-- -*- M2-comint -*- hash: 13527921062595685645

i1 : R = matrix {{1,1,2},{2,1,1}}

o1 = | 1 1 2 |
     | 2 1 1 |

              2       3
o1 : Matrix ZZ  <-- ZZ

i2 : C = posHull R

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of the cone => 2
      number of facets => 2
      number of rays => 2

o2 : Cone

i3 : ambDim C

o3 = 2

i4 : rays C

o4 = | 2 1 |
     | 1 2 |

              2       2
o4 : Matrix ZZ  <-- ZZ

i5 : HS = halfspaces C

o5 = | -1 2  |
     | 2  -1 |

              2       2
o5 : Matrix ZZ  <-- ZZ

i6 : R1 = R || matrix {{0,0,0}}

o6 = | 1 1 2 |
     | 2 1 1 |
     | 0 0 0 |

              3       3
o6 : Matrix ZZ  <-- ZZ

i7 : LS = matrix {{1},{1},{1}}

o7 = | 1 |
     | 1 |
     | 1 |

              3       1
o7 : Matrix ZZ  <-- ZZ

i8 : C1 = posHull(R1,LS)

o8 = {ambient dimension => 3           }
      dimension of lineality space => 1
      dimension of the cone => 3
      number of facets => 2
      number of rays => 2

o8 : Cone

i9 : rays C1

o9 = | 1  0  |
     | 0  1  |
     | -1 -1 |

              3       2
o9 : Matrix ZZ  <-- ZZ

i10 : HS = transpose R1

o10 = | 1 2 0 |
      | 1 1 0 |
      | 2 1 0 |

               3       3
o10 : Matrix ZZ  <-- ZZ

i11 : HP = matrix {{1,1,1}}

o11 = | 1 1 1 |

               1       3
o11 : Matrix ZZ  <-- ZZ

i12 : C2 = intersection(HS,HP)

o12 = {ambient dimension => 3           }
       dimension of lineality space => 0
       dimension of the cone => 2
       number of facets => 2
       number of rays => 2

o12 : Cone

i13 : rays C2

o13 = | 2  -1 |
      | -1 2  |
      | -1 -1 |

               3       2
o13 : Matrix ZZ  <-- ZZ

i14 : C3 = intersection HS

o14 = {ambient dimension => 3           }
       dimension of lineality space => 1
       dimension of the cone => 3
       number of facets => 2
       number of rays => 2

o14 : Cone

i15 : rays C3

o15 = | 2  -1 |
      | -1 2  |
      | 0  0  |

               3       2
o15 : Matrix ZZ  <-- ZZ

i16 : linSpace C3

o16 = | 0 |
      | 0 |
      | 1 |

               3       1
o16 : Matrix ZZ  <-- ZZ

i17 : C4 = posOrthant 3

o17 = {ambient dimension => 3           }
       dimension of lineality space => 0
       dimension of the cone => 3
       number of facets => 3
       number of rays => 3

o17 : Cone

i18 : rays C4

o18 = | 1 0 0 |
      | 0 1 0 |
      | 0 0 1 |

               3       3
o18 : Matrix ZZ  <-- ZZ

i19 : C5 = intersection(C1,C2)

o19 = {ambient dimension => 3           }
       dimension of lineality space => 0
       dimension of the cone => 2
       number of facets => 2
       number of rays => 2

o19 : Cone

i20 : rays C5

o20 = | 1  0  |
      | 0  1  |
      | -1 -1 |

               3       2
o20 : Matrix ZZ  <-- ZZ

i21 : C6 = posHull(C1,C2)

o21 = {ambient dimension => 3           }
       dimension of lineality space => 1
       dimension of the cone => 3
       number of facets => 2
       number of rays => 2

o21 : Cone

i22 : rays C6

o22 = | 2  -1 |
      | -1 2  |
      | -1 -1 |

               3       2
o22 : Matrix ZZ  <-- ZZ

i23 : linSpace C6

o23 = | 1 |
      | 1 |
      | 1 |

               3       1
o23 : Matrix ZZ  <-- ZZ

i24 : R2 = matrix {{2,-1},{-1,2},{-1,-1}}

o24 = | 2  -1 |
      | -1 2  |
      | -1 -1 |

               3       2
o24 : Matrix ZZ  <-- ZZ

i25 : C7 = posHull {R2,C3,C4}

o25 = {ambient dimension => 3           }
       dimension of lineality space => 1
       dimension of the cone => 3
       number of facets => 2
       number of rays => 2

o25 : Cone

i26 : rays C7

o26 = | 2  -1 |
      | -1 2  |
      | 0  0  |

               3       2
o26 : Matrix ZZ  <-- ZZ

i27 : linSpace C7

o27 = | 0 |
      | 0 |
      | 1 |

               3       1
o27 : Matrix ZZ  <-- ZZ

i28 : C6 == C1 + C2

o28 = true

i29 : P = crossPolytope 3

o29 = {ambient dimension => 3           }
       dimension of lineality space => 0
       dimension of polyhedron => 3
       number of facets => 8
       number of rays => 0
       number of vertices => 6

o29 : Polyhedron

i30 : P1 = C6 + P

o30 = {ambient dimension => 3           }
       dimension of lineality space => 1
       dimension of polyhedron => 3
       number of facets => 2
       number of rays => 2
       number of vertices => 1

o30 : Polyhedron

i31 : (vertices P1,rays P1)

o31 = (| -1/3 |, | 2  -1 |)
       | -1/3 |  | -1 2  |
       | 2/3  |  | -1 -1 |

o31 : Sequence

i32 : C8 = C * C1

o32 = {ambient dimension => 5           }
       dimension of lineality space => 1
       dimension of the cone => 5
       number of facets => 4
       number of rays => 4

o32 : Cone

i33 : rays C8

o33 = | 2 1 0  0  |
      | 1 2 0  0  |
      | 0 0 1  0  |
      | 0 0 0  1  |
      | 0 0 -1 -1 |

               5       4
o33 : Matrix ZZ  <-- ZZ

i34 : linSpace C8

o34 = | 0 |
      | 0 |
      | 1 |
      | 1 |
      | 1 |

               5       1
o34 : Matrix ZZ  <-- ZZ

i35 : ambDim C8

o35 = 5

i36 : fVector C8

o36 = {0, 1, 4, 6, 4, 1}

o36 : List

i37 : L = faces(1,C8)

o37 = {{ambient dimension => 5           }, {ambient dimension => 5         
        dimension of lineality space => 1    dimension of lineality space =>
        dimension of the cone => 4           dimension of the cone => 4     
        number of facets => 3                number of facets => 3          
        number of rays => 3                  number of rays => 3            
      -----------------------------------------------------------------------
       }, {ambient dimension => 5           }, {ambient dimension => 5      
      1    dimension of lineality space => 1    dimension of lineality space
           dimension of the cone => 4           dimension of the cone => 4
           number of facets => 3                number of facets => 3
           number of rays => 3                  number of rays => 3
      -----------------------------------------------------------------------
          }}
      => 1

o37 : List

i38 : apply(L,rays)

o38 = {| 2 0  0  |, | 1 0  0  |, | 2 1 0  |, | 2 1 0  |}
       | 1 0  0  |  | 2 0  0  |  | 1 2 0  |  | 1 2 0  |
       | 0 1  0  |  | 0 1  0  |  | 0 0 1  |  | 0 0 0  |
       | 0 0  1  |  | 0 0  1  |  | 0 0 0  |  | 0 0 1  |
       | 0 -1 -1 |  | 0 -1 -1 |  | 0 0 -1 |  | 0 0 -1 |

o38 : List

i39 : isSmooth C8

o39 = false

i40 : L = hilbertBasis C8

o40 = {| 0 |, | 0 |, | 0 |, | -1 |, | 0  |, | -1 |}
       | 0 |  | 0 |  | 0 |  | -1 |  | -1 |  | 0  |
       | 0 |  | 0 |  | 0 |  | -2 |  | -2 |  | -2 |
       | 1 |  | 2 |  | 1 |  | 0  |  | 0  |  | 0  |
       | 1 |  | 1 |  | 2 |  | 0  |  | 0  |  | 0  |

o40 : List

i41 : #L

o41 = 6

i42 : C9 = dualCone C8

o42 = {ambient dimension => 5           }
       dimension of lineality space => 0
       dimension of the cone => 4
       number of facets => 4
       number of rays => 4

o42 : Cone

i43 : rays C9

o43 = | 2  -1 0  0  |
      | -1 2  0  0  |
      | 0  0  2  -1 |
      | 0  0  -1 2  |
      | 0  0  -1 -1 |

               5       4
o43 : Matrix ZZ  <-- ZZ

i44 : 
