EUROCAL 1985: EUROCAL '85 pp 246-261

# An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space

• Dennis S. Arnon
• George E. Collins
• Scott McCallum
Algebraic Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)

## Abstract

Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space Er is a certain partition of Er into connected subsets compatible with the zeros of the polynomials. Each subset is a cell. Two cells of a cad are adjacent if their union is connected. In applications of cad's, one often wishes to know the pairs of adjacent cells. In a previous paper we gave an algorithm which determines the adjacent cells as it constructs a cad of the plane. We give such an algorithm here for three-dimensional space.

## Keywords

Boundary Point Limit Point Primitive Element Boundary Property Positive Degree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1. [ACM84a]
D. S. Arnon, G. E. Collins, S. McCallum ”Cylindrical algebraic decomposition I: the basic algorithm”, SIAM J. Comp, 13, (1984), pp. 865–877.Google Scholar
2. 2. [ACM84b]
D. S. Arnon, G. E. Collins, S. McCallum ”Cylindrical algebraic decomposition II: an adjacency algorithm for the plane”, SIAM J. Comp, 13, (1984), pp. 878–889.Google Scholar
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## Authors and Affiliations

• Dennis S. Arnon
• 1
• George E. Collins
• 2
• Scott McCallum
• 3
1. 1.Xerox PARCPalo Alto