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## Definitions <a id="numerics.defns">[[numerics.defns]]</a>
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Define `GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aN)` as follows:
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- `a1` when `N` is `1`, otherwise
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- `op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK),`
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`\phantom{op(}GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, ..., aN))` for
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any `K` where 1 < K+1 = M ≤ N.
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Define `GENERALIZED_SUM(op, a1, ..., aN)` as
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`GENERALIZED_NONCOMMUTATIVE_SUM(op, b1, ..., bN)`, where `b1, ..., bN`
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may be any permutation of `a1, ..., aN`.
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