<Appendix><Heading>Random functions</Heading> Here we describe some functions which allow to create several "random" objects. <Section><Heading>Random functions</Heading> <ManSection> <Func Name="RandomNumericalSemigroup" Arg="n,m"></Func> <Description> Returns a ``random" numerical semigroup with no more than <A>n</A> generators in [1..<A>m</A>]. <Example><![CDATA[ gap> RandomNumericalSemigroup(3,9); <Numerical semigroup with 3 generators> ]]></Example> </Description> </ManSection> <ManSection> <Func Name="RandomListForNS" Arg="n,m"></Func> <Description> Returns a set of length not greater than <A>n</A> of random integers in <A>[1..m]</A> whose GCD is 1. It is used to create "random" numerical semigroups. <Example><![CDATA[ gap> RandomListForNS(13,79); [ 22, 26, 29, 31, 34, 46, 53, 61, 62, 73, 76 ] ]]></Example> </Description> </ManSection> <ManSection> <Func Name="RandomModularNumericalSemigroup" Arg="k"></Func> <Description> Returns a ``random" modular numerical semigroup. <Example><![CDATA[ gap> RandomModularNumericalSemigroup(9); <Modular numerical semigroup satisfying 5x mod 6 <= x > ]]></Example> </Description> </ManSection> <ManSection> <Func Name="RandomProportionallyModularNumericalSemigroup" Arg="k"></Func> <Description> Returns a ``random" proportionally modular numerical semigroup (see <Ref Label="llab1" />). <Example><![CDATA[ gap> RandomProportionallyModularNumericalSemigroup(9); <Proportionally modular numerical semigroup satisfying 2x mod 3 <= 2x > ]]></Example> </Description> </ManSection> <ManSection> <Func Name="RandomListRepresentingSubAdditiveFunction" Arg="m, a"></Func> <Description> Produces a ``random" list representing a subadditive function (see <Ref Label="llab2" />) which is periodic with period <A>m</A> (or less). When possible, the images are in <A>[a..20*a]</A>. (Otherwise, the list of possible images is enlarged.) <Example><![CDATA[ gap> RandomListRepresentingSubAdditiveFunction(7,9); [ 173, 114, 67, 0 ] gap> RepresentsPeriodicSubAdditiveFunction(last); true ]]></Example> </Description> </ManSection> </Section> </Appendix>