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GenericCylindricalDecomposition

GenericCylindricalDecomposition
finds the full-dimensional part of the decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond to the successive , together with any hypersurfaces containing the rest of the region.
  • Lists or logical combinations of inequalities can be given.
Find a cylindrical decomposition of the full-dimensional part of the unit disk:
Find a cylindrical decomposition of the full-dimensional part of the unit disk:
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GenericCylindricalDecomposition gives a full-dimensional set of solutions and a hypersurface:
The hypersurface contains the difference between all solutions and the full-dimensional set:
There is no remaining hypersurface here:
Here the whole solution set is lower-dimensional:
Find solutions that are generic with respect to the first two variables:
The difference between the generic and full solution is contained in the blue cylindrical surface:
Plot a region described by inequalities:
The curves on the surface correspond to cylinder boundaries:
Computing full cylindrical decomposition takes longer and is not necessary to plot the picture:
RegionPlot3D uses a numerical method and gives a somewhat less-precise picture:
GenericCylindricalDecomposition finds the solution set up to lower-dimensional parts:
CylindricalDecomposition finds the complete solution set:
Reduce uses cylindrical decomposition to solve inequalities:
When the solution set is lower-dimensional, no solutions are found:
To find lower-dimensional solution sets, use CylindricalDecomposition:
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