1 | G := Group( |
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2 | (2, 3)(5, 6)(9, 10), (1, 5, 9, 10, 3)(2, 7, 8, 4, 6) |
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3 | );; |
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4 | Size(G); |
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5 | dimQ:=5; |
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6 | |
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7 | minidx:=SmallestMovedPoint(G); |
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8 | maxidx:=LargestMovedPoint(G); |
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9 | XZorbitsRepresentatives:=[];; |
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10 | for k in [dimQ..(maxidx-minidx+1)] do |
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11 | Print("Considering faces of cardinality ",k,"\n"); |
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12 | XZ := Combinations([minidx..maxidx],k);; |
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13 | Bahnen := OrbitsDomain(G,XZ,OnSets);; |
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14 | for i in [1..Size(Bahnen)] do |
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15 | Append(XZorbitsRepresentatives,[Bahnen[i][1]]); |
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16 | od; |
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17 | od; |
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18 | |
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19 | PrintTo("simplexOrbitRepresentativesG25.sing","list simplexOrbitRepresentatives = "); |
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20 | for k in [1..Size(XZorbitsRepresentatives)-1] do |
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21 | s:=String(XZorbitsRepresentatives[k]); |
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22 | s:=s{[2..Size(s)-1]}; |
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23 | AppendTo ("simplexOrbitRepresentativesG25.sing","intvec(",s,"),\n"); |
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24 | od; |
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25 | s:=String(XZorbitsRepresentatives[Size(XZorbitsRepresentatives)]); |
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26 | s:=s{[2..Size(s)-1]}; |
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27 | AppendTo ("simplexOrbitRepresentativesG25.sing","intvec(",s,");\n"); |
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28 | |
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29 | |
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30 | PrintTo("simplexSymmetryGroupG25.sing","list simplexSymmetryGroup = "); |
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31 | elementsG:=Elements(G); |
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32 | for i in [1..Size(elementsG)-1] do |
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33 | sigma:=elementsG[i]; |
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34 | l:=ListPerm(sigma,maxidx); |
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35 | l:=l{[minidx..maxidx]}; |
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36 | s:=String(l); |
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37 | s:=s{[2..Size(s)-1]}; |
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38 | AppendTo ("simplexSymmetryGroupG25.sing","permutationFromIntvec(intvec(",s,")),\n"); |
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39 | od; |
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40 | sigma:=elementsG[Size(elementsG)]; |
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41 | l:=ListPerm(sigma,maxidx); |
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42 | l:=l{[minidx..maxidx]}; |
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43 | s:=String(l); |
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44 | s:=s{[2..Size(s)-1]}; |
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45 | AppendTo ("simplexSymmetryGroupG25.sing","permutationFromIntvec(intvec(",s,"));\n"); |
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46 | |
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47 | |
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48 | PrintTo("elementsInTermsOfGeneratorsG25.sing","list generatorsG = "); |
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49 | L:=GeneratorsOfGroup(G); |
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50 | for i in [1..Size(L)-1] do |
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51 | sigma:=L[i]; |
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52 | l:=ListPerm(sigma,maxidx); |
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53 | l:=l{[minidx..maxidx]}; |
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54 | s:=String(l); |
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55 | s:=s{[2..Size(s)-1]}; |
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56 | AppendTo ("elementsInTermsOfGeneratorsG25.sing","permutationFromIntvec(intvec(",s,")),\n"); |
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57 | od; |
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58 | sigma:=L[Size(L)]; |
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59 | l:=ListPerm(sigma,maxidx); |
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60 | l:=l{[minidx..maxidx]}; |
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61 | s:=String(l); |
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62 | s:=s{[2..Size(s)-1]}; |
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63 | AppendTo ("elementsInTermsOfGeneratorsG25.sing","permutationFromIntvec(intvec(",s,"));\n"); |
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64 | |
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65 | AppendTo("elementsInTermsOfGeneratorsG25.sing","list elementsInTermsOfGenerators = "); |
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66 | hom:=EpimorphismFromFreeGroup(G); |
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67 | AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"\",\n"); |
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68 | for i in [2..Size(elementsG)-1] do |
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69 | sigma:=elementsG[i]; |
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70 | l:=PreImagesRepresentative(hom,sigma); |
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71 | s:=String(l); |
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72 | AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"",s,"\",\n"); |
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73 | od; |
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74 | sigma:=elementsG[Size(elementsG)]; |
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75 | l:=PreImagesRepresentative(hom,sigma); |
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76 | s:=String(l); |
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77 | AppendTo ("elementsInTermsOfGeneratorsG25.sing","\"",s,"\";\n"); |
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78 | |
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79 | |
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