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ISSAC
1989
Springer
77views Mathematics» more  ISSAC 1989»
13 years 9 months ago
A Parallel Implementation of the Cylindrical Algebraic Decomposition Algorithm
In this paper, we describe a parallelization scheme for Collins’ cylindrical algebraic decomposition algorithm for quantifier elimination in the theory of real closed fields. ...
B. David Saunders, Hong R. Lee, S. Kamal Abdali
ISSAC
2009
Springer
171views Mathematics» more  ISSAC 2009»
13 years 11 months ago
Computing cylindrical algebraic decomposition via triangular decomposition
Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approache...
Changbo Chen, Marc Moreno Maza, Bican Xia, Lu Yang
ISSAC
1992
Springer
95views Mathematics» more  ISSAC 1992»
13 years 9 months ago
Real Algebraic Closure of an Ordered Field: Implementation in Axiom
Real algebraic numbers appear in many Computer Algebra pro bJems. For inst ante the determination of a cylindrical algebraic decomposition for an euclidian space requires compu ti...
Renaud Rioboo
SODA
2008
ACM
106views Algorithms» more  SODA 2008»
13 years 6 months ago
Exact and efficient 2D-arrangements of arbitrary algebraic curves
We show how to compute the planar arrangement induced by segments of arbitrary algebraic curves with the Bentley-Ottmann sweep-line algorithm. The necessary geometric primitives r...
Arno Eigenwillig, Michael Kerber
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
13 years 11 months ago
Fast and exact geometric analysis of real algebraic plane curves
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert