1 | // -*- c++ -*- |
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2 | //***************************************************************************** |
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3 | /** @file cf_cyclo.cc |
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4 | * |
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5 | * @author Martin Lee |
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6 | * @date 29.01.2010 |
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7 | * |
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8 | * Compute cyclotomic polynomials and factorize integers by brute force |
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9 | * |
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10 | * @par Copyright: |
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11 | * (c) by The SINGULAR Team, see LICENSE file |
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12 | * |
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13 | **/ |
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14 | //***************************************************************************** |
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15 | |
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16 | #include "config.h" |
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17 | |
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18 | #include "canonicalform.h" |
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19 | #include "cf_primes.h" |
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20 | #include "cf_util.h" |
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21 | #include "cf_assert.h" |
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22 | |
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23 | #ifdef HAVE_NTL |
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24 | #include <NTL/ZZ.h> |
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25 | #endif |
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26 | |
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27 | |
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28 | /// integer factorization using table look-ups, |
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29 | /// function may fail if integer contains primes which exceed the largest prime |
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30 | /// in our table |
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31 | int* integerFactorizer (const long integer, int& length, bool& fail) |
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32 | { |
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33 | ASSERT (integer != 0 && integer != 1 && integer != -1, |
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34 | "non-zero non-unit expected"); |
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35 | int* result=NULL; |
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36 | length= 0; |
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37 | fail= false; |
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38 | int i= integer; |
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39 | if (integer < 0) |
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40 | i = -integer; |
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41 | |
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42 | int exp= 0; |
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43 | while ((i != 1) && (i%2 == 0)) |
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44 | { |
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45 | i /= 2; |
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46 | exp++; |
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47 | } |
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48 | if (exp != 0) |
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49 | { |
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50 | result= new int [exp]; |
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51 | for (int k= 0; k < exp; k++) |
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52 | result[k]= 2; |
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53 | length += exp; |
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54 | } |
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55 | if (i == 1) return result; |
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56 | |
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57 | long j= 0; |
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58 | exp= 0; |
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59 | int* buf; |
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60 | int next_prime; |
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61 | while ((i != 1) && (j < 31937)) |
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62 | { |
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63 | next_prime= cf_getPrime (j); |
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64 | while ((i != 1) && (i%next_prime == 0)) |
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65 | { |
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66 | i /= next_prime; |
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67 | exp++; |
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68 | } |
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69 | if (exp != 0) |
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70 | { |
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71 | buf= result; |
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72 | result= new int [length + exp]; |
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73 | for (int k= 0; k < length; k++) |
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74 | result [k]= buf[k]; |
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75 | for (int k= 0; k < exp; k++) |
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76 | result [k + length]= next_prime; |
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77 | length += exp; |
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78 | } |
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79 | exp= 0; |
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80 | j++; |
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81 | } |
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82 | if (j >= 31397) |
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83 | fail= true; |
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84 | ASSERT (j < 31397, "integer factorizer ran out of primes"); //sic |
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85 | return result; |
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86 | } |
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87 | |
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88 | /// make prime factorization distinct |
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89 | static inline |
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90 | int* makeDistinct (int* factors, const int factors_length, int& length) |
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91 | { |
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92 | length= 1; |
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93 | int* result= new int [length]; |
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94 | int* buf; |
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95 | result[0]= factors [0]; |
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96 | for (int i= 1; i < factors_length; i++) |
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97 | { |
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98 | if (factors[i - 1] != factors[i]) |
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99 | { |
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100 | buf= result; |
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101 | result= new int [length + 1]; |
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102 | for (int j= 0; j < length; j++) |
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103 | result[j]= buf [j]; |
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104 | result[length]= factors[i]; |
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105 | length++; |
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106 | } |
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107 | } |
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108 | return result; |
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109 | } |
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110 | |
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111 | /// compute the n-th cyclotomic polynomial, |
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112 | /// function may fail if integer_factorizer fails to factorize n |
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113 | CanonicalForm cyclotomicPoly (int n, bool& fail) |
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114 | { |
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115 | fail= false; |
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116 | Variable x= Variable (1); |
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117 | CanonicalForm result= x - 1; |
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118 | if (n == 1) |
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119 | return result; |
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120 | int* prime_factors; |
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121 | int prime_factors_length; |
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122 | int distinct_factors_length; |
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123 | prime_factors= integerFactorizer (n, prime_factors_length, fail); |
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124 | int* distinct_factors= makeDistinct (prime_factors, prime_factors_length, |
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125 | distinct_factors_length); |
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126 | if (fail) |
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127 | return 1; |
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128 | CanonicalForm buf; |
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129 | int prod= 1; |
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130 | for (int i= 0; i < distinct_factors_length; i++) |
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131 | { |
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132 | result= result (power (x, distinct_factors[i]), x)/result; |
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133 | prod *= distinct_factors[i]; |
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134 | } |
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135 | return result (power (x, n/prod), x); |
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136 | } |
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137 | |
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138 | #ifdef HAVE_NTL |
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139 | /// checks if alpha is a primitive element, alpha is assumed to be an algebraic |
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140 | /// variable over some finite prime field |
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141 | bool isPrimitive (const Variable& alpha, bool& fail) |
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142 | { |
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143 | int p= getCharacteristic(); |
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144 | CanonicalForm mipo= getMipo (alpha); |
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145 | int order= ipower(p, degree(mipo)) - 1; |
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146 | CanonicalForm cyclo= cyclotomicPoly (order, fail); |
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147 | if (fail) |
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148 | return false; |
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149 | if (mod(cyclo, mipo (Variable(1), alpha)) == 0) |
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150 | return true; |
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151 | else |
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152 | return false; |
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153 | } |
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154 | |
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155 | #endif |
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