[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