i1 : V = matrix {{0,2,-2,0},{-1,1,1,1}} o1 = | 0 2 -2 0 | | -1 1 1 1 | 2 4 o1 : Matrix ZZ <--- ZZ |
i2 : P = convexHull V o2 = P o2 : Polyhedron |
i3 : vertices P o3 = | 0 -2 2 | | -1 1 1 | 2 3 o3 : Matrix QQ <--- QQ |
i4 : (HS,v) = halfspaces P o4 = (| -1 -1 |, | 1 |) | 1 -1 | | 1 | | 0 1 | | 1 | o4 : Sequence |
i5 : hyperplanes P o5 = (0, 0) o5 : Sequence |
i6 : rays P o6 = 0 2 o6 : Matrix QQ <--- 0 |
i7 : linealitySpace P o7 = 0 2 o7 : Matrix QQ <--- 0 |
i8 : R = matrix {{1},{0},{0}} o8 = | 1 | | 0 | | 0 | 3 1 o8 : Matrix ZZ <--- ZZ |
i9 : V1 = V || matrix {{1,1,1,1}} o9 = | 0 2 -2 0 | | -1 1 1 1 | | 1 1 1 1 | 3 4 o9 : Matrix ZZ <--- ZZ |
i10 : P1 = convexHull(V1,R) o10 = P1 o10 : Polyhedron |
i11 : vertices P1 o11 = | 0 -2 | | -1 1 | | 1 1 | 3 2 o11 : Matrix QQ <--- QQ |
i12 : rays P1 o12 = | 1 | | 0 | | 0 | 3 1 o12 : Matrix QQ <--- QQ |
i13 : hyperplanes P1 o13 = (| 0 0 -1 |, | -1 |) o13 : Sequence |
i14 : HS = transpose (V || matrix {{-1,2,0,1}}) o14 = | 0 -1 -1 | | 2 1 2 | | -2 1 0 | | 0 1 1 | 4 3 o14 : Matrix ZZ <--- ZZ |
i15 : v = matrix {{1},{1},{1},{1}} o15 = | 1 | | 1 | | 1 | | 1 | 4 1 o15 : Matrix ZZ <--- ZZ |
i16 : hyperplanesTmp = matrix {{1,1,1}} o16 = | 1 1 1 | 1 3 o16 : Matrix ZZ <--- ZZ |
i17 : w = matrix {{3}} o17 = | 3 | 1 1 o17 : Matrix ZZ <--- ZZ |
i18 : P2 = intersection(HS,v,hyperplanesTmp,w) Warning: This method is deprecated. Please consider using polyhedronFromHData instead. o18 = P2 o18 : Polyhedron |
i19 : vertices P2 o19 = | 4 4 2 | | 9 5 5 | | -10 -6 -4 | 3 3 o19 : Matrix QQ <--- QQ |
i20 : P3 = intersection(HS,v) Warning: This method is deprecated. Please consider using polyhedronFromHData instead. o20 = P3 o20 : Polyhedron |
i21 : vertices P3 o21 = | 0 0 0 | | 1 1 -3 | | 0 -2 2 | 3 3 o21 : Matrix QQ <--- QQ |
i22 : linealitySpace P3 o22 = | 1 | | 2 | | -2 | 3 1 o22 : Matrix QQ <--- QQ |
i23 : P4 = hypercube(3,2) o23 = P4 o23 : Polyhedron |
i24 : vertices P4 o24 = | -2 2 -2 2 -2 2 -2 2 | | -2 -2 2 2 -2 -2 2 2 | | -2 -2 -2 -2 2 2 2 2 | 3 8 o24 : Matrix QQ <--- QQ |
i25 : P5 = crossPolytope(3,3) o25 = P5 o25 : Polyhedron |
i26 : vertices P5 o26 = | -3 3 0 0 0 0 | | 0 0 -3 3 0 0 | | 0 0 0 0 -3 3 | 3 6 o26 : Matrix QQ <--- QQ |
i27 : P6 = stdSimplex 2 o27 = P6 o27 : Polyhedron |
i28 : vertices P6 o28 = | 1 0 0 | | 0 1 0 | | 0 0 1 | 3 3 o28 : Matrix QQ <--- QQ |
i29 : P7 = convexHull(P4,P5) o29 = P7 o29 : Polyhedron |
i30 : vertices P7 o30 = | -3 3 0 0 0 -2 2 -2 2 -2 2 -2 2 0 | | 0 0 -3 3 0 -2 -2 2 2 -2 -2 2 2 0 | | 0 0 0 0 -3 -2 -2 -2 -2 2 2 2 2 3 | 3 14 o30 : Matrix QQ <--- QQ |
i31 : P8 = intersection(P4,P5) o31 = P8 o31 : Polyhedron |
i32 : vertices P8 o32 = | -1 1 -2 2 -2 2 -1 1 -1 1 0 0 -2 2 0 0 -2 2 0 0 -1 1 0 0 | | -2 -2 -1 -1 1 1 2 2 0 0 -1 1 0 0 -2 2 0 0 -2 2 0 0 -1 1 | | 0 0 0 0 0 0 0 0 -2 -2 -2 -2 -1 -1 -1 -1 1 1 1 1 2 2 2 2 | 3 24 o32 : Matrix QQ <--- QQ |
i33 : P9 = convexHull {(V1,R),P2,P6} o33 = P9 o33 : Polyhedron |
i34 : vertices P9 o34 = | 4 4 2 0 -2 | | 9 5 5 -1 1 | | -10 -6 -4 1 1 | 3 5 o34 : Matrix QQ <--- QQ |
i35 : Q = convexHull (-V) o35 = Q o35 : Polyhedron |
i36 : P10 = P + Q o36 = P10 o36 : Polyhedron |
i37 : vertices P10 o37 = | -4 4 -2 2 -2 2 | | 0 0 -2 -2 2 2 | 2 6 o37 : Matrix QQ <--- QQ |
i38 : (C,L,M) = minkSummandCone P10 o38 = (C, HashTable{0 => Polyhedron{...1...}}, | 1 0 |) 1 => Polyhedron{...1...} | 0 1 | 2 => Polyhedron{...1...} | 1 0 | 3 => Polyhedron{...1...} | 1 0 | 4 => Polyhedron{...1...} | 0 1 | o38 : Sequence |
i39 : apply(values L, vertices) o39 = {| 0 4 |, | 0 4 2 |, | 0 2 |, | 0 2 |, | 0 4 2 |} | 0 0 | | 0 0 -2 | | 0 2 | | 0 -2 | | 0 0 2 | o39 : List |
i40 : P11 = P * Q Warning: This method is deprecated. Please consider using polyhedronFromHData instead. o40 = P11 o40 : Polyhedron |
i41 : vertices P11 o41 = | 0 -2 2 0 -2 2 0 -2 2 | | -1 1 1 -1 1 1 -1 1 1 | | -2 -2 -2 2 2 2 0 0 0 | | -1 -1 -1 -1 -1 -1 1 1 1 | 4 9 o41 : Matrix QQ <--- QQ |
i42 : ambDim P11 o42 = 4 |
i43 : fVector P11 o43 = {9, 18, 15, 6, 1} o43 : List |
i44 : L = faces(1,P11) o44 = {({0, 1, 3, 4, 6, 7}, {}), ({0, 2, 3, 5, 6, 8}, {}), ({1, 2, 4, 5, 7, ----------------------------------------------------------------------- 8}, {}), ({0, 1, 2, 3, 4, 5}, {}), ({0, 1, 2, 6, 7, 8}, {}), ({3, 4, 5, ----------------------------------------------------------------------- 6, 7, 8}, {})} o44 : List |
i45 : vertP11 = vertices P11 o45 = | 0 -2 2 0 -2 2 0 -2 2 | | -1 1 1 -1 1 1 -1 1 1 | | -2 -2 -2 2 2 2 0 0 0 | | -1 -1 -1 -1 -1 -1 1 1 1 | 4 9 o45 : Matrix QQ <--- QQ |
i46 : apply(L, l -> vertP11_(l#0)) o46 = {| 0 -2 0 -2 0 -2 |, | 0 2 0 2 0 2 |, | -2 2 -2 2 -2 2 |, | | -1 1 -1 1 -1 1 | | -1 1 -1 1 -1 1 | | 1 1 1 1 1 1 | | | -2 -2 2 2 0 0 | | -2 -2 2 2 0 0 | | -2 -2 2 2 0 0 | | | -1 -1 -1 -1 1 1 | | -1 -1 -1 -1 1 1 | | -1 -1 -1 -1 1 1 | | ----------------------------------------------------------------------- 0 -2 2 0 -2 2 |, | 0 -2 2 0 -2 2 |, | 0 -2 2 0 -2 2 |} -1 1 1 -1 1 1 | | -1 1 1 -1 1 1 | | -1 1 1 -1 1 1 | -2 -2 -2 2 2 2 | | -2 -2 -2 0 0 0 | | 2 2 2 0 0 0 | -1 -1 -1 -1 -1 -1 | | -1 -1 -1 1 1 1 | | -1 -1 -1 1 1 1 | o46 : List |
i47 : L = latticePoints P11 o47 = {| 1 |, | -2 |, | 2 |, | 0 |, | 1 |, | -1 |, | 1 |, | -1 |, | 0 | 0 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 0 | | 0 | -2 | | -2 | | -2 | | 2 | | 2 | | -2 | | -2 | | -2 | | -2 | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 ----------------------------------------------------------------------- |, | 0 |, | 0 |, | 0 |, | 0 |, | 1 |, | -1 |, | 0 |, | 0 |, | 0 | | -1 | | 1 | | -1 | | -1 | | 0 | | 0 | | 0 | | -1 | | -1 | | -2 | | -2 | | -1 | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | -1 | | -1 | | -1 | | 0 | | -1 | | -1 | | -1 | | -1 | | 0 ----------------------------------------------------------------------- |, | 1 |, | -1 |, | 0 |, | 0 |, | -2 |, | 2 |, | -1 |, | 1 |, | 0 | | 0 | | 0 | | 0 | | -1 | | 1 | | 1 | | 1 | | 1 | | 1 | | -1 | | -1 | | -1 | | 0 | | -1 | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | 0 | | 1 | | -1 | | -1 | | -1 | | -1 | | -1 ----------------------------------------------------------------------- |, | 1 |, | -1 |, | 0 |, | 0 |, | 0 |, | 1 |, | -1 |, 0, | -2 |, | | | 0 | | 0 | | 0 | | -1 | | -1 | | 0 | | 0 | | 1 | | | | 0 | | 0 | | 0 | | 1 | | 1 | | 0 | | 0 | | -1 | | | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | 0 | | 0 | | ----------------------------------------------------------------------- 2 |, | -1 |, | 1 |, | 0 |, | 1 |, | -1 |, | 0 |, | -2 |, | 2 |, | 1 | | 1 | | 1 | | 1 | | 0 | | 0 | | 0 | | 1 | | 1 | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 1 | | 1 | | 1 | | -1 | | -1 | | ----------------------------------------------------------------------- -1 |, | 1 |, | 0 |, | 1 |, | -1 |, | 0 |, | 0 |, | 1 |, | -1 |, | 1 | | 1 | | 1 | | 0 | | 0 | | 0 | | -1 | | 0 | | 0 | | 0 | | 0 | | 0 | | 1 | | 1 | | 1 | | 2 | | 1 | | 1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | ----------------------------------------------------------------------- 0 |, | -2 |, | 2 |, | -1 |, | 1 |, | 0 |, | -2 |, | 2 |, | -1 |, | 1 |, 0 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | 1 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 1 | | 1 | | 1 | | 1 | ----------------------------------------------------------------------- | 0 |, | -2 |, | 2 |, | -1 |, | 1 |, | 0 |, | 1 |, | -1 |, | 0 |, | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 0 | | 0 | | 0 | | 0 | | 1 | | 1 | | 1 | | 1 | | 1 | | 2 | | 2 | | 2 | | 1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | ----------------------------------------------------------------------- | -2 |, | 2 |, | -1 |, | 1 |, | 0 |, | -2 |, | 2 |, | -1 |} | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 1 | | 2 | | 2 | | 2 | | 0 | | 0 | | 0 | | 0 | | 0 | | -1 | | -1 | | -1 | o47 : List |
i48 : #L o48 = 81 |
i49 : C = tailCone P1 o49 = C o49 : Cone |
i50 : rays C o50 = | 1 | | 0 | | 0 | 3 1 o50 : Matrix ZZ <--- ZZ |
i51 : P12 = polar P11 o51 = P12 o51 : Polyhedron |
i52 : vertices P12 o52 = | 1 -1 0 0 0 0 | | 1 1 -1 0 0 0 | | 0 0 0 0 1 -1 | | 0 0 0 1 -1 -1 | 4 6 o52 : Matrix QQ <--- QQ |