finds a decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond to the successive xi.
finds a decomposition of the result of applying the topological operation op to the region represented by the inequalities ineqs.
Details and Options
- CylindricalDecomposition assumes that all variables are real.
- Lists or logical combinations of inequalities can be given.
- CylindricalDecomposition returns inequalities whose bounds in general involve algebraic functions.
- The topological operation op can be one of:
"Boundary" boundary of the solution set "Closure" closure of the solution set "Interior" interior of the solution set "Exterior" exterior of the solution set "ClosureOfInterior" closure of the interior of the solution set "InteriorOfClosure" interior of the closure of the solution set "Components" connected components of the solution set
Examplesopen allclose all
Basic Examples (2)
Basic Uses (5)
Plot the individual cylinders using RegionPlot:
Topological Operations (5)
Generalizations & Extensions (4)
CylindricalDecomposition also allows quantified formulas:
This finds a decomposition using WorkingPrecision->1000, but the result may be incorrect:
Properties & Relations (8)
Use RegionPlot to visualize 2D semialgebraic sets:
Use RegionPlot3D to visualize 3D semialgebraic sets:
Resolve performs quantifier elimination and may avoid computing cylindrical decomposition:
Reduce in addition deals with different domains and transcendental functions:
Use FindInstance to find points that satisfy equations and inequalities:
SemialgebraicComponentInstances will give sample points in each cylinder:
CylindricalDecomposition merges several cylinders to get a more compact representation:
GenericCylindricalDecomposition will compute the full-dimensional part only: