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[Axiom-developer] [#187 trouble with tuples] Tuple, Product, Direct Prod
[Axiom-developer] [#187 trouble with tuples] Tuple, Product, Direct Product
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.
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden