Mignotte, Maurice 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) Cited in 1 ReviewCited in 39 Documents 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 Keywords:complexity; primality; factorization; polynomials Citations:Zbl 0679.12001 PDFBibTeX XMLCite \textit{M. Mignotte}, Mathematics for computer algebra. Transl. from the French by Catherine Mignotte. New York etc.: Springer-Verlag (1992; Zbl 0741.11002)