Singular Manual: minkowskiSum

| #### 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

User manual for Singular version 4-1-2p3, 2020, generated by texi2html.