pyro/ops/rings.py [135:155]:
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    def __init__(self, cache=None, dim_to_size=None):
        super().__init__(cache=cache)
        self._dim_to_size = {} if dim_to_size is None else dim_to_size

    def sumproduct(self, terms, dims):
        inputs = [term._pyro_dims for term in terms]
        output = ''.join(sorted(set(''.join(inputs)) - set(dims)))
        equation = ','.join(inputs) + '->' + output
        term = contract(equation, *terms, backend=self._backend)
        term._pyro_dims = output
        return term

    def product(self, term, ordinal):
        dims = term._pyro_dims
        for dim in sorted(ordinal, reverse=True):
            pos = dims.find(dim)
            if pos != -1:
                key = 'product', self._hash_by_id(term), dim
                if key in self._cache:
                    term = self._cache[key]
                else:
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pyro/ops/rings.py [186:206]:
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    def __init__(self, cache=None, dim_to_size=None):
        super().__init__(cache=cache)
        self._dim_to_size = {} if dim_to_size is None else dim_to_size

    def sumproduct(self, terms, dims):
        inputs = [term._pyro_dims for term in terms]
        output = ''.join(sorted(set(''.join(inputs)) - set(dims)))
        equation = ','.join(inputs) + '->' + output
        term = contract(equation, *terms, backend=self._backend)
        term._pyro_dims = output
        return term

    def product(self, term, ordinal):
        dims = term._pyro_dims
        for dim in sorted(ordinal, reverse=True):
            pos = dims.find(dim)
            if pos != -1:
                key = 'product', self._hash_by_id(term), dim
                if key in self._cache:
                    term = self._cache[key]
                else:
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