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TitleLower bounds for decomposable univariate wild polynomials
Author(s) Joachim von zur Gathen
TypeArticle in Journal
AbstractA univariate polynomial f over a field is decomposable if it is the composition f = g ∘ 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.
KeywordsComputer algebra, Wild polynomial decomposition, Finite fields, Combinatorics on polynomials
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717112001411
LanguageEnglish
JournalJournal of Symbolic Computation
Volume50
Number0
Pages409 - 430
Year2013
Edition0
Translation No
Refereed No
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