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#############################################################################
##
#W iterator.gi GAP4 package `Utils' Chris Wensley
##
#Y Copyright (C) 2015-2025, The GAP Group
##############################################################################
##
#M AllIsomorphismsIterator . . . . . . . . . . . . . . . for a pair of groups
#M DoAllIsomorphismsIterator . . . . . . . . . . . . . . for a pair of groups
#M AllIsomorphismsNumber . . . . . . . . . . . . . . . . for a pair of groups
#M AllIsomorphisms . . . . . . . . . . . . . . . . . . . for a pair of groups
##
BindGlobal( "NextIterator_AllIsomorphisms", function ( iter )
local a;
if not IsDoneIterator( iter ) then
a := NextIterator( iter!.autoIterator );
return CompositionMapping( iter!.firstiso, a );
fi;
Error( "iterator is exhausted" );
end );
BindGlobal( "IsDoneIterator_AllIsomorphisms",
iter -> IsDoneIterator( iter!.autoIterator ) );
BindGlobal( "ShallowCopy_AllIsomorphisms",
iter -> rec( firstiso := iter!.firstiso,
autoIterator := ShallowCopy( iter!.autoIterator ) ) );
BindGlobal( "DoAllIsomorphismsIterator",
function( G, H )
local iso, autoiter, iter;
if not IsGroup( G ) and IsGroup( H ) then
Error( "G,H should be groups" );
fi;
iso := IsomorphismGroups( G, H );
if ( iso = fail ) then
## there are no isomorphisms so return an empty iterator
return IteratorList( [ ] );
fi;
autoiter := Iterator( AutomorphismGroup( G ) );
iter := IteratorByFunctions(
rec( firstiso := iso,
autoIterator := ShallowCopy( autoiter ),
NextIterator := NextIterator_AllIsomorphisms,
IsDoneIterator := IsDoneIterator_AllIsomorphisms,
ShallowCopy := ShallowCopy_AllIsomorphisms ) );
return iter;
end );
InstallMethod( AllIsomorphismsIterator, "for a pair of groups",
[ IsGroup, IsGroup ], 0,
function( G, H )
return DoAllIsomorphismsIterator( G, H );
end );
InstallMethod( AllIsomorphisms, "for a pair of groups",
[ IsGroup, IsGroup ], 0,
function( G, H )
local iter, L, iso;
iter := AllIsomorphismsIterator( G, H );
if IsDoneIterator( iter ) then
return [ ];
fi;
L := [ ];
for iso in iter do
Add( L, iso );
od;
return L;
end );
InstallMethod( AllIsomorphismsNumber, "for a pair of groups",
[ IsGroup, IsGroup ], 0,
function( G, H )
local iter, n, iso;
iter := AllIsomorphismsIterator( G, H );
if IsDoneIterator( iter ) then
return 0;
fi;
n := 0;
for iso in iter do
n := n+1;
od;
return n;
end );
##############################################################################
##
#M AllSubgroupsIterator . . . . . . . . . . . . . . . . . . . . . for a group
#M DoAllSubgroupsIterator . . . . . . . . . . . . . . . . . . . . for a group
##
BindGlobal( "NextIterator_AllSubgroups", function ( iter )
local class, i;
if IsDoneIterator( iter!.subgpIterator ) then
class := NextIterator( iter!.classIterator );
iter!.class := class;
iter!.subgpIterator := IteratorList( [1..Size(class)] );
fi;
i := NextIterator( iter!.subgpIterator );
return iter!.class[i];
end );
BindGlobal( "IsDoneIterator_AllSubgroups",
iter -> IsDoneIterator( iter!.classIterator )
and IsDoneIterator( iter!.subgpIterator ) );
BindGlobal( "ShallowCopy_AllSubgroups",
iter -> rec( class := iter!.class,
classIterator := ShallowCopy( iter!.classIterator ),
subgpIterator := ShallowCopy( iter!.subgpIterator ) ) );
BindGlobal( "DoAllSubgroupsIterator",
function( G )
local lat, ccs, classIterator, subgpIterator, iter;
lat := LatticeSubgroups( G );
ccs := ConjugacyClassesSubgroups( lat );
classIterator := IteratorList( ccs );
subgpIterator := 0;
iter := IteratorByFunctions(
rec( class := 0,
classIterator := ShallowCopy( classIterator ),
subgpIterator := IteratorList( [ ] ),
NextIterator := NextIterator_AllSubgroups,
IsDoneIterator := IsDoneIterator_AllSubgroups,
ShallowCopy := ShallowCopy_AllSubgroups ) );
return iter;
end );
InstallMethod( AllSubgroupsIterator, "for a group", [ IsGroup ], 0,
function( G )
return DoAllSubgroupsIterator( G );
end );
##############################################################################
##
#M CartesianIterator . . . . . . . . . . . . . . . . . . . for two iterators
#M DoCartesianIterator . . . . . . . . . . . . . . . . . . for two iterators
##
BindGlobal( "NextIterator_CartesianIterator", function ( iter )
local first, second;
if IsDoneIterator( iter!.Iterator2Copy ) then
iter!.Iterator2Copy := ShallowCopy( iter!.Iterator2 );
first := NextIterator( iter!.Iterator1 );
iter!.first := first;
else
first := iter!.first;
fi;
second := NextIterator( iter!.Iterator2Copy );
return [ first, second ];
end );
BindGlobal( "IsDoneIterator_CartesianIterator",
iter -> IsDoneIterator( iter!.Iterator1 )
and IsDoneIterator( iter!.Iterator2Copy ) );
BindGlobal( "ShallowCopy_CartesianIterator",
iter -> rec( first := iter!.first,
Iterator1 := ShallowCopy( iter!.Iterator1 ),
Iterator2 := ShallowCopy( iter!.Iterator2 ),
Iterator2Copy := ShallowCopy( iter!.Iterator2Copy ) ) );
BindGlobal( "DoCartesianIterator",
function( iter1, iter2 )
local iter;
if IsDoneIterator( iter1 ) or IsDoneIterator( iter2 ) then
return IteratorList( [ ] );
fi;
iter := IteratorByFunctions(
rec( first := 0,
Iterator1 := ShallowCopy( iter1 ),
Iterator2 := ShallowCopy( iter2 ),
Iterator2Copy := IteratorList( [ ] ),
NextIterator := NextIterator_CartesianIterator,
IsDoneIterator := IsDoneIterator_CartesianIterator,
ShallowCopy := ShallowCopy_CartesianIterator ) );
return iter;
end );
InstallMethod( CartesianIterator, "for two iterators",
[ IsIterator, IsIterator ], 0,
function( iter1, iter2 )
return DoCartesianIterator( iter1, iter2 );
end );
##############################################################################
##
#M UnorderedPairsIterator . . . . . . . . . . . . . . . . . . for an iterator
#M DoUnorderedPairsIterator . . . . . . . . . . . . . . . . . for an iterator
##
BindGlobal( "NextIterator_UnorderedPairs", function ( iter )
local first, second;
if ( iter!.pos1 = iter!.pos2 ) then
iter!.Iterator1Copy := ShallowCopy( iter!.Iterator1 );
iter!.pos1 := 0;
second := NextIterator( iter!.Iterator2 );
iter!.pos2 := iter!.pos2 + 1;
iter!.second := second;
else
second := iter!.second;
fi;
first := NextIterator( iter!.Iterator1Copy );
iter!.pos1 := iter!.pos1 + 1;
return [ first, second ];
end );
BindGlobal( "IsDoneIterator_UnorderedPairs",
iter -> IsDoneIterator( iter!.Iterator2 )
and IsDoneIterator( iter!.Iterator1Copy ) );
BindGlobal( "ShallowCopy_UnorderedPairs",
iter -> rec( pos1 := iter!.pos1,
pos2 := iter!.pos2,
second := iter!.second,
Iterator1 := ShallowCopy( iter!.Iterator1 ),
Iterator2 := ShallowCopy( iter!.Iterator2 ),
Iterator1Copy := ShallowCopy( iter!.Iterator1Copy ) ) );
BindGlobal( "DoUnorderedPairsIterator",
function( iter0 )
local iter;
if IsDoneIterator( iter0 ) then
return IteratorList( [ ] );
fi;
iter := IteratorByFunctions(
rec( pos1 := 0,
pos2 := 0,
second := 0,
Iterator1 := ShallowCopy( iter0 ),
Iterator2 := ShallowCopy( iter0 ),
Iterator1Copy := ShallowCopy( iter0 ),
NextIterator := NextIterator_UnorderedPairs,
IsDoneIterator := IsDoneIterator_UnorderedPairs,
ShallowCopy := ShallowCopy_UnorderedPairs ) );
return iter;
end );
InstallMethod( UnorderedPairsIterator, "for an iterator", [ IsIterator ], 0,
function( iter0 )
return DoUnorderedPairsIterator( iter0 );
end );
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