Multivariate Polynomials

• Published in: Computer Algebra and Symbolic Computation pp. 219 - 282
• Main Author: Cohen, Joel S.
• Format: Book Chapter
• Language: English
• Published: United Kingdom A K Peters/CRC Press 2003; CRC Press LLC
• Subjects: Integral Domain; Iteration Scheme; Primitive Polynomials; Euclidean Property; Multivariate Polynomials; Main Variable; Polynomial Division; Auxiliary Variables; Division Process; Polynomial Domain; Greatest Common Divisor; Greatest Common Divisors; Multiplicative Inverse; Recursive Division; Content Computation; Polynomial Expansion; Irreducible Polynomial; Extended Euclidean Algorithm; Non-zero Polynomials; Unique Factorization Domain; Coefficient Domain; Gcd Computation; Variable Order
• ISBN: 9781568811598; 1568811594
• DOI: 10.1201/9781439863701-12

Most symbolic computation involves mathematical expressions that contain more than one symbol or generalized variable. In order to manipulate these expressions, we must extend the concepts and algorithms described in Chapter 4 to polynomials with several variables. This generalization is the subject of this chapter. It includes a description of coefficient domains and a recursive view of multivariate polynomials (Section 6.1), versions of polynomial division and expansion (Section 6.2), greatest common divisor algorithms (Section 6.3), and the extended Euclidean algorithm (Section 6.3).