# delta -- Boundary complex of cyclic polytope.

• Usage:
delta(d,R)
• Inputs:
• Outputs:

## Description

Boundary complex of a cyclic polytope of dimension d on the variables of R as vertices, i.e., Δ(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 = {x x x x , x x x x , x x x x , x x x x , x x x x , 0 1 2 3 0 1 3 4 1 2 3 4 0 1 4 5 1 2 4 5 ------------------------------------------------------------------------ x x x x , x x x x , x x x x , x x x x , x x x x , x 2 3 4 5 0 1 2 6 0 2 3 6 0 3 4 6 0 1 5 6 1 ------------------------------------------------------------------------ x x x , x x x x , x x x x , x x x x } 2 5 6 2 3 5 6 0 4 5 6 3 4 5 6 o3 : complex with 14 facets on the vertices x x x x x x x 0 1 2 3 4 5 6 i4 : fvector C o4 = {1, 7, 21, 28, 14, 0, 0, 0} o4 : List i5 : I=complexToIdeal C o5 = ideal (x x x , x x x , x x x , x x x , x x x , x x x , x x x ) 2 4 6 1 4 6 1 3 6 1 3 5 0 3 5 0 2 5 0 2 4 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)