Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
A cluster-based cylindrical algebraic decomposition algorithm
Journal of Symbolic Computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Isotopic triangulation of a real algebraic surface
Journal of Symbolic Computation
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
Journal of Symbolic Computation
On the isotopic meshing of an algebraic implicit surface
Journal of Symbolic Computation
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We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions (cad). Such adjacencies constitute a basis for determining all other cell adjacencies. Our new algorithms are local, being applicable to a specified 0D cell and the 1D cells described by specified polynomials. Particularly efficient algorithms are given for the 0D cells in spaces of dimensions two, three and four. Then an algorithm is given for a space of arbitrary dimension. This algorithm may on occasion report failure, but it can then be repeated with a modified isolating interval and a likelihood of success. Copyright 2002 Elsevier Science Ltd.