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Journals ACM Communications in Computer Algebra Volume 45 Issue 3/4

ACM Communications in Computer Algebra, Vol. 45, No. 3, Issue 177, September 2011 New software for computing asymptotics of multivariate generating functions Alexander Raichev Department of Computer Science University of Auckland Auckland, New Zealand, 1001 raichev@cs.auckland.ac.nz Abstract I introduce amgf, a new Sage software package for computing asymptotics of multivariate generating functions. It implements recent algorithms developed by Mark C. Wilson and me. The current version of amgf is under peer review for incorporation into Sage and is available from my website at www.cs. auckland.ac.nz/~raichev/research.html. Introduction Let F (x) = ˆNd F x 1 x d be a multivariate power series with complex coe ƒcients that converges in a 1 d neighborhood of the origin. Assume F = G/H for some functions G and H holomorphic in a neighborhood of the origin. For example, F could be the combinatorial generating function (1 ’ x1 ’ x2 ’ x1 x2 ) ’1 whose power series coe ƒcients F 1 , 2 (the Delannoy numbers) count the number of lattice paths from (0, 0) to ( 1 , 2 ) with allowable steps (1, 0), (0, 1) and (1, 1). Oftentimes one would like an asymptotic expansion for the coe

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New software for computing asymptotics of multivariate generating functions

Raichev, Alexander
ACM Communications in Computer Algebra , Volume 45 (3/4)
Association for Computing Machinery – Jan 23, 2012

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