Computational Algebraic Geometry as a Computational Science Elective

Computational algebraic geometry

Algebraic geometry is a powerful combination of algebra and geometry, with a rich history and many applications, both theoretical and practical. It also has an intimidating reputation. Hence it is important to have a variety of introductory texts at different levels of sophistication. We will see that Schenck's book offers an interesting path into this wonderful subject. 1. What is algebraic ge...

Computational Algebraic Geometry

38 COMPUTATIONAL and QUANTITATIVE REAL ALGEBRAIC GEOMETRY

Computational and quantitative real algebraic geometry studies various algorithmic and quantitative questions dealing with the real solutions of a system of equalities, inequalities, and inequations of polynomials over the real numbers. This emerging field is largely motivated by the power and elegance with which it solves a broad and general class of problems arising in robotics, vision, compu...

Bad Primes in Computational Algebraic Geometry

Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method is guaranteed to work if we use a sufficiently large set of good primes. In many applications, however, there is no efficient way of excluding bad primes. In...

Polyhedral and Algebraic Methods in Computational Geometry

Imagine that you get such certain awesome experience and knowledge by only reading a book. How can? It seems to be greater when a book can be the best thing to discover. Books now will appear in printed and soft file collection. One of them is this book polyhedral and algebraic methods in computational geometry. It is so usual with the printed books. However, many people sometimes have no space...