International Symposium on Symbolic and Algebraic Manipulation

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

Probabilistic algorithms for verification of polynomial identities

  • Jacob T. Schwartz
6. Polynomial Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


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.


Polynomial Identity Resultant System Real Zero Probabilistic Algorithm Mathematical Truth 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Jacob T. Schwartz
    • 1
  1. 1.Computer Science Department, Courant InstituteNew York UniversityUSA

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