### 4.24.1 polytopeViaPoints

`Syntax:`
  `polytopeViaPoints(` intmat V `)`
  `polytopeViaPoints(` intmat V, int flags `)`
`Type:`
  polytope
`Purpose:`
  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"gfanlib.so";
      // 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 p=polytopeViaPoints(V);
      p;
      ==> 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 **
      6,3,4,
      20,15,16,
      42,35,36;
      polytope p=polytopeViaPoints(V);
      ==> // ** redefining p **
      p;
      ==> 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 **
      1,0,0,
      0,1,0,
      0,0,1;
      polytope p=polytopeViaPoints(V);
      ==> // ** redefining p **
      p;
      ==> AMBIENT_DIM
      ==> 2
      ==> INEQUALITIES
      ==> 0,0,1,
      ==> 0,1,0,
      ==> 1,0,0
      ==> EQUATIONS
      ==>
      ==>

User manual for Singular version 4-0-3, 2016, generated by texi2html.