Set InfoText when computing Irr (#6275)

Whenever the `Irr` value gets computed for a group or a character table,
store in `InfoText` of the table which method was used.

And add an `Irr` method for the case that `IrrDixonSchneider` is known.
(We have at least one package with a method of higher rank than
the `IrrDixonSchneider` based method, so this makes sense.)

Author: ThomasBreuer

lib/ctblgrp.gi

@@ -290,7 +290,7 @@ local b;
     b:=List(b,i->i{d.invpermlist}); # permuted back
     r.niceBasis:=Immutable(b);
   fi;
-  Assert(1,Length(r.niceBasis)=Length(r.base));
+  Assert(1,Length(r.niceBasis)=Length(r.base), "in DxNiceBasis");
   return r.niceBasis;
 end );
 
@@ -657,7 +657,7 @@ BindGlobal( "DxEigenbase", function(M)
 
   minpol:=MinimalPolynomial(BaseDomain(M),M);
 
-  Assert(2,IsDuplicateFree(RootsOfUPol(minpol)));
+  Assert(2,IsDuplicateFree(RootsOfUPol(minpol)), "in DxEigenbase, 1");
   eigenvalues:=Set(RootsOfUPol(minpol));
   dim:=0;
   bases:=[];
@@ -674,7 +674,8 @@ BindGlobal( "DxEigenbase", function(M)
     Error("Failed to calculate eigenspaces.");
   fi;
 
-  Assert(3, ForAll([1..Length(bases)],j->bases[j]*M = bases[j]*eigenvalues[j]));
+  Assert(3, ForAll([1..Length(bases)],j->bases[j]*M = bases[j]*eigenvalues[j]),
+         "in DxEigenbase, 2");
   return rec(base:=bases,
              values:=eigenvalues);
 end );
@@ -791,7 +792,7 @@ InstallGlobalFunction(SplitStep,function(D,bestMat)
       base:=Matrix(BaseDomain(base[1]),base);
       eigenbase:=List(eigen.base,i->List(i,j->j*base));
 
-      Assert(1,Length(eigenbase)>1);
+      Assert(1,Length(eigenbase)>1, "in SplitStep");
 
       ra:=List(eigenbase,i->rec(base:=i,dim:=Length(i)));
 
@@ -2286,7 +2287,7 @@ local k,C,D,dsp;
   od;
 
   C:=DixontinI(D);
-  Assert(1,Length(C)=D.klanz);
+  Assert(1,Length(C)=D.klanz, "in IrrDixonSchneider");
   # SetIrr(OrdinaryCharacterTable(G),C);
   # (if `IrrDixonSchneider' is called explicitly,
   # we want to ignore the attribute)
@@ -2326,6 +2327,19 @@ InstallMethod( Irr,
     return irr;
     end );
 
+InstallMethod( Irr,
+    "for a group with known `IrrDixonSchneider'",
+    [ IsGroup and HasIrrDixonSchneider, IsZeroCyc ],
+    function( G, zero )
+    local irr, tbl;
+    irr:= IrrDixonSchneider( G );
+    tbl:= OrdinaryCharacterTable( G );
+    SetIrr( tbl, irr );
+    ComputeAllPowerMaps( tbl );
+    SetInfoText( tbl, "origin: Dixon's Algorithm" );
+    return irr;
+    end );
+
 
 #############################################################################
 ##
@@ -2360,7 +2374,8 @@ InstallMethod( Irr,
         fi;
       od;
     od;
-    Assert( 1, IsCollection( bijection ) and IsEmpty( cclnice ) );
+    Assert( 1, IsCollection( bijection ) and IsEmpty( cclnice ),
+            "in Irr via niceomorphism" );
 
     # Compute the values of the irreducibles of the nice object.
     irr:= List( Irr( nice ), ValuesOfClassFunction );
@@ -2374,6 +2389,7 @@ InstallMethod( Irr,
     od;
     irr:= List( irr, x -> Character( tbl, x ) );
     SetIrr( tbl, irr );
+    SetInfoText( tbl, "origin: via the nice monomorphism of the group" );
     return irr;
 end );
 

lib/ctblsolv.gi

@@ -657,7 +657,8 @@ InstallGlobalFunction( CoveringTriplesCharacters, function( G, z )
               CanonicalRepresentativeOfExternalSet( orb ) );
       if not zn in k then
         t:= StabilizerOfExternalSet( orb );
-        Assert( 1, IsIdenticalObj( Parent( t ), G ) );
+        Assert( 1, IsIdenticalObj( Parent( t ), G ),
+                "in CoveringTriplesCharacters" );
         h:= NaturalHomomorphismByNormalSubgroupNC( t, k );
         img:= ImagesSource( h );
         Append( r,
@@ -823,19 +824,23 @@ InstallMethod( Irr,
     "for a supersolvable group (Conlon's algorithm)",
     [ IsGroup and IsSupersolvableGroup, IsZeroCyc ],
     function( G, zero )
-    local irr;
+    local irr, tbl;
     irr:= IrrConlon( G );
-    SetIrr( OrdinaryCharacterTable( G ), irr );
+    tbl:= OrdinaryCharacterTable( G );
+    SetIrr( tbl, irr );
+    SetInfoText( tbl, "origin: Conlon's Algorithm" );
     return irr;
     end );
 
 InstallMethod( Irr,
     "for a supersolvable group with known `IrrConlon'",
     [ IsGroup and IsSupersolvableGroup and HasIrrConlon, IsZeroCyc ],
     function( G, zero )
-    local irr;
+    local irr, tbl;
     irr:= IrrConlon( G );
-    SetIrr( OrdinaryCharacterTable( G ), irr );
+    tbl:= OrdinaryCharacterTable( G );
+    SetIrr( tbl, irr );
+    SetInfoText( tbl, "origin: Conlon's Algorithm" );
     return irr;
     end );
 
@@ -853,6 +858,7 @@ InstallMethod( Irr,
     tbl:= OrdinaryCharacterTable( G );
     SetIrr( tbl, irr );
     ComputeAllPowerMaps( tbl );
+    SetInfoText( tbl, "origin: Baum-Clausen Algorithm" );
     return irr;
     end );
 
@@ -865,6 +871,7 @@ InstallMethod( Irr,
     tbl:= OrdinaryCharacterTable( G );
     SetIrr( tbl, irr );
     ComputeAllPowerMaps( tbl );
+    SetInfoText( tbl, "origin: Baum-Clausen Algorithm" );
     return irr;
     end );
 

lib/oprtpcgs.gi

@@ -174,7 +174,10 @@ end );
 
 InstallMethod( OrbitStabilizerAlgorithm,"for pcgs",true,
   [IsGroup,IsObject,IsObject,IsPcgs,
-     IsList,IsRecord],0,
+     IsList,IsRecord],
+  # rank above the method based on 'DoOrbitStabilizerAlgorithmStabsize'
+  {} -> RankFilter(IsGroup and IsFinite) - RankFilter(IsGroup),
+
 function(G,D,blist,pcgs,acts,pntact)
 local S,stab,i,pnt,act;
   pnt:=pntact.pnt;

tst/testinstall/ctbl.tst

@@ -1,4 +1,4 @@
-#@local g,t,lin
+#@local g,t,lin,G
 gap> START_TEST("ctbl.tst");
 
 # `ClassPositionsOf...' for the trivial group (which usually causes trouble)
@@ -433,5 +433,23 @@ true
 gap> HasIsIrreducibleCharacter( TrivialCharacter( SymmetricGroup( 4 ) ) );
 true
 
+# concurring 'Irr' methods
+gap> G:= SmallGroup( 24, 5 );;
+gap> IsSupersolvable( G );
+true
+gap> Irr( G );;
+gap> InfoText( OrdinaryCharacterTable( G ) );
+"origin: Baum-Clausen Algorithm"
+gap> G:= SmallGroup( 24, 5 );;
+gap> IsSupersolvable( G );
+true
+gap> IrrConlon( G );;  Irr( G );;
+gap> InfoText( OrdinaryCharacterTable( G ) );
+"origin: Conlon's Algorithm"
+gap> G:= SmallGroup( 24, 5 );;
+gap> IrrDixonSchneider( G );;  Irr( G );;
+gap> InfoText( OrdinaryCharacterTable( G ) );
+"origin: Dixon's Algorithm"
+
 ##
 gap> STOP_TEST( "ctbl.tst" );