PolyhedralSets/PolyhedralCones/Rays - Maple Help
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PolyhedralSets[PolyhedralCones]

  

Rays

  

returns the rays of a polyhedral cone

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Rays(pc)

Parameters

pc

-

PolyhedralCone

Description

• 

The command Rays(pc) returns the generating rays, as a list of list rational numbers, of the polyhedral cone pc.

Terminology

• 

A polyhedral cone in dimension d is the solution set of a system of homogeneous linear non-strict inequalities in d variables. Equivalently, this is the conical hull of finitely many vectors with d coordinates. Here, the base field is that of the real numbers.

• 

Suppose that C is  the conical hull of k vectors with d coordinates. Then C is given by the matrix V with k columns  and d columns, whose columns are the  k vectors. The dual cone of C is the polyhedral set in dimension d which is the solution set of the system of homogeneous linear inequalities, whose matrix is the transpose of the matrix V.

• 

The polyhedral cone C in dimension d is called simplicial if it is generated by d linearly independent vectors. A simplicial decomposition of C is a finite set of simplicial cones so that the union of their interiors (in the Euclidean topology) is equal to the interior of C.

• 

Note that a polyhedral cone C, as a polyhedral set, has a single vertex which is the origin. In practice, it is convenient to use the term polyhedral cone  for the translation of a polyhedral cone in the formal sense defined above. With this abuse of terminology, a polyhedral cone is given by a point (its apex, or vertex) and a number of vectors (its generating rays, or simply rays).

Examples

Define a polyhedral cone from its vertex and rays

(1)

Obtain its vertex

(2)

Obtain its rays

(3)

Define another polyhedral set

Define a polyhedral cone from the above polyhedral set

(4)

Obtain its vertex

(5)

Obtain its rays

(6)

Define another polyhedral set

Define a polyhedral cone from the above polyhedral set

(7)

Obtain its vertex

(8)

Obtain its rays

(9)

Compatibility

• 

The PolyhedralSets[PolyhedralCones][Rays] command was introduced in Maple 2025.

• 

For more information on Maple 2025 changes, see Updates in Maple 2025.

See Also

PolyhedralSets[PolyhedralCones][DualCone]

PolyhedralSets[PolyhedralCones][PolyhedralCone]

PolyhedralSets[PolyhedralCones][SimplicialDecomposition]

PolyhedralSets[PolyhedralCones][Vertex]

 


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