apery -- Compute the apery set, multiplicity and conductor

Synopsis

Usage:

A = apery L
Inputs:
- L, a list, of positive integers
Outputs:
- A, a hash table,

Description

The smallest nonzero element of s is the \emph{multiplicity}. The Apery set (really sequence) of a semigroup S is the the list {a_1..a_m-1} where a_i is the smallest element in s such that a_i = i mod m. The \emph{conductor} is 1 plus the largest element \emph{not} in S. We generally specify a semigroup by giving a list of positive integers L with gcd = 1, representing the semigroup of all sums of elements of L.

i1 : L = {3,5}

o1 = {3, 5}

o1 : List

i2 : apery L

o2 = HashTable{1 => 10                              }
               2 => 5
               "conductor" => 8
               "multiplicity" => 3
               "semigroup" => {0, 3, 5, 6, 8, 9, 10}

o2 : HashTable

Ways to use apery:

apery(List)

For the programmer

The object apery is a method function.

apery -- Compute the apery set, multiplicity and conductor

Synopsis

Description

See also

Ways to use apery:

For the programmer