Enhance support for very long transversals in a permutation group by forcing down huge index steps through an intermediate subgroup (#6114)

When computing a transversal in a permutation group force down huge index
steps, as they might lead to creation of infeasibly long bit lists.

Incidentally, this allows for Filtering classes in A_15.

Author: hulpke

lib/csetgrp.gi

@@ -1819,7 +1819,10 @@ DeclareRepresentation( "IsFactoredTransversalRep",
     # group, subgroup, list of transversals (descending)
 BindGlobal("FactoredTransversal",function(G,S,t)
 local trans,m,i;
-  Assert(1,ForAll([1..Length(t)-1],i->t[i]!.subgroup=t[i+1]!.group));
+  Assert(1,ForAll([1..Length(t)-1],
+                  i ->    (not IsBound(t[i]!.subgroup))
+                       or (not IsBound(t[i+1]!.group))
+                       or t[i]!.subgroup = t[i+1]!.group));
 
   m:=[1];
   for i in [Length(t),Length(t)-1..2] do

lib/csetperm.gi

@@ -42,7 +42,9 @@ end );
 ##
 #F  RightTransversalPermGroupConstructor( <filter>, <G>, <U> )  . constructor
 ##
-MAX_SIZE_TRANSVERSAL := 100000;
+MAX_SIZE_TRANSVERSAL := 100000; # try to keep transversals shorter than this
+BITLIST_LIMIT_TRANSVERSAL:=10^8; # absolutely must keep transversals
+ # shorter, as otheriwse too long bit lists might be produced
 
 # so far only orbits and perm groups -- TODO: Other deduced actions
 InstallGlobalFunction(ActionRefinedSeries,function(G,U)
@@ -121,11 +123,23 @@ BindGlobal( "RightTransversalPermGroupConstructor", function( filter, G, U )
             # go in biggish steps through the chain
             nc:=[ac[1]];
             nct:=[actions[1]];
-            for i in [3..Length(ac)] do
-              if Size(ac[i])/Size(Last(nc))>MAX_SIZE_TRANSVERSAL then
+            i:=3;
+            while i<=Length(ac) do
+              if Size(ac[i-1])/Size(nc[Length(nc)])
+                >BITLIST_LIMIT_TRANSVERSAL then
+                # the next step would be horrible -- insert
+                bpt:=AscendingChain(ac[i-1],nc[Length(nc)]:cheap);
+                bpt:=bpt{[2..Length(bpt)-1]};
+                ac:=Concatenation(ac{[1..i-2]},bpt,ac{[i-1..Length(ac)]});
+                actions:=Concatenation(actions{[1..i-2]},List(bpt,x->fail),
+                  actions{[i-1..Length(actions)]});
+              fi;
+
+              if Size(ac[i])/Size(nc[Length(nc)])>MAX_SIZE_TRANSVERSAL then
                 Add(nc,ac[i-1]);
                 Add(nct,actions[i-1]);
               fi;
+              i:=i+1;
             od;
             Add(nc,Last(ac));
             Add(nct,Last(actions));

tst/testinstall/listgen.tst

@@ -1,4 +1,4 @@
-#@local g,h,l,l2,p2,perm,t,filt,lcpy,permsp
+#@local g,h,l,l2,p2,perm,t,filt,lcpy,permsp,old_paras,G,U,tr
 gap> START_TEST("listgen.tst");
 gap> List( [ 1 .. 10 ], x -> x^2 );
 [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ]
@@ -156,6 +156,8 @@ gap> String( l );
 "[ 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ]"
 gap> String( [ 1 .. 10 ] );
 "[ 1 .. 10 ]"
+
+# right transversals
 gap> g:=Group((1,5)(2,6)(3,7)(4,8),(1,3)(2,4)(5,7)(6,8),(1,2)(3,4)(5,6)(7,8), 
 > (5,6)(7,8), (5,7)(6,8), (3,4)(7,8), (3,5)(4,6), (2,3)(6,7));;
 gap> h:=Subgroup(g,[(5,6)(7,8),(5,7)(6,8),(2,4)(6,8),(2,5)(4,7),(1,2)(3,4)]);;
@@ -167,5 +169,54 @@ true
 gap> p2:=Position(t,(5,7)(6,8));
 fail
 
+# right transversals, see pull request #6114
+gap> old_paras:= [ BITLIST_LIMIT_TRANSVERSAL, MAX_SIZE_TRANSVERSAL ];;
+gap> BITLIST_LIMIT_TRANSVERSAL:= 59;;
+gap> MAX_SIZE_TRANSVERSAL:= 59;;
+gap> G:= Group( [   # the group is equal to AtlasGroup( "J1" )
+>   (  1,262)(  2,107)(  3, 21)(  4,213)(  5,191)(  6, 22)(  7,133)
+>   (  8,234)(  9,232)( 10,151)( 11,139)( 12,176)( 13,202)( 14,253)( 15,222)
+>   ( 17,195)( 18,206)( 19, 68)( 20, 55)( 23,179)( 24,217)( 25,216)( 26,256)
+>   ( 27, 87)( 28, 70)( 29,131)( 30, 44)( 31,105)( 32,170)( 33, 77)( 34,104)
+>   ( 35,198)( 36,137)( 37,243)( 38, 56)( 39,124)( 40,223)( 41,134)( 43,174)
+>   ( 46, 51)( 47,128)( 48, 94)( 49,250)( 50,264)( 52,183)( 53,231)( 54,115)
+>   ( 57, 85)( 58,233)( 59,261)( 60, 95)( 61,235)( 62,177)( 63,249)( 64, 91)
+>   ( 65,247)( 66,155)( 69,219)( 71,237)( 72,211)( 73, 84)( 74,192)( 75,130)
+>   ( 76,251)( 79,260)( 80,112)( 81,193)( 82,156)( 83,242)( 86,238)( 88,143)
+>   ( 89,168)( 90,148)( 92,119)( 93,212)( 96,150)( 97,199)( 98,140)( 99,189)
+>   (100,180)(101,147)(102,111)(103,159)(106,162)(108,194)(109,166)(110,200)
+>   (113,120)(114,141)(116,182)(117,181)(118,225)(121,254)(122,125)(123,146)
+>   (126,208)(127,221)(129,210)(132,255)(136,175)(138,207)(142,240)(144,172)
+>   (145,185)(149,224)(152,169)(153,241)(154,190)(157,214)(158,161)(160,236)
+>   (163,239)(164,229)(165,230)(167,188)(171,258)(173,186)(178,245)(184,205)
+>   (187,228)(197,203)(201,252)(209,248)(215,259)(218,246)(220,227)(257,263)
+>   (265,266), (  1,146, 21)(  2,132, 82)(  4,156,166)(  5,242,253)
+>   (  6,107, 28)(  7,125, 76)(  8,245,130)(  9,174, 42)( 10,241,244)
+>   ( 11,264, 63)( 12,248,234)( 13, 36, 44)( 14,116,128)( 15, 47, 25)
+>   ( 16,178,112)( 17,170,110)( 18,197, 74)( 19,233,180)( 20,121, 96)
+>   ( 22,228,155)( 23, 48,173)( 24,201,187)( 26,136,190)( 27,212, 94)
+>   ( 29,175, 52)( 30, 77, 32)( 31,237, 34)( 33,226, 90)( 35,129, 54)
+>   ( 37,161,114)( 38,232, 87)( 39,219,192)( 40, 78,159)( 41,139, 71)
+>   ( 43,211,251)( 45,222,240)( 46, 97,135)( 49, 70,131)( 50,153,200)
+>   ( 51,186,209)( 53,203,216)( 55,169, 64)( 56,140,230)( 57,260,118)
+>   ( 58, 91,243)( 59,199,227)( 60,108,164)( 61,208,101)( 62,206,106)
+>   ( 65,103, 66)( 67, 95,205)( 68, 73,225)( 69,151,113)( 72,221,152)
+>   ( 75,143,202)( 79,217,254)( 80, 93,122)( 81,181,252)( 83,258,126)
+>   ( 84,163,177)( 85,154,213)( 86,182,196)( 88,133,215)( 89,117,247)
+>   ( 92,191,160)( 99,229,263)(100,138,188)(102,194,157)(105,149,184)
+>   (109,123,193)(111,137,183)(115,238,235)(119,167,147)(120,134,189)
+>   (124,185,265)(127,218,261)(141,231,210)(142,239,236)(144,224,249)
+>   (145,158,220)(148,214,172)(150,250,259)(162,257,256)(165,179,246)
+>   (176,195,266)(198,204,207)(223,262,255) ] );;
+gap> U:= TrivialSubgroup( G );;
+gap> tr:= RightTransversalPermGroupConstructor(
+>           IsRightTransversalPermGroupRep, G, U );;
+gap> Length( tr ) = Size( G );
+true
+gap> PositionCanonical( tr, GeneratorsOfGroup( G )[1] ) <= Length( tr );
+true
+gap> BITLIST_LIMIT_TRANSVERSAL:= old_paras[1];;
+gap> MAX_SIZE_TRANSVERSAL:= old_paras[2];;
+
 # that's all, folks
 gap> STOP_TEST("listgen.tst");