gap-system · cdwensley · Sep 28, 2022 · Sep 28, 2022 · Sep 29, 2022 · Sep 29, 2022
diff --git a/doc/ref/grpfp.xml b/doc/ref/grpfp.xml
@@ -486,7 +486,7 @@ gap> hom:=IsomorphismFpGroup(u);
 [ <[ [ 1, 1 ] ]|f2^-1*f1^-1> ] -> [ F1 ]
 gap> new:=Range(hom);
 <fp group on the generators [ F1 ]>
-gap> List(GeneratorsOfGroup(new),i->PreImagesRepresentative(hom,i));
+gap> List(GeneratorsOfGroup(new),i->PreImagesRepresentativeNC(hom,i));
 [ <[ [ 1, 1 ] ]|f2^-1*f1^-1> ]
 ]]></Example>
 <P/>
@@ -504,7 +504,7 @@ behave like ordinary words and no extra treatment should be necessary.
 <Example><![CDATA[
 gap> r:=Range(hom).1^10;
 F1^10
-gap> p:=PreImagesRepresentative(hom,r);
+gap> p:=PreImagesRepresentativeNC(hom,r);
 <[ [ 1, 10 ] ]|(f2^-1*f1^-1)^10>
 ]]></Example>
 

diff --git a/doc/ref/mapping.xml b/doc/ref/mapping.xml
@@ -1,6 +1,6 @@
 <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
 <!-- %% -->
-<!-- %A  mapping.xml                  GAP documentation              Thomas Breuer -->
+<!-- %A  mapping.xml               GAP documentation        Thomas Breuer -->
 <!-- %% -->
 <!-- %% -->
 <!-- %Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland -->

diff --git a/doc/ref/rws.xml b/doc/ref/rws.xml
@@ -174,7 +174,7 @@ gap> red:=ReducedForm(k,UnderlyingElement(melm));
 f1^-1^3*f2^-1*f1^2
 gap> melm:=ElementOfFpMonoid(FamilyObj(One(mon)),red);
 f1^-1^3*f2^-1*f1^2
-gap> gpelm:=PreImagesRepresentative(mhom,melm);
+gap> gpelm:=PreImagesRepresentativeNC(mhom,melm);
 f1^-3*f2^-1*f1^2
 gap> r=gpelm;
 true

diff --git a/doc/tut/group.xml b/doc/tut/group.xml
@@ -1,12 +1,12 @@
-<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
+<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
 <!-- %% -->
-<!-- %W  group.tex                 GAP documentation             Thomas Breuer -->
-<!-- %W                                                         & Frank Celler -->
-<!-- %W                                                     & Martin Schönert -->
-<!-- %W                                                       & Heiko Theißen -->
+<!-- %W  group.tex           GAP documentation               Thomas Breuer -->
+<!-- %W                                                     & Frank Celler -->
+<!-- %W                                                  & Martin Schönert -->
+<!-- %W                                                    & Heiko Theißen -->
 <!-- %% -->
 <!-- %% -->
-<!-- %Y  Copyright 1997,  Lehrstuhl D für Mathematik,  RWTH Aachen,   Germany -->
+<!-- %Y  Copyright 1997,  Lehrstuhl D für Mathematik, RWTH Aachen, Germany -->
 <!-- %% -->
 <!-- %%  This file contains a tutorial introduction to groups. -->
 <!-- %% -->
@@ -168,10 +168,9 @@ action domain of <C>norm</C>. (It only happens that both are subsets of the
 natural numbers.) We can now form  images and preimages under the natural
 homomorphism. The set of  preimages of an element under  <C>hom</C> is a coset
 modulo <C>elab</C>.
-We use the function <Ref Func="PreImages" BookName="ref"/> here because
-<C>hom</C> is not
-a bijection, so an  element of the range can   have several preimages  or
-none at all.
+We use the function <Ref Func="PreImages" BookName="ref"/> here 
+because <C>hom</C> is not a bijection, 
+so an element of the range can have several preimages or none at all.
 <P/>
 <Example><![CDATA[
 gap> ker:= Kernel( hom );
@@ -943,18 +942,20 @@ gap> PreImage( hom, TrivialSubgroup(s3) );  # the kernel
 Group([ (1,4)(2,3), (1,3)(2,4) ])
 ]]></Example>
 <P/>
-This homomorphism  from <M>S_4</M> onto  <M>S_3</M>  is well known  from elementary
-group theory.  Images   of elements and  subgroups  under   <C>hom</C> can  be
+This homomorphism  from <M>S_4</M> onto <M>S_3</M> is well known from 
+elementary group theory.  
+Images of elements and subgroups under <C>hom</C> can be
 calculated with the function <Ref Func="Image" BookName="ref"/>.
-But since the mapping <C>hom</C> is  not bijective, we  cannot use the
-function <Ref Func="PreImage" BookName="ref"/> for  preimages   of
-elements  (they can have   several preimages). Instead,   we have  to use
-<Ref Func="PreImagesRepresentative" BookName="ref"/>,
-which  returns  one  preimage if at  least one
-exists (and would  return <K>fail</K> if none  exists, which  cannot occur for
+But since the mapping <C>hom</C> is not bijective, we cannot use the
+function <Ref Func="PreImage" BookName="ref"/> for preimages of elements 
+(they can have several preimages).  
+Instead, we have to use 
+<Ref Func="PreImagesRepresentative" BookName="ref"/> 
+which returns one preimage if at least one exists 
+(and would return <K>fail</K> if none exists, which cannot occur for
 our surjective <C>hom</C>).
-On the other hand, we  can use <Ref Func="PreImage" BookName="ref"/> for the
-preimage of a set (which always exists, even if it  is empty).
+On the other hand, we can use <Ref Func="PreImage" BookName="ref"/> for the
+preimage of a set (which always exists, even if it is empty).
 <P/>
 Suppose we mistype the input when trying to construct a homomorphism as below.
 <P/>

diff --git a/lib/algebra.gi b/lib/algebra.gi
@@ -3647,7 +3647,7 @@ InstallMethod( CentralIdempotentsOfAlgebra,
 
       until k>Length(ideals);
 
-      id:= List( ids, e -> PreImagesRepresentative( hom, e ) );
+      id:= List( ids, e -> PreImagesRepresentativeNC( hom, e ) );
 
       # Now we lift the idempotents to the big algebra `A'. The
       # first idempotent is lifted as follows:

diff --git a/lib/algfp.gi b/lib/algfp.gi
@@ -705,7 +705,7 @@ InstallHandlingByNiceBasis( "IsFpAlgebraElementsSpace", rec(
       if hom = fail then
         TryNextMethod();
       fi;
-      return PreImagesRepresentative( hom, r );
+      return PreImagesRepresentativeNC( hom, r );
       end ) );
 
 

diff --git a/lib/alghom.gi b/lib/alghom.gi
@@ -576,18 +576,29 @@ InstallMethod( ImagesRepresentative,
 
 #############################################################################
 ##
-#M  PreImagesRepresentative( <map>, <elm> ) . . . . . .  for algebra g.m.b.i.
+#M  PreImagesRepresentativeNC( <map>, <elm> ) . . . . .  for algebra g.m.b.i.
 ##
-InstallMethod( PreImagesRepresentative,
+InstallMethod( PreImagesRepresentativeNC,
     "for algebra g.m.b.i., and element",
     FamRangeEqFamElm,
     [ IsGeneralMapping and IsAlgebraGeneralMappingByImagesDefaultRep,
       IsObject ],
     function( map, elm )
-    return PreImagesRepresentative( AsLeftModuleGeneralMappingByImages(map),
-                                    elm );
+        return PreImagesRepresentativeNC(
+                   AsLeftModuleGeneralMappingByImages(map), elm );
     end );
 
+## (13/05/26) commented this out to prevent infinite recursion in alghom.tst
+## InstallMethod( PreImagesRepresentativeNC,
+##     "for algebra g.m.b.i. knowing inverse, and element",
+##     FamRangeEqFamElm,
+##     [ IsGeneralMapping and IsAlgebraGeneralMappingByImagesDefaultRep
+##       and HasInverseGeneralMapping,
+##       IsObject ],
+##     function( map, elm )
+##         return ImagesRepresentative( InverseGeneralMapping(map), elm );
+##     end );
+
 
 #############################################################################
 ##
@@ -902,7 +913,7 @@ InstallMethod( ImagesRepresentative,
 
 #############################################################################
 ##
-#M  PreImagesRepresentative( <ophom>, <mat> )
+#M  PreImagesRepresentativeOperationAlgebraHomomorphism( <ophom>, <mat> )
 ##
 BindGlobal( "PreImagesRepresentativeOperationAlgebraHomomorphism", function( ophom, mat )
     if not IsBound( ophom!.basisImage ) then
@@ -915,7 +926,7 @@ BindGlobal( "PreImagesRepresentativeOperationAlgebraHomomorphism", function( oph
     return mat;
 end );
 
-InstallMethod( PreImagesRepresentative,
+InstallMethod( PreImagesRepresentativeNC,
     "for an operation algebra homomorphism, and an element",
     FamRangeEqFamElm,
     [ IsOperationAlgebraHomomorphismDefaultRep, IsMatrix ],
@@ -1076,9 +1087,9 @@ InstallMethod( ImagesRepresentative,
 
 #############################################################################
 ##
-#M  PreImagesRepresentative( <ophom>, <mat> )
+#M  PreImagesRepresentativeNC( <ophom>, <mat> )
 ##
-InstallMethod( PreImagesRepresentative,
+InstallMethod( PreImagesRepresentativeNC,
     "for an alg. hom. from f. p. algebra, and an element",
     FamRangeEqFamElm,
     [ IsAlgebraHomomorphismFromFpRep, IsMatrix ],

diff --git a/lib/alglie.gi b/lib/alglie.gi
@@ -34,7 +34,7 @@ InstallMethod( LieUpperCentralSeries,
       # under the natural homomorphism.
       Add( S, C );
       hom:= NaturalHomomorphismByIdeal( L, C );
-      C:= PreImages( hom, LieCentre( Range( hom ) ) );
+      C:= PreImagesNC( hom, LieCentre( Range( hom ) ) );
 #T we would like to get ideals!
 #T is it possible to teach the hom. that the preimage of an ideal is an ideal?
 
@@ -1057,7 +1057,7 @@ InstallMethod( PowerS,
 
     F:= LeftActingDomain( L );
     p:= Characteristic( F );
-    return List( [ 1 .. p-1 ], i -> PowerSi( F , i ) );
+    return List( [ 1 .. p-1 ], i -> PowerSi( F, i ) );
     end );
 
 
@@ -1385,7 +1385,7 @@ InstallMethod( CartanSubalgebra,
 ##
 ##  This function calculates a basis of the associative matrix algebra
 ##  generated by ad_L K, where <K> is a subalgebra of <L>.
-##  If {x_1,\ldots ,x_n} is a basis of K, then this algebra is spanned
+##  If {x_1,\ldots,x_n} is a basis of K, then this algebra is spanned
 ##  by all words
 ##                          ad x_{i_1}\cdots ad x_{i_t}
 ##  where t>0.
@@ -1706,7 +1706,7 @@ InstallMethod( LieSolvableRadical,
       quo:= ImagesSource( hom );
       r1:= LieSolvableRadical( quo );
       B:= BasisVectors( Basis( r1 ) );
-      B:= List( B, x -> PreImagesRepresentative( hom, x ) );
+      B:= List( B, x -> PreImagesRepresentativeNC( hom, x ) );
       Append( B, BasisVectors( Basis( n ) ) );
 
     fi;
@@ -2092,7 +2092,7 @@ InstallMethod( DirectSumDecomposition,
       SetRadicalOfAlgebra( Q, Subalgebra( Q, [ Zero( Q ) ] ) );
 
       id:= List( CentralIdempotentsOfAlgebra( Q ),
-                                x->PreImagesRepresentative(hom,x));
+                                x->PreImagesRepresentativeNC(hom,x));
 
       # Now we lift the idempotents to the big algebra `A'. The
       # first idempotent is lifted as follows:
@@ -2749,7 +2749,7 @@ InstallMethod( NonNilpotentElement,
 
       # Now `char F =0'.
       # In this case either `L' is nilpotent or one of the
-      # elements $L.1, \ldots , L.n, L.i + L.j; 1 \leq i < j$
+      # elements $L.1, \ldots, L.n, L.i + L.j; 1 \leq i < j$
       # is non nilpotent.
 
       for i in [ 1 .. n ] do
@@ -4017,9 +4017,9 @@ InstallMethod( ImagesRepresentative,
 
 ###########################################################################
 ##
-#M   PreImagesRepresentative( f, x )
+#M   PreImagesRepresentativeNC( f, x )
 ##
-InstallMethod( PreImagesRepresentative,
+InstallMethod( PreImagesRepresentativeNC,
     "for Fp to SCA mapping, and element",
     FamRangeEqFamElm,
     [ IsFptoSCAMorphism, IsSCAlgebraObj ], 0,
@@ -5567,33 +5567,33 @@ InstallMethod( JenningsLieAlgebra,
     # Construct the homogeneous components of `L':
 
     J:=JenningsSeries ( G );
-    Homs:= List ( [1..Length(J)-1] , x ->
+    Homs:= List ( [1..Length(J)-1], x ->
                   NaturalHomomorphismByNormalSubgroupNC( J[x], J[x+1] ));
-    grades := List ( Homs , Range );
+    grades := List ( Homs, Range );
     hom_pcg:= List( grades, IsomorphismSpecialPcGroup );
     pcgps:= List( hom_pcg, Range );
     gens := [];
     enum_gens:= [ ];
     pos := [];
     for i in [1.. Length(grades)] do
         tempgens:= GeneratorsOfGroup( pcgps[i] );
-        Append ( gens , tempgens);
+        Append ( gens, tempgens);
 
         # Record the number that each generator has in extrep.
         Add( enum_gens, List( tempgens, x -> ExtRepOfObj( x )[1] ) );
-        Append ( pos , List ( tempgens , x-> i ) );
+        Append ( pos, List ( tempgens, x-> i ) );
     od;
 
     # Construct the field and the multiplication table:
 
     dim:= Length(gens);
     p:= PrimePGroup( G );
     F:= GF( p );
-    T:= EmptySCTable( dim , Zero(F) , "antisymmetric" );
+    T:= EmptySCTable( dim, Zero(F), "antisymmetric" );
     pimgs := [];
     for i in [1..dim] do
-        a:= PreImagesRepresentative( Homs[pos[i]] ,
-                    PreImagesRepresentative( hom_pcg[pos[i]], gens[i] ) );
+        a:= PreImagesRepresentativeNC( Homs[pos[i]],
+                    PreImagesRepresentativeNC( hom_pcg[pos[i]], gens[i] ) );
 
         # calculate the p-th power image of `a':
 
@@ -5610,10 +5610,10 @@ InstallMethod( JenningsLieAlgebra,
                # Calculate the commutator [a,b], and map the result into
                # the correct homogeneous component.
 
-                b:= PreImagesRepresentative( Homs[pos[j]],
-                         PreImagesRepresentative( hom_pcg[pos[j]], gens[j] ));
+                b:= PreImagesRepresentativeNC( Homs[pos[j]],
+                      PreImagesRepresentativeNC( hom_pcg[pos[j]], gens[j] ));
                 c:= Image( hom_pcg[pos[i] + pos[j]],
-                           Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
+                      Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
                 e:= ExtRepOfObj(c);
                 co:=[];
                 for k in [1,3..Length(e)-1] do
@@ -5764,32 +5764,32 @@ InstallMethod( PCentralLieAlgebra,
 
     p:= PrimePGroup( G );
     J:= PCentralSeries( G, p );
-    Homs:= List ( [1..Length(J)-1] , x ->
+    Homs:= List ( [1..Length(J)-1], x ->
                   NaturalHomomorphismByNormalSubgroupNC( J[x], J[x+1] ));
-    grades := List ( Homs , Range );
+    grades := List ( Homs, Range );
     hom_pcg:= List( grades, IsomorphismSpecialPcGroup );
     pcgps:= List( hom_pcg, Range );
     gens := [];
     enum_gens:= [ ];
     pos := [];
     for i in [1.. Length(grades)] do
         tempgens:= GeneratorsOfGroup( pcgps[i] );
-        Append ( gens , tempgens);
+        Append ( gens, tempgens);
 
         # Record the number that each generator has in extrep.
         Add( enum_gens, List( tempgens, x -> ExtRepOfObj( x )[1] ) );
-        Append ( pos , List ( tempgens , x-> i ) );
+        Append ( pos, List ( tempgens, x-> i ) );
     od;
 
     # Construct the field and the multiplication table:
 
     dim:= Length(gens);
     F:= GF( p );
-    T:= EmptySCTable( dim , Zero(F) , "antisymmetric" );
+    T:= EmptySCTable( dim, Zero(F), "antisymmetric" );
     pimgs := [];
     for i in [1..dim] do
-        a:= PreImagesRepresentative( Homs[pos[i]] ,
-                    PreImagesRepresentative( hom_pcg[pos[i]], gens[i] ) );
+        a:= PreImagesRepresentativeNC( Homs[pos[i]],
+                    PreImagesRepresentativeNC( hom_pcg[pos[i]], gens[i] ) );
 
 
         # calculate the p-th power image of `a':
@@ -5807,10 +5807,10 @@ InstallMethod( PCentralLieAlgebra,
                # Calculate the commutator [a,b], and map the result into
                # the correct homogeneous component.
 
-                b:= PreImagesRepresentative( Homs[pos[j]],
-                         PreImagesRepresentative( hom_pcg[pos[j]], gens[j] ));
+                b:= PreImagesRepresentativeNC( Homs[pos[j]],
+                       PreImagesRepresentativeNC( hom_pcg[pos[j]], gens[j] ));
                 c:= Image( hom_pcg[pos[i] + pos[j]],
-                           Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
+                       Image(Homs[pos[i] + pos[j]], a^-1*b^-1*a*b) );
                 e:= ExtRepOfObj(c);
                 co:=[];
                 for k in [1,3..Length(e)-1] do

diff --git a/lib/algrep.gd b/lib/algrep.gd
@@ -697,10 +697,12 @@ DeclareOperation( "ModuleByRestriction", [ IsAlgebraModule, IsAlgebra ] );
 ##  <Oper Name="NaturalHomomorphismBySubAlgebraModule" Arg='V, W'/>
 ##
 ##  <Description>
-##  Here <A>V</A> must be a sub-algebra module of <A>V</A>. This function returns
-##  the projection from <A>V</A> onto <C><A>V</A>/<A>W</A></C>. It is a linear map, that is
-##  also a module homomorphism. As usual images can be formed with
-##  <C>Image( f, v )</C> and pre-images with <C>PreImagesRepresentative( f, u )</C>.
+##  Here <A>V</A> must be a sub-algebra module of <A>V</A>.
+##  This function returns
+##  the projection from <A>V</A> onto <C><A>V</A>/<A>W</A></C>.
+##  It is a linear map, that is also a module homomorphism.
+##  As usual images can be formed with <C>Image( f, v )</C>
+##  and pre-images with <C>PreImagesRepresentativeNC( f, u )</C>.
 ##  <P/>
 ##  The quotient module can also be formed
 ##  by entering <C><A>V</A>/<A>W</A></C>.
@@ -726,7 +728,7 @@ DeclareOperation( "ModuleByRestriction", [ IsAlgebraModule, IsAlgebra ] );
 ##  18 over Rationals>>
 ##  gap> v:= Basis( quo )[1];
 ##  [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]
-##  gap> PreImagesRepresentative( f, v );
+##  gap> PreImagesRepresentativeNC( f, v );
 ##  v.4
 ##  gap> Basis( C )[4]^v;
 ##  [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]