Algorithms for trigonometric polynomials

ABSTRACT

In this paper we present algorithms for simplifying ratios of trigonometric polynomials and algorithms for dividing, factoring and computing greatest common divisors of trigonometric polynomials, that is, polynomials in sin(x) and cos(x).

REFERENCES

• 1: Koepf, W., Bernig A., Melenk H. (1999) TRIGSIMP: A REDUCE Package for the Simplification and Factorization of Trigonometric and Hyperbolic Expressions. REDUCE 7 documentation.
• 2: Hungerford, T.W. (1980) Algebra, second edition, Graduate Texts in Mathematics, Springer-Verlag.
• 3: Roach, K. (1992), Trigonometric Factorization and Integration, Unpublished manuscript. Presented at the Maple Retreat, June, 1992.
• 4: Hale F. Trotter, An overlooked example of nonunique factorization, American Mathematical Monthly, v.95 n.4, p.339-342, April 1988 [doi>10.2307/2323570]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.5 Roots of Nonlinear Equations
          Subjects: Polynomials, methods for

General Terms:
Algorithms, Measurement, Performance, Theory, Verification