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Mathematics for computer algebra. Transl. from the French by Catherine Mignotte. (English) Zbl 0741.11002

New York etc.: Springer-Verlag. xiv, 346 p. (1992).
This is a translation of “Mathématiques pour le calcul formel” (1989; Zbl 0679.12001) but with some additional material.
The main topics of the book are as follows. Chapter 1: the elementary operations of arithmetic with special reference to multi-length working and complexity. Chapter 2: finite groups, primality and factorization. Chapter 3: polynomials and linear recursive sequences. Chapter 4: polynomials with complex coefficients and, in particular, bounds for size of factors, distribution of roots, and separation of roots. Chapter 5: polynomials with real coefficients, estimates of roots, and number of roots in a real interval. Chapter 6: polynomials over finite fields and factorization. Chapter 7: polynomials with integer coefficients and methods of factorization.
There are many exercises, some of which are supplements to the main text.
The book is easy to read, and the translation is good, with a few lapses, e.g. “rest” for “remainder” (p. 105), “decreases of” for “decreases by” (p. 196).
Reviewer: H.J.Godwin (Egham)

MSC:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
12-02 Research exposition (monographs, survey articles) pertaining to field theory
68-02 Research exposition (monographs, survey articles) pertaining to computer science
68W30 Symbolic computation and algebraic computation
12Y05 Computational aspects of field theory and polynomials (MSC2010)
11Y16 Number-theoretic algorithms; complexity
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
12D05 Polynomials in real and complex fields: factorization
11Y05 Factorization
11Y11 Primality
11C08 Polynomials in number theory
11T06 Polynomials over finite fields
13P05 Polynomials, factorization in commutative rings

Citations:

Zbl 0679.12001
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