Polynomial gcd computations over towers of algebraic extensions

  • Marc Moreno Maza
  • Renaud Rioboo
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 948)


Some methods for polynomial system solving require efficient techniques for computing univariate polynomial gcd over algebraic extensions of a field. Currently used techniques compute generic univariate polynomial gcd before specializing the result using algebraic relations in the ring of coefficients. This strategy generates very big intermediate data and fails for many problems. We present here a new approach which takes permanently into account those algebraic relations. It is based on a property of subresultant remainder sequences and leads to a great increase of the speed of computation and thus the size of accessible problems.


Polynomial gcd subresultants algebraic numbers triangular sets zero dimensional systems AXIOM 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marc Moreno Maza
    • 1
  • Renaud Rioboo
    • 1
  1. 1.LITP, Institut Blaise Pascal, Boite 168Université Pierre et Marie CurieParis Cedex 05

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