--- perm.spad.pamphlet	2006-06-04 12:36:44.000000000 +0200
+++ perm.spad.pamphlet.alt	2006-06-04 12:01:23.000000000 +0200
@@ -60,7 +60,7 @@
 )abbrev domain PERM Permutation
 ++ Authors: Johannes Grabmeier, Holger Gollan
 ++ Date Created: 19 May 1989
-++ Date Last Updated: 2 June 2006
+++ Date Last Updated: 24 May 1991
 ++ Basic Operations: _*, degree, movedPoints, cyclePartition, order,
 ++  numberOfCycles, sign, even?, odd?
 ++ Related Constructors: PermutationGroup, PermutationGroupExamples
@@ -96,16 +96,13 @@
       ++ listRepresentation(p) produces a representation {\em rep} of
       ++ the permutation p as a list of preimages and images, i.e
       ++ p maps {\em (rep.preimage).k} to {\em (rep.image).k} for all
-      ++ indices k. Elements of \spad{S} not in {\em (rep.preimage).k}
-      ++ are fixed points, and these are the only fixed points of the 
-      ++ permutation.
+      ++ indices k.
     coercePreimagesImages : List List S   ->  %
       ++ coercePreimagesImages(lls) coerces the representation {\em lls}
       ++ of a permutation as a list of preimages and images to a permutation.
-      ++ We assume that both preimage and image do not contain repetitions.
     coerce            :  List List S      ->  %
       ++ coerce(lls) coerces a list of cycles {\em lls} to a
-      ++ permutation, each cycle being a list with no
+      ++ permutation, each cycle being a list with not
       ++ repetitions, is coerced to the permutation, which maps
       ++ {\em ls.i} to {\em ls.i+1}, indices modulo the length of the list,
       ++ then these permutations are mutiplied.
@@ -159,24 +156,13 @@
         ++ whose image is given by {\em ls} and the preimage is fixed
         ++ to be {\em [1,...,n]}.
         ++ Note: {coerceImages(ls)=coercePreimagesImages([1,...,n],ls)}.
-        ++ We assume that both preimage and image do not contain repetitions.
 
   private ==> add
 
     -- representation of the object:
 
     Rep  := V L S
-@
-
-We represent a permutation as two lists of equal length representing preimages
-and images of moved points. I.e., fixed points do not occur in either of these
-lists. This enables us to compute the set of fixed points and the set of moved
-points easily.
 
-Note that this was not respected in versions before [[patch--50]] of this
-domain.
-
-<<domain PERM Permutation>>=
     -- import of domains and packages
 
     import OutputForm
@@ -281,35 +267,9 @@
       s : RECPRIM := [p.1,p.2]
 
     coercePreimagesImages preImageAndImage ==
-      preImage: List S := []
-      image: List S := []
-      for i in preImageAndImage.1 
-        for pi in preImageAndImage.2 repeat
-          if i ~= pi then
-            preImage := cons(i, preImage)
-            image := cons(pi, image)
-
-      [preImage, image]
-@ 
-
-This operation transforms a pair of preimages and images into an element of the
-domain. Since we assume that fixed points do not occur in the representation,
-we have to sort them out here. 
-
-Note that before [[patch--50]] this read
-\begin{verbatim}
-      coercePreimagesImages preImageAndImage ==
       p : % := [preImageAndImage.1,preImageAndImage.2]
-\end{verbatim}
-causing bugs when computing [[movedPoints]], [[fixedPoints]], [[even?]],
-[[odd?]], etc., as reported in Issue~\#295.
-
-The other coercion facilities check for fixed points. It also seems that [[*]]
-removes fixed points from its result.
 
-<<domain PERM Permutation>>=
-
-    movedPoints p == construct p.1
+    movedPoints p == construct p.1  --check on fixed points !!
 
     degree p ==  #movedPoints p
 
@@ -454,22 +414,14 @@
 
       coerceImages (image) ==
         preImage : L S := [i::S for i in 1..maxIndex image]
-        coercePreimagesImages [preImage,image]
-@
-
-Up to [[patch--50]] we did not check for duplicates.
+        p : % := [preImage,image]
 
-<<domain PERM Permutation>>=
     if S has Finite then
 
       coerceImages (image) ==
         preImage : L S := [index(i::PI)::S for i in 1..maxIndex image]
-        coercePreimagesImages [preImage,image]
-@
-
-Up to [[patch--50]] we did not check for duplicates.
+        p : % := [preImage,image]
 
-<<domain PERM Permutation>>=
       fixedPoints ( p ) == complement movedPoints p
 
       cyclePartition p ==