kunzMatrix -- determine the set of facet equations satisfied by a semigroup

Synopsis

Usage:

M = kunzMatrix L

M = kunzMatrix H
Inputs:
- L, a list,
- H, a hash table, such as produced by apery
Outputs:
- M, a matrix, of 0s and 1s

Description

The equations defining the facets of the homogeneous Kunz cone P_m^* are E_(i,j): a_i+a_j = a_(i+j mod m) for those (i,j) such that i+j != 0 mod m.

Given a list L generating the semigroups s with Apery set a = {a_1..a_i}, M = kunzMatrix L has a 1 in the (i,j) position if and only if a satisfies equation E_(i,j). Thus M = kunzMatrix L is a symmetric matrix of 0s and 1s that determines the face of the kunz cone P on which it lies.

i1 : L = {4,7}

o1 = {4, 7}

o1 : List

i2 : aperySet L

o2 = {21, 14, 7}

o2 : List

i3 : kunzMatrix L

o3 = | 0 0 0 |
     | 0 0 1 |
     | 0 1 1 |

              3       3
o3 : Matrix ZZ  <-- ZZ

Ways to use kunzMatrix:

kunzMatrix(HashTable)
kunzMatrix(List)

For the programmer

The object kunzMatrix is a method function.

kunzMatrix -- determine the set of facet equations satisfied by a semigroup

Synopsis

Description

See also

Ways to use kunzMatrix:

For the programmer