Refactor: Maybe GW should inherit from FGW instead of vice versa

[selmanozleyen]

I was wondering if it would make more sense to inherit GWProblem from FGWProblem since FGW kind of includes GW in itself. This is a problem since when GW inherites prepare it removes the linear arguments: (xy_callback etc.). And because of this we need to use CompoundProblem.prepare instead of super().prepare which is not ideal if you ask me.

moscot/src/moscot/problems/generic/_generic.py

Lines 581 to 592 in d54060a

	return CompoundProblem.prepare(
	self, # type: ignore[return-value, arg-type]
	key=key,
	xy=xy,
	x=x,
	y=y,
	policy=policy,
	cost=cost,
	a=a,
	b=b,
	**kwargs,
	)

[MUCDK]

so you would then throw NotImplementedError for all functions which are specific to the fused term?

[selmanozleyen]

But this problem also exists in current code. I can currently run

gwp[('0','1')].set_x(...)

because gwp[('0','1')] is a OTProblem, gwp itself doesn't have set_xy and others. If you are talking about other methods, I didn't notice any method that only FGWProblem itself implements except these

    @property
    def _base_problem_type(self) -> Type[B]:
        return OTProblem  # type: ignore[return-value]

    @property
    def _valid_policies(self) -> Tuple[Policy_t, ...]:
        return _constants.SEQUENTIAL, _constants.EXPLICIT, _constants.STAR  # type: ignore[return-value]

which are the same for both. So moving these to the parent class should work always.