KPolynomialASM -- compute the K Polynomial of an ASM variety

Synopsis

Usage:

KPolynomialASM A
Inputs:
- A, a matrix,

Description

Given a partial ASM $A$, compute the K-polynomial of its corresponding Ideal, defined as the numerator of its Hilbert series. The multidegree variables are indexed along rows.

i1 : A = matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}};

              4       4
o1 : Matrix ZZ  <-- ZZ

i2 : KPolynomialASM A

                      2                   3     2                2      3    
o2 = 1 - 3T  - T  + 3T  + 3T T  - T T  - T  - 3T T  + 3T T T  + T T  + T T  -
           0    1     0     0 1    1 2    0     0 1     0 1 2    1 2    0 1  
     ------------------------------------------------------------------------
       2           2      3         2 2      3 2
     3T T T  - 3T T T  + T T T  + 3T T T  - T T T
       0 1 2     0 1 2    0 1 2     0 1 2    0 1 2

o2 : ZZ[T ..T ]
         0   3

Ways to use KPolynomialASM :

KPolynomialASM(Matrix)

For the programmer

The object KPolynomialASM is a method function.