Add RandomLattice method

doc/digraph.xml

@@ -773,6 +773,18 @@ gap> RandomTournament(10);
 </ManSection>
 <#/GAPDoc>
 
+<#GAPDoc Label="RandomLattice">
+<ManSection>
+  <Oper Name="RandomLattice" Arg="n"/>
+  <Returns>A digraph.</Returns>
+  <Description>
+    If <A>n</A> is a positive integer, this function return a random lattice
+    with <A>m</A> vertices, where it is guaranteed that <A>m</A> is between
+    <A>n</A> and <C>2 * <A>n</A></C>. See <Ref Prop="IsLatticeDigraph"/>. <P/>
+  </Description>
+</ManSection>
+<#/GAPDoc>
+
 <#GAPDoc Label="ChainDigraph">
 <ManSection>
   <Oper Name="ChainDigraph" Arg="n"/>

doc/z-chap2.xml

@@ -65,6 +65,7 @@
     <#Include Label="RandomDigraph">
     <#Include Label="RandomMultiDigraph">
     <#Include Label="RandomTournament">
+    <#Include Label="RandomLattice">
   </Section>
 
   <Section><Heading>Standard examples</Heading>

gap/digraph.gd

@@ -132,6 +132,8 @@ DeclareConstructor("RandomTournamentCons", [IsDigraph, IsInt]);
 DeclareOperation("RandomTournament", [IsInt]);
 DeclareOperation("RandomTournament", [IsFunction, IsInt]);
 
+DeclareOperation("RandomLattice", [IsPosInt]);
+
 # No mutable analogues of the following because we will withdraw multidigraphs
 # the not too distant future!
 DeclareOperation("RandomMultiDigraph", [IsPosInt]);

gap/digraph.gi

@@ -1104,3 +1104,18 @@ InstallMethod(RandomTournament, "for a func and an integer",
 function(func, n)
   return RandomTournamentCons(func, n);
 end);
+
+InstallMethod(RandomLattice, "for a pos int",
+[IsPosInt],
+function(n)
+  local fam, rand_blist;
+
+  fam := [BlistList([1 .. n], [])];
+
+  while Length(fam) < n do
+    rand_blist := List([1 .. n], x -> Random([true, false]));
+    UniteSet(fam, List(fam, x -> UnionBlist(x, rand_blist)));
+  od;
+
+  return Digraph(fam, IsSubsetBlist);
+end);

tst/standard/digraph.tst

@@ -541,6 +541,99 @@ Error, the argument <n> must be a non-negative integer,
 gap> RandomTournament(IsMutableDigraph, 10);
 <mutable digraph with 10 vertices, 45 edges>
 
+#  RandomLattice
+gap> RandomLattice(25);;
+gap> RandomLattice(1);
+<digraph with 1 vertex, 1 edge>
+gap> RandomLattice(-1);
+Error, no method found! For debugging hints type ?Recovery from NoMethodFound
+Error, no 1st choice method found for `RandomLattice' on 1 arguments
+
+# The list of random lattice Digraph6Strings D was generated by running the following command
+# D := List([1 .. 100], x -> Digraph6String(RandomLattice(7)));
+gap> D := [
+> "&F~grwcIB?_", "&G~tSrCO{D?oC", "&F~kqG{IB?_", "&J~}jSpw`O~_t?a?{?g?o?_", "&H~zzIWxAGH?wB?G",
+> "&G~t[~DosD?oC", "&F~kqG{IB?_", "&H~z~IgrAGN?gB?G", "&I~|TR~DSKoP?{@OB?C", "&G~s[jFOcD?oC",
+> "&G~sc~EocF?oC", "&G~tSrCO{D?oC", "&F~kqG{IB?_", "&F~kqG{IB?_", "&I~|nqTFKKoP?{@OB?C",
+> "&I~|OrPCCNoP?{@OB?C", "&F~kqG{IB?_", "&G~tSrCO{D?oC", "&H~ynMWbAWN?gB?G", "&G~tSrCO{D?oC",
+> "&I~|Sr~DKLOP?{@OB?C", "&F~hrgcIB?_", "&G~s[rCOsD?oC", "&G~tCtCO{D?oC", "&F~lQG{IB?_",
+> "&F~hrgcIB?_", "&I~|DRrDKGOP?{@OB?C", "&F~jRWcIB?_", "&G~tSpCO{D?oC", "&F~mrGcMB?_",
+> "&F~iRwcMB?_", "&F~lQG{IB?_", "&F~lQG{IB?_", "&H~yhKw`BwH?wB?G", "&I~|zqdEKGO^?{@OB?C",
+> "&G~tSrCO{D?oC", "&G~tSrCO{D?oC", "&G~tSrCO{D?oC", "&F~kqG{IB?_", "&F~lQG{IB?_", "&G~skxCOcF?oC",
+> "&J~}dCggoo__~?a?{?g?o?_", "&F~lQG{IB?_", "&G~usdEocD?oC", "&G~tSrCO{D?oC", "&H~ybLG`BWH?wB?G",
+> "&F~irgcIB?_", "&I~|TRBCCNoT?{@OB?C", "&F~iqwcMB?_", "&H~yTHgxAGH?gB?G", "&F~nqg{IB?_",
+> "&I~|PRRCCNoR?{@OB?C", "&F~lqWcMB?_", "&J~}lKhgoo__~?e?s?g?o?_", "&F~nqW{IB?_", "&G~tSrCO{D?oC",
+> "&F~jrWkMB?_", "&G~vKpCO{D?oC", "&F~irgcIB?_", "&H~y~LwnAWN?gB?G", "&F~kqG{IB?_",
+> "&I~|zqdEKGO^?{@OB?C", "&G~t{`EocF?oC", "&H~zNGW~AGN?wB?G", "&H~zNGW~AgN?gB?G", "&F~nQgsIB?_",
+> "&F~hrwkMB?_", "&G~vkbEocF?oC", "&G~s{zCOkF?oC", "&F~grwkMB?_", "&G~tKtCO{D?oC", "&F~nqwsIB?_",
+> "&J~}jKpw_o~_r?a?{?g?o?_", "&F~nqg{IB?_", "&G~s{~DO{D?oC", "&G~tSrCO{D?oC",
+> "&K~~\\tGdCTBr@p?`?P?N?D?B?@", "&G~tSrCO{D?oC", "&H~zjKW`BwJ?gB?G", "&K~~PrG^FnAd@b?`?R?N?D?B?@",
+> "&H~ydKW`AWN?gB?G", "&F~lQG{IB?_", "&G~tSrCO{D?oC", "&H~zNGg~AGN?gB?G", "&G~u[bFocF?oC",
+> "&H~yrMwrAGN?wB?G", "&G~t{zEocF?oC", "&H~yhJw`BWH?wB?G", "&G~uk`FokF?oC", "&F~lqGcMB?_",
+> "&F~kqG{IB?_", "&G~sC~EocF?oC", "&F~lQG{IB?_", "&G~s[~EocF?oC", "&G~tKpCO{D?oC", "&F~jrGcMB?_",
+> "&I~|SrNCKNoR?{@OB?C", "&F~lQG{IB?_", "&F~irgcIB?_", "&F~kqG{IB?_"];;
+gap> D := List(D, x -> DigraphFromDigraph6String(x));;
+gap> iso := [];; 
+gap> iso_distr := [];;
+gap> eq := [];;
+gap> eq_distr := [];;
+gap> for i in [1 .. Length(D)] do
+>   iso_new := true;
+>   eq_new := true;
+>   for j in [1 .. Length(iso)] do
+>     if IsIsomorphicDigraph(D[i], iso[j]) then
+>       iso_distr[j] := iso_distr[j] + 1;
+>       iso_new := false;
+>       break;
+>     fi;
+>   od;
+>   for j in [1 .. Length(eq)] do
+>     if D[i] = eq[j] then
+>       eq_distr[j] := eq_distr[j] + 1;
+>       eq_new := false;
+>       break;
+>     fi;
+>   od;
+>   if iso_new then
+>     Add(iso, D[i]);
+>     Add(iso_distr, 1);
+>   fi;
+>   if eq_new then
+>     Add(eq, D[i]);
+>     Add(eq_distr, 1);
+>   fi;
+> od;
+
+# The total number of nonisomorphic digraphs generated, out of 100. 
+# It is known that there are 53 distinct lattices on 7 points according to OEIS A006966
+gap> Length(iso);
+41
+
+# The distribution of nonisomorhpic generated lattices. 
+# To the left is the number of times a particular lattice occurs among the randomly generated ones. 
+# To the right is how many distinct lattices have
+# this number of occurences.
+# So entry [3, 5] means that there were five distinct lattices each of which was generated 3 times.
+gap> Display(Collected(iso_distr));
+[ [   1,  26 ],
+  [   2,   7 ],
+  [   3,   3 ],
+  [   4,   1 ],
+  [   5,   2 ],
+  [  14,   1 ],
+  [  23,   1 ] ]
+
+# Same as above but for non-equal lattices
+gap> Length(eq);
+69
+gap> Display(Collected(eq_distr));
+[ [   1,  62 ],
+  [   2,   3 ],
+  [   3,   1 ],
+  [   8,   1 ],
+  [   9,   1 ],
+  [  12,   1 ] ]
+
 #  Equals (\=) for two digraphs
 gap> r1 := rec(DigraphNrVertices := 2, DigraphSource := [1, 1, 2], DigraphRange := [1, 2, 2]);;
 gap> r2 := rec(DigraphNrVertices := 2, DigraphSource := [1, 1, 2], DigraphRange := [2, 1, 2]);;