Algorithms to Solve Polynomial Systems

  • Victor A. Brumberg

Abstract

In most of the cases that actually occur solution of the polynomial systems is sought either in the form of Taylor expansions in powers of an independent argument or in pure trigonometric form with respect to some linear functions of this argument. We start with the first form. Let x1 (t),…, x N (t) be the functions satisfying the differential polynomial system
$$ \frac{{d{{x}_{i}}}}{{dt}} = {{F}_{i}}(x),i = 1,2, \ldots ,N $$
(4.1.1)
, F i (x) being power series with constant coefficients
$$ {F}_{i}(x) = \sum_{j=0}^{J}\sum F_{j_{{1}} \ldots j_{N}}^{(i)}x_{1}^{{j}_{1}}\ldots x_{N}^{{j}_{N}} $$
(4.1.2)
.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Victor A. Brumberg
    • 1
  1. 1.Russian Academy of SciencesInstitute of Applied AstronomySt. PetersburgRussia

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