Use class count, not instance

[connorjward]

No description provided.

[pbrubeck]

Follow-up: type(self).count += 1 reads the inherited value and writes the incremented one onto the subclass, so every subclass walks its own counter and prefixes still repeat across a hierarchy.

from petsctools import OptionsManager

class A(OptionsManager): pass
class B(A): pass

print([cls({}, default_prefix="firedrake_").options_prefix
       for cls in (A, B, A, B, OptionsManager, A)])

['firedrake_0_', 'firedrake_1_', 'firedrake_1_', 'firedrake_2_', 'firedrake_0_', 'firedrake_2_']

This is not hypothetical for Firedrake, which uses OptionsManager as a mixin:
NonlinearVariationalSolver(OptionsManager) → LinearVariationalSolver → LinearSolver,
and LinearEigensolver(OptionsManager). Building three of each in turn, against 729712d:

firedrake_1_ ['NVS']
firedrake_2_ ['LVS', 'NVS']                  <-- collision
firedrake_3_ ['LinearSolver', 'LVS', 'NVS']  <-- collision
firedrake_4_ ['LinearSolver', 'LVS']         <-- collision
firedrake_5_ ['LinearSolver']

So the option-inheritance hazard is weakened rather than removed: whether a solver built inside
another solver's inserted_options() picks up the outer solver's parameters now depends on how
many of each class were built beforehand. The tests that #52 turns green pass because that
particular pairing happens not to collide, not because collisions are gone — which makes the next
occurrence order-dependent and harder to pin down than the one this fixed.

Naming the class outright keeps one counter for the whole hierarchy:

options_prefix = f"{default_prefix}{OptionsManager.count}_"
OptionsManager.count += 1

Happy to reopen #53, which does that and adds a uniqueness assertion to test_options_prefix
(it fails on main either way), or leave it to you.

AI-assisted: found and checked with Claude Code.

[pbrubeck]

I guess the collision will go away when NLVS stops inheriting from OptionsManager

[connorjward]

You make a great point. We should be using OptionsManager.count. Please do reopen