# mPosHullFaces -- Faces of a positive hull.

## Description

Returns a list of

- a Matrix A with the rays of the positive hull of L in its rows

- a list of lists with the faces of the convex hull sorted by increasing dimension.

The rays of the faces are represented by the indices of the rows of A.

This uses the Convex functions posHull and faces.

The positive hull of L is required to be strictly convex.

 i1 : L= {{0,1,1,0,0},{0,1,0,1,0},{0,1,0,0,0},{1,0,0,0,1},{1,0,-1,-1,-1},{1,0,0,0,0}}; i2 : L=apply(L,vector) o2 = {| 0 |, | 0 |, | 0 |, | 1 |, | 1 |, | 1 |} | 1 | | 1 | | 1 | | 0 | | 0 | | 0 | | 1 | | 0 | | 0 | | 0 | | -1 | | 0 | | 0 | | 1 | | 0 | | 0 | | -1 | | 0 | | 0 | | 0 | | 0 | | 1 | | -1 | | 0 | o2 : List i3 : P=mPosHullFaces(L) o3 = {| 0 1 1 0 0 |, {{{}}, {{1}, {2}, {3}, {4}, {5}, {6}}, {{3, 5}, {3, | 0 1 0 1 0 | | 0 1 0 0 0 | | 1 0 0 0 1 | | 1 0 -1 -1 -1 | | 1 0 0 0 0 | ------------------------------------------------------------------------ 4}, {2, 3}, {1, 3}, {5, 6}, {4, 6}, {2, 6}, {1, 6}, {4, 5}, {2, 5}, {2, ------------------------------------------------------------------------ 4}, {1, 5}, {1, 4}, {1, 2}}, {{3, 4, 5}, {2, 3, 5}, {2, 3, 4}, {2, 4, ------------------------------------------------------------------------ 5}, {1, 3, 5}, {1, 3, 4}, {1, 4, 5}, {1, 2, 3}, {1, 2, 5}, {1, 2, 4}, ------------------------------------------------------------------------ {4, 5, 6}, {2, 5, 6}, {2, 4, 6}, {1, 5, 6}, {1, 4, 6}, {1, 2, 6}}, {{2, ------------------------------------------------------------------------ 3, 4, 5}, {1, 3, 4, 5}, {1, 2, 3, 5}, {1, 2, 3, 4}, {2, 4, 5, 6}, {1, 4, ------------------------------------------------------------------------ 5, 6}, {1, 2, 5, 6}, {1, 2, 4, 6}}, {{1, 2, 3, 4, 5, 6}}}} o3 : List

## Ways to use mPosHullFaces :

• "mPosHullFaces(List)"

## For the programmer

The object mPosHullFaces is .