CylindricalDecomposition

CylindricalDecomposition[ineqs,{x1,x2,}]

finds a decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond to the successive xi.

CylindricalDecomposition[ineqs,{x1,x2,},op]

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

Examples

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Basic Examples  (2)

Find a cylindrical decomposition of the unit disc:

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Find a cylindrical decomposition of the boundary of the unit disc:

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Scope  (10)

Generalizations & Extensions  (4)

Options  (1)

Applications  (2)

Properties & Relations  (8)

Possible Issues  (2)

Neat Examples  (1)

See Also

Reduce  Resolve  FindInstance  Discriminant  Resultant  SemialgebraicComponentInstances  GenericCylindricalDecomposition  GroebnerBasis  FullSimplify

Tutorials

Introduced in 2003
(5.0)
| Updated in 2017
(11.2)