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).
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 |