Geodesic
A fast algorithm for MacMahon's partition analysis
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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This paper deals with evaluating constant terms of a special class of rational functions, the Elliott-rational functions. The constant term of such a function can be read off immediately from its partial fraction decomposition. We combine the theory of iterated Laurent series and a new algorithm for partial fraction decompositions to obtain a fast algorithm for MacMahon's Omega calculus, which (partially) avoids the "run-time explosion" problem when eliminating several variables. We discuss the efficiency of our algorithm by investigating problems studied by Andrews and his coauthors; our running time is much less than that of their Omega package.
DOI : 10.37236/1811
Classification : 11Y60, 05A17 
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     author = {Guoce Xin},
     title = {A fast algorithm for {MacMahon's} partition analysis},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1811},
     zbl = {1066.11060},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1811/}
}
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Guoce Xin. A fast algorithm for MacMahon's partition analysis. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1811

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