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

- 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

## See also

- gaps -- The gap sequence of a semigroup

## Ways to use isGapSequence:

- `isGapSequence(List)`

## For the programmer

The object isGapSequence is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalSemigroups.m2:2857:0.