-- -*- M2-comint -*- {* hash: 1300917517 *}
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 QQ <--- QQ
i5 : HS = halfspaces C
o5 = | -1 2 |
| 2 -1 |
2 2
o5 : Matrix QQ <--- QQ
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 = | 0 0 |
| -1 1 |
| -2 -1 |
3 2
o9 : Matrix QQ <--- QQ
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 QQ <--- QQ
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 QQ <--- QQ
i16 : linSpace C3
o16 = | 0 |
| 0 |
| 1 |
3 1
o16 : Matrix QQ <--- QQ
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 QQ <--- QQ
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 QQ <--- QQ
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 = | 0 0 |
| 1 -1 |
| 0 -1 |
3 2
o22 : Matrix QQ <--- QQ
i23 : linSpace C6
o23 = | 1 |
| 1 |
| 1 |
3 1
o23 : Matrix QQ <--- QQ
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 QQ <--- QQ
i27 : linSpace C7
o27 = | 0 |
| 0 |
| 1 |
3 1
o27 : Matrix QQ <--- QQ
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 = (| 0 |, | 0 0 |)
| 0 | | 1 -1 |
| 1 | | 0 -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 0 0 |
| 0 0 -1 1 |
| 0 0 -2 -1 |
5 4
o33 : Matrix QQ <--- QQ
i34 : linSpace C8
o34 = | 0 |
| 0 |
| 1 |
| 1 |
| 1 |
5 1
o34 : Matrix QQ <--- QQ
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 0 0 | | 0 0 0 | | 0 0 0 | | 0 0 0 |
| 0 -1 1 | | 0 -1 1 | | 0 0 -1 | | 0 0 1 |
| 0 -2 -1 | | 0 -2 -1 | | 0 0 -2 | | 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 QQ <--- QQ
i44 :
