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WIP: mandarins
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@fingolfin @ssiccha
fingolfin authored and ssiccha committed Oct 28, 2020
1 parent cc9a051 commit 1c0ffe7
Showing 1 changed file with 98 additions and 18 deletions.
116 changes: 98 additions & 18 deletions gap/base/recognition.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -88,25 +88,25 @@ InstallMethod( ViewObj, "for recognition infos", [IsRecognitionInfo],

InstallGlobalFunction( RecognisePermGroup,
function(G)
return RecogniseGeneric(G, FindHomDbPerm, "", rec());
return RecogniseGeneric(G, FindHomDbPerm, "", rec(), fail);
end);

InstallGlobalFunction( RecogniseMatrixGroup,
function(G)
return RecogniseGeneric(G, FindHomDbMatrix, "", rec());
return RecogniseGeneric(G, FindHomDbMatrix, "", rec(), fail);
end);

InstallGlobalFunction( RecogniseProjectiveGroup,
function(G)
return RecogniseGeneric(G, FindHomDbProjective, "", rec());
return RecogniseGeneric(G, FindHomDbProjective, "", rec(), fail);
end);

InstallGlobalFunction( RecogniseGroup,
function(G)
if IsPermGroup(G) then
return RecogniseGeneric(G, FindHomDbPerm, "", rec());
return RecogniseGeneric(G, FindHomDbPerm, "", rec(), fail);
elif IsMatrixGroup(G) then
return RecogniseGeneric(G, FindHomDbMatrix, "", rec());
return RecogniseGeneric(G, FindHomDbMatrix, "", rec(), fail);
else
ErrorNoReturn("Only matrix and permutation groups are supported");
fi;
Expand Down Expand Up @@ -389,21 +389,31 @@ InstallGlobalFunction( PrintTreePos,
fi;
end );

NUM_MANDARINS := 100;

InstallGlobalFunction( RecogniseGeneric,
function(H, methoddb, depthString, knowledge)
function(H, methoddb, depthString, knowledge, mandarins)
# Assume all the generators have no memory!
local N,depth,done,i,l,ll,gensNmeth,allmethods,
proj1,proj2,ri,rifac,riker,s,x,y,z,succ,counter;
proj1,proj2,ri,rifac,riker,s,x,y,z,succ,counter,
kernelMandarins,factorMandarins,tmp;

depth := Length(depthString);

PrintTreePos("E",depthString,H);
Info(InfoRecog,4,"Recognising: ",H);

if Length(GeneratorsOfGroup(H)) = 0 then
# FIXME: shouldn't we just, like, finish here immediately?
H := Group([One(H)]);
fi;

if mandarins = fail then
Assert(0, depth = 0);
mandarins := List([1..NUM_MANDARINS], i -> PseudoRandom(H));
fi;


# Set up the record and the group object:
if IsIdenticalObj( methoddb, FindHomDbProjective ) then
ri := EmptyRecognitionInfoRecord(knowledge,H,true);
Expand Down Expand Up @@ -453,6 +463,20 @@ InstallGlobalFunction( RecogniseGeneric,
SetNiceGens(ri,GeneratorsOfGroup(H));
fi;
fi;

# check mandarins now
tmp := NiceGens(ri);
for x in mandarins do
s := SLPforElement(ri, x);
if s = fail then
# TODO: should not really happen
Error("Mandarins detected bad leaf");
fi;
# TODO: validate the SLP, too?
z := ResultOfStraightLineProgram(s, tmp);
Assert(0, ri!.isequal(x, z));
od;

# these two were set correctly by FindHomomorphism
if IsLeaf(ri) then SetFilterObj(ri,IsReady); fi;
# FIXME: settle what IsReady means *exactly*;
Expand All @@ -466,6 +490,18 @@ InstallGlobalFunction( RecogniseGeneric,

# The non-leaf case:
# In that case we know that ri now knows: homom plus additional data.

# map the mandarins
factorMandarins := [];
for x in mandarins do
y := ImageElm(Homom(ri), x);
if y = fail then
# TODO: deal with this properly
Error("Mandarins detected bad factor homom");
fi;
Add(factorMandarins, y);
#s := SLPforElement(ri, x);
od;

# Try to recognise the factor a few times, then give up:
counter := 0;
Expand Down Expand Up @@ -493,7 +529,7 @@ InstallGlobalFunction( RecogniseGeneric,

rifac := RecogniseGeneric(
Group(List(GeneratorsOfGroup(H), x->ImageElm(Homom(ri),x))),
methodsforfactor(ri), depthString, forfactor(ri) ); # TODO: change forfactor to hintsForFactor??)
methodsforfactor(ri), depthString, forfactor(ri), factorMandarins ); # TODO: change forfactor to hintsForFactor??)
Remove(depthString);
PrintTreePos("F",depthString,H);
SetRIFac(ri,rifac);
Expand Down Expand Up @@ -535,7 +571,7 @@ InstallGlobalFunction( RecogniseGeneric,
Sort(l,SortFunctionWithMemory); # this favours "shorter" memories!
# FIXME: For projective groups different matrices might stand
# for the same element, we might overlook this here!
# remove duplicates:
# remove duplicates and trivial entries:
ll := [];
for i in [1..Length(l)] do
if not isone(ri)(l[i]) and
Expand All @@ -545,17 +581,59 @@ InstallGlobalFunction( RecogniseGeneric,
od;
SetgensN(ri,ll);
fi;

# evaluate mandarins to get kernel mandarins
kernelMandarins := [];
for i in [1..Length(mandarins)] do
x := mandarins[i];
y := factorMandarins[i];
s := SLPforElement(rifac, y);
if s = fail then
Error("TODO: no SLP for factor");
fi;
z := ResultOfStraightLineProgram(s, pregensfac(ri));
if not ri!.isequal(x, z) then
Add( kernelMandarins, x / z );
fi;
od;
# kernelMandarins := rifac!.kernelMandarins

if Length(gensN(ri)) = 0 then
# We found out that N is the trivial group!
# In this case we do nothing, kernel is fail indicating this.
Info(InfoRecog,2,"Found trivial kernel (depth=",depth,").");
SetRIKer(ri,fail);
# We have to learn from the factor, what our nice generators are:
SetNiceGens(ri,pregensfac(ri));
SetFilterObj(ri,IsReady);
if InfoLevel(InfoRecog) = 1 and depth = 0 then Print("\n"); fi;
# StopStoringRandEls(ri);
return ri;

if Length(kernelMandarins) <> 0 then
# ooops, mandarins disagree
if gensNmeth.method = FindKernelDoNothing then
Error("Mandarins detected bad kernel, but gensNmeth is FindKernelDoNothing");
elif IsBound(ri!.leavegensNuntouched) then
Error("Mandarins detected bad kernel, but leavegensNuntouched is set");
else
# we need to
# WARNING: do NOT add the mandarin here, even though it may seem tempting.
# But (a) they don't have memory, and (b) we need them to stay "clean",
# if we start using them for computations, this destroys out assumption
# about their independency
succ := FindKernelFastNormalClosure(ri,5,5);
Info(InfoRecog,2,"Have now ",Length(gensN(ri)),
" generators for kernel, recognising...");
# TODO: we should check if we found non-trivial gens now, and also clean out
# duplicates etc.; possibly by replicating the code we use above
if succ = false then
ErrorNoReturn("Very bad: factor was wrongly recognised and we ",
"found out too late");
fi;
fi;
else
Info(InfoRecog,2,"Found trivial kernel (depth=",depth,").");
SetRIKer(ri,fail);
# We have to learn from the factor, what our nice generators are:
SetNiceGens(ri,pregensfac(ri));
SetFilterObj(ri,IsReady);
if InfoLevel(InfoRecog) = 1 and depth = 0 then Print("\n"); fi;
# StopStoringRandEls(ri);
return ri;
fi;
fi;

Info(InfoRecog,2,"Going to the kernel (depth=",depth,").");
Expand All @@ -568,13 +646,15 @@ InstallGlobalFunction( RecogniseGeneric,
N := Group(StripMemory(gensN(ri)));

Add(depthString,'K');
riker := RecogniseGeneric( N, methoddb, depthString, forkernel(ri) );
riker := RecogniseGeneric( N, methoddb, depthString, forkernel(ri), kernelMandarins );
Remove(depthString);
PrintTreePos("K",depthString,H);
SetRIKer(ri,riker);
SetRIParent(riker,ri);
Info(InfoRecog,2,"Back from kernel (depth=",depth,").");

# TODO: verify kernelMandarins

done := true;
if IsReady(riker) and immediateverification(ri) then
# Do an immediate verification:
Expand Down

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