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D.13.4.34 isSmooth
Procedure from library polymake.lib (see polymake_lib).
- Usage:
- isSmooth(c); c cone
isSmooth(f); f fan
isSmooth(p); p polytope
- Return:
- 1, if the input is smooth; 0 otherwise
Example:
| 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);
==> 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
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