isSymmetric -- test whether the semigroup generated by L is symmetric

Synopsis

Usage:

t = isSymmetric L
Inputs:
- L, a list,
Outputs:
- t, a Boolean value,

Description

Suppose that c = conductor S, so that c-1 is the last gap. If x in S, and x<c then c-1-x must be a gap, so the number g of gaps <c is at least the number of semigroup elements e < c. The semigroup is called \emph{symmetric} if g = e, or equivalently if the semigroup ring is Gorenstein. Thus for example any semigroup generated by just 2 elements is symmetric.

i1 : isSymmetric{3,4,5}

o1 = false

i2 : isSymmetric{3, 5}

o2 = true

i3 : gaps {3,5}

o3 = {1, 2, 4, 7}

o3 : List

i4 : mu {3,5}

o4 = {3, 1}

o4 : List

Ways to use isSymmetric:

isSymmetric(List)

For the programmer

The object isSymmetric is a method function.

isSymmetric -- test whether the semigroup generated by L is symmetric

Synopsis

Description

See also

Ways to use isSymmetric:

For the programmer