Ebook: Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra: with 91 illustrations
- Genre: Mathematics // Algebra
- Series: Undergraduate texts in mathematics
- Year: 2006
- Publisher: Springer
- City: New York
- Edition: 2nd ed
- Language: English
- djvu
The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered it the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric Theorem proving.
In preparing a new edition of "Ideals, Varieties and Algorithms" the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple, Mathematica and REDUCE.