naiveChirotope -- compute the chirotope of a configuration via determinants in Macaulay2

• Usage:

  C = naiveChirotope A

• Inputs:
  • A, a matrix,
• Optional inputs:
  • Homogenize => a Boolean value, default value true, if true (default), augment $A$ with a final row of $1$'s before computing (treating columns of $A$ as a point set); if false, treat the columns of $A$ as a vector configuration as-is
• Outputs:
  • C, an instance of the type Chirotope,

i1 : A = transpose matrix {{0,3},{0,1},{-1,-1},{1,-1},{-4,-2},{4,-2}}

o1 = | 0 0 -1 1  -4 4  |
     | 3 1 -1 -1 -2 -2 |

              2       6
o1 : Matrix ZZ  <-- ZZ

i2 : chirotope A == naiveChirotope A

o2 = true