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Using Algebraic Geometry
David A. Cox,John Little,Donal O'Shea +2 more
- 01 Jan 1998
TL;DR: The Berlekamp-Massey-Sakata Decoding Algorithm is used for solving Polynomial Equations and for computations in Local Rings.
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Abstract: Introduction.- Solving Polynomial Equations.- Resultants.- Computation in Local Rings.- Modules.- Free Resolutions.- Polytopes, Resultants, and Equations.- Integer Programming, Combinatorics, and Splines.- Algebraic Coding Theory.- The Berlekamp-Massey-Sakata Decoding Algorithm.
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Locating and counting equilibria of the Kuramoto model with rank one coupling
TL;DR: An algorithm to locate only the real solutions of the Kuramoto model, thereby shortening computation time by several orders of magnitude in certain situations and conjecture an upper bound on the maximum number of equilibria for any number of oscillators which generalizes the known cases and is obtained on a range of explicitly provided natural frequencies.
Real solution isolation with multiplicity of zero-dimensional triangular systems
Zhihai Zhang,Tian Fang,Bican Xia +2 more
TL;DR: In this paper, the authors define the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that their definition is equivalent to the classical definition of local intersection multiplicity.
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The Voronoi Diagram of Circles and Its Application to the Visualization of the Growth of Particles
François Anton,Darka Mioc,Christopher M. Gold +2 more
- 13 Feb 2009
TL;DR: This paper shows how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix.
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What is the Role of Algebra in Applied Mathematics
David A. Cox
- 01 Jan 2005
TL;DR: The relationship between algebra and applied mathematics has been explored in this paper, where the authors explore some aspects of this relation in the hope of provoking useful discussions between pure and applied Mathematics.
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Kinematic analysis of Five-DOF (3T2R) parallel mechanisms with identical limb structures
Mehdi Tale Masouleh
- 01 Jan 2010
TL;DR: This thesis can be regarded as a guideline of the application of algebraic geometry in the kinematic analysis of parallel mechanisms and aims to validate and refine the obtained results, a state of the art which can be applied to other cases.
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