Multivariate Polynomials

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...

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Vydáno v:Computer Algebra and Symbolic Computation s. 219 - 282
Hlavní autor: Cohen, Joel S.
Médium: Kapitola
Jazyk:angličtina
Vydáno: United Kingdom A K Peters/CRC Press 2003
CRC Press LLC
Témata:
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
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Shrnutí: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).
ISBN:9781568811598
1568811594
DOI:10.1201/9781439863701-12