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

## Synopsis

• Usage:
P = polyhedronFromHData(I, v)
P = polyhedronFromHData(I, v, E, w)
• Inputs:
• I, , The inequalities
• v, , The right hand side of the inequalities
• E, , The equations
• w, , The right hand side of the equations
• Outputs:

## 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 :

• polyhedronFromHData(Matrix,Matrix)
• polyhedronFromHData(Matrix,Matrix,Matrix,Matrix)