30 lines
906 B
Markdown
30 lines
906 B
Markdown
[numerics.defns]
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# 26 Algorithms library [[algorithms]](./#algorithms)
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## 26.10 Generalized numeric operations [[numeric.ops]](numeric.ops#numerics.defns)
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### 26.10.2 Definitions [numerics.defns]
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12270)
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Define *GENERALIZED_NONCOMMUTATIVE_SUM*(op, a1, …, aN) as follows:
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- [(1.1)](#1.1)
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a1 when N is 1, otherwise
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- [(1.2)](#1.2)
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op(*GENERALIZED_NONCOMMUTATIVE_SUM*(op, a1, …, aK),
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op(*GENERALIZED_NONCOMMUTATIVE_SUM*(op, aM, …, aN)) for any K where 1<K+1=Mâ¤N[.](#1.2.sentence-2)
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12284)
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Define *GENERALIZED_SUM*(op, a1, …, aN) as*GENERALIZED_NONCOMMUTATIVE_SUM*(op, b1, …, bN),
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whereb1, …, bN may be any permutation of a1, …, aN[.](#2.sentence-1)
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