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#############################################################################
##
##
#W yapb.gi Ferret Package Chris Jefferson
##
## Installation file for functions of the Ferret package.
##
#Y Copyright (C) 2013-2014 University of St. Andrews, North Haugh,
#Y St. Andrews, Fife KY16 9SS, Scotland
##

####
# Functions and variables beginning '_YAPB' are only called
# from C++ by YAPB.
####

_YAPB_Globals := [];

# Have a copy of this in each thread in HPCGAP
# This store references to variables we are using inside ferret,
# to make sure they don't get garbage collected.
if IsBound( MakeThreadLocal ) then
 MakeThreadLocal("_YAPB_Globals");
fi;

_YAPB_addRef := function(obj)
 Add(_YAPB_Globals, obj);
end;

_YAPB_checkRef := function(obj)
 return ForAny(_YAPB_Globals, x -> IsIdenticalObj(x, obj));
end;

_YAPB_clearRefs := function()
 _YAPB_Globals := [];
end;

_YAPB_getPermTo := function(sc, i)
 local current_perm, current_pos, base_val;
 base_val := sc.orbit[1];
 if not(IsBound(sc.transversal[i])) then
 return fail;
 fi;
 current_perm := sc.transversal[i];
 current_pos := i^current_perm;
 while (current_pos <> base_val)
 do
 current_perm := current_perm * sc.transversal[current_pos];
 current_pos := i^current_perm;
 od;
 return current_perm;
end;

_YAPB_inGroup := function(p, g)
 return (p in g);
end;

_YAPB_isGroupConj := function(p, g)
 return g^p = g;
end;

_YAPB_getOrbitPart := function(g, maxval)
 return OrbitsDomain(Group(g.generators), [1..maxval]);
end;

_YAPB_getBlockList := function(sc)
 local blocks, g, orbs, b, o;
 g := Group(sc.generators);
 orbs := Orbits(g);
 blocks := [];
 for o in orbs
 do
 b := RepresentativesMinimalBlocks(g,o);
 if b[1] <> o then
 Append(blocks, b);
 fi;
 od;

 return List(blocks, x->Orbit(g,Set(x),OnSets));
end;

_YAPB_FixedOrbits := function(group, domainsize, fixedpoints)
 return OrbitsDomain(Stabilizer(group, fixedpoints, OnTuples), [1..domainsize]);
end;

_YAPB_RepresentElement := function(group, list1, list2)
 local res;
 res := RepresentativeAction(group, list1, list2, OnTuples);
 if(res = fail) then
 return fail;
 fi;
 return ListPerm(res);
end;

_YAPB_getInfoFerret := function()
 return InfoLevel(InfoFerret);
end;

_YAPB_getInfoFerretDebug := function()
 return InfoLevel(InfoFerretDebug);
end;

_YAPB_fillRepElements := function(G, orb)
 local val, g, reps, buildorb, gens;
 reps := [];
 reps[orb[1]] := ();
 buildorb := [orb[1]];
 gens := GeneratorsOfGroup(G);
 for val in buildorb do
 for g in gens do
 if not IsBound(reps[val^g]) then
 reps[val^g] := reps[val] * g;
 Add(buildorb, val^g);
 fi;
od;
 od;
 return reps;
end;

_YAPB_stabTime := 0;

_YAPB_getOrbitalList := function(sc, maxval)
local G, cutoff,
 orb, orbitsG, iorb, graph, graphlist, val, p, i, orbsizes, orbpos, innerorblist, orbitsizes,
 biggestOrbit, skippedOneLargeOrbit, orbreps, stabtime;

 if IsGroup(sc) then
 G := sc;
 else
 G := GroupStabChain(sc);
 fi;

 cutoff := infinity;

graphlist := [];
orbitsG := Orbits(G,[1..maxval]);

orbsizes := [];
orbpos := [];
# Efficiently store size of orbits of values
for orb in [1..Length(orbitsG)] do
 for i in orbitsG[orb] do
 orbsizes[i] := Size(orbitsG[orb]);
 orbpos[i] := orb;
 od;
od;

 stabtime := NanosecondsSinceEpoch();
innerorblist := List(orbitsG, o -> Orbits(Stabilizer(G, o[1]), [1..LargestMovedPoint(G)]));
 _YAPB_stabTime := _YAPB_stabTime + (NanosecondsSinceEpoch() - stabtime);

 orbitsizes := List([1..Length(orbitsG)],
 x -> List(innerorblist[x], y -> Size(orbitsG[x])*Size(y)));

biggestOrbit := Maximum(Flat(orbitsizes));

skippedOneLargeOrbit := false;

for i in [1..Size(orbitsG)] do
 orb := orbitsG[i];
 orbreps := [];
 for iorb in innerorblist[i] do
 if (Size(orb) * Size(iorb) = biggestOrbit and not skippedOneLargeOrbit) then
 skippedOneLargeOrbit := true;
 else
 if (Size(orb) * Size(iorb) <= cutoff) and
 # orbit size unchanged
 not(Size(iorb) = orbsizes[iorb[1]]) and
 # orbit size only removed one point
 not(orbpos[orb[1]] = orbpos[iorb[1]] and Size(iorb) + 1 = orbsizes[iorb[1]]) and
 # don't want to take the fixed point orbit
 not(orb[1] = iorb[1] and Size(iorb) = 1)
 then
 graph := List([1..LargestMovedPoint(G)], x -> []);
 if IsEmpty(orbreps) then
 orbreps := _YAPB_fillRepElements(G, orb);
 fi;
 for val in orb do
 p := orbreps[val];
 graph[val] := List(iorb, x -> x^p);
 od;
 Add(graphlist, graph);
 fi;
 fi;
 od;
od;
return graphlist;
end;

#####
# END OF FUNCTIONS CALLED FROM C++ CODE
#####

#############################################################################
##
##
## <#GAPDoc Label="ConStabilize">
## <ManSection>
## <Func Name="ConStabilize" Arg="object, action" Label="for an object and an action"/>
## <Func Name="ConStabilize" Arg="object, n" Label="for a transformation or partial perm"/>
##
## <Description>
## This function creates a Constraint which can be given to <Ref Func="Solve" />.
## It does not perform any useful actions by itself
## 
## In the first form this represents the group which stabilises <A>object</A>
## under <A>action</A>.
## The currently allowed actions are <C>OnSets</C>, <C>OnSetsSets</C>, <C>OnSetsDisjointSets</C>,
## <C>OnSetsTuples</C>, <C>OnTuples</C>, <C>OnPairs</C> and <C>OnDirectedGraph</C>.
## 
## In the second form it represents the stabilizer of a partial perm
## or transformation in the symmetric group on <A>n</A> points.
##
##
## </Description>
## </ManSection>
## <#/GAPDoc>
InstallMethod(ConStabilize, [IsList, IsFunction],
function(list, op)
 if op = OnSets then
 return rec(constraint := "SetStab",
 arg := list,
 max := MaximumList(list, 0));
 fi;

 if op = OnSetsDisjointSets then
 return rec(constraint := "SetSetStab",
 arg := list,
 max := MaximumList(List(list, x -> MaximumList(x, 0)),0));
 fi;

 if op = OnSetsSets then
 return rec(constraint := "OverlappingSetSetStab",
 arg := list,
 max := MaximumList(List(list, x -> MaximumList(x, 0)),0));
 fi;

 if op = OnSetsTuples then
 return rec(constraint := "SetTupleStab",
 arg := list,
 max := MaximumList(List(list, x -> MaximumList(x, 0)),0));
 fi;

 if op = OnTuples or op = OnPairs then
 return rec(constraint := "ListStab",
 arg := list,
 max := MaximumList(list, 0));
 fi;

 if op = OnTuplesTuples then
 return rec(constraint := "ListStab",
 arg := Concatenation(list),
 max := MaximumList(Concatenation(list), 0));
 fi;

 if op = OnTuplesSets then
 return List(list, x -> ConStabilize(x, OnSets));
 fi;

 if op = OnDirectedGraph then
 return rec(constraint := "DirectedGraph",
 arg := list,
 max := Length(list));
 fi;

 if op = OnEdgeColouredDirectedGraph then
 return rec(constraint := "EdgeColouredDirectedGraph",
 arg := list,
 max := Length(list));
 fi;

 Error("Do not understand:", op);
end);

InstallMethod(ConStabilize, [IsList, IsFunction, IsRecord],
 function(list, op, useroptions)
 local con, options;

 if Size(RecNames(useroptions)) = 0 then
 return ConStabilize(list, op);
 fi;

 if op = OnEdgeColouredDirectedGraph then
 con := rec(constraint := "EdgeColouredDirectedGraph",
 arg := list,
 max := Length(list));
 elif op = OnDirectedGraph then
 con := rec(constraint := "DirectedGraph",
 arg := list,
 max := Length(list));
 else
 ErrorNoReturn("No record argument allowed for " + op);
 fi;

 useroptions := _FerretHelperFuncs.fillUserValues(
 rec(start_path_length := 1,
 normal_path_length := 1), useroptions);

 con.start_path_length := useroptions.start_path_length;
 con.normal_path_length := useroptions.normal_path_length;

 return con;
 end);



InstallMethod(ConStabilize, [IsPosInt, IsFunction],
function(i, op)
 if op = OnPoints then
 return rec(constraint := "SetStab",
 arg := [i],
 max := i);
 fi;

 Error("Do not understand:", op);
end);

InstallMethod(ConStabilize, [IsTransformation, IsPosInt],
function(t, i)
 return ConStabilize(List([1..i], x -> [x^t]), OnDirectedGraph);
end);

InstallMethod(ConStabilize, [IsPartialPerm, IsPosInt],
function(pp, m)
 local l, i;
 l := List([1..m], x -> []);
 for i in [1..m] do
 if i^pp <> 0 then
 Add(l[i], i^pp);
 fi;
 od;
 return ConStabilize(l, OnDirectedGraph);
end);

#############################################################################
##
##
## <#GAPDoc Label="ConInGroup">
## <ManSection>
## <Func Name="ConInGroup" Arg="G"/>
##
## <Description>
## This function creates a Constraint which can be given to <Ref Func="Solve" />.
## It does not perform any useful actions by itself
## 
## Represents the set of permutations in a permutation group <A>G</A>, as an
## argument for
## <Ref Func="Solve" />.
## </Description>
## </ManSection>
## <#/GAPDoc>
InstallMethod(ConInGroup, [IsPermGroup],
function(G)
 return ConInGroup(G, rec() );
end);

# Inefficient, StabChain, BlockStabChain, OrbStabChain, BlockOrbStabChain, UnorderedStabChain

InstallMethod(ConInGroup, [IsPermGroup, IsRecord],
function(G, useroptions)

 useroptions := _FerretHelperFuncs.fillUserValues(
 rec(orbits := "always", blocks := "never", orbitals := "never"), useroptions);

 # We special case the identity group, because it is a pain
 if IsTrivial(G) then
 return rec(constraint:="FixAllPoints", max := 1);
 else
 return rec(constraint:= "Generators_StabChain",
 arg := G,
 orbits := useroptions.orbits,
 blocks := useroptions.blocks,
 orbitals := useroptions.orbitals,
 max := LargestMovedPoint(G));
 fi;
end);

InstallGlobalFunction( OnDirectedGraph, function(graph, perm)
 local newgraph, list, i, j;
 newgraph := [];
 for i in [1..Length(graph)] do
 list := [];
 for j in [1..Length(graph[i])] do
 Add(list, (graph[i][j])^perm);
 od;
 if i^perm > Length(graph) then
 ErrorNoReturn("perm invalid on graph");
 fi;
 newgraph[i^perm] := Set(list);
 od;
 return newgraph;
end );

InstallGlobalFunction( OnEdgeColouredDirectedGraph, function(graph, perm)
 local newgraph, list, i, j;
 newgraph := [];
 for i in [1..Length(graph)] do
 list := [];
 for j in [1..Length(graph[i])] do
 Add(list, [(graph[i][j][1])^perm, graph[i][j][2]]);
 od;
 if i^perm > Length(graph) then
 ErrorNoReturn("perm invalid on graph");
 fi;
 newgraph[i^perm] := Set(list);
 od;
 return newgraph;
end );

_FERRET_DEFAULT_OPTIONS := MakeImmutable(rec(searchValueHeuristic := "RBase",
 searchFirstBranchValueHeuristic := "RBase",
 rbaseCellHeuristic := "smallest",
 rbaseValueHeuristic := "smallest",
 stats := false,
 nodeLimit := false,
 recreturn := false,
 only_find_generators := true,
 just_rbase := false
 ));

#############################################################################
##
##
## <#GAPDoc Label="Solve">
## <ManSection>
## <Func Name="Solve" Arg="constraints [,rec]"/>
##
## <Description>
## Finds the intersection of the list <A>Constraints</A>.
##
## Each member of <A>constraints</A> should be a group or coset
## generated by one of <Ref Func="ConInGroup" /> or
## <Ref Func="ConStabilize" Label="for an object and an action"/>.
##
## The optional second argument allows configuration options to be
## passed in. These follow options are supported:
##
## <List>
## <C>rbaseCellHeuristic</C> (default "smallest")
## <Item>
## The cell to be branched on. This is the option which will most
## effect the time taken to search. the default is usually best.
##
## Other options are: "First" (first cell), "Largest" (largest cell),
## "smallest2" (the 2nd smallest cell), "random" (a random cell)
## and "randomsmallest" (one of the smallest cells, chosen randomly)
## </Item>
## <C>rbaseValueHeuristic</C> (default "smallest")
## <Item>
## Choose which cell to branch on within a cell. While this will
## generally make a big difference to search, it is hard to predict
## the best value, and small changes to the problem will change the
## best heuristic. Options are the same as <C>rbaseCellHeuristic</C>.
## </Item>
## <C>searchValueHeuristic</C> (default <K>RBase</K>)
## <Item>
## The order to branch during search. In general the best order
## is very hard to predict. Options are "RBase", "InvRBase",
## "Random", "Sorted" or "Nosort" (which uses the order the values
## naturally end up in by the algorithm).
## </Item>
## <C>searchFirstBranchValueHeuristic</C> (default <K>RBase</K>)
## <Item>
## Choose the search order used just on the left-most branches of
## search. Allows the same options as <C>searchValueHeuristic</C>
## </Item>
## <C>stats</C> (default <C>false</C>)
## <Item>
## Change the return value to provide a range of information about how
## search performed (implies <C>recreturn</C>). This information will
## change between releases.
## </Item>
## <C>nodeLimit</C> (default <C>false</C>) 
## <Item>
## Either false, or an integer which places a limit on the amount
## of search which should be performed. WARNING: When this option is set
## to an integer, Ferret will return the current best answer when the limit
## is reached, which may be a subgroup of the actual result. To know if this
## limit was reached, set <C>stats</C> to true, and check the nodes.
## </Item>
## <C>recreturn</C> (default <C>false</C>) 
## <Item>
## Return a record containing private information, rather than the group.
## </Item>
## <C>only_find_generators</C> (default <C>true</C>)
## <Item>
## By default only find the generators of the group. If false, then
## find all members of the group. This option is only useful for testing.
## If 'true', then sets 'recreturn' to true.
## </Item>
## </List>
##
##
## </Description>
## </ManSection>
## <#/GAPDoc>
InstallGlobalFunction( Solve, function( arg )
 local maxpoint, record, l, options, useroptions,
 constraints, name, buildStabChain, retgrp;
 l := Length(arg);
 if l = 0 or l > 2 then
 Error( "usage: Solve(<C>[, <options>])");
 fi;

 constraints := Filtered(Flat(arg[1]), x -> x.max > 0);

 if Length(constraints) = 0 then
 Error("Cannot create infinite group in Solve");
 fi;

 maxpoint := Maximum(List(constraints, x -> x.max));

 # YAPB++ requires at least 2 points. We solve this in this way
 # because it makes sure we return all the various things
 # users might want (an rbase, etc).
 if maxpoint < 2 then
 Add(constraints, rec(constraint:="FixAllPoints", max := 2));
 maxpoint := 2;
 fi;

 if l = 2 then
 useroptions := arg[2];
 else
 useroptions := rec();
 fi;

 options := _FerretHelperFuncs.fillUserValues(_FERRET_DEFAULT_OPTIONS,
 useroptions);

 options.size := maxpoint;

 if options.stats or options.just_rbase then
 options.recreturn := true;
 fi;

_YAPB_stabTime := 0;
 record := YAPB_SOLVE(constraints, options);
 if IsBound(record.timing) then
 record.timing[1].stabInOrbFinding := _YAPB_stabTime;
fi;
 _YAPB_clearRefs();

 # We now stitch together a stabilizer chain from the return values of YAPB++
 buildStabChain := function(gens, gen_map)
 local sc, current_val, start_of_range, i;
 current_val := gen_map[1][1];
 start_of_range := 1;
 sc := EmptyStabChain(gens, ());
 for i in [2..Length(gen_map)] do
 if gen_map[i][1] <> current_val then
 InsertTrivialStabilizer(sc, current_val);
 AddGeneratorsExtendSchreierTree(sc, gens{[start_of_range..i-1]});
 current_val := gen_map[i][1];
 start_of_range := i;
 fi;
 od;
 InsertTrivialStabilizer(sc, current_val);
 AddGeneratorsExtendSchreierTree(sc, gens{[start_of_range..Length(gens)]});
 return sc;
 end;

 if options.recreturn then
 return record;
 else
 if record.generators = [()] then # just to avoid having to make code work in this case
 retgrp := Group(());
 StabChainMutable(retgrp);
 else
 retgrp := Group(record.generators);
 SetStabChainMutable(retgrp, buildStabChain(record.generators, record.generators_map));
 fi;

 Size(retgrp);
 return retgrp;
 fi;

end );
#E files.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here

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