delta -- Boundary complex of cyclic polytope.

Synopsis

Usage:

delta(d,R)
Inputs:
- d, an integer, positive
- R, a polynomial ring,
Outputs:
- an abstract simplicial complex,

Description

Boundary complex of a cyclic polytope of dimension d on the variables of R as vertices, i.e., $\Delta(d,m)$ if m is the number of variables of R.

i1 : K=QQ;

i2 : R=K[x_0..x_6];

i3 : C=delta(4,R)

o3 = simplicialComplex | x_3x_4x_5x_6 x_0x_4x_5x_6 x_2x_3x_5x_6 x_1x_2x_5x_6 x_0x_1x_5x_6 x_0x_3x_4x_6 x_0x_2x_3x_6 x_0x_1x_2x_6 x_2x_3x_4x_5 x_1x_2x_4x_5 x_0x_1x_4x_5 x_1x_2x_3x_4 x_0x_1x_3x_4 x_0x_1x_2x_3 |

o3 : SimplicialComplex

i4 : fVector C

o4 = {1, 7, 21, 28, 14}

o4 : List

i5 : I=ideal C

o5 = ideal (x x x , x x x , x x x , x x x , x x x , x x x , x x x )
             0 2 4   0 2 5   0 3 5   1 3 5   1 3 6   1 4 6   2 4 6

o5 : Ideal of R

i6 : betti res I

            0 1 2 3
o6 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o6 : BettiTally

Ways to use delta :

delta(ZZ,PolynomialRing)

For the programmer

The object delta is a method function.