* algebra/permgrps.spad.pamphlet (PermutationGroup): Rename

	movedPoints to support.  Adjust call eval.
	* algebra/perm.spad.pamphlet (PermutationCategory): Now extend
	Eltable.  Remove eval.  Rename movedPoints to support.
	(Permutation): Adjust.
	* algebra/irsn.spad.pamphlet (listPermutationIrrRepSymNatPackage): 
	Change call to eval to elt.
	* algebra/rep1.spad.pamphlet: Likewise.

4 files changed, 31 insertions, 37 deletions

diff --git a/src/algebra/irsn.spad.pamphlet b/src/algebra/irsn.spad.pamphlet
index 95d9a257..5b2a4f48 100644
--- a/src/algebra/irsn.spad.pamphlet
+++ b/src/algebra/irsn.spad.pamphlet
@@ -171,7 +171,7 @@ IrrRepSymNatPackage(): public == private where
     listPermutation(pi) ==
       li : L I := nil$(L I)
       for k in n..1 by -1 repeat
-        li := cons(eval(pi,k)$(PERM I),li)
+        li := cons(pi.k,li)
       li
 
     signum(numberOfRowTableau, numberOfColumnTableau,pi) ==
diff --git a/src/algebra/perm.spad.pamphlet b/src/algebra/perm.spad.pamphlet
index 69f33f83..2dd9da5b 100644
--- a/src/algebra/perm.spad.pamphlet
+++ b/src/algebra/perm.spad.pamphlet
@@ -15,7 +15,7 @@
 ++ Authors:  Holger Gollan, Johannes Grabmeier, Gerhard Schneider
 ++ Date Created: 27 July 1989
 ++ Date Last Updated: 29 March 1990
-++ Basic Operations: cycle, cycles, eval, orbit
+++ Basic Operations: cycle, cycles, orbit
 ++ Related Constructors: PermutationGroup, PermutationGroupExamples
 ++ Also See: RepresentationTheoryPackage1
 ++ AMS Classifications:
@@ -24,7 +24,8 @@
 ++ Description: PermutationCategory provides a categorial environment
 ++  for subgroups of bijections of a set (i.e. permutations)
 
-PermutationCategory(S:SetCategory): Category  ==  Group with
+PermutationCategory(S:SetCategory): Category ==
+  Join(Group,Eltable(S,S)) with
     cycle   :  List S       ->  %
       ++ cycle(ls) coerces a cycle {\em ls}, i.e. a list with not
       ++ repetitions to a permutation, which maps {\em ls.i} to
@@ -37,12 +38,9 @@ PermutationCategory(S:SetCategory): Category  ==  Group with
       ++ {\em ls.i} to {\em ls.i+1}, indices modulo the length of the list,
       ++ then these permutations are mutiplied.
       ++ Error: if repetitions occur in one cycle.
-    eval  :  (%,S)          ->  S
-      ++ eval(p, el) returns the image of {\em el} under the
-      ++ permutation p.
-    elt  :  (%,S)          ->  S
-      ++ elt(p, el) returns the image of {\em el} under the
-      ++ permutation p.
+    support: % -> Set S
+      ++ \spad{support p} returns the set of points not fixed by the
+      ++ permutation \spad{p}.
     orbit :  (%,S)          ->  Set S
       ++ orbit(p, el) returns the orbit of {\em el} under the
       ++ permutation p, i.e. the set which is given by applications of
@@ -61,7 +59,7 @@ PermutationCategory(S:SetCategory): Category  ==  Group with
 ++ Authors: Johannes Grabmeier, Holger Gollan
 ++ Date Created: 19 May 1989
 ++ Date Last Updated: 2 June 2006
-++ Basic Operations: _*, degree, movedPoints, cyclePartition, order,
+++ Basic Operations: _*, degree, support, cyclePartition, order,
 ++  numberOfCycles, sign, even?, odd?
 ++ Related Constructors: PermutationGroup, PermutationGroupExamples
 ++ Also See: RepresentationTheoryPackage1
@@ -126,8 +124,6 @@ Permutation(S:SetCategory): public == private where
     degree            :  %                ->  NonNegativeInteger
       ++ degree(p) retuns the number of points moved by the
       ++ permutation p.
-    movedPoints       :  %                ->  Set S
-      ++ movedPoints(p) returns the set of points moved by the permutation p.
     cyclePartition    :  %                ->  Partition
       ++ cyclePartition(p) returns the cycle structure of a permutation
       ++ p including cycles of length 1 only if S is finite.
@@ -300,7 +296,7 @@ Note that before [[patch--50]] this read
       coercePreimagesImages preImageAndImage ==
       p : % := [preImageAndImage.1,preImageAndImage.2]
 \end{verbatim}
-causing bugs when computing [[movedPoints]], [[fixedPoints]], [[even?]],
+causing bugs when computing [[support]], [[fixedPoints]], [[even?]],
 [[odd?]], etc., as reported in Issue~\#295.
 
 The other coercion facilities check for fixed points. It also seems that [[*]]
@@ -308,7 +304,7 @@ removes fixed points from its result.
 
 <<TEST PERM>>=
   p := coercePreimagesImages([[1,2,3],[1,2,3]])
-  movedPoints p    -- should return {}
+  support p        -- should return {}
   even? p          -- should return true
   p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4
   fixedPoints p    -- should return {2}
@@ -319,9 +315,9 @@ removes fixed points from its result.
 
 <<domain PERM Permutation>>=
 
-    movedPoints p == construct p.1
+    support p == construct p.1
 
-    degree p ==  #movedPoints p
+    degree p ==  #support p
 
     p = q ==
       #(preimp := p.1) ~= #(preimq := q.1) => false
@@ -334,12 +330,12 @@ removes fixed points from its result.
     orbit(p ,el) ==
       -- start with a 1-element list:
       out : Set S := brace list el
-      el2 := eval(p, el)
+      el2 := p(el)
       while el2 ~= el repeat
         -- be carefull: insert adds one element
         -- as side effect to out
         insert!(el2, out)
-        el2 := eval(p, el2)
+        el2 := p(el2)
       out
 
     cyclePartition p ==
@@ -450,13 +446,11 @@ removes fixed points from its result.
 
     inv p  == [p.2, p.1]
 
-    eval(p, el) ==
+    elt(p,el) ==
       pos := position(el, p.1)
       pos = 0 => el
       (p.2).pos
 
-    elt(p, el) == eval(p, el)
-
     numberOfCycles p == #coerceToCycle(p, false)
 
 
@@ -480,7 +474,7 @@ Up to [[patch--50]] we did not check for duplicates.
 Up to [[patch--50]] we did not check for duplicates.
 
 <<domain PERM Permutation>>=
-      fixedPoints ( p ) == complement movedPoints p
+      fixedPoints ( p ) == complement support p
 
       cyclePartition p ==
         pt := partition([#c::PI for c in coerceToCycle(p, false)])$Partition
diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet
index 5d69a574..98e2ab75 100644
--- a/src/algebra/permgrps.spad.pamphlet
+++ b/src/algebra/permgrps.spad.pamphlet
@@ -116,8 +116,8 @@ PermutationGroup(S:SetCategory): public == private where
       ++ wordInGenerators(p,gp) returns the word for the permutation p
       ++ in the original generators of the group {\em gp},
       ++ represented by the indices of the list, given by {\em generators}.
-    movedPoints      : %         -> FSET S
-      ++ movedPoints(gp) returns the points moved by the group {\em gp}.
+    support      : %         -> FSET S
+      ++ support(gp) returns the points moved by the group {\em gp}.
     <              : (%,%)     -> B
       ++ gp1 < gp2 returns true if and only if {\em gp1}
       ++ is a proper subgroup of {\em gp2}.
@@ -261,7 +261,7 @@ PermutationGroup(S:SetCategory): public == private where
           newList  := nil()$(L S)
           workList := orbitList.pos
           for j in #workList..1 by -1 repeat
-            newList := cons ( eval ( gen , workList.j ) , newList )
+            newList := cons (gen(workList.j) , newList )
           if not member?( newList , orbitList ) then
             orbitList := cons ( newList , orbitList )
             pos  := pos + 1
@@ -298,10 +298,10 @@ PermutationGroup(S:SetCategory): public == private where
       true
 
     pointList(group : %) : L S ==
-      support : FSET S :=  brace()   -- empty set !!
+      s : FSET S :=  brace()   -- empty set !!
       for perm in group.gens repeat
-        support := union(support, movedPoints perm)
-      parts support
+        s := union(s, support perm)
+      parts s
 
     orbitWithSvc ( group : L V NNI , point : NNI ) : REC ==
       -- compute orbit with Schreier vector, "-2" means not in the orbit,
@@ -469,7 +469,7 @@ PermutationGroup(S:SetCategory): public == private where
       for ggg in 1..#gp repeat
         q := new(degree,0)$(V NNI)
         for i in 1..degree repeat
-          newEl := eval ( gp.ggg , supp.i )
+          newEl := elt(gp.ggg,supp.i)
           pos2  := position ( newEl , supp )
           q.i   := pos2 pretend NNI
         newGroup := cons ( q , newGroup )
@@ -597,7 +597,7 @@ PermutationGroup(S:SetCategory): public == private where
       -- internal membership testing
       supp     := pointList gp
       outlist := nil()$(L NNI)
-      mP : L S := parts movedPoints p
+      mP : L S := parts support p
       for x in mP repeat
         not member? (x, supp) => return [ false , nil()$(L NNI) ]
       if flag then
@@ -617,7 +617,7 @@ PermutationGroup(S:SetCategory): public == private where
       degree := # supp
       pp := new(degree,0)$(V NNI)
       for i in 1..degree repeat
-        el   := eval ( p , supp.i )
+        el   := p(supp.i)
         pos  := position ( el , supp )
         pp.i := pos::NNI
       words := nil()$(L L NNI)
@@ -649,7 +649,7 @@ PermutationGroup(S:SetCategory): public == private where
 
     elt ( gp , i ) == (gp.gens).i
 
-    movedPoints ( gp ) == brace pointList gp
+    support ( gp ) == brace pointList gp
 
     random ( group , maximalNumberOfFactors ) ==
       maximalNumberOfFactors < 1 => 1$(PERM S)
@@ -707,7 +707,7 @@ PermutationGroup(S:SetCategory): public == private where
       outSet
 
     orbits ( gp ) ==
-      spp    := movedPoints gp
+      spp    := support gp
       orbits := nil()$(L FSET S)
       while cardinality spp > 0 repeat
         el       := extract! spp
@@ -734,17 +734,17 @@ PermutationGroup(S:SetCategory): public == private where
       shortenWord ( outlist , gp )
 
     gp1 < gp2 ==
-      not empty? difference ( movedPoints gp1 , movedPoints gp2 ) => false
+      not empty? difference ( support gp1 , support gp2 ) => false
       not subgroup ( gp1 , gp2 ) => false
       order gp1 = order gp2 => false
       true
 
     gp1 <= gp2 ==
-      not empty?  difference ( movedPoints gp1 , movedPoints gp2 ) => false
+      not empty?  difference ( support gp1 , support gp2 ) => false
       subgroup ( gp1 , gp2 )
 
     gp1 = gp2 ==
-      movedPoints gp1 ~= movedPoints gp2 => false
+      support gp1 ~= support gp2 => false
       if #(gp1.gens) <= #(gp2.gens) then
         not subgroup ( gp1 , gp2 ) => return false
       else
diff --git a/src/algebra/rep1.spad.pamphlet b/src/algebra/rep1.spad.pamphlet
index f26ae02c..dde33bc9 100644
--- a/src/algebra/rep1.spad.pamphlet
+++ b/src/algebra/rep1.spad.pamphlet
@@ -302,7 +302,7 @@ RepresentationPackage1(R): public == private where
        -- permutations are assumed to permute {1,2,...,n}
        a : M I := zero(n :: NNI, n :: NNI)
        for i in 1..n repeat
-          a(eval(p,i)$(PERM I),i) := 1
+          a(p.i,i) := 1
        a