Overview of the SumTools Package - Maple Programming Help

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Overview of the SumTools Package

 

Calling Sequence

Description

References

Calling Sequence

SumTools[command](arguments)

command(arguments)

Description

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The SumTools package contains commands that help find closed forms of definite and indefinite sums. The package consists of three commands and three subpackages.

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Each command in the SumTools package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

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To display the help page for a particular SumTools command, see Getting Help with a Command in a Package.

Commands for Computing Closed Forms of Definite and Indefinite Sums

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SumTools[Summation]: compute closed forms of definite and indefinite sums

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SumTools[DefiniteSummation]: compute closed forms of definite sums

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SumTools[IndefiniteSummation]: compute closed forms of indefinite sums

Tools for Computing Closed Forms of Indefinite sums: The IndefiniteSum Subpackage

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SumTools[IndefiniteSum][AccurateSummation]: compute indefinite sums using the method of accurate summation

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SumTools[IndefiniteSum][AddIndefiniteSum]: library extension mechanism

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SumTools[IndefiniteSum][HomotopySum]: compute indefinite sums of expressions containing unspecified functions

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SumTools[IndefiniteSum][Hypergeometric]: compute indefinite sums of hypergeometric terms

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SumTools[IndefiniteSum][Indefinite]: compute closed forms of indefinite sums

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SumTools[IndefiniteSum][Polynomial]: compute indefinite sums of polynomials

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SumTools[IndefiniteSum][Rational]: compute indefinite sums of rational functions

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SumTools[IndefiniteSum][RemoveIndefiniteSum]: library extension mechanism

Tools for Computing Closed Forms of Definite Sums: The DefiniteSum Subpackage

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SumTools[DefiniteSum][CreativeTelescoping]: compute closed forms of definite sums using the creative telescoping method

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SumTools[DefiniteSum][Definite]: compute closed forms of definite sums

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SumTools[DefiniteSum][pFqToStandardFunctions]: compute closed forms of definite sums using the conversion method where the hypergeometric series is used as an intermediate representation

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SumTools[DefiniteSum][SummableSpace]: compute all sequences satisfying a given first order recurrence that are summable by either Gosper's algorithm or the accurate summation algorithm

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SumTools[DefiniteSum][Telescoping]: compute closed forms of definite sums using the classical telescoping method

Tools for Working with Hypergeometric Terms: The Hypergeometric Subpackage

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Normal forms of rational functions and hypergeometric terms:

  

SumTools[Hypergeometric][EfficientRepresentation],

  

SumTools[Hypergeometric][MultiplicativeDecomposition],

  

SumTools[Hypergeometric][PolynomialNormalForm],

  

SumTools[Hypergeometric][RationalCanonicalForm],

  

SumTools[Hypergeometric][RegularGammaForm],

  

SumTools[Hypergeometric][SumDecomposition]

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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][MinimalTelescoper],

  

SumTools[Hypergeometric][MinimalZpair],

  

SumTools[Hypergeometric][Zeilberger],

  

SumTools[Hypergeometric][ZeilbergerRecurrence],

  

SumTools[Hypergeometric][ZpairDirect]

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Applications:

  

SumTools[Hypergeometric][DefiniteSum],

  

SumTools[Hypergeometric][IndefiniteSum],

  

SumTools[Hypergeometric][WZMethod]

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Other functions:

  

SumTools[Hypergeometric][AreSimilar],

  

SumTools[Hypergeometric][ConjugateRTerm],

  

SumTools[Hypergeometric][BottomSequence],

  

SumTools[Hypergeometric][IsHolonomic],

  

SumTools[Hypergeometric][IsHypergeometricTerm],

  

SumTools[Hypergeometric][IsProperHypergeometricTerm],

  

SumTools[Hypergeometric][Verify]

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).

See Also

LREtools

rsolve

sum

sumtools

UsingPackages

with