cayley -- constructs the Cayley sum of polytopes

Synopsis

Usage:

cayley(P1,P2),

cayley(P1,P2,k),

cayley(P1,P2,P3),

cayley(P1,P2,P3,k),

cayley(L),

cayley(L,k),

cayley(M1,M2),

cayley(M1,M2,k),

cayley(M1,M2,M3),

cayley(M1,M2,M3,k)
Inputs:
- P1, a convex polyhedron,
- P2, a convex polyhedron,
- P3, a convex polyhedron,
- M1, a matrix,
- M2, a matrix,
- M3, a matrix,
- k, an integer,
- L, a list,
Outputs:
- a convex polyhedron,

Description

Given polytopes P and Q the function computes the cayley sum of P and Q.

i1 : P=convexHull(matrix{{0,1}});

i2 : Q=convexHull(matrix{{0,2}});

i3 : C=cayley(P,Q)

o3 = C

o3 : Polyhedron

i4 : vertices C

o4 = | 0 1 0 2 |
     | 0 0 1 1 |

              2       4
o4 : Matrix QQ  <-- QQ

One can also construct the Cayley polytope of order k by specifying the positive integer k.

i5 : C=cayley(P,Q,3)

o5 = C

o5 : Polyhedron

i6 : vertices C

o6 = | 0 1 0 2 |
     | 0 0 3 3 |

              2       4
o6 : Matrix QQ  <-- QQ

You can also compute the Cayley sum of several polytopes of any order, by placing the polytopes in a list.

i7 : C=cayley({P,Q,Q,P,P},2)

o7 = C

o7 : Polyhedron

i8 : vertices C

o8 = | 0 1 0 2 0 2 0 1 0 1 |
     | 0 0 2 2 0 0 0 0 0 0 |
     | 0 0 0 0 2 2 0 0 0 0 |
     | 0 0 0 0 0 0 2 2 0 0 |
     | 0 0 0 0 0 0 0 0 2 2 |

              5       10
o8 : Matrix QQ  <-- QQ

Ways to use cayley :

cayley(List)
cayley(List,ZZ)
cayley(Matrix,Matrix)
cayley(Matrix,Matrix,Matrix)
cayley(Matrix,Matrix,Matrix,ZZ)
cayley(Matrix,Matrix,ZZ)
cayley(Polyhedron,Polyhedron)
cayley(Polyhedron,Polyhedron,Polyhedron)
cayley(Polyhedron,Polyhedron,Polyhedron,ZZ)
cayley(Polyhedron,Polyhedron,ZZ)

For the programmer

The object cayley is a method function.

cayley -- constructs the Cayley sum of polytopes

Synopsis

Description

See also

Ways to use cayley :

For the programmer