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Finding the number of distinct real roots of sparse polynomials of the form p(x,xn)

  • Daniel Richardson
Conference paper
Part of the Progress in Mathematics book series (PM, volume 109)

Abstract

Cylindrical decomposition and false derivatives are used to find the number of distinct real solutions of a polynomial with integral coefficients p(x, x n ), where n is large. The computation time depends only poly normally on the size of the problem, where this is defined to be the maximum of d, log(n) and log(C), where d is the total degree of p(x, y), assumed to be small relative to n, and C is the maximum of the absolute values of the coefficients.

Keywords

Real Root Decimal Place Algebraic Number Total Degree Complete Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1993

Authors and Affiliations

  • Daniel Richardson
    • 1
  1. 1.Department of MathematicsUniversity of BathBathEngland

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