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Shiftless decomposition and polynomial-time rational summation
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Proceedings of the 2003 international symposium on Symbolic and algebraic computation table of contents
Philadelphia, PA, USA
Pages: 119 - 126  
Year of Publication: 2003
ISBN:1-58113-641-2
Authors
J. Gerhard  Maplesoft, Waterloo, ON, Canada
M. Giesbrecht  University of Waterloo, Waterloo, ON, Canada
A. Storjohann  University of Waterloo, Waterloo, ON, Canada
E. V. Zima  University of Waterloo, Waterloo, ON, Canada
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
ACM: Association for Computing Machinery
Publisher
ACM  New York, NY, USA
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ABSTRACT

New algorithms are presented for computing the dispersion set of two polynomials over Q and for shiftless factorization. Together with a summability criterion by Abramov, these are applied to get a polynomial-time algorithm for indefinite rational summation, using a sparse representation of the output.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
S.A. Abramov. On the summation of rational functions. U.S.S.R. Comput. Maths. Math. Phys. 11, pp. 324--330, 1971. Transl. from Zh. vychisl. mat. mat. fiz. 11, pp. 1071--1075, 1971.
 
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S.A. Abramov. The rational component of the solution of a first-order linear recurrence relation with a rational right-hand side. U.S.S.R. Comput. Maths. Math. Phys. 15, pp. 216--221, 1975. Transl. from Zh. vychisl. mat. mat. fiz. 15, pp. 1035--1039, 1975.
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J. Gerhard. Modular algorithms in symbolic summation and symbolic integration. PhD thesis, Universität Paderborn, Germany, 2001.
 
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R.W. Gosper. Decision procedures for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. U.S.A. 75(1), pp. 40--42, 1978.
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M. van Hoeij. Factoring polynomials and the knapsack problem. J. Number Theory. 95, pp. 167-189, 2002.
 
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J.B. Rosser and L. Schoenfeld. Approximate formulas for some functions of prime numbers. Ill. J. Math. 6, pp. 64--94, 1962.
 
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R. Pirastu. On combinatorial identities: symbolic summation and umbral calculus. PhD thesis, Johannes Kepler Universität Linz, Austria, July 1996.


Collaborative Colleagues:
J. Gerhard: colleagues
M. Giesbrecht: colleagues
A. Storjohann: colleagues
E. V. Zima: colleagues