Dear all,
I'm not absolutely sure what the type of expression$CombinatorialSpecies in axiom-portcombinat/src/species.as.nw *should* be. It is supposed to return an "expression" for the grammar that defines the species. Of course, in some cases, this expression really is a rational function, or maybe an algebraic function, sometimes a holonomic function, maybe we can give a defining differential equation, but sometimes it won't have any structure we can describe well at all. The point is, that only the "functor" (in the aldor/axiom sense) that produces the CombinatorialSpecies will know, and often, it will depend on the arguments given to the functor. I guess, the best way to deal with it is to leave it as it is, i.e., make it return a "SpeciesExpression", which allows all sorts of "operators". We can then make SpeciesExpression clever and decide whether a given SpeciesExpression can be "retract"ed to a better domain. We can possibly have some Boolean constants exported by CombinatorialSpecies that return whether a species is "rational", "algebraic", "holonomic", etc. (I use quotes, since I want to alert you that thisis stronger than the generating series being rational, algebraic, etc.) The good news is, that we can decide for two species built using CharacteristicSpecies, Plus, Times and Compose whether they are equal or not. There exists a normal form! See Karl Aberer: http://lsirpeople.epfl.ch/aberer/PAPERS/P1990-01.pdf I wonder whether there is already a "better" normal form. This certainly should be investigated. Martin ------------------------------------------------------------------------- Take Surveys. Earn Cash. Influence the Future of IT Join SourceForge.net's Techsay panel and you'll get the chance to share your opinions on IT & business topics through brief surveys - and earn cash http://www.techsay.com/default.php?page=join.php&p=sourceforge&CID=DEVDEV _______________________________________________ Aldor-combinat-devel mailing list Aldor-combinat-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/aldor-combinat-devel
