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D.15.18.18 groupActionOnHashes
Procedure from library gitfan.lib (see gitfan_lib).
- Usage:
- groupActionOnHashes(Asigma,OCmov); Asigma: list, OCmov: list of list of cones
- Purpose:
- From the list of orbits of orbitcones, and the symmetry group represenation given by the matrices in Asigma, compute the corresponding permutation representation of the symmetry group on the orbit cones. The permutations are specified in a map representation of length the sum of the size of the orbits of OCmov.
- Return:
- list of permutations
Example:
| | LIB "gitfan.lib";
ring R = 0,T(1..10),wp(1,1,1,1,1,1,1,1,1,1);
ideal J =
T(5)*T(10)-T(6)*T(9)+T(7)*T(8),
T(1)*T(9)-T(2)*T(7)+T(4)*T(5),
T(1)*T(8)-T(2)*T(6)+T(3)*T(5),
T(1)*T(10)-T(3)*T(7)+T(4)*T(6),
T(2)*T(10)-T(3)*T(9)+T(4)*T(8);
intmat Q[5][10] =
1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
0, 1, 1, 0, 0, 0, -1, 1, 0, 0,
0, 1, 0, 1, 0, -1, 0, 0, 1, 0,
0, 0, 1, 1, -1, 0, 0, 0, 0, 1;
list AF= afaces(J);
list OC = orbitCones(AF,Q);
list generatorsG = permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )),
permutationFromIntvec(intvec( 5, 7, 1, 6, 9, 2, 8, 4, 10, 3 ));
list Asigmagens = groupActionOnQImage(generatorsG,Q);
groupActionOnHashes(Asigmagens,list(OC));
==> [1]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 \
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 5\
4 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 \
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 1\
09 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 12\
7 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145\
146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 \
164 165 166 167 168 169 170 171 172|
==> | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 44 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 0 0 0 120 0 0 0 124 0\
126 127 128 129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 86 0 0 0 90 0 92 93 \
94 95 0 0 0 0 0 0 0 137 0 0 0 141 0 143 144 145 14\
6 0 0 0 0 0 0 153 155 154 156 0 163 165 164 166 0 158 160\
159 161 0 168 170 169 171 172|
==>
==> [2]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 \
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 5\
4 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 \
91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 1\
09 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 12\
7 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145\
146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 \
164 165 166 167 168 169 170 171 172|
==> | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 120 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 0 0 0 126 0 0 0 128 0\
44 124 127 129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0 0 0 0 165 0 0 0 163 0 141 90 1\
64 166 0 0 0 0 0 0 0 155 0 0 0 153 0 137 86 154 15\
6 0 0 0 0 0 0 144 93 160 170 0 143 92 158 168 0 145 94\
159 171 0 146 95 161 169 172|
==>
list simplexSymmetryGroup = G25Action();
list orb = findOrbits(simplexSymmetryGroup,nrows(Q));
list simplexOrbitRepresentatives;
for (int i=1;i<=size(orb);i++){simplexOrbitRepresentatives[i]=orb[i][1];}
list afaceOrbitRepresentatives=afaces(J,simplexOrbitRepresentatives);
list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits);
list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q);
list listOfMinimalOrbitConeOrbits = minimalOrbitConeOrbits(listOfOrbitConeOrbits);
list Asigma = groupActionOnQImage(simplexSymmetryGroup,Q);
groupActionOnHashes(Asigma,listOfOrbitConeOrbits);
==> [1]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\
25|
==>
==> [2]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 2 4 3 5 7 6 9 8 10 11 13 12 14 16 15 17 19 18 23 24 25 20 21\
22|
==>
==> [3]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 3 2 4 6 5 7 8 10 9 12 11 13 15 14 16 20 21 22 17 18 19 23 25\
24|
==>
==> [4]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 4 2 3 7 5 6 9 10 8 13 11 12 16 14 15 23 24 25 17 19 18 20 22\
21|
==>
==> [5]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 3 4 2 6 7 5 10 8 9 12 13 11 15 16 14 20 22 21 23 25 24 17 18\
19|
==>
==> [6]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 4 3 2 7 6 5 10 9 8 13 12 11 16 15 14 23 25 24 20 22 21 17 19\
18|
==>
==> [7]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 5 6 7 2 3 4 8 9 10 14 15 16 11 12 13 17 19 18 20 22 21 23 25\
24|
==>
==> [8]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 5 7 6 2 4 3 9 8 10 14 16 15 11 13 12 17 18 19 23 25 24 20 22\
21|
==>
==> [9]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 6 5 7 3 2 4 8 10 9 15 14 16 12 11 13 20 22 21 17 19 18 23 24\
25|
==>
==> [10]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 7 5 6 4 2 3 9 10 8 16 14 15 13 11 12 23 25 24 17 18 19 20 21\
22|
==>
==> [11]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 6 7 5 3 4 2 10 8 9 15 16 14 12 13 11 20 21 22 23 24 25 17 19\
18|
==>
==> [12]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 1 7 6 5 4 3 2 10 9 8 16 15 14 13 12 11 23 24 25 20 21 22 17 18\
19|
==>
==> [13]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 1 3 4 5 8 9 6 7 10 11 13 12 17 18 19 14 15 16 21 20 22 24 23\
25|
==>
==> [14]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 1 4 3 5 9 8 7 6 10 11 12 13 17 19 18 14 16 15 24 23 25 21 20\
22|
==>
==> [15]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 1 2 4 6 8 10 5 7 9 12 13 11 20 21 22 15 14 16 18 17 19 25 23\
24|
==>
==> [16]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 1 2 3 7 9 10 5 6 8 13 12 11 23 24 25 16 14 15 19 17 18 22 20\
21|
==>
==> [17]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 1 4 2 6 10 8 7 5 9 12 11 13 20 22 21 15 16 14 25 23 24 18 17\
19|
==>
==> [18]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 1 3 2 7 10 9 6 5 8 13 11 12 23 25 24 16 15 14 22 20 21 19 17\
18|
==>
==> [19]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 1 6 7 2 8 9 3 4 10 14 16 15 17 19 18 11 12 13 22 20 21 25 23\
24|
==>
==> [20]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 1 7 6 2 9 8 4 3 10 14 15 16 17 18 19 11 13 12 25 23 24 22 20\
21|
==>
==> [21]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 1 5 7 3 8 10 2 4 9 15 16 14 20 22 21 12 11 13 19 17 18 24 23\
25|
==>
==> [22]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 1 5 6 4 9 10 2 3 8 16 15 14 23 25 24 13 11 12 18 17 19 21 20\
22|
==>
==> [23]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 1 7 5 3 10 8 4 2 9 15 14 16 20 21 22 12 13 11 24 23 25 19 17\
18|
==>
==> [24]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 1 6 5 4 10 9 3 2 8 16 14 15 23 24 25 13 12 11 21 20 22 18 17\
19|
==>
==> [25]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 3 1 4 8 5 9 6 10 7 13 11 12 18 17 19 21 20 22 14 15 16 24 25\
23|
==>
==> [26]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 4 1 3 9 5 8 7 10 6 12 11 13 19 17 18 24 23 25 14 16 15 21 22\
20|
==>
==> [27]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 2 1 4 8 6 10 5 9 7 13 12 11 21 20 22 18 17 19 15 14 16 25 24\
23|
==>
==> [28]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 2 1 3 9 7 10 5 8 6 12 13 11 24 23 25 19 17 18 16 14 15 22 21\
20|
==>
==> [29]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 4 1 2 10 6 8 7 9 5 11 12 13 22 20 21 25 23 24 15 16 14 18 19\
17|
==>
==> [30]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 3 1 2 10 7 9 6 8 5 11 13 12 25 23 24 22 20 21 16 15 14 19 18\
17|
==>
==> [31]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 6 1 7 8 2 9 3 10 4 16 14 15 19 17 18 22 20 21 11 12 13 25 24\
23|
==>
==> [32]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 7 1 6 9 2 8 4 10 3 15 14 16 18 17 19 25 23 24 11 13 12 22 21\
20|
==>
==> [33]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 5 1 7 8 3 10 2 9 4 16 15 14 22 20 21 19 17 18 12 11 13 24 25\
23|
==>
==> [34]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 5 1 6 9 4 10 2 8 3 15 16 14 25 23 24 18 17 19 13 11 12 21 22\
20|
==>
==> [35]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 7 1 5 10 3 8 4 9 2 14 15 16 21 20 22 24 23 25 12 13 11 19 18\
17|
==>
==> [36]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 6 1 5 10 4 9 3 8 2 14 16 15 24 23 25 21 20 22 13 12 11 18 19\
17|
==>
==> [37]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 3 4 1 8 9 5 10 6 7 13 12 11 18 19 17 21 22 20 24 25 23 14 15\
16|
==>
==> [38]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 4 3 1 9 8 5 10 7 6 12 13 11 19 18 17 24 25 23 21 22 20 14 16\
15|
==>
==> [39]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 2 4 1 8 10 6 9 5 7 13 11 12 21 22 20 18 19 17 25 24 23 15 14\
16|
==>
==> [40]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 2 3 1 9 10 7 8 5 6 12 11 13 24 25 23 19 18 17 22 21 20 16 14\
15|
==>
==> [41]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 4 2 1 10 8 6 9 7 5 11 13 12 22 21 20 25 24 23 18 19 17 15 16\
14|
==>
==> [42]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 3 2 1 10 9 7 8 6 5 11 12 13 25 24 23 22 21 20 19 18 17 16 15\
14|
==>
==> [43]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 6 7 1 8 9 2 10 3 4 16 15 14 19 18 17 22 21 20 25 24 23 11 12\
13|
==>
==> [44]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 7 6 1 9 8 2 10 4 3 15 16 14 18 19 17 25 24 23 22 21 20 11 13\
12|
==>
==> [45]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 5 7 1 8 10 3 9 2 4 16 14 15 22 21 20 19 18 17 24 25 23 12 11\
13|
==>
==> [46]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 5 6 1 9 10 4 8 2 3 15 14 16 25 24 23 18 19 17 21 22 20 13 11\
12|
==>
==> [47]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 7 5 1 10 8 3 9 4 2 14 16 15 21 22 20 24 25 23 19 18 17 12 13\
11|
==>
==> [48]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 6 5 1 10 9 4 8 3 2 14 15 16 24 25 23 21 22 20 18 19 17 13 12\
11|
==>
==> [49]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 5 8 9 1 3 4 6 7 10 17 18 19 11 13 12 14 16 15 21 22 20 24 25\
23|
==>
==> [50]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 5 9 8 1 4 3 7 6 10 17 19 18 11 12 13 14 15 16 24 25 23 21 22\
20|
==>
==> [51]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 2 8 9 1 6 7 3 4 10 17 19 18 14 16 15 11 13 12 22 21 20 25 24\
23|
==>
==> [52]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 2 9 8 1 7 6 4 3 10 17 18 19 14 15 16 11 12 13 25 24 23 22 21\
20|
==>
==> [53]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 6 8 10 1 2 4 5 7 9 20 21 22 12 13 11 15 16 14 18 19 17 25 24\
23|
==>
==> [54]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 7 9 10 1 2 3 5 6 8 23 24 25 13 12 11 16 15 14 19 18 17 22 21\
20|
==>
==> [55]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 6 10 8 1 4 2 7 5 9 20 22 21 12 11 13 15 14 16 25 24 23 18 19\
17|
==>
==> [56]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 7 10 9 1 3 2 6 5 8 23 25 24 13 11 12 16 14 15 22 21 20 19 18\
17|
==>
==> [57]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 3 8 10 1 5 7 2 4 9 20 22 21 15 16 14 12 13 11 19 18 17 24 25\
23|
==>
==> [58]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 4 9 10 1 5 6 2 3 8 23 25 24 16 15 14 13 12 11 18 19 17 21 22\
20|
==>
==> [59]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 3 10 8 1 7 5 4 2 9 20 21 22 15 14 16 12 11 13 24 25 23 19 18\
17|
==>
==> [60]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 4 10 9 1 6 5 3 2 8 23 24 25 16 14 15 13 11 12 21 22 20 18 19\
17|
==>
==> [61]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 8 5 9 3 1 4 6 10 7 18 17 19 13 11 12 21 22 20 14 16 15 24 23\
25|
==>
==> [62]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 9 5 8 4 1 3 7 10 6 19 17 18 12 11 13 24 25 23 14 15 16 21 20\
22|
==>
==> [63]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 8 2 9 6 1 7 3 10 4 19 17 18 16 14 15 22 21 20 11 13 12 25 23\
24|
==>
==> [64]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 9 2 8 7 1 6 4 10 3 18 17 19 15 14 16 25 24 23 11 12 13 22 20\
21|
==>
==> [65]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 8 6 10 2 1 4 5 9 7 21 20 22 13 12 11 18 19 17 15 16 14 25 23\
24|
==>
==> [66]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 9 7 10 2 1 3 5 8 6 24 23 25 12 13 11 19 18 17 16 15 14 22 20\
21|
==>
==> [67]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 10 6 8 4 1 2 7 9 5 22 20 21 11 12 13 25 24 23 15 14 16 18 17\
19|
==>
==> [68]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 10 7 9 3 1 2 6 8 5 25 23 24 11 13 12 22 21 20 16 14 15 19 17\
18|
==>
==> [69]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 8 3 10 5 1 7 2 9 4 22 20 21 16 15 14 19 18 17 12 13 11 24 23\
25|
==>
==> [70]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 9 4 10 5 1 6 2 8 3 25 23 24 15 16 14 18 19 17 13 12 11 21 20\
22|
==>
==> [71]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 10 3 8 7 1 5 4 9 2 21 20 22 14 15 16 24 25 23 12 11 13 19 17\
18|
==>
==> [72]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 10 4 9 6 1 5 3 8 2 24 23 25 14 16 15 21 22 20 13 11 12 18 17\
19|
==>
==> [73]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 8 9 5 3 4 1 10 6 7 18 19 17 13 12 11 21 20 22 24 23 25 14 16\
15|
==>
==> [74]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 2 9 8 5 4 3 1 10 7 6 19 18 17 12 13 11 24 23 25 21 20 22 14 15\
16|
==>
==> [75]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 8 9 2 6 7 1 10 3 4 19 18 17 16 15 14 22 20 21 25 23 24 11 13\
12|
==>
==> [76]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 5 9 8 2 7 6 1 10 4 3 18 19 17 15 16 14 25 23 24 22 20 21 11 12\
13|
==>
==> [77]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 8 10 6 2 4 1 9 5 7 21 22 20 13 11 12 18 17 19 25 23 24 15 16\
14|
==>
==> [78]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 9 10 7 2 3 1 8 5 6 24 25 23 12 11 13 19 17 18 22 20 21 16 15\
14|
==>
==> [79]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 3 10 8 6 4 2 1 9 7 5 22 21 20 11 13 12 25 23 24 18 17 19 15 14\
16|
==>
==> [80]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 4 10 9 7 3 2 1 8 6 5 25 24 23 11 12 13 22 20 21 19 17 18 16 14\
15|
==>
==> [81]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 8 10 3 5 7 1 9 2 4 22 21 20 16 14 15 19 17 18 24 23 25 12 13\
11|
==>
==> [82]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 9 10 4 5 6 1 8 2 3 25 24 23 15 14 16 18 17 19 21 20 22 13 12\
11|
==>
==> [83]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 6 10 8 3 7 5 1 9 4 2 21 22 20 14 16 15 24 23 25 19 17 18 12 11\
13|
==>
==> [84]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 7 10 9 4 6 5 1 8 3 2 24 25 23 14 15 16 21 20 22 18 17 19 13 11\
12|
==>
==> [85]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 2 5 9 3 6 10 1 4 7 18 19 17 21 22 20 13 11 12 16 14 15 23 24\
25|
==>
==> [86]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 2 5 8 4 7 10 1 3 6 19 18 17 24 25 23 12 11 13 15 14 16 20 21\
22|
==>
==> [87]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 5 2 9 6 3 10 1 7 4 19 18 17 22 21 20 16 14 15 13 11 12 23 25\
24|
==>
==> [88]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 5 2 8 7 4 10 1 6 3 18 19 17 25 24 23 15 14 16 12 11 13 20 22\
21|
==>
==> [89]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 3 6 10 2 5 9 1 4 7 21 22 20 18 19 17 13 12 11 16 15 14 23 25\
24|
==>
==> [90]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 4 7 10 2 5 8 1 3 6 24 25 23 19 18 17 12 13 11 15 16 14 20 22\
21|
==>
==> [91]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 6 3 10 5 2 9 1 7 4 22 21 20 19 18 17 16 15 14 13 12 11 23 24\
25|
==>
==> [92]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 7 4 10 5 2 8 1 6 3 25 24 23 18 19 17 15 16 14 12 13 11 20 21\
22|
==>
==> [93]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 3 6 8 4 7 9 1 2 5 22 21 20 25 24 23 11 12 13 14 15 16 17 18\
19|
==>
==> [94]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 4 7 9 3 6 8 1 2 5 25 24 23 22 21 20 11 13 12 14 16 15 17 19\
18|
==>
==> [95]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 6 3 8 7 4 9 1 5 2 21 22 20 24 25 23 14 15 16 11 12 13 17 19\
18|
==>
==> [96]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 7 4 9 6 3 8 1 5 2 24 25 23 21 22 20 14 16 15 11 13 12 17 18\
19|
==>
==> [97]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 2 9 5 3 10 6 4 1 7 18 17 19 21 20 22 13 12 11 23 24 25 16 14\
15|
==>
==> [98]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 2 8 5 4 10 7 3 1 6 19 17 18 24 23 25 12 13 11 20 21 22 15 14\
16|
==>
==> [99]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 5 9 2 6 10 3 7 1 4 19 17 18 22 20 21 16 15 14 23 25 24 13 11\
12|
==>
==> [100]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 5 8 2 7 10 4 6 1 3 18 17 19 25 23 24 15 16 14 20 22 21 12 11\
13|
==>
==> [101]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 3 10 6 2 9 5 4 1 7 21 20 22 18 17 19 13 11 12 23 25 24 16 15\
14|
==>
==> [102]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 4 10 7 2 8 5 3 1 6 24 23 25 19 17 18 12 11 13 20 22 21 15 16\
14|
==>
==> [103]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 6 10 3 5 9 2 7 1 4 22 20 21 19 17 18 16 14 15 23 24 25 13 12\
11|
==>
==> [104]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 7 10 4 5 8 2 6 1 3 25 23 24 18 17 19 15 14 16 20 21 22 12 13\
11|
==>
==> [105]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 3 8 6 4 9 7 2 1 5 22 20 21 25 23 24 11 13 12 17 18 19 14 15\
16|
==>
==> [106]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 4 9 7 3 8 6 2 1 5 25 23 24 22 20 21 11 12 13 17 19 18 14 16\
15|
==>
==> [107]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 6 8 3 7 9 4 5 1 2 21 20 22 24 23 25 14 16 15 17 19 18 11 12\
13|
==>
==> [108]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 7 9 4 6 8 3 5 1 2 24 23 25 21 20 22 14 15 16 17 18 19 11 13\
12|
==>
==> [109]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 9 2 5 10 3 6 4 7 1 17 18 19 20 21 22 23 24 25 13 12 11 16 15\
14|
==>
==> [110]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 8 2 5 10 4 7 3 6 1 17 19 18 23 24 25 20 21 22 12 13 11 15 16\
14|
==>
==> [111]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 9 5 2 10 6 3 7 4 1 17 19 18 20 22 21 23 25 24 16 15 14 13 12\
11|
==>
==> [112]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 8 5 2 10 7 4 6 3 1 17 18 19 23 25 24 20 22 21 15 16 14 12 13\
11|
==>
==> [113]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 10 3 6 9 2 5 4 7 1 20 21 22 17 18 19 23 25 24 13 11 12 16 14\
15|
==>
==> [114]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 10 4 7 8 2 5 3 6 1 23 24 25 17 19 18 20 22 21 12 11 13 15 14\
16|
==>
==> [115]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 8 10 6 3 9 5 2 7 4 1 20 22 21 17 19 18 23 24 25 16 14 15 13 11\
12|
==>
==> [116]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 9 10 7 4 8 5 2 6 3 1 23 25 24 17 18 19 20 21 22 15 14 16 12 11\
13|
==>
==> [117]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 8 3 6 9 4 7 2 5 1 20 22 21 23 25 24 17 18 19 11 13 12 14 16\
15|
==>
==> [118]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 9 4 7 8 3 6 2 5 1 23 25 24 20 22 21 17 19 18 11 12 13 14 15\
16|
==>
==> [119]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 8 6 3 9 7 4 5 2 1 20 21 22 23 24 25 17 19 18 14 16 15 11 13\
12|
==>
==> [120]:
==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\
24 25|
==> | 10 9 7 4 8 6 3 5 2 1 23 24 25 20 21 22 17 18 19 14 15 16 11 12\
13|
==>
|
|
Online Manual
