slackMatrix -- computes the slack matrix of a given realization

Synopsis

• Usage:

  S = slackMatrix V

  S = slackMatrix M

  S = slackMatrix P

  S = slackMatrix C

• Inputs:
  • V, a list, a list of vertices of a polytope, or the vectors of a linear matroid
  • M, a matroid, a matroid
  • P, a convex polyhedron, a polytope
  • C, a convex rational cone, a cone
• Optional inputs:
  • Object => ..., default value polytope, specify combinatorial object
• Outputs:
  • S, a matrix, a slack matrix of the realization

Description

i1 : V = {{0, 0}, {0, 1}, {1, 1}, {1, 0}};

i2 : SP = slackMatrix V

Order of vertices is 
{{0, 0}, {1, 0}, {0, 1}, {1, 1}}

o2 = | 0 1 0 1 |
     | 1 0 0 1 |
     | 0 1 1 0 |
     | 1 0 1 0 |

              4        4
o2 : Matrix QQ  <--- QQ

i3 : SM = slackMatrix(V, Object => "matroid")

o3 = | -1 -1 0 -1 0  0  |
     | -1 0  1 0  1  0  |
     | 0  1  1 0  0  -1 |
     | 0  0  0 -1 -1 -1 |

              4        6
o3 : Matrix ZZ  <--- ZZ

i4 : C = posHull(matrix{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}});

i5 : S = slackMatrix C

Order of rays is 
{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

o5 = | 1 0 0 |
     | 0 1 0 |
     | 0 0 1 |

              3        3
o5 : Matrix ZZ  <--- ZZ

Caveat

See also

• symbolicSlackMatrix -- computes the symbolic slack matrix
• Object -- select the combinatorial object which the input should be interpreted as