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-rw-r--r--src/algebra/permgrps.spad.pamphlet28
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], _