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I'm working on an algorithm where a lot of things are summed. My paper has the words "summed", "summation", etc. all over the place.

I've recently found that actually, the algorithm will work differently and maybe better with other binary operations than addition. Is there a more graceful word for "iterated binary operation"?

For instance, I could change "Sum the weights of all the edges on the route" to "Use one of the iterated binary operations previously defined over the weights of all the edges on the routes". Is there a more graceful way to talk about this stuff?

Andrés E. Caicedo
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Jehan
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    It depends both on the nature of the operation and the iteration. Many examples exist of expressions that are viewed as left or right associative: the expression 8 - 5 - 3 - 7 can give -7 (left) or -1 (right). Other iterations involve a full binary tree, say a_(n+1) is op (a_n,b_n) and b_(n+1) is op (b_n,a_n). You might see what names are used in the literature you reference. Max Alekseyev had a recent preprint on generating sequences which phrased things in general terms. You might check it out. Gerhard "It's Linked Somewhere On MathOverflow" Paseman, 2016.06.03. – Gerhard Paseman Jun 04 '16 at 01:56
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    You may start with an axiomatic definition. Only then one/we may think of the name. – Włodzimierz Holsztyński Jun 04 '16 at 03:02
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    Does this binary operation have properties that fit into some well-known context? For instance, if the operation makes the set of operands into an abelian group, then you could continue to call it "summation". – Nate Eldredge Jun 04 '16 at 04:55
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    With no conditions at all assumed on the binary operation, iterated binary operations are called magmatic operations. – Gabriel C. Drummond-Cole Jun 04 '16 at 05:18
  • The Wikipedia article on Iterated binary operation does not mention another name. – Martin Sleziak Jun 04 '16 at 06:48
  • Warner, Modern Algebra Sec 18, calls it the composite, but it's an obscure term IMO. – Bart Michels Jan 20 '18 at 12:45

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