B. Random functions

Here we describe some functions which allow to create several "random" objects.

B.1 Random functions

B.1-1 RandomNumericalSemigroup
> RandomNumericalSemigroup( n, m )( attribute )

Returns a ``random" numerical semigroup with no more than n generators in [1..m].


gap> RandomNumericalSemigroup(3,9);
<Numerical semigroup with 3 generators>

B.1-2 RandomListForNS
> RandomListForNS( n, m )( attribute )

Returns a set of length not greater than n of random integers in [1..m] whose GCD is 1. It is used to create "random" numerical semigroups.


gap> RandomListForNS(13,79);
[ 22, 26, 29, 31, 34, 46, 53, 61, 62, 73, 76 ]

B.1-3 RandomModularNumericalSemigroup
> RandomModularNumericalSemigroup( k )( attribute )

Returns a ``random" modular numerical semigroup.


gap> RandomModularNumericalSemigroup(9);
<Modular numerical semigroup satisfying 5x mod 6 <= x >

B.1-4 RandomProportionallyModularNumericalSemigroup
> RandomProportionallyModularNumericalSemigroup( k )( attribute )

Returns a ``random" proportionally modular numerical semigroup (see 1.).


gap> RandomProportionallyModularNumericalSemigroup(9);
<Proportionally modular numerical semigroup satisfying 2x mod 3 <= 2x >

B.1-5 RandomListRepresentingSubAdditiveFunction
> RandomListRepresentingSubAdditiveFunction( m, a )( attribute )

Produces a ``random" list representing a subadditive function (see 1.) which is periodic with period m (or less). When possible, the images are in [a..20*a]. (Otherwise, the list of possible images is enlarged.)


gap> RandomListRepresentingSubAdditiveFunction(7,9);
[ 173, 114, 67, 0 ]
gap> RepresentsPeriodicSubAdditiveFunction(last);
true




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