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D.13.3.18 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 representation 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|
==> 


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            User manual for Singular version 4.3.1, 2022, generated by texi2html.