-- -*- M2-comint -*- hash: 11451332872744094205

i1 : C = posHull matrix {{1,0,0},{0,1,0},{0,0,1}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o1 : Cone

i2 : F = fan C

o2 = {ambient dimension => 3         }
      number of generating cones => 1
      number of rays => 3
      top dimension of the cones => 3

o2 : Fan

i3 : maxCones F

o3 = {{ambient dimension => 3           }}
       dimension of lineality space => 0
       dimension of the cone => 3
       number of facets => 3
       number of rays => 3

o3 : List

i4 : C1 = posHull matrix {{1,0,0},{1,1,0},{0,0,-1}}

o4 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o4 : Cone

i5 : commonFace(C,C1)

o5 = false

i6 : (b,C2) = areCompatible(C,C1)

o6 = (false, {ambient dimension => 3           })
              dimension of lineality space => 0
              dimension of the cone => 2
              number of facets => 2
              number of rays => 2

o6 : Sequence

i7 : rays C2

o7 = | 0 1 |
     | 1 1 |
     | 0 0 |

              3       2
o7 : Matrix ZZ  <-- ZZ

i8 : C1 = posHull matrix {{1,0,0},{0,1,0},{0,0,-1}}

o8 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o8 : Cone

i9 : F = addCone(C1,F)

o9 = {ambient dimension => 3         }
      number of generating cones => 2
      number of rays => 4
      top dimension of the cones => 3

o9 : Fan

i10 : C2 = posHull matrix {{-1,0,0},{0,1,0},{0,0,1}};

i11 : C3 = posHull matrix {{-1,0,0},{0,1,0},{0,0,-1}};

i12 : C4 = posHull matrix {{-1,0,0},{0,-1,0},{0,0,1}};

i13 : C5 = posHull matrix {{-1,0,0},{0,-1,0},{0,0,-1}};

i14 : F1 = fan {C2,C3,C4,C5}

o14 = {ambient dimension => 3         }
       number of generating cones => 4
       number of rays => 5
       top dimension of the cones => 3

o14 : Fan

i15 : C6 = posHull matrix {{1,0,0},{0,-1,0},{0,0,1}};

i16 : C7 = posHull matrix {{1,0,0},{0,-1,0},{0,0,-1}};

i17 : F1 = addCone( {C6,C7}, F1)

o17 = {ambient dimension => 3         }
       number of generating cones => 6
       number of rays => 6
       top dimension of the cones => 3

o17 : Fan

i18 : F1 = addCone(F,F1)

o18 = {ambient dimension => 3         }
       number of generating cones => 8
       number of rays => 6
       top dimension of the cones => 3

o18 : Fan

i19 : P = hypercube 4

o19 = {ambient dimension => 4           }
       dimension of lineality space => 0
       dimension of polyhedron => 4
       number of facets => 8
       number of rays => 0
       number of vertices => 16

o19 : Polyhedron

i20 : F2 = normalFan P

o20 = {ambient dimension => 4          }
       number of generating cones => 16
       number of rays => 8
       top dimension of the cones => 4

o20 : Fan

i21 : F3 = fan {posHull matrix {{1}},posHull matrix {{-1}}}

o21 = {ambient dimension => 1         }
       number of generating cones => 2
       number of rays => 2
       top dimension of the cones => 1

o21 : Fan

i22 : F1 = F3 * F1

o22 = {ambient dimension => 4          }
       number of generating cones => 16
       number of rays => 8
       top dimension of the cones => 4

o22 : Fan

i23 : ambDim F1

o23 = 4

i24 : F1 == F2

o24 = true

i25 : 
