Singular

LIB "polymake.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
intmat M1[2][2]=
1,0,
0,1;
cone c1 = coneViaPoints(M1);
isSmooth(c1);
==> 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
intmat M2[3][3]=
1,0,
1,2;
cone c2 = coneViaPoints(M2);
fan F1 = emptyFan(2);
insertCone(F1,c1);
isSmooth(F1);
==> 1
fan F2 = emptyFan(3);
insertCone(F2,c2);
isSmooth(F2);
==> 1
intmat Mp[3][3]=
1,-2,-3,
1,1,0,
1,0,1;
polytope p = polytopeViaPoints(Mp);
isSmooth(p);
==> polymake: used package cdd
==>   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
==> 
==> 0
fan F = normalFan(p);
isSmooth(F);
==> 0
intmat Mq[4][3]=
1,2,0,
1,0,1,
1,2,1,
1,0,0;
polytope q = polytopeViaPoints(Mq);
isSmooth(q);
==> 1