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D.16.2.20 isSmooth

Syntax:
Polymake::isSmooth( cone c )
Polymake::isSmooth( fan f )
Polymake::isSmooth( polytope p )
Type:
int
Purpose:
1 if c, f or p is smooth, 0 otherwise.
Example:
 
  LIB"polymake.lib";
==> Welcome to polymake
==> Copyright (c) 1997-2012
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
  intmat M[2][2]=1,0, 0,1;
  cone c1 = coneViaPoints(M);
  Polymake::isSmooth(c1);
==> 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
==> 
==> 1
  intmat N[3][3]=1,0, 1,2;
  cone c2 = coneViaPoints(N);
  Polymake::isSmooth(c2);
==> 1
  intmat M[2][2]=1,0, 0,1;
==> // ** redefining M **
  cone c = coneViaPoints(M);
  fan F1 = emptyFan(2);
  insertCone(F1,c);
  Polymake::isSmooth(F1);
==> 1
  intmat N[3][3]=1,-2,-3, 1,1,0, 1,0,1;
==> // ** redefining N **
  polytope q = polytopeViaPoints(N);
  fan F2 = Polymake::normalFan(q);
  Polymake::isSmooth(F2);
==> 0
  intmat M[4][3]=1,2,0, 1,0,1, 1,2,1, 1,0,0;
==> // ** redefining M **
  polytope p = polytopeViaPoints(M);
  Polymake::isSmooth(p);
==> polymake: used package lrslib
==>   Implementation of the reverse search algorithm of Avis and Fukuda.
==>   Copyright by David Avis.
==>   http://cgm.cs.mcgill.ca/~avis/lrs.html
==> 
==> 1
  intmat N[3][3]=1,-2,-3, 1,1,0, 1,0,1;
==> // ** redefining N **
  polytope q = polytopeViaPoints(N);
==> // ** redefining q **
  Polymake::isSmooth(q);
==> 0