proximum -- computes the proximum of the Polyhedron/Cone to a point in euclidean metric

Synopsis

Usage:

q = proximum(p,P)

q = proximum(p,C)
Inputs:
- p, a matrix, over ZZ or QQ with only one column representing a point
- P, a convex polyhedron
- C, a convex rational cone
Outputs:
- q, a matrix, over QQ with only one column representing the closest point

For a point p and a Polyhedron P or a Cone C, proximum computes the point in P or C with minimal euclidean distance to p.

i1 : P = crossPolytope 3

o1 = P

o1 : Polyhedron

i2 : p = matrix {{1},{2},{3}}

o2 = | 1 |
     | 2 |
     | 3 |

              3        1
o2 : Matrix ZZ  <--- ZZ

i3 : q = proximum(p,P)

o3 = | 0 |
     | 0 |
     | 1 |

              3        1
o3 : Matrix QQ  <--- QQ