Fundamental Problems of Algorithmic Algebra de Chee Keng Yap

Fundamental Problems of Algorithmic Algebra

Chee Keng Yap

Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics.

Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more.
Features
� Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system
� Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor
� Aims to be self-contained in its mathematical development
� Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students

Citește tot Restrânge

Descriere

Computer Algebra systems represent a rapidly growing application of computer science to all areas of scientific research and computation. Well-known computer algebra systems such as Maple, Macsyma, Mathematica and REDUCE are now a basic tool on most computers. Underlying these systems are efficient algorithms for various algebraic operations. The field of Computer Algebra, or Algorithmic Algebra, constitute the study of these algorithms and their properties, andrepresents a rich intersection of theoretical computer science with very classical mathematics. Yap's book focuses on a collection of core problems in this area; in effect, they are the computational versions of the classical Fundamental Problem of Algebra and its derivatives. It attempts to beself-contained in its mathematical development while addressing the algorithmic aspects of problems. General prerequesites for the book, beyond some mathematical sophistication, is a course in modern algebra. A course in the analysis of algorithms would also increase the appreciation of some of the themes on efficiency. The book is intended for a first course in algorithmic algebra (or computer algebra) for advanced undergraduates or beginning graduate students in computer science. Additionally, it will be a useful reference for professionals in this field.