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Trading order for degree in creative telescoping.

Shaoshi Chen1, Manuel Kauers2

  • 1Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA.

Journal of Symbolic Computation
|November 6, 2015
PubMed
Summary
This summary is machine-generated.

Creative telescoping for hyperexponential terms generates differential equations where lower orders have higher degrees. This study derives degree bounding formulas to optimize creative telescoping performance and analyze its asymptotic complexity.

Keywords:
Definite integrationHyperexponential termsZeilberger’s algorithm

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Area of Science:

  • Computer Algebra
  • Symbolic Computation
  • Differential Equations

Background:

  • Creative telescoping is a method for finding closed-form solutions to summations.
  • Hyperexponential terms are a class of functions frequently encountered in symbolic computation.

Purpose of the Study:

  • To analyze the properties of differential equations generated by creative telescoping for hyperexponential terms.
  • To derive formulas bounding the degree of these equations based on their order.
  • To explore applications in optimizing creative telescoping algorithms.

Main Methods:

  • Analysis of differential equations arising from creative telescoping.
  • Derivation of degree bounding formulas as a function of equation order.
  • Investigation of asymptotic complexity bounds.

Main Results:

  • Established an inverse relationship between the order and degree of output equations.
  • Derived explicit degree bounding formulas for creative telescoping.
  • Identified potential for performance improvements in creative telescoping implementations.

Conclusions:

  • The derived formulas provide crucial insights into the behavior of creative telescoping for hyperexponential terms.
  • Understanding degree-order relationships can lead to more efficient symbolic computation algorithms.
  • This work contributes to the theoretical foundation of automated mathematical problem-solving.