<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _deltasummation(term, ranges, i_range):
 """Partially execute a summation for `term` with a Kronecker Delta for one of the summation indices. This implements the solution to the core sub-problem in :func:`indexed_sum_over_kronecker` Args: term (QuantumExpression):
 term of the sum ranges (list):
 list of all summation index ranges (class:`IndexRangeBase` instances) i_range (int):
 list-index of element in `ranges` which should be eliminated Returns: ``(result, flag)`` where `result` is a list of ``(new_term, new_ranges)`` tuples and `flag` is an integer. There are three possible cases, indicated by the returned `flag`. Consider the following setup:: 1. If executing the sum produces a single non-zero term, result will be ``[(new_term, new_ranges)]`` where `new_ranges` contains the input `ranges` without the eliminated range specified by `i_range`. This should be the most common case for calls to:func:`_deltasummation`:: 2. If executing the sum for the index symbol specified via `index_range` does not reduce the sum, the result will be the list ``[(term, ranges)]`` with unchanged `term` and `ranges`:: This case also covers if there is no Kroncker delta in the term:: 3. If `term` does not contain a Kronecker delta as a factor, but in a sum that can be expanded, the result will be a list of expansion. In this case, `:func:`_deltasummation` should be called again for every tuple in the list, with the same `i_range`:: """

    from qnet.algebra.core.abstract_quantum_algebra import QuantumExpression
    idx = ranges[i_range].index_symbol
    summands = _expand_delta(term, idx)
    if len(summands) > 1:
        return [(summand, ranges) for summand in summands], 3
    else:
        delta, expr = _extract_delta(summands[0], idx)
    if not delta:
        return [(term, ranges)], 2
    solns = sympy.solve(delta.args[0] - delta.args[1], idx)
    assert len(solns) > 0  # I can't think of an example that might cause this
    #     if len(solns) == 0:
    #         return [(term._zero, [])], 4
    if len(solns) != 1:
        return [(term, ranges)], 2
    value = solns[0]
    new_term = expr.substitute({idx: value})
    if _RESOLVE_KRONECKER_WITH_PIECEWISE:
        new_term *= ranges[i_range].piecewise_one(value)
    assert isinstance(new_term, QuantumExpression)
    return [(new_term, ranges[:i_range] + ranges[i_range+1:])], 1