# arrangement(String,PolynomialRing) -- look up a built-in hyperplane arrangement

## Synopsis

• Function: arrangement
• Usage:
arrangement(s) or arrangement(s,R) or arrangement(s,k)
• Inputs:
• s, , the name of a built-in arrangement
• R, , an optional coordinate ring for the arrangement
• Outputs:
• , the hyperplane arrangement named s.

## Description

The built-in arrangements are stored in a global HashTable called arrangementLibrary. Accordingly, the user can see what arrangements are available by examining the keys:
 i1 : keys arrangementLibrary o1 = {prism, bracelet, nonFano, Ziegler1, Ziegler2, braid, Pappus, (9_3)_2, ------------------------------------------------------------------------ notTame, Hessian, X2, X3, MacLane, Desargues} o1 : List i2 : R = QQ[x,y,z]; i3 : A = arrangement("Pappus",R) o3 = {x, y, z, x - y, y - z, x - y - z, 2x + y + z, 2x + y - z, 2x - 5y + z} o3 : Hyperplane Arrangement  i4 : poincare A 2 3 o4 = 1 + 9T + 27T + 19T o4 : ZZ[T] i5 : isDecomposable A o5 = false i6 : A = arrangement("prism", ZZ/101) -- can also specify coefficient ring o6 = {x , x , x , x , x + x + x , x + x + x } 1 2 3 4 1 2 4 1 3 4 o6 : Hyperplane Arrangement  i7 : ring A ZZ o7 = ---[x ..x ] 101 1 4 o7 : PolynomialRing

## Caveat

The arrangements MacLane and Hessian are defined over ZZ/31627, where 6419 is a cube root of unity.