tmp/tmpokxwb_d_/{from.md → to.md}
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### Definitions <a id="numerics.defns">[[numerics.defns]]</a>
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Define `GENERALIZED_NONCOMMUTATIVE_SUM(op, a1,
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- `a1` when `N` is `1`, otherwise
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- `op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1,
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`\phantom{op(}GENERALIZED_NONCOMMUTATIVE_SUM(op, aM,
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Define `GENERALIZED_SUM(op, a1,
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`GENERALIZED_NONCOMMUTATIVE_SUM(op, b1,
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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 any
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`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` may
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be any permutation of `a1, …, aN`.
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