# euler(Flat)

## Synopsis

• Function: euler
• Usage:
euler(F) or euler(A)
• Inputs:
• F, , a flat
• Outputs:
• k, an integer, the beta invariant of the flat F or arrangement A

## Description

The beta invariant of an arrangement A is, by definition, the Euler characteristic of complement of A in complex projective space.

The beta invariant of a flat F is the beta invariant of the restriction of A to F.

 i1 : A = typeA(3) o1 = {x - x , x - x , x - x , x - x , x - x , x - x } 1 2 1 3 1 4 2 3 2 4 3 4 o1 : Hyperplane Arrangement  i2 : euler A -- for a real arrangement, equals number of bounded chambers o2 = 2