1 | /* |
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2 | * gfan_symmetry.h |
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3 | * |
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4 | * Created on: Oct 22, 2010 |
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5 | * Author: anders |
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6 | */ |
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7 | |
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8 | #ifndef GFANLIB_SYMMETRY_H_INCLUDED |
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9 | #define GFANLIB_SYMMETRY_H_INCLUDED |
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10 | |
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11 | #include <set> |
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12 | #include "gfanlib_vector.h" |
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13 | #include "gfanlib_matrix.h" |
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14 | |
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15 | namespace gfan{ |
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16 | |
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17 | /** |
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18 | * The permutation class represents an element in the symmetric group S_n. |
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19 | */ |
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20 | class Permutation:public IntVector |
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21 | { |
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22 | // IntVector data; |
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23 | public: |
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24 | /** |
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25 | * Returns true if a contains the elements from 0 up to a.size()-1. |
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26 | */ |
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27 | static bool isPermutation(IntVector const &a); |
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28 | /** |
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29 | * Returns true if all rows of the matrix contains the elements 0 up to m.getWidth()-1. |
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30 | */ |
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31 | static bool arePermutations(IntMatrix const &m); |
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32 | /** |
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33 | * Generates the identity permutation on n elements. |
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34 | */ |
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35 | Permutation(int n): |
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36 | IntVector(n) |
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37 | { |
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38 | for(int i=0;i<n;i++)(*this)[i]=i; |
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39 | } |
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40 | /** |
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41 | * Generates a permutation from the vector v. The ith entry of v tells |
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42 | * If the check flag is set to true, then it is checked whether the vector represents |
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43 | * a permutation. If not, the code fails with an assertion. |
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44 | */ |
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45 | Permutation(IntVector const &v, bool check=true): |
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46 | IntVector(v) |
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47 | { |
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48 | if(check)assert(isPermutation(v)); |
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49 | } |
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50 | |
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51 | static Permutation transposition(int n, int i, int j) |
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52 | { |
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53 | IntVector ret(n); |
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54 | for(int k=0;k<n;k++)ret[k]=k; |
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55 | ret[i]=j; |
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56 | ret[j]=i; |
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57 | return Permutation(ret); |
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58 | } |
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59 | static Permutation cycle(int n) |
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60 | { |
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61 | IntVector a(n); |
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62 | for(int i=0;i<n-1;i++)a[i]=i+1; |
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63 | a[n-1]=0; |
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64 | return Permutation(a); |
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65 | } |
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66 | IntVector toIntVector()const |
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67 | { |
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68 | return IntVector(*this); |
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69 | } |
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70 | |
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71 | int sizeOfBaseSet()const |
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72 | { |
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73 | return size(); |
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74 | } |
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75 | Permutation inverse()const; |
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76 | |
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77 | /** |
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78 | * Apply the permutation |
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79 | */ |
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80 | Permutation apply(Permutation const &p)const; |
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81 | IntVector apply(IntVector const &v)const; |
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82 | ZVector apply(ZVector const &v)const; |
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83 | ZMatrix apply(ZMatrix const &m)const; |
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84 | Permutation applyInverse(Permutation const &p)const; |
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85 | IntVector applyInverse(IntVector const &v)const; |
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86 | ZVector applyInverse(ZVector const &v)const; |
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87 | ZMatrix applyInverse(ZMatrix const &m)const; |
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88 | |
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89 | /** |
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90 | The set of vectors which are not improved lexicographically when |
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91 | perm is applied to them is convex. Its closure is a |
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92 | halfspace. This routine returns the inner normal of this |
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93 | halfspace. The only exception is if perm is the identity then the |
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94 | zero vector is returned. |
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95 | */ |
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96 | ZVector fundamentalDomainInequality()const; |
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97 | }; |
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98 | |
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99 | /** |
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100 | * This object represents a subgroup of the symmetric group S_n. |
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101 | */ |
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102 | |
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103 | class SymmetryGroup{ |
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104 | int byteTableHeight; |
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105 | class Trie *trie; |
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106 | public: |
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107 | typedef std::set<Permutation/*,LexicographicTermOrder*/> ElementContainer; |
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108 | ElementContainer elements;//Make this private |
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109 | int size()const |
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110 | { |
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111 | return elements.size(); |
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112 | } |
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113 | int sizeOfBaseSet()const; |
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114 | /** |
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115 | The set of vectors which cannot be improved lexicographically by |
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116 | applying an element from the group is a convex set. Its closure |
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117 | is a polyhedral cone. This routine returns a set of inequalities |
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118 | The returned list does not contain the zero vector. |
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119 | */ |
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120 | ZMatrix fundamentalDomainInequalities()const; |
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121 | SymmetryGroup(int n); |
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122 | void computeClosure(Permutation const &v); |
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123 | void computeClosure(IntMatrix const &l); |
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124 | IntMatrix getGenerators()const; |
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125 | int orbitSize(ZVector const &stable)const; |
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126 | bool isTrivial()const; |
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127 | /** |
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128 | The symmetry group acts on vectors by permuting the entries. The |
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129 | following routine returns a unique representative for the orbit |
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130 | containing v. This makes it easy to check if two elements are in |
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131 | the same orbit. The permutation used to get this representative |
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132 | is stored in *usedPermutation (if pointer not 0). |
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133 | */ |
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134 | ZVector orbitRepresentative(ZVector const &v, Permutation *usedPermutation=0)const; |
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135 | /** |
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136 | This routine works as orbitRepresentative() except that the |
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137 | symmetry group considered is only the subgroup keeping the vector |
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138 | fixed fixed. |
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139 | */ |
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140 | ZVector orbitRepresentativeFixing(ZVector const &v, ZVector const &fixed)const; |
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141 | |
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142 | // Methods for highly optimized symmetry group computations: |
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143 | void createTrie(); |
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144 | }; |
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145 | /** |
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146 | * Sorts v and returns the number of swaps performed. |
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147 | */ |
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148 | int mergeSort(IntVector &v); |
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149 | } |
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150 | |
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151 | |
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152 | |
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153 | |
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154 | #endif /* GFAN_SYMMETRY_H_ */ |
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