Efficient Absolute Factorization of Polynomials with Parametric Coefficients
- Authors: Chistov A.L.1
-
Affiliations:
- St.Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 224, No 2 (2017)
- Pages: 360-384
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239598
- DOI: https://doi.org/10.1007/s10958-017-3422-4
- ID: 239598
Cite item
Abstract
Consider a polynomial with parametric coefficients. We show that the variety of parameters can be represented as a union of strata. For values of the parameters from each stratum, the decomposition of this polynomial into absolutely irreducible factors is given by algebraic formulas depending only on the stratum. Each stratum is a quasiprojective algebraic variety. This variety and the corresponding output are given by polynomials of degrees at most D with D = d′dO(1) where d′, d are bounds on the degrees of the input polynomials. The number of strata is polynomial in the size of the input data. Thus, here we avoid double exponential upper bounds for 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