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D.13.2.33 polytopeViaPoints
Procedure from library gfan.lib (see gfan_lib).
- Usage:
- polytopeViaPoints(V [, flags]); intmat V, int flags
- Return:
- polytope which is the intersection of the cone generated by the row vectors
of V with the hyperplane, in which the first coordinate equals 1;
flags may be 0 or 1,
if flags is 1, then program assumes that each row vector of M generates a ray in the cone,
if flags is 0, then program computes that information itself
Example:
| | LIB "gfan.lib";
// This is a polytope in R^2 generated by (0,0), (1,0), (0,1), (0,0);
intmat V[4][3]=
1,0,0,
1,1,0,
1,0,1,
1,1,1;
polytope p1=polytopeViaPoints(V);
p1;
==> AMBIENT_DIM
==> 2
==> INEQUALITIES
==> 0, 0, 1,
==> 0, 1, 0,
==> 1,-1, 0,
==> 1, 0,-1
==> EQUATIONS
==>
==>
// This is a polytope in R^2 generated by (1/2,2/3), (3/4,4/5), (5/6,6/7):
intmat V[3][3]=
==> // ** redefining V (intmat V[3][3]=) ./examples/polytopeViaPoints.sing:11
6,3,4,
20,15,16,
42,35,36;
polytope p2=polytopeViaPoints(V);
p2;
==> AMBIENT_DIM
==> 2
==> INEQUALITIES
==> -10,-24, 35,
==> -6, -8, 15,
==> 8, 12,-21
==> EQUATIONS
==>
==>
// This polytope is the positive orthant in R^2:
// (0,1,0) and (0,0,1) imply that the polytope is unbounded in that direction
intmat V[3][3]=
==> // ** redefining V (intmat V[3][3]=) ./examples/polytopeViaPoints.sing:19
1,0,0,
0,1,0,
0,0,1;
polytope p3=polytopeViaPoints(V);
p3;
==> AMBIENT_DIM
==> 2
==> INEQUALITIES
==> 0,0,1,
==> 0,1,0,
==> 1,0,0
==> EQUATIONS
==>
==>
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