Description
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra develops the connection between polynomial equations, algebraic varieties, and ideals from a computational perspective. It introduces Gröbner bases and their applications to solving polynomial systems, ideal membership, and elimination theory, followed by the algebra–geometry correspondence and polynomial and rational functions on varieties. Further topics include robotics and automatic geometric theorem proving, invariant theory of finite groups, projective algebraic geometry, and the dimension of a variety. The book combines theoretical results with algorithms, examples, exercises, and computer-based methods, making it suitable for undergraduate study and for students beginning work in computational algebraic geometry and commutative algebra.
