The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Grobner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature."

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas-...

This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002.

The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in...

This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001.

The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.

Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas-...

This book constitutes the refereed proceedings of the 4th International Conference on Algebraic Informatics, CAI 2011, held in Linz, Austria, in June 2011.
The 12 revised full papers presented together with 4 invited articles were carefully reviewed and selected from numerous submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical...