On testing the divisibility of lacunary polynomials by cyclotomic polynomials
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- by Michael Filaseta and Andrzej Schinzel PDF
- Math. Comp. 73 (2004), 957-965 Request permission
Abstract:
An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficient-exponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.References
- J. H. Conway and A. J. Jones, Trigonometric Diophantine equations (On vanishing sums of roots of unity), Acta Arith. 30 (1976), no. 3, 229–240. MR 422149, DOI 10.4064/aa-30-3-229-240
Additional Information
- Michael Filaseta
- Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29218
- MR Author ID: 66800
- Email: filaseta@math.sc.edu
- Andrzej Schinzel
- Affiliation: Institute of Mathematics of the Polish Academy of Sciences, P.O. Box 137, ul. Śniadeckich 8, 00-950 Warszawa 10, Poland
- Email: a.schinzel@impan.gov.pl
- Received by editor(s): October 1, 1998
- Received by editor(s) in revised form: December 15, 2002
- Published electronically: August 5, 2003
- Additional Notes: The first author gratefully acknowledges support from the National Security Agency and the National Science Foundation
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 957-965
- MSC (2000): Primary 13P05, 12Y05, 11Y16, 11C08
- DOI: https://doi.org/10.1090/S0025-5718-03-01589-8
- MathSciNet review: 2031418