De-duplicate some functions (#5657)

hpcgap/lib/ffeconway.gi

@@ -1214,34 +1214,6 @@ InstallMethod( LogFFE,
         [ IsFFE and IsCoeffsModConwayPolRep, IsFFE and IsInternalRep],
         DoDLog );
 
-#############################################################################
-##
-#M  Order -- multiplicative order of an FFE
-##
-
-
-InstallMethod( Order,
-        [IsFFE],
-        function(z)
-    local   p,  d,  ord,  facs,  f,  i,  o;
-    p := Characteristic(z);
-    d := DegreeFFE(z);
-    ord := p^d-1;
-    facs := Collected(Factors(Integers,ord));
-    for f in facs do
-        for i in [1..f[2]] do
-            o := ord/f[1];
-            if not IsOne(z^o) then
-                break;
-            fi;
-            ord := o;
-        od;
-    od;
-    return ord;
-end);
-
-
-
 #############################################################################
 ##
 #M LargeGaloisField(p,d) -- construct GFs in this size range

lib/algebra.gi

@@ -2843,10 +2843,8 @@ InstallMethod( Basis,
 ##
 #M  Basis( <A> )  . . . . . .  basis from FLMLOR gens. for associative FLMLOR
 ##
-InstallMethod( Basis,
-    "for an associative FLMLOR",
-    [ IsFLMLOR and IsAssociative ],
-        function( A )
+BindGlobal("BasisLieAlgebraAndAssociativeFLMOR",
+    function( A )
     local  mb;
 
     # If generators as left module are known
@@ -2864,8 +2862,11 @@ InstallMethod( Basis,
              Zero( A ),
              infinity );
     return ImmutableBasis( mb, A );
-
     end );
+InstallMethod( Basis,
+    "for an associative FLMLOR",
+    [ IsFLMLOR and IsAssociative ],
+    BasisLieAlgebraAndAssociativeFLMOR );
 
 
 #############################################################################
@@ -2906,25 +2907,7 @@ InstallMethod( Basis,
 InstallMethod( Basis,
     "for a Lie algebra",
     [ IsLieAlgebra ],
-    function( A )
-    local  mb;
-
-    # If generators as left module are known
-    # we do not need to multiply at all.
-    if HasGeneratorsOfLeftModule( A ) then
-      TryNextMethod();
-    fi;
-
-    mb:= MutableBasisOfClosureUnderAction(
-             LeftActingDomain( A ),
-             GeneratorsOfLeftOperatorRing( A ),
-             "left",
-             GeneratorsOfLeftOperatorRing( A ),
-             \*,
-             Zero( A ),
-             infinity );
-    return ImmutableBasis( mb, A );
-    end );
+    BasisLieAlgebraAndAssociativeFLMOR );
 
 
 #############################################################################

lib/alglie.gi

@@ -3776,6 +3776,44 @@ end );
 ##  For the algorithm we refer to C. Reutenauer, Free Lie Algebras, Clarendon
 ##  Press, Oxford, 1993.
 ##
+DeclareGlobalName( "IsLyndonT" );
+
+BindGlobal( "IsLyndonT",
+function( t )
+
+    # This function tests whether the bracketed expression `t' is
+    # a Lyndon tree.
+
+    local w,w1,w2,b,y;
+
+    if not IsList( t ) then return true; fi;
+
+    w:= Flat( t );
+    if IsList( t[1] ) then
+        w1:= Flat( t[1] );
+        b:= false;
+    else
+        w1:= [ t[1] ];
+        b:=true;
+    fi;
+    if IsList( t[2] ) then
+        w2:= Flat( t[2] );
+    else
+        w2:= [ t[2] ];
+    fi;
+
+    if w<w2 and w1<w2 then
+        if not b then
+            y:= Flat( [ t[1][2] ] );
+            if y  < w2 then return false; fi;
+        fi;
+    else
+        return false;
+    fi;
+
+    return IsLyndonT(t[1]) and IsLyndonT(t[2]);
+end);
+
 InstallMethod( NormalizedElementOfMagmaRingModuloRelations,
      "for family of free Lie algebra elements, and list",
      true,
@@ -3790,52 +3828,14 @@ InstallMethod( NormalizedElementOfMagmaRingModuloRelations,
                ll,              #List
                zero,            #The zero element of the field
                tlist,           #List of elements of the free Lie algebra
-               Dcopy,IsLyndonT; #Two functions
+               Dcopy;           #Two functions
 
          Dcopy:=function( l )
 
            if not IsList(l) then return ShallowCopy( l ); fi;
            return List( l, Dcopy );
          end;
 
-         IsLyndonT:= function( t )
-
-            # This function tests whether the bracketed expression `t' is
-            # a Lyndon tree.
-
-             local w,w1,w2,b,y;
-
-             if not IsList( t ) then return true; fi;
-
-             w:= Flat( t );
-             if IsList( t[1] ) then
-               w1:= Flat( t[1] );
-               b:= false;
-             else
-               w1:= [ t[1] ];
-               b:=true;
-             fi;
-             if IsList( t[2] ) then
-               w2:= Flat( t[2] );
-             else
-               w2:= [ t[2] ];
-             fi;
-
-             if w<w2 and w1<w2 then
-               if not b then
-                 y:= Flat( [ t[1][2] ] );
-                 if y  < w2 then return false; fi;
-               fi;
-             else
-               return false;
-             fi;
-
-             if not IsLyndonT( t[1] ) then return false; fi;
-             if not IsLyndonT( t[2] ) then return false; fi;
-             return true;
-
-         end;
-
          zero:= descr[1];
          todo:= [ ];
          i:= 1;
@@ -4038,48 +4038,10 @@ InstallMethod( PreImagesRepresentative,
 
     function( f, x )
 
-    local   IsLyndonT,  dim,  e,  gens,  imgs,  b1,  b2,  levs,
+    local   dim,  e,  gens,  imgs,  b1,  b2,  levs,
             brackets,  sp,  deg,  newlev,  newbracks,  d,  br1,  br2,
             i,  j,  a,  b,  c,  z,  imz,  cf;
 
-    IsLyndonT:= function( t )
-
-        # This function tests whether the bracketed expression `t' is
-        # a Lyndon tree.
-
-        local w,w1,w2,b,y;
-
-        if not IsList( t ) then return true; fi;
-
-        w:= Flat( t );
-        if IsList( t[1] ) then
-            w1:= Flat( t[1] );
-            b:= false;
-        else
-            w1:= [ t[1] ];
-            b:=true;
-        fi;
-        if IsList( t[2] ) then
-            w2:= Flat( t[2] );
-        else
-            w2:= [ t[2] ];
-        fi;
-
-        if w<w2 and w1<w2 then
-            if not b then
-                y:= Flat( [ t[1][2] ] );
-                if y  < w2 then return false; fi;
-            fi;
-        else
-            return false;
-        fi;
-
-        if not IsLyndonT( t[1] ) then return false; fi;
-        if not IsLyndonT( t[2] ) then return false; fi;
-        return true;
-
-    end;
-
     if not IsBound( f!.bases ) then
 
         # We find bases of the source and the range that are mapped to

lib/ffeconway.gi

@@ -1184,33 +1184,6 @@ InstallMethod( LogFFE,
         [ IsFFE and IsCoeffsModConwayPolRep, IsFFE and IsInternalRep],
         DoDLog );
 
-#############################################################################
-##
-#M  Order -- multiplicative order of an FFE
-##
-
-
-InstallMethod( Order,
-        [IsFFE],
-        function(z)
-    local   p,  d,  ord,  facs,  f,  i,  o;
-    p := Characteristic(z);
-    d := DegreeFFE(z);
-    ord := p^d-1;
-    facs := Collected(Factors(Integers,ord));
-    for f in facs do
-        for i in [1..f[2]] do
-            o := ord/f[1];
-            if not IsOne(z^o) then
-                break;
-            fi;
-            ord := o;
-        od;
-    od;
-    return ord;
-end);
-
-
 
 #############################################################################
 ##

lib/grppc.gi

@@ -1491,18 +1491,7 @@ local G,           # common parent
     if eas=fail then
         home:=PcgsElementaryAbelianSeries([G,NT]);
         eas:=EANormalSeriesByPcgs(home);
-        cent:=function(pcgs,grpg,Npcgs,dep)
-              local i,j;
-                for i in grpg do
-                  for j in Npcgs do
-                    if DepthOfPcElement(pcgs,Comm(j,i))<dep then
-                      return false;
-                    fi;
-                  od;
-                od;
-                return true;
-              end;
-
+        cent:=PcClassFactorCentralityTest;
     fi;
     indstep:=IndicesEANormalSteps(home);