basis lie in a common university. Then refine
is_commutative to mean that the universe is a commuative ring, and only then
commute factors automatically.

Second, after the above is resolved, the sort function for comparison
should call universe() (not base_ring) and use some sensible defaults,
before resorting to that mess of code in the current sort method.

Component: basic arithmetic

Keywords: editor_wstein

Issue created by migration from https://trac.sagemath.org/ticket/2460

[garyfurnish]

comment:4

Attachment: trac_2460.patch.gz

[garyfurnish]

comment:5

There is a possibility that fixing commutativity may other things.

[garyfurnish]

comment:6

There are non-trivial issues involved with fixing this (namely, moving things to the universe causes issues with repr and commutes, and I can't find a way to fix those issues without refactoring other code to make this work well, so this should probably see some discussion.