# Singular

#### D.16.2.31 minkowskiSum

`Syntax:`
`Polymake::minkowskiSum(` polytope p, polytope q `)`
`Polymake::minkowskiSum(` polytope p, cone c `)`
`Polymake::minkowskiSum(` cone c, polytope q `)`
`Polymake::minkowskiSum(` cone c, cone d `)`
`Assume:`
same ambient dimension.
`Type:`
polytope
`Purpose:`
the Minkowski sum of the two input arguments.
`Note:`
The Minkowski sum of two cones is just the cone generated by their union.
`Example:`
 ``` LIB"polymake.lib"; ==> Welcome to polymake ==> Copyright (c) 1997-2012 ==> 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); polytope pq = Polymake::minkowskiSum(p,q); ==> polymake: used package cddlib ==> Implementation of the double description method of Motzkin et al. ==> Copyright by Komei Fukuda. ==> http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html ==> pq; ==> AMBIENT_DIM ==> 3 ==> INEQUALITIES ==> 1,-1,-1, 0, ==> 1,-1,-1, 2, ==> 1,-1, 1, 0, ==> 1, 0, 0,-1, ==> 1, 0, 0, 1, ==> 1, 0, 2,-1, ==> 1, 1,-1, 0, ==> 1, 2, 0,-1 ==> EQUATIONS ==> ==> ```