# Singular

#### D.13.2.45 minkowskiSum

Procedure from library `polymake.lib` (see polymake_lib).

Usage:
minkowskiSum(c,d); c cone, d cone
minkowskiSum(c,q); c cone, q polytope
minkowskiSum(p,d); p polytope, d cone
minkowskiSum(p,q); p polytope, q polytope

Assume:
input arguments have the same ambient dimension

Return:
cone, if both inputs are cones; polytope, otherwise
the minkowski sum of the two input arguments

Example:
 ```LIB "polymake.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org intmat M[3][4]= 1,1,0,0, 1,0,1,0, 1,0,0,0; intmat N[3][4]= 1,0,0,1, 1,-1,-1,-1, 1,0,0,0; polytope p = polytopeViaPoints(M); polytope q = polytopeViaPoints(N); vertices(minkowskiSum(p,q)); ==> polymake: used package ppl ==> The Parma Polyhedra Library (PPL): A C++ library for convex polyhedra ==> and other numerical abstractions. ==> http://www.cs.unipr.it/ppl/ ==> ==> 1, 0, 1, 0, ==> 1, 1, 0, 0, ==> 1, 1, 0, 1, ==> 1, 0,-1,-1, ==> 1,-1,-1,-1, ==> 1, 0, 0, 1, ==> 1, 0, 1, 1, ==> 1,-1, 0,-1 ```