conductor(List) -- conductor of a semigroup

Synopsis

Function: conductor
Usage:

c = conductor L
Inputs:
- L, a list, of generators of a semigroup
Outputs:
- c, an integer, conductor of the semigroups

Description

Semigroups in this package are additively closed cofinite subsets of ZZ_{>= 0}. The conductor is the smallest element c such that c+i is in the semigroup for all i >= 0. For a semigroup generated by two elements a,b, the conductor is (a-1)(b-1), but for semigroups with more generators there is no known formula.

i1 : conductor {3,5}

o1 = 8

i2 : conductor {5, 7, 9, 13}

o2 = 12

Ways to use this method: