• Corpus ID: 117501871

# A Fast Algorithm for Partial Fraction Decompositions

@article{Xin2004AFA,
title={A Fast Algorithm for Partial Fraction Decompositions},
author={Guoce Xin},
journal={arXiv: Combinatorics},
year={2004}
}
• G. Xin
• Published 14 August 2004
• Mathematics
• arXiv: Combinatorics
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the rational function. The new algorithms use less storage space, and are suitable for parallel programming. We also discuss full partial fraction decompositions.
2 Citations
A Fast Algorithm for MacMahon's Partition Analysis
• G. Xin
• Mathematics, Computer Science
Electron. J. Comb.
• 2004
The theory of iterated Laurent series and a new algorithm for partial fraction decompositions are combined to obtain a fast algorithm for MacMahon's Omega calculus, which (partially) avoids the "run-time explosion" problem when eliminating several variables.
An Efficient Representation for Large Arrays of Rational Expressions ∗
The paper describes a method of representing an n-dimensional array of rational expressions as an (n + 1)-dimensional array of scalars and shows how this representation readily supports the

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