Franz,
On Wed, Oct 21, 2009 at 9:59 AM, you wrote: > On Sat, Oct 17, 2009 at 09:57:43AM +0100, Bertfried Fauser wrote: >> Bases of symmetric function Hopf algebras: > At the moment we concentrate on > PowerSum, Elementary, Complete, Schur symmetric functions. > This is always the same algebra with different basis. > > All these bases are indexed by Partition, > therefore I suggest the following model > (of course more general bases will need other implementations). > For SymmetricFunctions We need products > inner, outer ...: (%,%)->% > > and coproducts: > coinner, coouter ...: % -> TensorPower(2,...,%) > I worry about the situation in which we must write something like: outerProduct: (%:TensorPower(n,...),%:TensorPower(m,...)) -> TensorPower(n+m, ... ) I think this will cause some difficulty. If this can be solved by a recursive definition something like below, I think that would be quite beautiful. > All these products are defined on the basis and then linearly extended, > the latter code is always the same. Therefore I propose > > SymmetricFunction(R:CommutativeRing,B:SymmetricFunctionBasisCategory) > with > inner, outer:(%,%)->% > coinner,couter:%->TensorPower(2,...,%) > add > inner(x,y) = bilinearExtend(inner$B,x,y) > > SymmetricFunctionBasisCategory == with > inner:(%,%) -> SymmetricFunction(Integer,%) > ... > > then all there is to do is to implement the different bases, > the linear extensions are always the same. > The above code however is recursive: > SymmetricFunction uses SymmetricFunctionBasisCategory > and SymmstricFunctionBasisCategory uses SymmetricFunction. > > Apparently the spad compiler accepts this. > ... Yes, this is a very important feature of spad! > > However I suspect problems when the file is split. > How can this be solved? > Compiling together is preferred. Then the compiler can automatically solve the recursion. If you must split the code, the usual approach is to use a kind of iterative bootstrap: Define one of the categories twice, first a dummy one without the recursion, then the one that depends on it, finally re-define the first one. Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ 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 fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
