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These notes describe Leinartas's algorithm for multivariate partial fraction decompositions and employ an implementation thereof in Sage.
E. K. Leĭnartas, Factorization of rational functions of several variables into partial fractions , Soviet Math. (Iz. VUZ) (1978), no. 10(22), 35–38. MR MR522760 (80c:32002)
1978
Earlier work this paper cites.
I. A. Aĭzenberg and A. P. Yuzhakov, Integral representations and residues in multidimensional complex analysis , Translations of Mathematical Monographs, vol. 58, American Mathematical Society, Providence, RI, 1983, Translated from the Russian by H. H. McFaden, Translation edited by Lev J. Leifman. MR MR735793 (85a:32006)
1983
Earlier work this paper cites.
Richard Ehrenborg and Gian-Carlo Rota, Apolarity and canonical forms for homogeneous polynomials , European J. Combin. 14
1993
Earlier work this paper cites.
David Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms , third ed., Undergraduate Texts in Mathematics, Springer, New York, 2007, An introduction to computational algebraic geometry and commutative algebra. MR 2290010 (2007h:13036)
2007
Cited alongside, same era.
Jesús A. De Loera, Jon Lee, Peter N. Malkin, and Susan Margulies, Hilbert’s Nullstellensatz and an algorithm for proving combinatorial infeasibility , ISSAC 2008, ACM, New York, 2008, pp. 197–206. MR 2513506 (2010j:05385)
2008
Cited alongside, same era.
David R. Stoutemyer, Multivariate partial fraction expansion , ACM Commun. Comput. Algebra 42
2008
Cited alongside, same era.
Neeraj Kayal, The complexity of the annihilating polynomial , Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity (Washington, DC, USA), CCC ’09, IEEE Computer Society, 2009, pp. 184–193
2009
Later among the works it cites.
Alexander Raichev and Mark C. Wilson, Asymptotics of coefficients of multivariate generating functions: improvements for multiple points , Online Journal of Analytic Combinatorics (2012)
2012
Closest in time.
W. A. Stein et al., Sage Mathematics Software (Version 5.0) , The Sage Development Team, 2012, http://www.sagemath.org
2012
Closest in time.
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