diff options
Diffstat (limited to 'src/algebra/permgrps.spad.pamphlet')
| -rw-r--r-- | src/algebra/permgrps.spad.pamphlet | 28 |
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], _ |