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[Axiom-developer] [#187 trouble with tuples] Tuple, Product, Direct Prod

From: wyscc
Subject: [Axiom-developer] [#187 trouble with tuples] Tuple, Product, Direct Product
Date: Fri, 01 Jul 2005 19:50:48 -0500

Product can be looked up in hyperdoc. It is listed in Appendix C (p. 613 of 
Axiom (paper) Book; p. 1028 of eBook). Tuple is more like Direct Product since 
the entries must come from the same domain. However, Product  constructs only 
Cartesian product of two domains; Direct Product requires a dimension 
parameter; whereas Tuple does not (arbitrary length). Also Tuple is only a 
linear aggregate (or PRIMARR) and has no algebraic structure. Direct product 
exists in many categories. 

So, a tuple is not an element of Product (it is a Cartesian product in a loose 
mathematical sense: Tuple S is actually the infinite union of 
DirectProduct(n,S) over all n.

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