Lower bounds for decomposable univariate wild polynomials
A univariate polynomial f over a field is decomposable if it is the composition f = g o h of two polynomials g and h whose degree is at least 2. The tame case, where the field characteristic p does not divide the degree n of f, is reasonably well understood. The wild case, where p divides n, is more challenging. We present an efficient algorithm for this case that computes a decomposition, if one exists. It works for most but not all inputs, and provides a reasonable lower bound on the number of decomposable polynomials over a finite field. This is a central ingredient in finding a good approximation to this number. (C) 2012 Elsevier B.V. All rights reserved.
finite fields computer algebra wild polynomial decomposition combinatorics on polynomials