Bivariate Factorizations via Galois Theory, with Application to Exceptional Polynomials
Copyright policy )Bivariate Factorizations via Galois Theory, with Application to Exceptional Polynomials
A method for factoring polynomials of the shape \(f(X)-f(Y)\) where \(f\) is a univariate polynomial over a field is presented. The problem is connected with Galois theory. The method is applied to the family of exceptional polynomials \(f\) discovered by \textit{H. W. Lenstra} jun. and \textit{M. Zieve} in 1995 [Finite Fields and Applications, Glasgow 1995, Lond. Math. Soc. Lect. Note Ser. 233, 209-218 (1996; Zbl 0871.11087)]. The exceptional polynomials are connected with permutation polynomials.
- University of Southern California United States
- University of California System United States
Algebra and Number Theory, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Symbolic computation and algebraic computation, exceptional polynomials
Algebra and Number Theory, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Symbolic computation and algebraic computation, exceptional polynomials
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