cmVolumes -- Computes the Chern-Mather volumes of a projective toric variety

Synopsis

• Usage:

  cmVolumes(A)

• Inputs:
  • A, a matrix, a full rank integer matrix with the vector (1,1,...,1) in its row space defining a projective toric variety X_A
• Optional inputs:
  • ForceAmat (missing documentation) => a Boolean value, default value false, if A defines a codimension two toric variety a faster method will be used by default, setting this to true forces the general purpose method
  • Output (missing documentation) => a list, default value List, this can be set to HashTable to return a HashTable with all computed values
  • TextOutput (missing documentation) => ..., default value "Quiet",
• Outputs:
  • cmv, a list, the Chern-Mather volumes of the projective toric variety X_A, ordered from dimension X_A to dimension zero.

Description

i1 : A=matrix{{0, 0, 0, 1, 1,5}, {7,0, 1, 3, 0, -2},{1,1, 1, 1, 1, 1}}

o1 = | 0 0 0 1 1 5  |
     | 7 0 1 3 0 -2 |
     | 1 1 1 1 1 1  |

              3       6
o1 : Matrix ZZ  <-- ZZ

i2 : cmVolumes(A)


o2 = {35, 20, -12}

o2 : List

i3 : A=matrix{{3, 0, 0, 1, 1,2}, {3,5,0,2,1,3},{0, 1, 2, 0, 2,0},{1, 1, 1, 1, 1,1}}

o3 = | 3 0 0 1 1 2 |
     | 3 5 0 2 1 3 |
     | 0 1 2 0 2 0 |
     | 1 1 1 1 1 1 |

              4       6
o3 : Matrix ZZ  <-- ZZ

i4 : cm=cmVolumes(A)


o4 = {28, 31, 23, 20}

o4 : List