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Implementation of \Gamma_0 congruence subgroups of SL_3(Z) #146

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Merged
grahamknockillaree merged 4 commits into from
Jan 31, 2026
Merged

Implementation of \Gamma_0 congruence subgroups of SL_3(Z) #146

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e6aaa58
Add functions to compute finite projective spaces
giuliao27 Jan 13, 2026
abbdac2
Add implementation for non-prime m
giuliao27 Jan 13, 2026
a639804
Add implementation of Gamma0 for SL3
giuliao27 Jan 13, 2026
8e87db5
Add SL3ZSubgroupTree
giuliao27 Jan 29, 2026
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80 changes: 80 additions & 0 deletions lib/Orru/HAP_SL3ZSubgroupTree_fast.gi
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@@ -0,0 +1,80 @@
#descrive come i generatori di un gruppo agiscono sui coset di un sottogruppo.

InstallGlobalFunction(HAP_SL3ZSubgroupTree_fast,
function(G)
local ambientGenerators, tree, InGmodU, Ugrp, S, T, U, v, p, g, s, n, q, vv, leaves, genTriples, generators, InLowDegreeNodesModG, csts, cnt, vertex2word, one, triple2word, i, j, u,c, a, b;

S := [ [1,0,1], [0,-1,-1], [0,1,0] ];
T := [ [0,1,0], [0,0,1], [1,0,0]];
U := [[0,1,0], [1,0,0], [-1,-1,-1]];

ambientGenerators := [S,T,U];
one := IdentityMat(3); #to change? stabilizers to consider
Ugrp := G!.ugrp;
Ugrp := Elements( Ugrp );
tree := [ ];
genTriples := [ ];
cnt := 1;
leaves := NewDictionary( S, true, SL( 3, Integers ) );
csts := [ ];
csts[G!.cosetPos( one )] := 1;
AddDictionary( leaves, one, G!.cosetPos( one ) );
InLowDegreeNodesModG := function ( g )
local pos;
pos := G!.cosetPos( g );
if not IsBound( csts[pos] ) then
return false;
else
;
return pos;
fi;
return;
end;
while Size( leaves ) > 0 do
vv := 1 * leaves!.entries[1];
v := vv[1];
p := G!.cosetPos( v );
for s in [ 1 .. Length( ambientGenerators ) ] do
g := ambientGenerators[s] * v;
q := InLowDegreeNodesModG( g );
if q = false then
q := G!.cosetPos( g );
AddDictionary( leaves, g, q );
csts[q] := 1;
tree[q] := [ p, s ];
else
Add( genTriples, [ p, s, v, g ] );
fi;
od;
RemoveDictionary( leaves, v );
od;
vertex2word := function ( v )
local word;
word := one;
while IsBound( tree[v] ) do
word := word * ambientGenerators[tree[v][2]];
v := tree[v][1];
od;
return word;
end;
triple2word := function ( x )
local u, uu, g, q, c;
for u in Ugrp do
c := x[4] ^ -1 * u * vertex2word( G!.cosetPos( x[4] ) );
if G!.membership( c ) then
return c;
fi;
od;
return fail;
end;
genTriples := List( genTriples, function ( x )
return triple2word( x );
end );
genTriples := List( genTriples, function ( x )
return Minimum( x, x ^ -1 );
end );
genTriples := SSortedList( genTriples );
G!.tree := tree;
G!.GeneratorsOfMagmaWithInverses := genTriples;
return tree;
end);
7 changes: 5 additions & 2 deletions lib/Orru/decsOrru.gd
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@@ -1,5 +1,8 @@
IsHapCongruenceSubgroup:=NewFilter("IsHapCongruenceSubgroup");;
DeclareGlobalFunction("HAP_GenericCongruenceSubgroup");
DeclareGlobalFunction("FiniteProjectiveLine");
DeclareGlobalFunction("FiniteProjectivePlane");
DeclareGlobalFunction("HAP_SL3ZSubgroupTree_fast");
DeclareOperation("HAPCongruenceSubgroupGamma0",[IsInt,IsInt]);
DeclareOperation("HAPCongruenceSubgroupTree",[IsHapCongruenceSubgroup]);

Expand All @@ -9,13 +12,13 @@ InstallMethod( ViewObj,
10000000, #Ensures that this method is chosen
function(G)
Print(G!.name," of ",G!.fam);
end);
end);

InstallMethod( PrintObj,
"for HapCongruenceSubgroup",
[IsHapCongruenceSubgroup and IsGroup],
100000000, #Ensures that this method is chosen
function(G)
Print(G!.name," of ",G!.fam);
end);
end);

88 changes: 88 additions & 0 deletions lib/Orru/finiteProjectiveSpaces.gi
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@@ -0,0 +1,88 @@
InstallGlobalFunction(FiniteProjectiveLine,
function(n)
local UnitEls, x, y, i, c, d, u, UnitsAction, Representatives,
RepOf, r, v, w, m, min;

UnitEls := Units(Integers mod n);

UnitsAction := function(c, u)
local uu;
uu :=Int (u);
return List(c, x -> (uu * x) mod n);
end;

Representatives := [];

RepOf := [];
for x in [1..n] do
RepOf[x] := [];
od;

for x in [0..n-1] do
for y in [0..n-1] do
if Gcd(x,y,n) = 1 then
v := [x,y];
if not IsBound(RepOf[x+1][y+1]) then
m := Orbit(UnitEls,v,UnitsAction);
min := Minimum(m);
AddSet(Representatives,min);
for w in m + 1 do
RepOf[w[1]][w[2]] := min;
od;
fi;
fi;
od;
od;

return rec(
Reps := Set(Representatives),
RepOf:= RepOf
);
end);

InstallGlobalFunction(FiniteProjectivePlane,
function(n)
local UnitEls, x, y, z, i, c, d, u, UnitsAction, Representatives,
RepOf, r, v, w, m, min;

UnitEls := Units(Integers mod n);

UnitsAction := function(c, u)
local uu;
uu :=Int (u);
return List(c, x -> (uu * x) mod n);
end;

Representatives := [];

RepOf := [];
for x in [1..n] do
RepOf[x] := [];
for y in [1..n] do
RepOf[x][y] := [];
od;
od;

for x in [0..n-1] do
for y in [0..n-1] do
for z in [0..n-1] do
if Gcd(x,y,z,n) = 1 then
v := [x,y,z];
if not IsBound(RepOf[x+1][y+1][z+1]) then
m := Orbit(UnitEls,v,UnitsAction);
min := Minimum(m);
AddSet(Representatives,min);
for w in m + 1 do
RepOf[w[1]][w[2]][w[3]] := min;
od;
fi;
fi;
od;
od;
od;

return rec(
Reps := Set(Representatives),
RepOf:= RepOf
);
end);
2 changes: 2 additions & 0 deletions lib/Orru/initOrru.gi
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@@ -1 +1,3 @@
ReadPackageHap( "lib/Orru/subgroups.gi");
ReadPackageHap( "lib/Orru/finiteProjectiveSpaces.gi");
ReadPackageHap( "lib/Orru/HAP_SL3ZSubgroupTree_fast.gi");
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