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Endpaper: FRPOLY: A benchmark revisited

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LISP and Symbolic Computation

Abstract

The FRPOLY Lisp performance benchmark [3] was based on a circa-1968 piece of code for computing powers of polynomials. We address two questions: (a) What algorithm would you use if you really wanted to compute powers of polynomials fast? and (b) Given that Common Lisp supports many types of data structures other than the simple lists used for the benchmark, what more efficient representations might be appropriate to use for polynomials?

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References

  1. Davenport, J., Siret, Y., and Tournier, E.Computer Algebra Systems and Algorithms for Algebraic Computation. Academic Press, (1988).

  2. Fateman, Richard J.On the Computation of Powers of Sparse Polynomials. Studies in Applied Math (53), No. 2, (June 1974) 145–155.

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  3. Gabriel, Richard P.Performance and Evaluation of Lisp Systems. MIT Press (1985).

  4. Probst, David K. and Alagar, Vangalur S.A Family of Algorithms for Powering Sparse Polynomials.SIAM J. Comput. (8), No. 4, (1979), 626–644. Corrigendum, andSIAM J. Comput. (9) No. 2, (1980) 439.

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Fateman, R.J. Endpaper: FRPOLY: A benchmark revisited. Lisp and Symbolic Computation 4, 155–164 (1991). https://doi.org/10.1007/BF01813018

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  • DOI: https://doi.org/10.1007/BF01813018

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