On approximate irreducibility of polynomials in several variables

Authors:
Erich Kaltofen;John May
Affiliations:
North Carolina State University, Raleigh, NC;North Carolina State University, Raleigh, NC
Venue:
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Year:
2003

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Abstract

We study the problem of bounding a polynomial away from polynomials which are absolutely irreducible. Such separation bounds are useful for testing whether a numerical polynomial is absolutely irreducible, given a certain tolerance on its coefficients. Using an absolute irreducibility criterion due to Ruppert, we are able to find useful separation bounds, in several norms, for bivariate polynomials. We also use Ruppert's criterion to derive new, more effective Noether forms for polynomials of arbitrarily many variables. These forms lead to small separation bounds for polynomials of arbitrarily many variables.