Lazy species

[mantepse]

We provide an implementation of combinatorial species based on the lazy series framework and #38446.

[mantepse]

@tscrim, I'm not sure whether this is the best way to do it. I tried to create a separate class SumSpeciesElement inheriting from LazySpeciesElement that only overrides the method structures (and will override generating_series, etc.), but got stuck.

I think I would like to turn the result of super()._add_(other) into a SumSpeciesElement instance.

[mantepse]

One other thing: I am not sure, but perhaps it would actually be nice to take some decisions of LazyModuleElement._add_ into account. For example, if one of the arguments is zero, I might not want to return a SumSpeciesElement, but rather the other summand.

However, this smells badly like duplicating a lot of code.

[mantepse]

Rethinking this: I guess it happens next to never that we are in one of the cases treated specially by LazyModuleElement._add_ (or _mul_, etc.) So maybe my afterthought is thinking about the empty set.

[mantepse]

Does the following look correct to you? At least it works. I admit that the arguments super requires are not super-clear to me.

class LazySpeciesElement(LazyCompletionGradedAlgebraElement):
...
    def _add_(self, other):
        return SumSpeciesElement(self, other)
...
class SumSpeciesElement(LazySpeciesElement):
    def __init__(self, left, right):
        self._left = left
        self._right = right
        coeff_stream = super(LazySpeciesElement, type(left))._add_(left, right)._coeff_stream
        super().__init__(self.parent(), coeff_stream)

    def structures(self, labels):
        yield from self._left.structures(labels)
        yield from self._right.structures(labels)