Technical References

Aaron Meurer edited this page Mar 12, 2011 · 2 revisions
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This page lists articles and websites that have provided useful information (or just inspiration) for developing SymPy. Papers describing interesting algorithms that have not yet been implemented in SymPy may also be listed here.

Computer algebra (general)

Limits

  • Gruntz, D. On Computing Limits in a Symbolic Manipulation System. Doctoral thesis. Zürich: Swiss Federal Institute of Technology, 1996. (gruntz.pdf)
  • See also Ondřej's presentation (pages 17-20) given at Sage Days 6 in Bristol, UK, that explains the gist of the Gruntz algorithm

Symbolic integration

  • K. Geddes, L.Stefanus, On the Risch-Norman Integration Method and its Implementation in Maple, Proceedings of ISSAC'89, ACM Press, 212-217.
  • J. H. Davenport, On the Parallel Risch Algorithm (I), Proceedings of EUROCAM'82, LNCS 144, Springer, 144-157.
  • J. H. Davenport, On the Parallel Risch Algorithm (III): Use of Tangents, SIGSAM Bulletin 16 (1982), 3-6.
  • J. H. Davenport, B. M. Trager, On the Parallel Risch Algorithm (II), ACM Transactions on Mathematical Software 11 (1985), 356-362.
  • Manuel Bronstein Poor Man's Integrator

Solving (q-)recurrences

  • S. A. Abramov, M. Bronstein and M. Petkovsek, On polynomial solutions of linear operator equations, in: T. Levelt, ed., Proc. ISSAC '95, ACM Press, New York, 1995, 290-296.
  • M. Petkovsek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symbolic Computation, 14 (1992), 243-264.
  • S. A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, in: T. Levelt, ed., Proc. ISSAC '95, ACM Press, New York, 1995, 285-289.
  • M. Petkovsek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symbolic Computation, 14 (1992), 243-264.
  • M. Petkovsek, H. S. Wilf, D. Zeilberger, A = B, 1996.

Partial fraction decomposition

  • M. Bronstein, B. Salvy, Full partial fraction decomposition of rational functions, in: M. Bronstein, ed., Proceedings ISSAC '93, ACM Press, Kiev, Ukraine, 1993, pp. 157-160.