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This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision.Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and...

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. This title covers theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources.

Spectral techniques to explore point clouds in Euclidean space, with applications to collective coordinates in structural biology.- Rational parametrizations, intersection theory, and Newton polytopes.- Some discrete properties of the space of line transversals to disjoint balls.- Algebraic geometry and kinematics.- Rational offset surfaces and their modeling applications.- A list of challenges for real algebraic plane curve visualization software.- A subdivision method for arrangement computation of semi-algebraic curves.- Invariant-based characterization of the relative position of two...