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inria-00538839, version 1

Geometric predicates as arrangements of hypersurfaces: Application to comparison of algebraic numbers

George Tzoumas () 1

Fall School Shapes, Geometry, and Algebra - SAGA 2010 (2010)

  • 1:  VEGAS (INRIA Lorraine - LORIA)

  • INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) France

Bibliographic reference

  • Type of document: Documents associated with scientific events (Tutorial, poster/pres./preface, short paper, conference digest, …)
  • Domain: Computer Science/Computational Geometry
  • Title: Geometric predicates as arrangements of hypersurfaces: Application to comparison of algebraic numbers
  • Abstract: A lot of geometric predicates can be formulated as an arrangement of hypersurfaces (algebraic varieties) in a high-dimensional space, where each cell of the arrangement corresponds to an outcome of the predicate, and an evaluation of the predicate maps to point-location queries in this arrangement. To do this successfully, the arrangement has to be decomposed by the aid of subsidiary hypersurfaces, the degree of which plays a fundamental role in the algebraic complexity of the predicate, with respect to the input coefficients. For example, the widely used predicate of root comparison of quadratic polynomials can be mapped to an arrangement of lines and a parabola. For cubics, it becomes an arrangement of planes and a quartic surface, when a monic polynomial of degree d is represented as a point in R^d. Minimizing the degree of the subsidiary equations is an outstanding open problem.
  • Full text language: English
  • Audience: international
  • Popular scientific document: No
  • Conference title: Fall School Shapes, Geometry, and Algebra - SAGA 2010
  • Conference city: Kolympari
  • Country: Greece
  • Conference date: 2010-10-04
  • Conference date (end): 2010-10-08
  • Type of document: Poster

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  • inria-00538839, version 1
  • http://hal.inria.fr/inria-00538839
  • oai:hal.inria.fr:inria-00538839
  • From: George Tzoumas <>
  • Submitted on: Tuesday, 23 November 2010 14:06:00
  • Updated on: Thursday, 2 December 2010 11:15:46