Bill Page <bill.p...@newsynthesis.org> writes: [...]
| > It is an obscure binary relation, much of which not related to | > the actual mathematics that OpenAxiom wants to deal with. | > That is part of the reasons why it is not glorified into a category | > of its own. | | In OpenAxiom 'before?' is exported by SetCategory | | (1) -> )di op before? | | There is one exposed function called before? : | [1] (D,D) -> Boolean from D if D has SETCAT | | In FriCAS it is exported by the category 'Comparable' | | (1) -> )di op smaller? | | There is one unexposed function called smaller? : | [1] (D,D) -> Boolean from D if D has COMPAR | | and it is inherit by OrderedSet it from Comparable. Note: In FriCAS | not all domains in OrderedSet are Comparable. OpenAxiom did not introduce a dedicated category just for 'before?', as you would find elsewhere. And most domains just don't care about 'before?' If a domain has a natural ordering, then the implementation of before? will use that -- without the author ever having to notice. Otherwise, we do something else he does not need to know about. It is a purely implementation detail artifact, which in an ideal world no OpenAxiom user should ever have to hear of. And I would like to keep it that way. | > It is an obscure relation that is best ignored by most users | > (including library writers.) Only OpenAxiom *runtime system* | > developers (not the library developers) have to care about it. | > | | Could you explain why you say only run-time system developers have to | care about it? Are you claiming that this order relation it is not | important for "mathematical" algorithms? It is not important for their mathematical semantics. The only times it matters is when we a particular algorithm happens to critically depend on that ordering. But, in that case, I would look twice at the algorithm instead of trying to glorify 'before?' -- Gaby ------------------------------------------------------------------------------ Come build with us! The BlackBerry® Developer Conference in SF, CA is the only developer event you need to attend this year. Jumpstart your developing skills, take BlackBerry mobile applications to market and stay ahead of the curve. Join us from November 9-12, 2009. Register now! http://p.sf.net/sfu/devconf _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
