✦ LIBER ✦
Quantifier Elimination for Trigonometric Polynomials by Cylindrical Trigonometric Decomposition
✍ Scribed by Petru Pau; Josef Schicho
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 320 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
Given a formula Φ in r variables, some of them quantified and/or occurring as arguments in trigonometric functions, we consider in this paper the problem of finding a quantifierfree formula equivalent to Φ.
We present an algorithm that first computes a decomposition of the space so that the polynomials occurring in Φ are sign-invariant over each cell of this decomposition. Then the cells over which Φ is true are collected: their description gives a quantifier-free formula equivalent to Φ. The algorithm is an adaption of a well-known algorithm for the same problem with polynomial functions.