Bill Page <[email protected]> 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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
