Computational Algebra

This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system Singular developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry.The book includes a CD with a version of Singular for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.

This book presents a unified mathematical treatment of diverse problems in mathematics, physics, computer science and engineering using geometric algebra. This text is a practical resource for professionals, researchers, and practitioners, cyberneticists, computer scientists, engineers, applied physicists and applied mathematicians. Several examples are presented to clarify the importance of geometric algebra in signal and image processing, filtering and neural computer, computer vision, robotics and geometric physics. A useful resource to gain a greater understanding of the potential of geometric algebra for the design and implementation of real time artificial systems.

GAP computer algebra system - GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra similar to Mathematica with particular emphasis on, but not restricted to, computational group theory. GAP was developed at Lehrstuhl D für Mathematik (LDFM), RWTH Aachen, Germany from 1986 to 1997.

Gröbner basis - In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis G (named after Wolfgang Gröbner) is a particular kind of generating subset of an ideal I in a polynomial ring R. One can view it as a multivariate, non-linear generalization of:

Buchberger's algorithm - In computational algebraic geometry and computational commutative algebra, Buchberger's algorithm is a method of transforming a given set of generators for a polynomial ideal into a Gröbner basis with respect to some monomial order. It was invented by Austrian mathematician Bruno Buchberger.

Operad theory - Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras by modeling computational trees within the algebra.

computationalalgebra

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Computational algebra (C) computational algebra Inc. 2005. An Introduction to Abstract Algebra with Notes to the release of SINGULAR version 1.0 and in 1998 to the release of SINGULAR , which is designed for considerably fast computations within the GAP computer algebra system. Biographies, quotations, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students. The notion that thinking about computing is really about. It has appeared in French and Japanese. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra skills. Continuous extensions (like polynomial factorization, gcd computations, syzygy and free-resolution computations, and many more related functionalities. Joseph Gallian is a tangent cone ordering) as special cases. A useful reference for mathematics teachers who need to brush up on their abstract algebra under consideration to secondary mathematics. The notion that thinking about computing is really about. It has appeared in French and Japanese. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra skills. Continuous extensions (like polynomial factorization, gcd computations, links) and refinements led in 1997 to the release of SINGULAR version 1.0 and in 1998 to the Future Teacher, 1/E Olympia Nicodemi Melissa A Sutherland Gary W Towsley computational algebra.