Polynomial Simplification with Side Relations

• Published in: Computer Algebra and Symbolic Computation pp. 315 - 366
• Main Author: Cohen, Joel S.
• Format: Book Chapter
• Language: English
• Published: United Kingdom A K Peters/CRC Press 2003; CRC Press LLC
• Subjects: Multivariate Polynomials; Rational; Reduction Step; Division Process; Principal Ideal; Greatest Common Divisor; Multiplicative Inverse; Hilbert Basis Theorem; Grobner Basis; Computer Algebra Systems; Simplification Algorithm; Non-zero Remainder; Buchberger's Algorithm; Algebraic Number; Divisor Sequence; Constant Polynomial; Non-zero Polynomials; Minimal Polynomials; Nonzero Polynomials; Side Relations; Variable Order; Polynomial Simplification; Multiple Division
• ISBN: 9781568811598; 1568811594
• DOI: 10.1201/9781439863701-14

In Section 4.3 we considered the simplification of polynomials with symbols for algebraic numbers that are defined as the solutions of polynomial equations. In Section 6.2 we considered the simplification of multivariate polynomials with respect to a single polynomial side relation. In this chapter we again consider the polynomial simplification problem but this time allow for several multivariate polynomial side relations that may have symbols in common. Because of this, the supporting mathematical theory is more involved than the material in Sections 4.3 and 6.2. The algorithm in this chapter is a generalization of the algorithms in these earlier sections.