  
  [1XB Random functions[0X
  
  Here  we  describe  some  functions  which  allow to create several "random"
  objects.
  
  
  [1XB.1 Random functions[0X
  
  [1XB.1-1 RandomNumericalSemigroup[0m
  
  [2X> RandomNumericalSemigroup( [0X[3Xn, m[0X[2X ) _________________________________[0Xfunction
  
  Returns  a  ``random"  numerical semigroup with no more than [3Xn[0m generators in
  [1..[3Xm[0m].
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> RandomNumericalSemigroup(3,9);[0X
    [4X<Numerical semigroup with 3 generators>[0X
  [4X------------------------------------------------------------------[0X
  
  [1XB.1-2 RandomListForNS[0m
  
  [2X> RandomListForNS( [0X[3Xn, m[0X[2X ) __________________________________________[0Xfunction
  
  Returns  a  set  of  length  not greater than [3Xn[0m of random integers in [3X[1..m][0m
  whose GCD is 1. It is used to create "random" numerical semigroups.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> RandomListForNS(13,79);[0X
    [4X[ 22, 26, 29, 31, 34, 46, 53, 61, 62, 73, 76 ][0X
  [4X------------------------------------------------------------------[0X
  
  [1XB.1-3 RandomModularNumericalSemigroup[0m
  
  [2X> RandomModularNumericalSemigroup( [0X[3Xk[0X[2X ) _____________________________[0Xfunction
  
  Returns a ``random" modular numerical semigroup.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> RandomModularNumericalSemigroup(9);[0X
    [4X<Modular numerical semigroup satisfying 5x mod 6 <= x >[0X
  [4X------------------------------------------------------------------[0X
  
  [1XB.1-4 RandomProportionallyModularNumericalSemigroup[0m
  
  [2X> RandomProportionallyModularNumericalSemigroup( [0X[3Xk[0X[2X ) _______________[0Xfunction
  
  Returns a ``random" proportionally modular numerical semigroup (see [14X1.[0m).
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> RandomProportionallyModularNumericalSemigroup(9);[0X
    [4X<Proportionally modular numerical semigroup satisfying 2x mod 3 <= 2x >[0X
  [4X------------------------------------------------------------------[0X
  
  [1XB.1-5 RandomListRepresentingSubAdditiveFunction[0m
  
  [2X> RandomListRepresentingSubAdditiveFunction( [0X[3Xm, a[0X[2X ) ________________[0Xfunction
  
  Produces a ``random" list representing a subadditive function (see [14X1.[0m) which
  is  periodic  with  period  [3Xm[0m  (or  less).  When possible, the images are in
  [3X[a..20*a][0m. (Otherwise, the list of possible images is enlarged.)
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> RandomListRepresentingSubAdditiveFunction(7,9);[0X
    [4X[ 173, 114, 67, 0 ][0X
    [4Xgap> RepresentsPeriodicSubAdditiveFunction(last);[0X
    [4Xtrue[0X
  [4X------------------------------------------------------------------[0X
  
