Computer Algebra pp 189-220

# Arithmetic in Basic Algebraic Domains

• G. E. Collins
• M. Mignotte
• F. Winkler
Part of the Computing Supplementa book series (COMPUTING, volume 4)

## Abstract

This chapter is devoted to the arithmetic Operations, essentially addition, multiplication, exponentiation, division, gcd calculation and evaluation, on the basic algebraic domains. The algorithms for these basic domains are those most frequently used in any Computer algebra system. Therefore the best known algorithms, from a computational point of view, are presented. The basic domains considered here are the rational integers, the rational numbers, integers modulo m, Gaussian integers, polynomials, rational functions, power series, finite fields and P-adic numbers. Bounds on the maximum, minimum and average Computing time (t +, t -, t*) for the various algorithms are given.

## Keywords

Great Common Divisor Rational Integer Modular Exponentiation Average Computing Time Modular Arithmetic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• G. E. Collins
• 1
• M. Mignotte
• 2
• F. Winkler
• 3
2. 2.Centre de Calcul de l’EsplanadeUniversite Louis PasteurStrasbourg CédexFrance
3. 3.Institut für MathematikJohannes-Kepler-Universität LinzLinzAustria