We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower degree. More precisely, we derive degree bounding formulas which allow to estimate the degree of the output equations of creative telescoping as a function of the order. As an application, we show how the knowledge of this formula can be used to optimize the runtime of creative telescoping implementations, and we deduce bounds on the asymptotic complexity of creative telescoping for hyperexponential terms.
| Original language | English |
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| Number of pages | 31 |
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| Publication status | Published - 2011 |
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| Name | arXiv.org |
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| No. | 1108.4508 |
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- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101009 Geometry
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101006 Differential geometry
- 101003 Applied geometry
- 102025 Distributed systems
- Computation in Informatics and Mathematics