Burcin Erocal wrote: > On Thu, 13 Nov 2008 04:09:56 -0600 > Jason Grout <[EMAIL PROTECTED]> wrote: > >> Burcin Erocal wrote: >> >>> >>> Returning to the question of how Sage plans to handle this, the >>> short answer is "I am working on it." :) >>> >> Yeah! >> >> >>> We will have a completely new implementation of summation, >>> independent of the one in Maxima. At the moment I have an >>> implementation of the theoretical framework which lets you solve >>> much more complicated sums than the ones above. Unfortunately, >>> coming up with an interface that spares the user from the gory >>> details of the theory will still be a challenge. Thus, it will be >>> some time before these problems are handled natively in Sage, but >>> then Sage will (hopefully) be more capable than the others out >>> there. >> >> Is there any chance you could make this work available so people >> could experiment with it, test it, and if desired, give suggestions >> for an interface? On the other hand, I understand if the work is >> still at a "I need to work on this alone" stage. > > In this case, there is a huge gap between theory and the user. It > is not like giving the ratio of the consecutive terms of your > summand as an argument to Gosper's algorithm. Unless you want to get > into research in this area, the code is useless for now. > > Nevertheless, I will start implementing a simple user interface, > which I hope will help me handle more complex expressions as > well. After I have the basic framework to construct the algebraic > objects I work with, given the symbolic expressions, I will start > submitting patches. >
I would love to see this done in Sage. The few times that I fire up Maple is using the SumTools Package: > Introduction to the SumTools Package > > Calling Sequence > > SumTools[function](args) > > function(args) > > Description > > The SumTools package contains functions that help find closed forms of > definite and indefinite sums. The package consists of three functions > and three subpackages. > > Functions for Computing Closed Forms of Definite and Indefinite Sums > > SumTools[Summation]: compute closed forms of definite and indefinite sums > > SumTools[DefiniteSummation]: compute closed forms of definite sums > > SumTools[IndefiniteSummation]: compute closed forms of indefinite sums > > Tools for Computing Closed Forms of Indefinite sums: The IndefiniteSum > Subpackage > > SumTools[IndefiniteSum][AccurateSummation]: compute indefinite sums > using the method of accurate summation > > SumTools[IndefiniteSum][AddIndefiniteSum]: library extension mechanism > > SumTools[IndefiniteSum][Hypergeometric]: compute indefinite sums of > hypergeometric terms > > SumTools[IndefiniteSum][Indefinite]: compute closed forms of indefinite sums > > SumTools[IndefiniteSum][Polynomial]: compute indefinite sums of polynomials > > SumTools[IndefiniteSum][Rational]: compute indefinite sums of rational > functions > > SumTools[IndefiniteSum][RemoveIndefiniteSum]: library extension mechanism > > Tools for Computing Closed Forms of Definite Sums: The DefiniteSum Subpackage > > SumTools[DefiniteSum][CreativeTelescoping]: compute closed forms of > definite sums using the creative telescoping method > > SumTools[DefiniteSum][Definite]: compute closed forms of definite sums > > SumTools[DefiniteSum][pFqToStandardFunctions]: compute closed forms of > definite sums using the conversion method where the hypergeometric > series is used as an intermediate representation > > SumTools[DefiniteSum][Telescoping]: compute closed forms of definite > sums using the classical telescoping method > > Tools for Working with Hypergeometric Terms: The Hypergeometric Subpackage > > Normal forms of rational functions and hypergeometric terms: > > SumTools[Hypergeometric][MultiplicativeDecomposition], > SumTools[Hypergeometric][PolynomialNormalForm], > SumTools[Hypergeometric][RationalCanonicalForm], > SumTools[Hypergeometric][SumDecomposition] > > Algorithms for definite and indefinite sums of hypergeometric type: > > SumTools[Hypergeometric][ExtendedGosper], > SumTools[Hypergeometric][ExtendedZeilberger], > SumTools[Hypergeometric][Gosper], > SumTools[Hypergeometric][IsZApplicable], > SumTools[Hypergeometric][KoepfGosper], > SumTools[Hypergeometric][KoepfZeilberger], > SumTools[Hypergeometric][LowerBound], > SumTools[Hypergeometric][MinimalZpair], > SumTools[Hypergeometric][Zeilberger], > SumTools[Hypergeometric][ZeilbergerRecurrence], > SumTools[Hypergeometric][ZpairDirect] > > Applications: > > SumTools[Hypergeometric][DefiniteSum], > SumTools[Hypergeometric][IndefiniteSum], > SumTools[Hypergeometric][WZMethod] > > Other functions: > > SumTools[Hypergeometric][AreSimilar], > SumTools[Hypergeometric][ConjugateRTerm], > SumTools[Hypergeometric][IsHolonomic], > SumTools[Hypergeometric][IsHypergeometricTerm], > SumTools[Hypergeometric][IsProperHypergeometricTerm], > SumTools[Hypergeometric][Verify] > > Accessing SumTools Package Functions > > Each function in the SumTools package can be accessed by using either > the long form or the short form of the function name in the command > calling sequence. > > Getting Help > > To display the help page for a particular SumTools function, see > Getting Help with a Function in a Package. > > See Also > > LREtools, rsolve, sum, UsingPackages, with > > References > > Abramov, S.A.; Carette, J.J.; Geddes, K.O.; and Le, H.Q. "Symbolic > Summation in Maple." Technical Report CS-2002-32, School of Computer > Science, University of Waterloo, Ontario, Canada. (2002). Jaap --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
