Compute power maps when irreducibles were computed without them (#6141)

- add a helper function `ComputeAllPowerMaps`,
- compute all power maps in `InducedCyclic` if they are not yet available,
- compute all power maps in the `Irr` methods based on `IrrBaumClausen`

Since #6134, more character tables use `IrrBaumClausen`,
and the power maps are not automatically computed fr such tables.
Thus we call `ComputeAllPowerMaps` in this situation,
because computing individual power map values later on is more expensive.

(The way *how* `ComputeAllPowerMaps` proceeds is just a temporary hack.)

Author: ThomasBreuer

lib/ctblfuns.gi

@@ -3133,6 +3133,11 @@ InstallMethod( InducedCyclic,
           j,
           single;
 
+    if HasUnderlyingGroup( tbl ) then
+      # Precompute the power maps if possible.
+      ComputeAllPowerMaps( tbl );
+    fi;
+
     centralizers:= SizesCentralizers( tbl );
     orders:= OrdersClassRepresentatives( tbl );
     independent:= List( orders, ReturnTrue );

lib/ctblgrp.gd

@@ -470,3 +470,5 @@ DeclareGlobalFunction("RepresentationsPermutationIrreducibleCharacters");
 ##  <#/GAPDoc>
 ##
 DeclareGlobalFunction("NthRootsInGroup");
+
+DeclareGlobalName( "ComputeAllPowerMaps" );

lib/ctblgrp.gi

@@ -139,9 +139,10 @@ local p,primes,i,cl,spr,j,allpowermaps,pm,ex;
   od;
 
   for p in primes do
-    allpowermaps[p]:=List(D.classrange,i->ShallowCopy(D.classrange));
-    allpowermaps[p][1]:=1;
-    #allpowermaps[p]:=InitPowerMap(D.characterTable,p);
+    if not IsBound( allpowermaps[p] ) then
+      allpowermaps[p]:=List(D.classrange,i->ShallowCopy(D.classrange));
+      allpowermaps[p][1]:=1;
+    fi;
   od;
 
   for p in primes do
@@ -200,6 +201,27 @@ fi;
   od;
 end );
 
+
+#############################################################################
+##
+#F  ComputeAllPowerMaps( <tbl> )
+##
+##  Computing all power maps is cheaper than successively computing some
+##  values of individual power maps.
+##  The current code is a hack.
+##  (Apparently 'DxCalcAllPowerMaps' is much faster than other available
+##  functions.)
+##  It should be improved as soon as we have a general tool for the
+##  identification of conjugacy classes.
+##
+BindGlobal( "ComputeAllPowerMaps", function( tbl )
+  tbl:= UnderlyingGroup( tbl );
+  if not HasDixonRecord( tbl ) then
+    DxCalcAllPowerMaps( DixonRecord( tbl ) );
+  fi;
+end );
+
+
 #############################################################################
 ##
 #F  DxCalcPrimeClasses(<D>)

lib/ctblsolv.gi

@@ -848,19 +848,23 @@ InstallMethod( Irr,
     "for a supersolvable group (Baum-Clausen algorithm)",
     [ IsGroup and IsSupersolvableGroup, IsZeroCyc ],
     function( G, zero )
-    local irr;
+    local irr, tbl;
     irr:= IrrBaumClausen( G );
-    SetIrr( OrdinaryCharacterTable( G ), irr );
+    tbl:= OrdinaryCharacterTable( G );
+    SetIrr( tbl, irr );
+    ComputeAllPowerMaps( tbl );
     return irr;
     end );
 
 InstallMethod( Irr,
     "for a supersolvable group with known `IrrBaumClausen'",
     [ IsGroup and IsSupersolvableGroup and HasIrrBaumClausen, IsZeroCyc ],
     function( G, zero )
-    local irr;
+    local irr, tbl;
     irr:= IrrBaumClausen( G );
-    SetIrr( OrdinaryCharacterTable( G ), irr );
+    tbl:= OrdinaryCharacterTable( G );
+    SetIrr( tbl, irr );
+    ComputeAllPowerMaps( tbl );
     return irr;
     end );
 

tst/testinstall/ctbl.tst

@@ -313,6 +313,7 @@ C2
         2  1  1
 
           1a 2a
+       2P 1a 1a
        2
 X.1    ?   1  1
 X.2    ?   1 -1