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cppdraft/numerics/defns.md

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