next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Polyhedra :: polyhedronFromHData

polyhedronFromHData -- Constructing a polyhedron from its H-representation, i.e. inequalities and equations

Synopsis

Description

Constructs a polyhedron from inequalities and equations. Uses the negative halfspace defined by the equations, the normal vectors of every inequality point outside the polyhedron.

The polyhedron is defined by {x∈ℝ | I * x≤v, E * x=w}.

Please see V- and H-representation on the conventions we use for cones and polyhedra.

i1 : S = simplex 2

o1 = S

o1 : Polyhedron
i2 : facets S

o2 = (| -1 0  |, | 0 |)
      | 0  -1 |  | 0 |
      | 1  1  |  | 1 |

o2 : Sequence
i3 : SCopy = polyhedronFromHData facets S

o3 = SCopy

o3 : Polyhedron
i4 : assert(vertices S == vertices SCopy)
i5 : S = stdSimplex 2

o5 = S

o5 : Polyhedron
i6 : facets S

o6 = (| -1 0  0  |, 0)
      | 0  -1 0  |
      | 0  0  -1 |

o6 : Sequence
i7 : hyperplanes S

o7 = (| 1 1 1 |, | 1 |)

o7 : Sequence
i8 : SCopy = polyhedronFromHData(join(facets S, hyperplanes S))

o8 = SCopy

o8 : Polyhedron
i9 : assert(vertices S == vertices SCopy)

Ways to use polyhedronFromHData :