Clean up SpecializationMorphism

[jdemeyer]

Depends on #23337

CC: @tscrim

Component: algebra

Author: Travis Scrimshaw, Jeroen Demeyer

Branch/Commit: 6766161

Reviewer: Jeroen Demeyer, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/23343

[jdemeyer]

New commits:

ee4548f	Use variable names instead of symbolic variables
e938684	Handling flatten.py and some mild cleanup.

[jdemeyer]

Branch: u/tscrim/ticket/var_names_not_symbolic_names-23337

[jdemeyer]

Commit: e938684

[jdemeyer]

Dependencies: #23337

[jdemeyer]

Description changed:

--- 
+++ 
@@ -1 +1,6 @@
+It is checking the keys in `D`, which are actual variables and hence, do not compare with the string values. So the variable names all get included when constructing `new_vars` on this line:
 
+```python
+new_vars = [[[t for t in v if t not in newD.keys()], b] for v,b in old_vars]
+```
+I think I see a good way to fix this. I also am going to do a slight bit of cleanup of that method.

[jdemeyer]

comment:3

Since you are cleaning this up anyway, I would prefer if you could also move the changes from #10483 to flatten.py to this branch. For example, it would allow to test whether the changes here are compatible with #10483.

[tscrim]

comment:4

I don't think they are really compatible. Instead, I think these changes should replace those in #10483. The changes of #10483 rely on strings for keys rather than variables, which (in principle) would not work if a variable name is repeated (I haven't explicitly tested that this works in my code or if this is [suppose to be] a supported feature).