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» Exact numerical computation in algebra and geometry
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ICMS
2010
13 years 3 months ago
Exact Geometric and Algebraic Computations in CGAL
We summarize recent progress and on-going developments for exact geometric and algebraic computations within the Computational Geometry Algorithms Library (Cgal). We detail the exi...
Menelaos I. Karavelas
AI
2008
Springer
13 years 5 months ago
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra. There are many models of this alge...
Jürg Kohlas, Nic Wilson
AMC
2010
114views more  AMC 2010»
13 years 5 months ago
Witness sets of projections
Elimination is a basic algebraic operation which geometrically corresponds to projections. This article describes using the numerical algebraic geometric concept of witness sets t...
Jonathan D. Hauenstein, Andrew J. Sommese
COMPGEOM
2004
ACM
13 years 9 months ago
Complete, exact, and efficient computations with cubic curves
The Bentley-Ottmann sweep-line method can be used to compute the arrangement of planar curves provided a number of geometric primitives operating on the curves are available. We d...
Arno Eigenwillig, Lutz Kettner, Elmar Schömer...
COMPGEOM
2005
ACM
13 years 7 months ago
On the exact computation of the topology of real algebraic curves
We consider the problem of computing a representation of the plane graph induced by one (or more) algebraic curves in the real plane. We make no assumptions about the curves, in p...
Raimund Seidel, Nicola Wolpert