Systems with Parameters, or Efficiently Solving Systems of Polynomial Equations 33 Years Later. II
- Authors: Chistov A.L.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 240, No 5 (2019)
- Pages: 594-616
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242798
- DOI: https://doi.org/10.1007/s10958-019-04378-8
- ID: 242798
Cite item
Abstract
Consider a system of polynomial equations with parametric coefficients over an arbitrary ground field. We show that the variety of parameters can be represented as a union of strata. For values of the parameters from each stratum, the solutions of the system are given by algebraic formulas depending only on this stratum. Each stratum is a quasiprojective algebraic variety with degree bounded from above by a subexponential function in the size of the input data. The number of strata is also subexponential in the size of the input data. Thus, here we avoid double exponential upper bounds on the degrees and solve a long-standing problem
About the authors
A. L. Chistov
St. Petersburg Department of Steklov Institute of Mathematics
Author for correspondence.
Email: alch@pdmi.ras.ru
Russian Federation, St. Petersburg