isGapSequence -- test whether a list of integers can be the list of gaps of a semigroup

Synopsis

Usage:

L = isGapSequence G
Inputs:
- G, a list,
Outputs:
- L, a Boolean value,
- L, a list,

Description

The function isGapSequence returns either false or a list of generators of the semigroup of which the sequence is the gap sequence. Note that the gap sequence of a semigroup of multiplicity m begins with 1..m-1, and ends with the Frobenius number c-1, where c is the conductor.

i1 : G = {1,2,3,4,6,9,11,14}

o1 = {1, 2, 3, 4, 6, 9, 11, 14}

o1 : List

i2 : isGapSequence G

o2 = false

i3 : G = {1,2,3,4,6,9,11}

o3 = {1, 2, 3, 4, 6, 9, 11}

o3 : List

i4 : S = isGapSequence G

o4 = {5, 7, 8}

o4 : List

i5 : G == gaps S

o5 = true

Ways to use isGapSequence:

isGapSequence(List)

For the programmer

The object isGapSequence is a method function.

isGapSequence -- test whether a list of integers can be the list of gaps of a semigroup

Synopsis

Description

See also

Ways to use isGapSequence:

For the programmer