Replace `^=' with `~='.

1 files changed, 14 insertions, 14 deletions

diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet
index 0b3fa62d..ee97d7ed 100644
--- a/src/algebra/permgrps.spad.pamphlet
+++ b/src/algebra/permgrps.spad.pamphlet
@@ -218,7 +218,7 @@ PermutationGroup(S:SetCategory): public == private where
         flag := false
         while pointer > 1 repeat
           pointer := ( pointer - 1 )::NNI
-          if newlw.pointer ^= test then
+          if newlw.pointer ~= test then
             -- don't get a trivial element, try next
             test := newlw.pointer
             anzahl := 1
@@ -294,7 +294,7 @@ PermutationGroup(S:SetCategory): public == private where
 
     testIdentity ( p : V NNI ) : B ==
       -- internal test for identity
-      for i in 1..degree repeat qelt(p,i) ^= i => return false
+      for i in 1..degree repeat qelt(p,i) ~= i => return false
       true
 
     pointList(group : %) : L S ==
@@ -346,14 +346,14 @@ PermutationGroup(S:SetCategory): public == private where
         ort := orbitWithSvc ( group , i )
         k   := ort.orb
         k1  := # k
-        if k1 ^= 1 then leave
+        if k1 ~= 1 then leave
       gpsgs := nil()$(L V NNI)
       words2 := nil()$(L L NNI)
       gplength : NNI := #group
-      for jj in 1..gplength repeat if (group.jj).i ^= i then leave
+      for jj in 1..gplength repeat if (group.jj).i ~= i then leave
       for k in 1..gplength repeat
         el2 := group.k
-        if el2.i ^= i then
+        if el2.i ~= i then
           gpsgs := cons ( el2 , gpsgs )
           if wordProblem then words2 := cons ( words.k , words2 )
         else
@@ -432,7 +432,7 @@ PermutationGroup(S:SetCategory): public == private where
               pt2  := baseLength - j + 1
               sgs2 := append ( sgs2 , out.j )
               obs2 := orbitWithSvc ( sgs2 , baseOfGroup.pt2 )
-              if # obs2.orb ^= orbitLength.j then
+              if # obs2.orb ~= orbitLength.j then
                 test := false
                 leave
             if test then
@@ -541,7 +541,7 @@ PermutationGroup(S:SetCategory): public == private where
             word := shortenWord ( word , group )
           if newBasePoint then
             for i in 1..degree repeat
-              if z.i ^= i then
+              if z.i ~= i then
                 baseOfGroup := append ( baseOfGroup , [ i ] )
                 leave
             out := cons (list  z, out )
@@ -739,7 +739,7 @@ PermutationGroup(S:SetCategory): public == private where
       subgroup ( gp1 , gp2 )
 
     gp1 = gp2 ==
-      movedPoints gp1 ^= movedPoints gp2 => false
+      movedPoints gp1 ~= movedPoints gp2 => false
       if #(gp1.gens) <= #(gp2.gens) then
         not subgroup ( gp1 , gp2 ) => return false
       else
@@ -1007,7 +1007,7 @@ PermutationGroupExamples():public == private where
       mathieu11(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 11 => error "Exactly 11 integers for mathieu11 needed !"
+        #l ~= 11 => error "Exactly 11 integers for mathieu11 needed !"
         a:L L I:=[[l.1,l.10],[l.2,l.8],[l.3,l.11],[l.5,l.7]]
         llli2gp [a,[[l.1,l.4,l.7,l.6],[l.2,l.11,l.10,l.9]]]
 
@@ -1016,7 +1016,7 @@ PermutationGroupExamples():public == private where
       mathieu12(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 12 => error "Exactly 12 integers for mathieu12 needed !"
+        #l ~= 12 => error "Exactly 12 integers for mathieu12 needed !"
         a:L L I:=
           [[l.1,l.2,l.3,l.4,l.5,l.6,l.7,l.8,l.9,l.10,l.11]]
         llli2gp [a,[[l.1,l.6,l.5,l.8,l.3,l.7,l.4,l.2,l.9,l.10],[l.11,l.12]]]
@@ -1026,7 +1026,7 @@ PermutationGroupExamples():public == private where
       mathieu22(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 22 => error "Exactly 22 integers for mathieu22 needed !"
+        #l ~= 22 => error "Exactly 22 integers for mathieu22 needed !"
         a:L L I:=[[l.1,l.2,l.4,l.8,l.16,l.9,l.18,l.13,l.3,l.6,l.12],   _
           [l.5,l.10,l.20,l.17,l.11,l.22,l.21,l.19,l.15,l.7,l.14]]
         b:L L I:= [[l.1,l.2,l.6,l.18],[l.3,l.15],[l.5,l.8,l.21,l.13],   _
@@ -1038,7 +1038,7 @@ PermutationGroupExamples():public == private where
       mathieu23(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 23 => error "Exactly 23 integers for mathieu23 needed !"
+        #l ~= 23 => error "Exactly 23 integers for mathieu23 needed !"
         a:L L I:= [[l.1,l.2,l.3,l.4,l.5,l.6,l.7,l.8,l.9,l.10,l.11,l.12,l.13,l.14,_
                    l.15,l.16,l.17,l.18,l.19,l.20,l.21,l.22,l.23]]
         b:L L I:= [[l.2,l.16,l.9,l.6,l.8],[l.3,l.12,l.13,l.18,l.4],              _
@@ -1050,7 +1050,7 @@ PermutationGroupExamples():public == private where
       mathieu24(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 24 => error "Exactly 24 integers for mathieu24 needed !"
+        #l ~= 24 => error "Exactly 24 integers for mathieu24 needed !"
         a:L L I:= [[l.1,l.16,l.10,l.22,l.24],[l.2,l.12,l.18,l.21,l.7],          _
                    [l.4,l.5,l.8,l.6,l.17],[l.9,l.11,l.13,l.19,l.15]]
         b:L L I:= [[l.1,l.22,l.13,l.14,l.6,l.20,l.3,l.21,l.8,l.11],[l.2,l.10],  _
@@ -1062,7 +1062,7 @@ PermutationGroupExamples():public == private where
       janko2(l:L I):PERMGRP I ==
       -- permutations derived from the ATLAS
         l:=removeDuplicates l
-        #l ^= 100 => error "Exactly 100 integers for janko2 needed !"
+        #l ~= 100 => error "Exactly 100 integers for janko2 needed !"
         a:L L I:=[                                                            _
                  [l.2,l.3,l.4,l.5,l.6,l.7,l.8],                               _
                  [l.9,l.10,l.11,l.12,l.13,l.14,l.15],                         _