GAP (NumericalSgps) - Appendix B: Random functions

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B Random functions
B.1 Random functions
B.1-1 RandomNumericalSemigroup
B.1-2 RandomListForNS
B.1-3 RandomModularNumericalSemigroup
B.1-4 RandomProportionallyModularNumericalSemigroup
B.1-5 RandomListRepresentingSubAdditiveFunction

### 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, a[, b] ) | ( function )

Returns a ``random" numerical semigroup with no more than n generators in [1..a] (or in [a..b], if b is present).

    gap> RandomNumericalSemigroup(3,9);
    <Numerical semigroup with 3 generators>
    gap> RandomNumericalSemigroup(3,9,55);
    <Numerical semigroup with 3 generators>

##### B.1-2 RandomListForNS

`‣ RandomListForNS`( n, a, b ) | ( function )

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

    gap> RandomListForNS(13,1,79);
    [ 22, 26, 29, 31, 34, 46, 53, 61, 62, 73, 76 ]

##### B.1-3 RandomModularNumericalSemigroup

`‣ RandomModularNumericalSemigroup`( k[, m] ) | ( function )

Returns a ``random" modular numerical semigroup S(a,b) with a le k (see 1.) and multiplicity at least m, were m is the second argument, which may not be present..

    gap> RandomModularNumericalSemigroup(9);
    <Modular numerical semigroup satisfying 5x mod 6 <= x >
    gap> RandomModularNumericalSemigroup(10,25);
    <Modular numerical semigroup satisfying 4x mod 157 <= x >

##### B.1-4 RandomProportionallyModularNumericalSemigroup

`‣ RandomProportionallyModularNumericalSemigroup`( k[, m] ) | ( function )

Returns a ``random" proportionally modular numerical semigroup S(a,b,c) with a le k (see 1.) and multiplicity at least m, were m is the second argument, which may not be present.

    gap> RandomProportionallyModularNumericalSemigroup(9);
    <Proportionally modular numerical semigroup satisfying 2x mod 3 <= 2x >
    gap> RandomProportionallyModularNumericalSemigroup(10,25);
    <Proportionally modular numerical semigroup satisfying 6x mod 681 <= 2x >

##### B.1-5 RandomListRepresentingSubAdditiveFunction

`‣ RandomListRepresentingSubAdditiveFunction`( m, a ) | ( function )

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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