BUILT-IN MATHEMATICA SYMBOL

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.

MORE INFORMATION

GenericCylindricalDecomposition assumes that all variables are real.

Lists or logical combinations of inequalities can be given.

GenericCylindricalDecomposition returns inequalities whose bounds in general involve algebraic functions.

EXAMPLES

CLOSE ALL

Basic Examples (1)

Find a cylindrical decomposition of the full-dimensional part of the unit disk:

In[1]:=

Out[1]=

Scope (3)

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:

Generalizations & Extensions (1)

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:

Applications (1)

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:

Properties & Relations (3)

GenericCylindricalDecomposition finds the solution set up to lower-dimensional parts:

CylindricalDecomposition finds the complete solution set:

Reduce uses cylindrical decomposition to solve inequalities:

Possible Issues (1)

When the solution set is lower-dimensional, no solutions are found:

To find lower-dimensional solution sets, use CylindricalDecomposition: