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Holonomic functions in mathematica

Published: 28 January 2014 Publication History

Abstract

We present the Mathematica package HolonomicFunctions which provides a powerful framework for the automatic manipulation of multivariate holonomic functions, in the spirit of Zeilberger's holonomic systems approach. Its top-level functionalities are: converting a mathematical expression into a holonomic description, executing holonomic closure properties, and creative telescoping for general holonomic functions. To achieve these goals, many other, lower-level, functionalities had to be implemented which were not available in the Mathematica system: finding rational solutions of linear systems of (q-) difference / differential equations, noncommutative arithmetic in Ore algebras and computing Gröbner bases in such domains.

References

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Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, and Guoce Xin. Hermite reduction and creative telescoping for hyperexponential functions. In Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), New York, NY, USA, 2013. ACM. To appear (preprint on arXiv:1301.5038).
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Frédéric Chyzak. An extension of Zeilberger's fast algorithm to general holonomic functions. Discrete Mathematics, 217(1-3):115--134, 2000.
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Frédéric Chyzak, Manuel Kauers, and Bruno Salvy. A non-holonomic systems approach to special function identities. In Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), pages 111--118, New York, NY, USA, 2009. ACM.
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Stavros Garoufalidis and Christoph Koutschan. Twisting q-holonomic sequences by complex roots of unity. In Joris van der Hoeven and Mark van Hoeij, editors, Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), pages 179--186. ACM, 2012.
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Christoph Koutschan. A fast approach to creative telescoping. Mathematics in Computer Science, 4(2-3):259--266, 2010.
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Christoph Koutschan. HolonomicFunctions (user's guide). Technical Report 10-01, RISC Report Series, Johannes Kepler University, Linz, Austria, 2010. http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/.
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Cited By

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  • (2024)Hypergeometric-type sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102328125(102328)Online publication date: Nov-2024
  • (2020)An extension of the method of brackets. Part 2Open Mathematics10.1515/math-2020-006218:1(983-995)Online publication date: 16-Sep-2020
  • (2016)Efficient Algorithms for Mixed Creative TelscopingProceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930907(127-134)Online publication date: 20-Jul-2016

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 47, Issue 3/4
September/December 2013
116 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/2576802
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 January 2014
Published in SIGSAM-CCA Volume 47, Issue 3/4

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Cited By

View all
  • (2024)Hypergeometric-type sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102328125(102328)Online publication date: Nov-2024
  • (2020)An extension of the method of brackets. Part 2Open Mathematics10.1515/math-2020-006218:1(983-995)Online publication date: 16-Sep-2020
  • (2016)Efficient Algorithms for Mixed Creative TelscopingProceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930907(127-134)Online publication date: 20-Jul-2016

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