Elsevier

Information Processing Letters

Volume 39, Issue 5, 13 September 1991, Pages 231-236
Information Processing Letters

Trigonometric polynomials with simple roots

https://doi.org/10.1016/0020-0190(91)90020-IGet rights and content

Abstract

Trogonometric polynimials frequently occur applications in physics, numerical analysis and engineering, since each periodic function can be approximated by a trigonometric polynomial. Additionally, there are many analogies between trigonometric and standard algebraic polynomials. Algorithms in computer algebra depend on methods for the square-free decomposition of polynomials. These methods use polynomial division and cannot be applied directly to trigonometric polynomials. Let P denote the set of odd multiples of π. A trigonometric polynomial T is a reduced representation of a trigonometric polynomial T if the set of zeros of T in CP is the same as the set of zeros of T in CP, and if all zero s of T are simple zeros. It is shown that a reduced representation of a trigonometric polynomial with rational or algebraic coefficients can be found in polynomial time.

References (4)

There are more references available in the full text version of this article.

Author's address: Robotics Laboratory, Computer Science Department, Standford University, Standford, CA 94305, U.S.A.

View full text