Skip to content

Enhance NumberSmallGroups(<order>, <filter>) by avoiding to list the groups whose count we want #73

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
fingolfin merged 1 commit into from
Aug 16, 2026
Merged

Enhance NumberSmallGroups(<order>, <filter>) by avoiding to list the groups whose count we want #73

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
11 changes: 8 additions & 3 deletions CHANGES.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,12 +1,17 @@
This file describes changes in the smallgrp package.

# Unreleased

- Optimized `NumberSmallGroups` to be much faster in certain cases, for
example `NumberSmallGroups(1536, IsSolvableGroup, true)` is now instant
instead of running for 90 seconds.

# 1.6.0 (2026-08-09)

- Require GAP 4.12
- `NumberSmallGroups` now accepts a list of orders and the selection
criteria of `AllSmallGroups`, as in `NumberSmallGroups(96, IsAbelian)`.
It counts by listing the ids, so it costs what `IdsOfAllSmallGroups`
costs (issue #68)
criteria of `AllSmallGroups`, as in `NumberSmallGroups(96, IsAbelian)`
(issue #68)
- Selection by `IsAbelian`, `IsNilpotentGroup`, `IsSupersolvableGroup`,
`IsSolvableGroup`, `RankPGroup` and `PClassPGroup` now avoids
constructing the groups for most orders which had no precomputed data,
Expand Down
273 changes: 184 additions & 89 deletions gap/small.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -83,6 +83,15 @@ NUMBER_SMALL_GROUPS_FUNCS := [ ];
##
SELECT_SMALL_GROUPS_FUNCS := [ ];

#############################################################################
##
#F COUNT_SMALL_GROUPS_FUNCS
##
## A layer may install a function here to count a selection rather than
## list it, taking <size>, <funcs>, <vals>, <inforec> and <idList>. Without
## one the groups are listed and the list measured.
COUNT_SMALL_GROUPS_FUNCS := [ ];

#############################################################################
##
#F SMALL_IDS_EXPAND( <ids> )
Expand Down Expand Up @@ -345,6 +354,77 @@ SMALL_GROUPS_SIMPLIFY_QUERY := function( funcs, vals )
return rec( funcs := newfuncs, vals := newvals );
end;

#############################################################################
##
#F SMALL_GROUPS_PARSE_QUERY( argl )
##
## turns the arguments of 'AllSmallGroups' and its kin into a record with
## the components 'sizes', 'idList', 'funcs' and 'vals', the latter two as
## 'SMALL_GROUPS_SIMPLIFY_QUERY' leaves them.
SMALL_GROUPS_PARSE_QUERY := function( argl )
local sizes, i, funcs, vals, hasSizes, pos, idList, query;

sizes := [ ];
hasSizes := false;
idList := fail;

for i in [ 1 .. Length( argl ) ] do
if i = 1 and argl[ i ] = Size then
;
elif ( not hasSizes ) and IsList( argl[ i ] )
and Length( sizes ) = 1 then
idList := argl[ i ];
elif ( not hasSizes ) and IsList( argl[ i ] ) then
Append( sizes, argl[ i ] );
elif ( not hasSizes ) and IsPosInt( argl[ i ] ) then
Add( sizes, argl[ i ] );
elif ( not hasSizes ) and sizes <> [] and IsFunction( argl[i] ) then
hasSizes := true;
funcs := [ argl[ i ] ];
vals := [ [ ] ];
pos := 1;
elif not hasSizes then
Error( "usage: AllSmallGroups / OneSmallGroup(\n",
" Size, [ sizes ],\n",
" function1, [ values1 ],\n",
" function2, [ values2 ], ... )" );
elif vals[ pos ] <> [ ] and IsFunction( argl[ i ] ) then
pos := pos + 1;
funcs[ pos ] := argl[ i ];
vals[ pos ] := [ ];
elif IsFunction( argl[ i ] ) then
vals[ pos ] := [ true ];
pos := pos + 1;
funcs[ pos ] := argl[ i ];
vals[ pos ] := [ ];
elif IsList( argl[ i ] ) and vals[ pos ] = [ ] then
vals[ pos ] := argl[ i ];
elif IsList( argl[ i ] ) and IsInt( argl[ i ][ 1 ] ) and
IsList( vals[ pos ][ 1 ] ) and IsInt( vals[ pos ][1][ 1 ] ) then
Add( vals[ pos ], argl[ i ] );
elif IsList( argl[ i ] ) and IsInt( argl[ i ][ 1 ] ) and
IsInt( vals[ pos ][ 1 ] ) then
vals[ pos ] := [ vals[ pos ], argl[ i ] ];
else
Add( vals[ pos ], argl[ i ] );
fi;
od;

if sizes <> [ ] and ( not IsBound( vals ) ) then
funcs := [ ];
vals := [ ];
elif vals[ pos ] = [ ] then
vals[ pos ] := [ true ];
fi;

query := SMALL_GROUPS_SIMPLIFY_QUERY( funcs, vals );
funcs := query.funcs;
vals := query.vals;

return rec( sizes := sizes, idList := idList,
funcs := query.funcs, vals := query.vals );
end;

#############################################################################
##
#F SMALL_GROUPS_PROPERTIES_FUNCS
Expand Down Expand Up @@ -499,6 +579,28 @@ SMALL_GROUPS_PROPERTY_IDS := function( size, inforec, funcs, vals )
return rec( ids := ids, funcs := evalfuncs, vals := evalvals );
end;

#############################################################################
##
#F SMALL_GROUPS_LIBRARY_NUMBER( size, i )
##
## the number the library stores 'SmallGroup( size, i )' under. The two
## differ for the orders 3^7, 5^7, 7^7 and 11^7; see
## 'SMALL_GROUPS_OLD_ORDER'.
SMALL_GROUPS_LIBRARY_NUMBER := function( size, i )
if SMALL_GROUPS_OLD_ORDER then
return i;
elif size = 3^7 then
return SMALLGP_PERM3( i );
elif size = 5^7 then
return SMALLGP_PERM5( i );
elif size = 7^7 then
return SMALLGP_PERM7( i );
elif size = 11^7 then
return SMALLGP_PERM11( i );
fi;
return i;
end;

#############################################################################
##
#F SMALL_GROUPS_SELECT_GENERIC( size, funcs, vals, inforec, all, id, idList )
Expand All @@ -508,7 +610,7 @@ end;
## them.
SMALL_GROUPS_SELECT_GENERIC := function( size, funcs, vals, inforec,
all, id, idList )
local result, i, g, ok, j, sel, range, nid;
local result, i, g, ok, j, sel, range;

if not IsBound( inforec.number ) then
inforec := NUMBER_SMALL_GROUPS_FUNCS[ inforec.func ]( size, inforec);
Expand Down Expand Up @@ -538,20 +640,8 @@ SMALL_GROUPS_SELECT_GENERIC := function( size, funcs, vals, inforec,

result := [ ];
for i in range do
nid:=i;
if not SMALL_GROUPS_OLD_ORDER then
if size = 3^7 then
nid := SMALLGP_PERM3(i);
elif size = 5^7 then
nid := SMALLGP_PERM5(i);
elif size = 7^7 then
nid := SMALLGP_PERM7(i);
elif size = 11^7 then
nid := SMALLGP_PERM11(i);
fi;
fi;

g := SMALL_GROUP_FUNCS[ inforec.func ]( size, nid, inforec );
g := SMALL_GROUP_FUNCS[ inforec.func ](
size, SMALL_GROUPS_LIBRARY_NUMBER( size, i ), inforec );
SetIdGroup( g, [ size, i ] );
ok := true;
for j in [ 1 .. Length( funcs ) ] do
Expand All @@ -573,6 +663,74 @@ SMALL_GROUPS_SELECT_GENERIC := function( size, funcs, vals, inforec,
fi;
end;

#############################################################################
##
#F SMALL_GROUPS_COUNT_GENERIC( size, funcs, vals, inforec, idList )
##
## how many groups 'SMALL_GROUPS_SELECT_GENERIC' would return, without
## building the list.
SMALL_GROUPS_COUNT_GENERIC := function( size, funcs, vals, inforec, idList )
local sel, range, n, i, g;

if not IsBound( inforec.number ) then
inforec := NUMBER_SMALL_GROUPS_FUNCS[ inforec.func ]( size, inforec );
fi;
sel := SMALL_GROUPS_PROPERTY_IDS( size, inforec, funcs, vals );

if idList = fail then
if sel.funcs = [ ] then
return Sum( sel.ids, run -> SMALL_IDS_LAST( run )
- SMALL_IDS_FIRST( run ) + 1 );
fi;
range := SMALL_IDS_EXPAND( sel.ids );
else
range := Filtered( idList, x -> SMALL_IDS_MEMBER( sel.ids, x ) );
if sel.funcs = [ ] then
return Length( range );
fi;
fi;

n := 0;
for i in range do
g := SMALL_GROUP_FUNCS[ inforec.func ](
size, SMALL_GROUPS_LIBRARY_NUMBER( size, i ), inforec );
SetIdGroup( g, [ size, i ] );
if ForAll( [ 1 .. Length( sel.funcs ) ],
j -> sel.funcs[ j ]( g ) in sel.vals[ j ] ) then
n := n + 1;
fi;
od;
return n;
end;

#############################################################################
##
#F SMALL_GROUPS_COUNT( argl )
##
## the number of groups the selection <argl> describes.
SMALL_GROUPS_COUNT := function( argl )
local query, n, size, inforec;

query := SMALL_GROUPS_PARSE_QUERY( argl );
n := 0;
for size in query.sizes do
inforec := SMALL_AVAILABLE( size );
if inforec = fail then
Error( "NumberSmallGroups: groups of order ", size,
" not available" );
fi;
if IsBound( COUNT_SMALL_GROUPS_FUNCS[ inforec.func ] ) then
n := n + COUNT_SMALL_GROUPS_FUNCS[ inforec.func ]
( size, query.funcs, query.vals, inforec, query.idList );
else
n := n + Length( SELECT_SMALL_GROUPS_FUNCS[ inforec.func ]
( size, query.funcs, query.vals, inforec,
true, true, query.idList ) );
fi;
od;
return n;
end;

#############################################################################
##
#V SMALL_GROUP_LIB
Expand All @@ -597,7 +755,7 @@ PROPERTIES_SMALL_GROUPS := [ ];
## an PcGroup, if the group is soluble and a permutation group otherwise.
## If the groups of this size are not installed, it will return an error.
InstallGlobalFunction( SmallGroup, function( arg )
local inforec, g, size, i, nid;
local inforec, g, size, i;

if Length( arg ) = 1 then
if not IsList( arg[1] ) or Length( arg[1] ) <> 2 then
Expand All @@ -618,19 +776,8 @@ InstallGlobalFunction( SmallGroup, function( arg )
if inforec = fail then
Error( "the library of groups of size ", size, " is not available" );
fi;
nid := i;
if not SMALL_GROUPS_OLD_ORDER then
if size = 3^7 then
nid := SMALLGP_PERM3(i);
elif size = 5^7 then
nid := SMALLGP_PERM5(i);
elif size = 7^7 then
nid := SMALLGP_PERM7(i);
elif size = 11^7 then
nid := SMALLGP_PERM11(i);
fi;
fi;
g := SMALL_GROUP_FUNCS[ inforec.func ]( size, nid, inforec );
g := SMALL_GROUP_FUNCS[ inforec.func ](
size, SMALL_GROUPS_LIBRARY_NUMBER( size, i ), inforec );
SetIdGroup( g, [ size, i ] );
IsPGroup( g );
return g;
Expand Down Expand Up @@ -695,74 +842,22 @@ InstallGlobalFunction( NumberSmallGroups, function( arg )
Error( "usage: NumberSmallGroups( order )" );
fi;

# so far counting the groups is not cheaper than listing their ids
return Length( SelectSmallGroups( arg, true, true ) );
return SMALL_GROUPS_COUNT( arg );
end );

#############################################################################
##
#F SelectSmallGroups( argl, all, id )
##
InstallGlobalFunction( SelectSmallGroups, function( argl, all, id )
local sizes, size, i, funcs, vals, gs, inforec, result, hasSizes, pos,
idList, query;

sizes := [ ];
hasSizes := false;
idList := fail;

for i in [ 1 .. Length( argl ) ] do
if i = 1 and argl[ i ] = Size then
;
elif ( not hasSizes ) and IsList( argl[ i ] )
and Length( sizes ) = 1 then
idList := argl[ i ];
elif ( not hasSizes ) and IsList( argl[ i ] ) then
Append( sizes, argl[ i ] );
elif ( not hasSizes ) and IsPosInt( argl[ i ] ) then
Add( sizes, argl[ i ] );
elif ( not hasSizes ) and sizes <> [] and IsFunction( argl[i] ) then
hasSizes := true;
funcs := [ argl[ i ] ];
vals := [ [ ] ];
pos := 1;
elif not hasSizes then
Error( "usage: AllSmallGroups / OneSmallGroup(\n",
" Size, [ sizes ],\n",
" function1, [ values1 ],\n",
" function2, [ values2 ], ... )" );
elif vals[ pos ] <> [ ] and IsFunction( argl[ i ] ) then
pos := pos + 1;
funcs[ pos ] := argl[ i ];
vals[ pos ] := [ ];
elif IsFunction( argl[ i ] ) then
vals[ pos ] := [ true ];
pos := pos + 1;
funcs[ pos ] := argl[ i ];
vals[ pos ] := [ ];
elif IsList( argl[ i ] ) and vals[ pos ] = [ ] then
vals[ pos ] := argl[ i ];
elif IsList( argl[ i ] ) and IsInt( argl[ i ][ 1 ] ) and
IsList( vals[ pos ][ 1 ] ) and IsInt( vals[ pos ][1][ 1 ] ) then
Add( vals[ pos ], argl[ i ] );
elif IsList( argl[ i ] ) and IsInt( argl[ i ][ 1 ] ) and
IsInt( vals[ pos ][ 1 ] ) then
vals[ pos ] := [ vals[ pos ], argl[ i ] ];
else
Add( vals[ pos ], argl[ i ] );
fi;
od;

if sizes <> [ ] and ( not IsBound( vals ) ) then
funcs := [ ];
vals := [ ];
elif vals[ pos ] = [ ] then
vals[ pos ] := [ true ];
fi;
InstallGlobalFunction( SelectSmallGroups, function( argl, all, id )
local query, sizes, funcs, vals, idList, size, gs, inforec, result;

query := SMALL_GROUPS_SIMPLIFY_QUERY( funcs, vals );
funcs := query.funcs;
vals := query.vals;
query := SMALL_GROUPS_PARSE_QUERY( argl );
sizes := query.sizes;
funcs := query.funcs;
vals := query.vals;
idList := query.idList;

result := [ ];
for size in sizes do
Expand Down
4 changes: 3 additions & 1 deletion small10/smlgp10.g
View file
Open in desktop

Some generated files are not rendered by default. Learn more about how customized files appear on GitHub.

3 changes: 2 additions & 1 deletion small11/smlgp11.g
View file
Open in desktop

Some generated files are not rendered by default. Learn more about how customized files appear on GitHub.

Loading