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# Exec("date");Rewritability(AlternatingGroup(5),10);time;Exec("date");
Rewritability:=function(G,limit)
local eltsG, s, A, orbsA, x, q, n, isnrw, nrw, S, i, j, u, K, y, orbsK, v, tw;
eltsG:=Filtered( G, s -> s <> () );
A:=AutomorphismGroup(G);
orbsA:=Orbits(A,G);
x:=Filtered( List(orbsA, q -> q[1] ), q -> q <> () );
x:=List( x, q -> [q] );
n:=1;
repeat
n:=n+1;
Print("Started enumeration of NRW of length ", n, "\n");
nrw:=[];
S := SymmetricGroup( n );
S := Filtered( S, s -> s <> () );
for i in [1..Length(x)] do
# Print( i, "/", Length(nrw), "\r");
u := x[i];
K:=Stabilizer(A,u[1]);
for j in [ 2 .. Length(u) ] do
K:=Intersection( K, Stabilizer( A,u[j] ) );
if Size(K) = 1 then
y := eltsG;
break;
fi;
od;
if Size(K) > 1 then
orbsK:=Orbits(K,G);
y:=Filtered( List(orbsK, q -> q[1] ), q -> q <> () );
fi;
tw := u;
for v in y do
tw[n] := v;
isnrw:=true;
for s in S do
if Product(tw)=Product(Permuted(tw,s)) then
isnrw := false;
break;
fi;
od;
if isnrw then
Add( nrw, ShallowCopy(tw) );
fi;
od;
od;
Print( Length(nrw), " NRW of length ", n, " constructed\n");
if nrw=[] then
return n;
fi;
x := ShallowCopy( nrw );
until n=limit;
return fail;
end;
# Exec("date");RewritabilityWithCache(AlternatingGroup(5),10);time;Exec("date");
RewritabilityWithCache:=function(G,limit)
local eltsG, s, A, orbsA, x, q, n, isnrw, nrw, S, i, j, u, K, y, orbsK, v, tw;
eltsG:=Filtered( G, s -> s <> () );
A:=AutomorphismGroup(G);
orbsA:=Orbits(A,G);
x:=Filtered( List(orbsA, q -> q[1] ), q -> q <> () );
x:=List( x, q -> [ [ q ], Stabilizer( A,q ) ] );
n:=1;
repeat
n:=n+1;
Print("Started enumeration of NRW of length ", n, "\n");
nrw:=[];
S := SymmetricGroup( n );
S := Filtered( S, s -> s <> () );
for i in [1..Length(x)] do
# Print( i, "/", Length(nrw), "\r");
u := x[i][1];
K := x[i][2];
if Size(K) = 1 then
y := eltsG;
else
orbsK:=Orbits(K,G);
y:=Filtered( List(orbsK, q -> q[1] ), q -> q <> () );
fi;
tw := u;
for v in y do
tw[n] := v;
isnrw:=true;
for s in S do
if Product(tw)=Product(Permuted(tw,s)) then
isnrw := false;
break;
fi;
od;
if isnrw then
Add( nrw, [ ShallowCopy(tw), Intersection( K, Stabilizer( A,v ) ) ] );
fi;
od;
od;
Print( Length(nrw), " NRW of length ", n, " constructed\n");
if nrw=[] then
return n;
fi;
x := ShallowCopy( nrw );
until n=limit;
return fail;
end;
RewritabilityWorker:=function( a )
local G, w, stab, limit, x ,eltsG, s, A, orbsA, q, n, isnrw, nrw, S,
i, j, u, K, y, orbsK, v, tw, res, g;
G:=a[1];
w:=a[2];
stab:=a[3];
limit:=a[4];
eltsG:=Filtered( G, s -> s <> () );
A:=AutomorphismGroup(G);
if stab=[] then
x:=[ [ w, Subgroup(A, [One(A)] ) ] ];
else
x:=[ [ w, Subgroup( A, List(stab, g -> GroupHomomorphismByImages( G, G, g[1], g[2] ) ) ) ] ];
fi;
#orbsA:=Orbits(A,G);
#x:=Filtered( List(orbsA, q -> q[1] ), q -> q <> () );
#x:=List( x, q -> [ [ q ], Stabilizer( A,q ) ] );
n:=Length(w);
res:=[];
repeat
n:=n+1;
Print("Started enumeration of NRW of length ", n, " on worker\n");
nrw:=[];
S := SymmetricGroup( n );
S := Filtered( S, s -> s <> () );
for i in [1..Length(x)] do
# Print( i, "/", Length(nrw), "\r");
u := x[i][1];
K := x[i][2];
if Size(K) = 1 then
y := eltsG;
else
orbsK:=Orbits(K,G);
y:=Filtered( List(orbsK, q -> q[1] ), q -> q <> () );
fi;
tw := u;
for v in y do
tw[n] := v;
isnrw:=true;
for s in S do
if Product(tw)=Product(Permuted(tw,s)) then
isnrw := false;
break;
fi;
od;
if isnrw then
Add( nrw, [ ShallowCopy(tw), Intersection( K, Stabilizer( A,v ) ) ] );
fi;
od;
od;
Print( Length(nrw), " NRW of length ", n, " constructed on worker\n");
res[n]:=Length(nrw);
if nrw=[] then
return res;
fi;
x := ShallowCopy( nrw );
until n=limit;
return res;
end;
RewritabilityParallel:=function(G,limit,depth)
local eltsG, s, A, orbsA, x, q, n, isnrw, nrw, S,
i, j, u, K, y, orbsK, v, tw, res, res1, w, r;
if depth<3 then
Error("the third argument should be bigger than 2 \n");
fi;
eltsG:=Filtered( G, s -> s <> () );
A:=AutomorphismGroup(G);
orbsA:=Orbits(A,G);
x:=Filtered( List(orbsA, q -> q[1] ), q -> q <> () );
x:=List( x, q -> [ [ q ], Stabilizer( A,q ) ] );
n:=1;
res:=[];
repeat
n:=n+1;
Print("Started enumeration of NRW of length ", n, "\n");
if n>=depth then
res1 := Sum( ParListWithSCSCP(
List( x, w -> [ G, w[1], List( GeneratorsOfGroup(w[2]),MappingGeneratorsImages), limit ] ),
"RewritabilityWorker" ) );
res := res + Concatenation( ListWithIdenticalEntries( n-1, 0), res1 );
return res;
else
nrw:=[];
S := SymmetricGroup( n );
S := Filtered( S, s -> s <> () );
for i in [1..Length(x)] do
# Print( i, "/", Length(nrw), "\r");
u := x[i][1];
K := x[i][2];
if Size(K) = 1 then
y := eltsG;
else
orbsK:=Orbits(K,G);
y:=Filtered( List(orbsK, q -> q[1] ), q -> q <> () );
fi;
tw := u;
for v in y do
tw[n] := v;
isnrw:=true;
for s in S do
if Product(tw)=Product(Permuted(tw,s)) then
isnrw := false;
break;
fi;
od;
if isnrw then
Add( nrw, [ ShallowCopy(tw), Intersection( K, Stabilizer( A,v ) ) ] );
fi;
od;
od;
fi;
Print( Length(nrw), " NRW of length ", n, " constructed\n");
res[n]:=Length(nrw);
if nrw=[] then
return res;
fi;
x := ShallowCopy( nrw );
until n=limit;
return res;
end;
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