socle -- elements of the semigroup that are in the socle mod the multiplicity

Synopsis

Usage:

socle L
Inputs:
- L, a list, generators of a semigroup
Outputs:
- L, a list, subset of the Apery set representing the socle mod the multiplicity

Description

Let S = semigroup L be a numerical semigroup with minimal non-zero element m, and consider the artinian ring A(s) = k[{t^i : i in s]/(t^m). The socle of A(s) is the sum of the minimal nonzero ideals, and socle L is a set of generators of the socle

i1 : L = {3,7}

o1 = {3, 7}

o1 : List

i2 : s = semigroup L

o2 = {0, 3, 6, 7, 9, 10, 12, 13, 14}

o2 : List

i3 : socle L

o3 = {14}

o3 : List

i4 : L = {3,4,5}

o4 = {3, 4, 5}

o4 : List

i5 : s = semigroup L

o5 = {0, 3, 4, 5}

o5 : List

i6 : socle L

o6 = {4, 5}

o6 : List

Ways to use socle:

socle(List)

For the programmer

The object socle is a method function.

socle -- elements of the semigroup that are in the socle mod the multiplicity

Synopsis

Description

See also

Ways to use socle:

For the programmer