Arithmetic of Polynomials, Rational Functions, and Power Series

K. O. Geddes, S. R. Czapor and G. Labahn
Additional contact information
K. O. Geddes: University of Waterloo
S. R. Czapor: Laurentian University
G. Labahn: University of Waterloo

Chapter Chapter 4 in Algorithms for Computer Algebra, 1992, pp 111-149 from Springer

Abstract: Abstract In Chapter 2 we introduced the basic algebraic domains which are of interest to computer algebra. This was followed by the representation problem, that is, the problem of how elements of these algebras are to be represented in a computer environment. Having described the types of objects along with the various representation issues, there follows the problem of implementing the various algebraic operations that define the algebras. In this chapter we describe the arithmetic operations of addition, subtraction, multiplication, and division for these domains. In particular, we describe these fundamental operations in the ring of integers modulo n, the ring of formal power series over a field, and the ring of polynomials over an integral domain along with their quotient fields. The latter includes the domain of multiprecision integers and rational numbers.

Keywords: Power Series; Discrete Fourier Transform; Arithmetic Operation; Computer Algebra; Modular Representation (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-585-33247-5_4

Ordering information: This item can be ordered from
http://www.springer.com/9780585332475

DOI: 10.1007/978-0-585-33247-5_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().