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International Symposium on Symbolic and Algebraic Manipulation

EUROSAM 1979: Symbolic and Algebraic Computation pp 200–215Cite as

Probabilistic algorithms for verification of polynomial identities

  • 6. Polynomial Algorithms
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

Abstract

The startling success of the Rabin-Strassen-Solovay primality algorithm, togehter with the intriguing foundational possibility that axioms of randomness may constitute a useful fundamental source of mathematical truth independent of the standard axiomatic structure of mathematics, suggests a vigorous search for probabilistic algorithms. In illustration of this observation, we present various fast probabilistic algorithms, with probability of correctness guaranteed a priori, for testing polynomial identities and properties of systems of polynomials. Ancillary fast algorithms for calculating resultants and Sturm sequences are given. Theorems of elementary geometry can be proved much more efficiently by the techniques presented than by any known artificial intelligence approach.

This work is supported under NSF Grant MCS-76-00116 from the National Science Foundation, and U. S. Department of Energy Contract No. EY-76-C-02-3077.

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Authors and Affiliations

  1. Computer Science Department, Courant Institute, New York University, USA

    Jacob T. Schwartz

Authors
  1. Jacob T. Schwartz
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Edward W. Ng

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© 1979 Springer-Verlag Berlin Heidelberg

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Schwartz, J.T. (1979). Probabilistic algorithms for verification of polynomial identities. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_72

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  • DOI: https://doi.org/10.1007/3-540-09519-5_72

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

  • eBook Packages: Springer Book Archive

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