Fundamental Problems of Algorithmic Algebra

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 andrepresents 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, thefundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features DT Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system DT Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor DT Aims to be self-contained in its mathematical development DT Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students