Elements of computer algebra with applications.

*(English)*Zbl 0675.68001
Wiley-Interscience Publication. New York etc.: John Wiley & Sons. xv, 425 p. £33.75; $ 54.00 (1989).

The book under review is more a monograph than a textbook, although its origin was a senior/graduate course of computer algebra.

It contains several topics which represent the author’s experience in the domain of computer algebra. Thus, it contains, for instance, an extension of the Sylvester method for computing polynomial remainder, Sturm and Vincent methods for isolating the real roots of a polynomial equation, methods of factorization of polynomials over the integers. Some applications in cryptography are presented.

The book is preceded by a mathematical introduction devoted to standard methods and algorithms. However, one should not expect any links with, for example, constructive mathematics. As the implementation tools the computer algebra system MAPLE is recommended. The book is endowed with numerous examples, programming exercises and quite complete bibliography.

Concluding, the book is typical for the present state of affairs in computer algebra, that is, particular methods and algorithms dominate the theory, if there is any.

It contains several topics which represent the author’s experience in the domain of computer algebra. Thus, it contains, for instance, an extension of the Sylvester method for computing polynomial remainder, Sturm and Vincent methods for isolating the real roots of a polynomial equation, methods of factorization of polynomials over the integers. Some applications in cryptography are presented.

The book is preceded by a mathematical introduction devoted to standard methods and algorithms. However, one should not expect any links with, for example, constructive mathematics. As the implementation tools the computer algebra system MAPLE is recommended. The book is endowed with numerous examples, programming exercises and quite complete bibliography.

Concluding, the book is typical for the present state of affairs in computer algebra, that is, particular methods and algorithms dominate the theory, if there is any.

Reviewer: P.Kruszyński

##### MSC:

68-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science |

12-04 | Software, source code, etc. for problems pertaining to field theory |

11-04 | Software, source code, etc. for problems pertaining to number theory |

68W30 | Symbolic computation and algebraic computation |