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, a string, the name of a built-in arrangement
- R, a polynomial ring, an optional coordinate ring for the arrangement
Outputs:
- a hyperplane arrangement, 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.