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A new framework in quantum chemistry has been proposed recently (``An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the ...
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Magma Computational Algebra System Magma is a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment for defining and working with structures such as groups, rings, fields, modules, algebras, schemes, curves ...Home | Mathematics
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Apr 14, 2018 · My research brings together methods from number theory, algebraic geometry, dynamical systems, arithmetic geometry, computational number theory, and computational algebraic geometry. Recently I have been heavily involved in improving the computational tools for dynamical systems in the computer algebra system Sage.
Geometric algebra is a consistent computational framework in which to de-fine geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits coordinate-free specification of computational constructions. It contains primitives of any dimensionality (rather than just vec-tors). Algebra provides the mathematical tools to find unknown quantities from related known ones, the famous quadratic equation being a familiar example. The subject interacts with all of mathematics as well as many applied fields. For instance, symmetries of pyramids or cubes, or indeed any object, can be viewed through the lens of algebra.
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Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These ...
Course Description. Computational Photography is concerned with overcoming the limitations of traditional photography with computation: in optics, sensors, and geometry; and even in composition, style, and human interfaces.
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Persistent homology, a new branch of algebraic topology, is able to bridge the gap between traditional topology and geometry by incorporating certain geometric features into topological invariants. Computational topology promises potentially revolutionary approaches to physical sciences.
She is also interested in computational algebra problems. Professor Judy Walker works in algebraic coding theory. Much of her work uses techniques from number theory, algebraic geometry and graph theory. She has worked with algebraic geometric codes over rings and the relationship between weight measures on these codes and exponential sums.
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algebraic geometry, the study of solutions to systems of polynomial equations, is a tool for scientists and engineers. Moreover, relations between concepts aris-ing in science and engineering are often described by polynomials. Whatever their source, once polynomials enter the picture, notions from algebraic geometry— A First Course In Computational Algebraic Geometry. Download and Read online A First Course In Computational Algebraic Geometry ebooks in PDF, epub, Tuebl Mobi, Kindle Book. Get Free A First Course In Computational Algebraic Geometry Textbook and unlimited access to our library by created an account. Fast Download speed and ads Free!
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Computational Geometry We work on efficient algorithms in computational geometry. We also make our algorithmic results available in mature software libraries such as CGAL .
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computational algebraic geometry techniques. Because of the local structure of bifurcation problems we have to use the computations in local rings instead of common polynomial ring. Hence the monomial ordering, Gr¨obner basis, division algorithm and buchberger algorithm are substituted by the similar concepts in local rings. We have develop a ...
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Computer Algebra for Geometry Algebraic varieties are defined by polynomial equations. Computer algebra methods for solving systems of polynomial equations and similar problems form the basis for a computational theory of Algebraic Geometry. From the preface of J. R. Sendra, F. Winkler, S. Pérez-Díaz.These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of ...
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