1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file cfNewtonPolygon.cc |
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5 | * |
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6 | * This file provides functions to compute the Newton polygon of a bivariate |
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7 | * polynomial |
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8 | * |
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9 | * @author Martin Lee |
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10 | * |
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11 | **/ |
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12 | /*****************************************************************************/ |
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13 | |
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14 | |
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15 | #include "config.h" |
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16 | |
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17 | |
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18 | #include "cf_assert.h" |
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19 | |
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20 | #include <stdlib.h> |
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21 | |
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22 | #include "canonicalform.h" |
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23 | #include "cf_iter.h" |
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24 | #include "cf_algorithm.h" |
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25 | #include "cf_primes.h" |
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26 | #include "cf_reval.h" |
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27 | #include "cf_factory.h" |
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28 | #include "gfops.h" |
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29 | #include "cfNewtonPolygon.h" |
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30 | #include "templates/ftmpl_functions.h" |
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31 | |
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32 | static |
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33 | void translate (int** points, int* point, int sizePoints) //make point to 0 |
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34 | { |
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35 | for (int i= 0; i < sizePoints; i++) |
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36 | { |
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37 | points[i] [0] -= point [0]; |
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38 | points[i] [1] -= point [1]; |
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39 | } |
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40 | } |
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41 | |
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42 | static |
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43 | int smallestPointIndex (int** points, int sizePoints) |
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44 | { |
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45 | int min= 0; |
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46 | for (int i= 1; i < sizePoints; i++) |
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47 | { |
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48 | if (points[i][0] < points[min][0] || |
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49 | (points[i] [0] == points[min] [0] && points[i] [1] < points[min] [1])) |
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50 | min= i; |
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51 | } |
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52 | return min; |
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53 | } |
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54 | |
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55 | static |
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56 | void swap (int** points, int i, int j) |
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57 | { |
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58 | int* tmp= points[i]; |
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59 | points[i]= points[j]; |
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60 | points[j]= tmp; |
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61 | } |
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62 | |
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63 | static |
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64 | bool isLess (int* point1, int* point2) |
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65 | { |
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66 | long area= point1[0]*point2[1]- point1[1]*point2[0]; |
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67 | if (area > 0) return true; |
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68 | if (area == 0) |
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69 | { |
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70 | return (abs (point1[0]) + abs (point1[1]) > |
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71 | abs (point2[0]) + abs (point2[1])); |
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72 | } |
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73 | return false; |
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74 | } |
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75 | |
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76 | static |
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77 | void quickSort (int lo, int hi, int** points) |
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78 | { |
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79 | int i= lo, j= hi; |
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80 | int* point= new int [2]; |
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81 | point [0]= points [(lo+hi)/2] [0]; |
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82 | point [1]= points [(lo+hi)/2] [1]; |
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83 | while (i <= j) |
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84 | { |
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85 | while (isLess (points [i], point) && i < hi) i++; |
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86 | while (isLess (point, points[j]) && j > lo) j--; |
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87 | if (i <= j) |
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88 | { |
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89 | swap (points, i, j); |
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90 | i++; |
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91 | j--; |
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92 | } |
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93 | } |
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94 | delete [] point; |
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95 | if (lo < j) quickSort (lo, j, points); |
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96 | if (i < hi) quickSort (i, hi, points); |
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97 | } |
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98 | |
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99 | static |
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100 | void sort (int** points, int sizePoints) |
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101 | { |
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102 | quickSort (1, sizePoints - 1, points); |
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103 | } |
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104 | |
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105 | // check whether p2 is convex |
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106 | static |
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107 | bool isConvex (int* point1, int* point2, int* point3) |
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108 | { |
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109 | long relArea= (point1[0] - point2[0])*(point3[1] - point2[1]) - |
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110 | (point1[1] - point2[1])*(point3[0] - point2[0]); |
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111 | if (relArea < 0) |
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112 | return true; |
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113 | if (relArea == 0) |
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114 | { |
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115 | return !(abs (point1[0] - point3[0]) + abs (point1[1] - point3[1]) >= |
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116 | (abs (point2[0] - point1[0]) + abs (point2[1] - point1[1]) + |
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117 | abs (point2[0] - point3[0]) + abs (point2[1] - point3[1]))); |
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118 | } |
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119 | return false; |
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120 | } |
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121 | |
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122 | static |
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123 | bool isConvex (int** points, int i) |
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124 | { |
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125 | return isConvex (points[i - 1], points [i], points [i + 1]); |
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126 | } |
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127 | |
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128 | int grahamScan (int** points, int sizePoints) |
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129 | { |
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130 | swap (points, 0, smallestPointIndex (points, sizePoints)); |
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131 | int * minusPoint= new int [2]; |
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132 | minusPoint [0]= points[0] [0]; |
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133 | minusPoint [1]= points[0] [1]; |
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134 | translate (points, minusPoint, sizePoints); |
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135 | sort (points, sizePoints); |
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136 | minusPoint[0]= - minusPoint[0]; |
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137 | minusPoint[1]= - minusPoint[1]; |
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138 | translate (points, minusPoint, sizePoints); //reverse translation |
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139 | delete [] minusPoint; |
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140 | int i= 3, k= 3; |
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141 | while (k < sizePoints) |
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142 | { |
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143 | swap (points, i, k); |
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144 | while (!isConvex (points, i - 1)) |
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145 | { |
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146 | swap (points, i - 1, i); |
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147 | i--; |
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148 | } |
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149 | k++; |
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150 | i++; |
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151 | } |
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152 | if (i + 1 <= sizePoints || i == sizePoints) |
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153 | { |
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154 | long relArea= |
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155 | (points [i-2][0] - points [i-1][0])*(points [0][1] - points [i-1][1])- |
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156 | (points [i-2][1] - points [i-1][1])*(points [0][0] - points [i-1][0]); |
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157 | if (relArea == 0) |
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158 | { |
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159 | if (abs (points [i-2][0] - points [0][0]) + |
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160 | abs (points [i-2][1] - points [0][1]) >= |
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161 | abs (points [i-1][0] - points [i-2][0]) + |
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162 | abs (points [i-1][1] - points [i-2][1]) + |
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163 | abs (points [i-1][0] - points [0][0]) + |
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164 | abs (points [i-1][1] - points [0][1])) |
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165 | i--; |
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166 | } |
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167 | } |
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168 | return i; |
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169 | } |
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170 | |
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171 | //points[i] [0] is x-coordinate, points [i] [1] is y-coordinate |
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172 | int polygon (int** points, int sizePoints) |
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173 | { |
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174 | if (sizePoints < 3) return sizePoints; |
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175 | return grahamScan (points, sizePoints); |
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176 | } |
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177 | |
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178 | static |
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179 | int* getDegrees (const CanonicalForm& F, int& sizeOfOutput) |
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180 | { |
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181 | if (F.inCoeffDomain()) |
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182 | { |
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183 | int* result= new int [1]; |
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184 | result [0]= 0; |
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185 | sizeOfOutput= 1; |
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186 | return result; |
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187 | } |
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188 | sizeOfOutput= size (F); |
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189 | int* result= new int [sizeOfOutput]; |
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190 | int j= 0; |
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191 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
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192 | result [j]= i.exp(); |
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193 | return result; |
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194 | } |
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195 | |
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196 | //get points in Z^2 whose convex hull is the Newton polygon |
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197 | int ** getPoints (const CanonicalForm& F, int& n) |
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198 | { |
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199 | n= size (F); |
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200 | int ** points= new int* [n]; |
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201 | for (int i= 0; i < n; i++) |
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202 | points [i]= new int [2]; |
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203 | |
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204 | int j= 0; |
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205 | int * buf; |
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206 | int bufSize; |
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207 | if (F.isUnivariate() && F.level() == 1) |
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208 | { |
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209 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
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210 | { |
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211 | points [j] [0]= i.exp(); |
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212 | points [j] [1]= 0; |
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213 | } |
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214 | return points; |
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215 | } |
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216 | for (CFIterator i= F; i.hasTerms(); i++) |
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217 | { |
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218 | buf= getDegrees (i.coeff(), bufSize); |
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219 | for (int k= 0; k < bufSize; k++, j++) |
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220 | { |
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221 | points [j] [0]= i.exp(); |
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222 | points [j] [1]= buf [k]; |
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223 | } |
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224 | delete [] buf; |
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225 | } |
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226 | return points; |
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227 | } |
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228 | |
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229 | int ** |
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230 | merge (int ** points1, int sizePoints1, int ** points2, int sizePoints2, |
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231 | int& sizeResult) |
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232 | { |
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233 | int i, j; |
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234 | sizeResult= sizePoints1+sizePoints2; |
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235 | for (i= 0; i < sizePoints1; i++) |
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236 | { |
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237 | for (j= 0; j < sizePoints2; j++) |
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238 | { |
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239 | if (points1[i][0] != points2[j][0]) |
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240 | continue; |
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241 | else |
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242 | { |
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243 | if (points1[i][1] != points2[j][1]) |
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244 | continue; |
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245 | else |
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246 | { |
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247 | points2[j][0]= -1; |
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248 | points2[j][1]= -1; |
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249 | sizeResult--; |
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250 | } |
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251 | } |
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252 | } |
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253 | } |
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254 | if (sizeResult == 0) |
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255 | return points1; |
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256 | |
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257 | int ** result= new int *[sizeResult]; |
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258 | for (i= 0; i < sizeResult; i++) |
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259 | result [i]= new int [2]; |
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260 | |
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261 | int k= 0; |
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262 | for (i= 0; i < sizePoints1; i++, k++) |
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263 | { |
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264 | result[k][0]= points1[i][0]; |
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265 | result[k][1]= points1[i][1]; |
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266 | } |
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267 | for (i= 0; i < sizePoints2; i++) |
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268 | { |
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269 | if (points2[i][0] < 0) |
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270 | continue; |
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271 | else |
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272 | { |
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273 | result[k][0]= points2[i][0]; |
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274 | result[k][1]= points2[i][1]; |
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275 | k++; |
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276 | } |
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277 | } |
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278 | return result; |
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279 | } |
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280 | |
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281 | // assumes a bivariate poly as input |
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282 | int ** newtonPolygon (const CanonicalForm& F, int& sizeOfNewtonPoly) |
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283 | { |
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284 | int sizeF= size (F); |
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285 | int ** points= new int* [sizeF]; |
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286 | for (int i= 0; i < sizeF; i++) |
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287 | points [i]= new int [2]; |
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288 | int j= 0; |
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289 | int * buf; |
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290 | int bufSize; |
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291 | for (CFIterator i= F; i.hasTerms(); i++) |
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292 | { |
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293 | buf= getDegrees (i.coeff(), bufSize); |
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294 | for (int k= 0; k < bufSize; k++, j++) |
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295 | { |
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296 | points [j] [0]= i.exp(); |
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297 | points [j] [1]= buf [k]; |
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298 | } |
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299 | delete [] buf; |
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300 | } |
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301 | |
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302 | int n= polygon (points, sizeF); |
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303 | |
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304 | int ** result= new int* [n]; |
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305 | for (int i= 0; i < n; i++) |
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306 | { |
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307 | result [i]= new int [2]; |
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308 | result [i] [0]= points [i] [0]; |
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309 | result [i] [1]= points [i] [1]; |
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310 | } |
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311 | |
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312 | sizeOfNewtonPoly= n; |
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313 | for (int i= 0; i < sizeF; i++) |
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314 | delete [] points[i]; |
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315 | delete [] points; |
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316 | |
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317 | return result; |
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318 | } |
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319 | |
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320 | // assumes a bivariate polys as input |
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321 | int ** newtonPolygon (const CanonicalForm& F, const CanonicalForm& G, |
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322 | int& sizeOfNewtonPoly) |
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323 | { |
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324 | int sizeF= size (F); |
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325 | int ** pointsF= new int* [sizeF]; |
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326 | for (int i= 0; i < sizeF; i++) |
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327 | pointsF [i]= new int [2]; |
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328 | int j= 0; |
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329 | int * buf; |
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330 | int bufSize; |
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331 | for (CFIterator i= F; i.hasTerms(); i++) |
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332 | { |
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333 | buf= getDegrees (i.coeff(), bufSize); |
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334 | for (int k= 0; k < bufSize; k++, j++) |
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335 | { |
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336 | pointsF [j] [0]= i.exp(); |
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337 | pointsF [j] [1]= buf [k]; |
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338 | } |
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339 | delete [] buf; |
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340 | } |
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341 | |
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342 | int sizeG= size (G); |
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343 | int ** pointsG= new int* [sizeG]; |
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344 | for (int i= 0; i < sizeG; i++) |
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345 | pointsG [i]= new int [2]; |
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346 | j= 0; |
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347 | for (CFIterator i= G; i.hasTerms(); i++) |
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348 | { |
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349 | buf= getDegrees (i.coeff(), bufSize); |
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350 | for (int k= 0; k < bufSize; k++, j++) |
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351 | { |
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352 | pointsG [j] [0]= i.exp(); |
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353 | pointsG [j] [1]= buf [k]; |
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354 | } |
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355 | delete [] buf; |
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356 | } |
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357 | |
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358 | int sizePoints; |
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359 | int ** points= merge (pointsF, sizeF, pointsG, sizeG, sizePoints); |
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360 | |
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361 | int n= polygon (points, sizePoints); |
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362 | |
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363 | int ** result= new int* [n]; |
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364 | for (int i= 0; i < n; i++) |
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365 | { |
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366 | result [i]= new int [2]; |
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367 | result [i] [0]= points [i] [0]; |
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368 | result [i] [1]= points [i] [1]; |
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369 | } |
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370 | |
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371 | sizeOfNewtonPoly= n; |
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372 | for (int i= 0; i < sizeF; i++) |
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373 | delete [] pointsF[i]; |
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374 | delete [] pointsF; |
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375 | for (int i= 0; i < sizeG; i++) |
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376 | delete [] pointsG[i]; |
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377 | delete [] pointsG; |
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378 | |
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379 | return result; |
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380 | } |
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381 | |
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382 | // assumes first sizePoints entries of points form a Newton polygon |
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383 | bool isInPolygon (int ** points, int sizePoints, int* point) |
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384 | { |
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385 | int ** buf= new int* [sizePoints + 1]; |
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386 | for (int i= 0; i < sizePoints; i++) |
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387 | { |
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388 | buf [i]= new int [2]; |
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389 | buf [i] [0]= points [i] [0]; |
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390 | buf [i] [1]= points [i] [1]; |
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391 | } |
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392 | buf [sizePoints]= new int [2]; |
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393 | buf [sizePoints] [0]= point [0]; |
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394 | buf [sizePoints] [1]= point [1]; |
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395 | int sizeBuf= sizePoints + 1; |
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396 | |
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397 | swap (buf, 0, smallestPointIndex (buf, sizeBuf)); |
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398 | int * minusPoint= new int [2]; |
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399 | minusPoint [0]= buf[0] [0]; |
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400 | minusPoint [1]= buf[0] [1]; |
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401 | translate (buf, minusPoint, sizeBuf); |
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402 | sort (buf, sizeBuf); |
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403 | minusPoint[0]= - minusPoint[0]; |
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404 | minusPoint[1]= - minusPoint[1]; |
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405 | translate (buf, minusPoint, sizeBuf); //reverse translation |
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406 | delete [] minusPoint; |
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407 | |
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408 | if (buf [0] [0] == point [0] && buf [0] [1] == point [1]) |
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409 | { |
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410 | for (int i= 0; i < sizeBuf; i++) |
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411 | delete [] buf[i]; |
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412 | delete [] buf; |
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413 | return false; |
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414 | } |
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415 | |
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416 | for (int i= 1; i < sizeBuf-1; i++) |
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417 | { |
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418 | if (buf [i] [0] == point [0] && buf [i] [1] == point [1]) |
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419 | { |
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420 | bool result= !isConvex (buf, i); |
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421 | for (int i= 0; i < sizeBuf; i++) |
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422 | delete [] buf [i]; |
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423 | delete [] buf; |
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424 | return result; |
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425 | } |
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426 | } |
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427 | |
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428 | if (buf [sizeBuf - 1] [0] == point [0] && buf [sizeBuf-1] [1] == point [1]) |
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429 | { |
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430 | buf [1] [0]= point [0]; |
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431 | buf [1] [1]= point [1]; |
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432 | buf [2] [0]= buf [0] [0]; |
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433 | buf [2] [1]= buf [0] [1]; |
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434 | buf [0] [0]= buf [sizeBuf-2] [0]; |
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435 | buf [0] [1]= buf [sizeBuf-2] [1]; |
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436 | bool result= !isConvex (buf, 1); |
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437 | for (int i= 0; i < sizeBuf; i++) |
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438 | delete [] buf [i]; |
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439 | delete [] buf; |
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440 | return result; |
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441 | } |
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442 | for (int i= 0; i < sizeBuf; i++) |
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443 | delete [] buf [i]; |
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444 | delete [] buf; |
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445 | |
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446 | return false; |
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447 | } |
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448 | |
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449 | void lambda (int** points, int sizePoints) |
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450 | { |
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451 | for (int i= 0; i < sizePoints; i++) |
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452 | points [i] [1]= points [i] [1] - points [i] [0]; |
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453 | } |
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454 | |
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455 | void lambdaInverse (int** points, int sizePoints) |
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456 | { |
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457 | for (int i= 0; i < sizePoints; i++) |
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458 | points [i] [1]= points [i] [1] + points [i] [0]; |
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459 | } |
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460 | |
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461 | void tau (int** points, int sizePoints, int k) |
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462 | { |
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463 | for (int i= 0; i < sizePoints; i++) |
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464 | points [i] [1]= points [i] [1] + k; |
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465 | } |
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466 | |
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467 | void mu (int** points, int sizePoints) |
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468 | { |
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469 | int tmp; |
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470 | for (int i= 0; i < sizePoints; i++) |
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471 | { |
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472 | tmp= points [i] [0]; |
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473 | points [i] [0]= points [i] [1]; |
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474 | points [i] [1]= tmp; |
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475 | } |
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476 | } |
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477 | |
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478 | void getMaxMin (int** points, int sizePoints, int& minDiff, int& minSum, |
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479 | int& maxDiff, int& maxSum, int& maxX, int& maxY |
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480 | ) |
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481 | { |
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482 | minDiff= points [0] [1] - points [0] [0]; |
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483 | minSum= points [0] [1] + points [0] [0]; |
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484 | maxDiff= points [0] [1] - points [0] [0]; |
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485 | maxSum= points [0] [1] + points [0] [0]; |
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486 | maxX= points [0] [1]; |
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487 | maxY= points [0] [0]; |
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488 | int diff, sum; |
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489 | for (int i= 1; i < sizePoints; i++) |
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490 | { |
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491 | diff= points [i] [1] - points [i] [0]; |
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492 | sum= points [i] [1] + points [i] [0]; |
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493 | minDiff= tmin (minDiff, diff); |
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494 | minSum= tmin (minSum, sum); |
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495 | maxDiff= tmax (maxDiff, diff); |
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496 | maxSum= tmax (maxSum, sum); |
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497 | maxX= tmax (maxX, points [i] [1]); |
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498 | maxY= tmax (maxY, points [i] [0]); |
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499 | } |
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500 | } |
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501 | |
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502 | void mpz_mat_mul (const mpz_t* N, mpz_t*& M) |
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503 | { |
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504 | mpz_t * tmp= new mpz_t[4]; |
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505 | |
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506 | mpz_init_set (tmp[0], N[0]); |
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507 | mpz_mul (tmp[0], tmp[0], M[0]); |
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508 | mpz_addmul (tmp[0], N[1], M[2]); |
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509 | |
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510 | mpz_init_set (tmp[1], N[0]); |
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511 | mpz_mul (tmp[1], tmp[1], M[1]); |
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512 | mpz_addmul (tmp[1], N[1], M[3]); |
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513 | |
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514 | mpz_init_set (tmp[2], N[2]); |
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515 | mpz_mul (tmp[2], tmp[2], M[0]); |
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516 | mpz_addmul (tmp[2], N[3], M[2]); |
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517 | |
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518 | mpz_init_set (tmp[3], N[2]); |
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519 | mpz_mul (tmp[3], tmp[3], M[1]); |
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520 | mpz_addmul (tmp[3], N[3], M[3]); |
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521 | |
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522 | mpz_set (M[0], tmp[0]); |
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523 | mpz_set (M[1], tmp[1]); |
---|
524 | mpz_set (M[2], tmp[2]); |
---|
525 | mpz_set (M[3], tmp[3]); |
---|
526 | |
---|
527 | mpz_clear (tmp[0]); |
---|
528 | mpz_clear (tmp[1]); |
---|
529 | mpz_clear (tmp[2]); |
---|
530 | mpz_clear (tmp[3]); |
---|
531 | |
---|
532 | delete [] tmp; |
---|
533 | } |
---|
534 | |
---|
535 | void mpz_mat_inv (mpz_t*& M) |
---|
536 | { |
---|
537 | mpz_t det; |
---|
538 | mpz_init_set (det, M[0]); |
---|
539 | mpz_mul (det, det, M[3]); |
---|
540 | mpz_submul (det, M[1], M[2]); |
---|
541 | |
---|
542 | mpz_t tmp; |
---|
543 | mpz_init_set (tmp, M[0]); |
---|
544 | mpz_divexact (tmp, tmp, det); |
---|
545 | mpz_set (M[0], M[3]); |
---|
546 | mpz_divexact (M[0], M[0], det); |
---|
547 | mpz_set (M[3], tmp); |
---|
548 | |
---|
549 | mpz_neg (M[1], M[1]); |
---|
550 | mpz_divexact (M[1], M[1], det); |
---|
551 | mpz_neg (M[2], M[2]); |
---|
552 | mpz_divexact (M[2], M[2], det); |
---|
553 | |
---|
554 | mpz_clear (det); |
---|
555 | mpz_clear (tmp); |
---|
556 | } |
---|
557 | |
---|
558 | void convexDense(int** points, int sizePoints, mpz_t*& M, mpz_t*& A) |
---|
559 | { |
---|
560 | if (sizePoints < 3) |
---|
561 | { |
---|
562 | if (sizePoints == 2) |
---|
563 | { |
---|
564 | mpz_t u,v,g,maxX,maxY; |
---|
565 | mpz_init (u); |
---|
566 | mpz_init (v); |
---|
567 | mpz_init (g); |
---|
568 | mpz_init_set_si (maxX, |
---|
569 | (points[1][1] < points[0][1])?points[0][1]:points[1][1]); |
---|
570 | mpz_init_set_si (maxY, |
---|
571 | (points[1][0] < points[0][0])?points[0][0]:points[1][0]); |
---|
572 | mpz_gcdext (g, u, v, maxX, maxY); |
---|
573 | if (points [0] [1] != points [0] [0] && points [1] [0] != points [1] [1]) |
---|
574 | { |
---|
575 | mpz_set (A[0], u); |
---|
576 | mpz_mul (A[0], A[0], maxX); |
---|
577 | mpz_set (M[2], maxY); |
---|
578 | mpz_divexact (M[2], M[2], g); |
---|
579 | mpz_set (A[1], M[2]); |
---|
580 | mpz_neg (A[1], A[1]); |
---|
581 | mpz_mul (A[1], A[1], maxX); |
---|
582 | mpz_neg (u, u); |
---|
583 | mpz_set (M[0], u); |
---|
584 | mpz_set (M[1], v); |
---|
585 | mpz_set (M[3], maxX); |
---|
586 | mpz_divexact (M[3], M[3], g); |
---|
587 | } |
---|
588 | else |
---|
589 | { |
---|
590 | mpz_set (M[0], u); |
---|
591 | mpz_set (M[1], v); |
---|
592 | mpz_set (M[2], maxY); |
---|
593 | mpz_divexact (M[2], M[2], g); |
---|
594 | mpz_neg (M[2], M[2]); |
---|
595 | mpz_set (M[3], maxX); |
---|
596 | mpz_divexact (M[3], M[3], g); |
---|
597 | } |
---|
598 | mpz_clear (u); |
---|
599 | mpz_clear (v); |
---|
600 | mpz_clear (g); |
---|
601 | mpz_clear (maxX); |
---|
602 | mpz_clear (maxY); |
---|
603 | } |
---|
604 | else if (sizePoints == 1) |
---|
605 | { |
---|
606 | mpz_set_si (M[0], 1); |
---|
607 | mpz_set_si (M[3], 1); |
---|
608 | } |
---|
609 | return; |
---|
610 | } |
---|
611 | mpz_set_si (M[0], 1); |
---|
612 | mpz_set_si (M[3], 1); |
---|
613 | |
---|
614 | mpz_t * Mu= new mpz_t[4]; |
---|
615 | mpz_init_set_si (Mu[1], 1); |
---|
616 | mpz_init_set_si (Mu[2], 1); |
---|
617 | mpz_init (Mu[0]); |
---|
618 | mpz_init (Mu[3]); |
---|
619 | |
---|
620 | mpz_t * Lambda= new mpz_t[4]; |
---|
621 | mpz_init_set_si (Lambda[0], 1); |
---|
622 | mpz_init_set_si (Lambda[1], -1); |
---|
623 | mpz_init_set_si (Lambda[3], 1); |
---|
624 | mpz_init (Lambda[2]); |
---|
625 | |
---|
626 | mpz_t * InverseLambda= new mpz_t[4]; |
---|
627 | mpz_init_set_si (InverseLambda[0], 1); |
---|
628 | mpz_init_set_si (InverseLambda[1], 1); |
---|
629 | mpz_init_set_si (InverseLambda[3], 1); |
---|
630 | mpz_init (InverseLambda[2]); |
---|
631 | |
---|
632 | mpz_t tmp; |
---|
633 | mpz_init (tmp); |
---|
634 | int minDiff, minSum, maxDiff, maxSum, maxX, maxY, b, d, f, h; |
---|
635 | getMaxMin(points, sizePoints, minDiff, minSum, maxDiff, maxSum, maxX, maxY); |
---|
636 | do |
---|
637 | { |
---|
638 | if (maxX < maxY) |
---|
639 | { |
---|
640 | mu (points, sizePoints); |
---|
641 | |
---|
642 | mpz_mat_mul (Mu, M); |
---|
643 | |
---|
644 | mpz_set (tmp, A[0]); |
---|
645 | mpz_set (A[0], A[1]); |
---|
646 | mpz_set (A[1], tmp); |
---|
647 | } |
---|
648 | getMaxMin(points, sizePoints, minDiff, minSum, maxDiff, maxSum, maxX, maxY); |
---|
649 | b= maxX - maxDiff; |
---|
650 | d= maxX + maxY - maxSum; |
---|
651 | f= maxY + minDiff; |
---|
652 | h= minSum; |
---|
653 | if (b + f > maxY) |
---|
654 | { |
---|
655 | lambda (points, sizePoints); |
---|
656 | tau (points, sizePoints, maxY - f); |
---|
657 | |
---|
658 | mpz_mat_mul (Lambda, M); |
---|
659 | |
---|
660 | if (maxY-f > 0) |
---|
661 | mpz_add_ui (A[0], A[0], maxY-f); |
---|
662 | else |
---|
663 | mpz_add_ui (A[0], A[0], f-maxY); |
---|
664 | maxX= maxX + maxY - b - f; |
---|
665 | } |
---|
666 | else if (d + h > maxY) |
---|
667 | { |
---|
668 | lambdaInverse (points, sizePoints); |
---|
669 | tau (points, sizePoints, -h); |
---|
670 | |
---|
671 | mpz_mat_mul (InverseLambda, M); |
---|
672 | |
---|
673 | if (h < 0) |
---|
674 | mpz_add_ui (A[0], A[0], -h); |
---|
675 | else |
---|
676 | mpz_sub_ui (A[0], A[0], h); |
---|
677 | maxX= maxX + maxY - d - h; |
---|
678 | } |
---|
679 | else |
---|
680 | { |
---|
681 | mpz_clear (tmp); |
---|
682 | mpz_clear (Mu[0]); |
---|
683 | mpz_clear (Mu[1]); |
---|
684 | mpz_clear (Mu[2]); |
---|
685 | mpz_clear (Mu[3]); |
---|
686 | delete [] Mu; |
---|
687 | |
---|
688 | mpz_clear (Lambda[0]); |
---|
689 | mpz_clear (Lambda[1]); |
---|
690 | mpz_clear (Lambda[2]); |
---|
691 | mpz_clear (Lambda[3]); |
---|
692 | delete [] Lambda; |
---|
693 | |
---|
694 | mpz_clear (InverseLambda[0]); |
---|
695 | mpz_clear (InverseLambda[1]); |
---|
696 | mpz_clear (InverseLambda[2]); |
---|
697 | mpz_clear (InverseLambda[3]); |
---|
698 | delete [] InverseLambda; |
---|
699 | |
---|
700 | return; |
---|
701 | } |
---|
702 | } while (1); |
---|
703 | } |
---|
704 | |
---|
705 | CanonicalForm |
---|
706 | compress (const CanonicalForm& F, mpz_t*& M, mpz_t*& A, bool computeMA) |
---|
707 | { |
---|
708 | int n; |
---|
709 | int ** newtonPolyg= NULL; |
---|
710 | if (computeMA) |
---|
711 | { |
---|
712 | newtonPolyg= newtonPolygon (F, n); |
---|
713 | convexDense (newtonPolyg, n, M, A); |
---|
714 | } |
---|
715 | |
---|
716 | CanonicalForm result= 0; |
---|
717 | Variable x= Variable (1); |
---|
718 | Variable y= Variable (2); |
---|
719 | |
---|
720 | mpz_t expX, expY, minExpX, minExpY; |
---|
721 | mpz_init (expX); |
---|
722 | mpz_init (expY); |
---|
723 | mpz_init (minExpX); |
---|
724 | mpz_init (minExpY); |
---|
725 | |
---|
726 | int k= 0; |
---|
727 | Variable alpha; |
---|
728 | mpz_t * exps= new mpz_t [2*size (F)]; |
---|
729 | int exps_maxcount=0; |
---|
730 | int count= 0; |
---|
731 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
732 | { |
---|
733 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
734 | { |
---|
735 | mpz_set (expX, A[0]); |
---|
736 | mpz_set (expY, A[1]); |
---|
737 | mpz_addmul_ui (expX, M[1], i.exp()); |
---|
738 | mpz_addmul_ui (expY, M[3], i.exp()); |
---|
739 | |
---|
740 | if (k == 0) |
---|
741 | { |
---|
742 | mpz_set (minExpX, expX); |
---|
743 | mpz_set (minExpY, expY); |
---|
744 | k= 1; |
---|
745 | } |
---|
746 | else |
---|
747 | { |
---|
748 | if (mpz_cmp (minExpY, expY) > 0) |
---|
749 | mpz_set (minExpY, expY); |
---|
750 | if (mpz_cmp (minExpX, expX) > 0) |
---|
751 | mpz_set (minExpX, expX); |
---|
752 | } |
---|
753 | mpz_init_set (exps[count], expX); |
---|
754 | count++; |
---|
755 | mpz_init_set (exps[count], expY); |
---|
756 | exps_maxcount=count; |
---|
757 | count++; |
---|
758 | continue; |
---|
759 | } |
---|
760 | CFIterator j= i.coeff(); |
---|
761 | if (k == 0) |
---|
762 | { |
---|
763 | mpz_set (expX, A[0]); |
---|
764 | mpz_addmul_ui (expX, M[1], i.exp()); |
---|
765 | mpz_addmul_ui (expX, M[0], j.exp()); |
---|
766 | |
---|
767 | mpz_set (expY, A[1]); |
---|
768 | mpz_addmul_ui (expY, M[3], i.exp()); |
---|
769 | mpz_addmul_ui (expY, M[2], j.exp()); |
---|
770 | |
---|
771 | mpz_set (minExpX, expX); |
---|
772 | mpz_set (minExpY, expY); |
---|
773 | mpz_init_set (exps[count], expX); |
---|
774 | count++; |
---|
775 | mpz_init_set (exps[count], expY); |
---|
776 | exps_maxcount=count; |
---|
777 | count++; |
---|
778 | j++; |
---|
779 | k= 1; |
---|
780 | } |
---|
781 | |
---|
782 | for (; j.hasTerms(); j++) |
---|
783 | { |
---|
784 | mpz_set (expX, A[0]); |
---|
785 | mpz_addmul_ui (expX, M[1], i.exp()); |
---|
786 | mpz_addmul_ui (expX, M[0], j.exp()); |
---|
787 | |
---|
788 | mpz_set (expY, A[1]); |
---|
789 | mpz_addmul_ui (expY, M[3], i.exp()); |
---|
790 | mpz_addmul_ui (expY, M[2], j.exp()); |
---|
791 | |
---|
792 | mpz_init_set (exps[count], expX); |
---|
793 | count++; |
---|
794 | mpz_init_set (exps[count], expY); |
---|
795 | exps_maxcount=count; |
---|
796 | count++; |
---|
797 | if (mpz_cmp (minExpY, expY) > 0) |
---|
798 | mpz_set (minExpY, expY); |
---|
799 | if (mpz_cmp (minExpX, expX) > 0) |
---|
800 | mpz_set (minExpX, expX); |
---|
801 | } |
---|
802 | } |
---|
803 | |
---|
804 | count= 0; |
---|
805 | int mExpX= mpz_get_si (minExpX); |
---|
806 | int mExpY= mpz_get_si (minExpY); |
---|
807 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
808 | { |
---|
809 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
810 | { |
---|
811 | result += i.coeff()*power (x, mpz_get_si (exps[count])-mExpX)* |
---|
812 | power (y, mpz_get_si (exps[count+1])-mExpY); |
---|
813 | count += 2; |
---|
814 | continue; |
---|
815 | } |
---|
816 | CFIterator j= i.coeff(); |
---|
817 | for (; j.hasTerms(); j++) |
---|
818 | { |
---|
819 | result += j.coeff()*power (x, mpz_get_si (exps[count])-mExpX)* |
---|
820 | power (y, mpz_get_si (exps[count+1])-mExpY); |
---|
821 | count += 2; |
---|
822 | } |
---|
823 | } |
---|
824 | |
---|
825 | CanonicalForm tmp= LC (result); |
---|
826 | if (tmp.inPolyDomain() && degree (tmp) <= 0) |
---|
827 | { |
---|
828 | int d= degree (result); |
---|
829 | Variable x= result.mvar(); |
---|
830 | result -= tmp*power (x, d); |
---|
831 | result += Lc (tmp)*power (x, d); |
---|
832 | } |
---|
833 | |
---|
834 | if (computeMA) |
---|
835 | { |
---|
836 | for (int i= 0; i < n; i++) |
---|
837 | delete [] newtonPolyg [i]; |
---|
838 | delete [] newtonPolyg; |
---|
839 | mpz_mat_inv (M); |
---|
840 | } |
---|
841 | |
---|
842 | for(int tt=exps_maxcount;tt>=0;tt--) mpz_clear(exps[tt]); |
---|
843 | delete [] exps; |
---|
844 | mpz_clear (expX); |
---|
845 | mpz_clear (expY); |
---|
846 | mpz_clear (minExpX); |
---|
847 | mpz_clear (minExpY); |
---|
848 | |
---|
849 | return result; |
---|
850 | } |
---|
851 | |
---|
852 | CanonicalForm |
---|
853 | decompress (const CanonicalForm& F, const mpz_t* inverseM, const mpz_t * A) |
---|
854 | { |
---|
855 | CanonicalForm result= 0; |
---|
856 | Variable x= Variable (1); |
---|
857 | Variable y= Variable (2); |
---|
858 | |
---|
859 | mpz_t expX, expY, minExpX, minExpY; |
---|
860 | mpz_init (expX); |
---|
861 | mpz_init (expY); |
---|
862 | mpz_init (minExpX); |
---|
863 | mpz_init (minExpY); |
---|
864 | |
---|
865 | mpz_t * exps= new mpz_t [2*size(F)]; |
---|
866 | int max_exps=0; |
---|
867 | int count= 0; |
---|
868 | if (F.isUnivariate() && F.level() == 1) |
---|
869 | { |
---|
870 | CFIterator i= F; |
---|
871 | |
---|
872 | mpz_set_si (expX, i.exp()); |
---|
873 | mpz_sub (expX, expX, A[0]); |
---|
874 | mpz_mul (expX, expX, inverseM[0]); |
---|
875 | mpz_submul (expX, inverseM[1], A[1]); |
---|
876 | |
---|
877 | mpz_set_si (expY, i.exp()); |
---|
878 | mpz_sub (expY, expY, A[0]); |
---|
879 | mpz_mul (expY, expY, inverseM[2]); |
---|
880 | mpz_submul (expY, inverseM[3], A[1]); |
---|
881 | |
---|
882 | mpz_set (minExpX, expX); |
---|
883 | mpz_set (minExpY, expY); |
---|
884 | |
---|
885 | mpz_init_set (exps[count], expX); |
---|
886 | count++; |
---|
887 | mpz_init_set (exps[count], expY); |
---|
888 | count++; |
---|
889 | max_exps=count; |
---|
890 | |
---|
891 | i++; |
---|
892 | for (; i.hasTerms(); i++) |
---|
893 | { |
---|
894 | mpz_set_si (expX, i.exp()); |
---|
895 | mpz_sub (expX, expX, A[0]); |
---|
896 | mpz_mul (expX, expX, inverseM[0]); |
---|
897 | mpz_submul (expX, inverseM[1], A[1]); |
---|
898 | |
---|
899 | mpz_set_si (expY, i.exp()); |
---|
900 | mpz_sub (expY, expY, A[0]); |
---|
901 | mpz_mul (expY, expY, inverseM[2]); |
---|
902 | mpz_submul (expY, inverseM[3], A[1]); |
---|
903 | |
---|
904 | mpz_init_set (exps[count], expX); |
---|
905 | count++; |
---|
906 | mpz_init_set (exps[count], expY); |
---|
907 | max_exps=count; |
---|
908 | count++; |
---|
909 | |
---|
910 | if (mpz_cmp (minExpY, expY) > 0) |
---|
911 | mpz_set (minExpY, expY); |
---|
912 | if (mpz_cmp (minExpX, expX) > 0) |
---|
913 | mpz_set (minExpX, expX); |
---|
914 | } |
---|
915 | |
---|
916 | int mExpX= mpz_get_si (minExpX); |
---|
917 | int mExpY= mpz_get_si (minExpY); |
---|
918 | count= 0; |
---|
919 | for (i= F; i.hasTerms(); i++) |
---|
920 | { |
---|
921 | result += i.coeff()*power (x, mpz_get_si (exps[count])-mExpX)* |
---|
922 | power (y, mpz_get_si (exps[count+1])-mExpY); |
---|
923 | max_exps=count+1; |
---|
924 | count += 2; |
---|
925 | } |
---|
926 | |
---|
927 | mpz_clear (expX); |
---|
928 | mpz_clear (expY); |
---|
929 | mpz_clear (minExpX); |
---|
930 | mpz_clear (minExpY); |
---|
931 | |
---|
932 | for(int tt=max_exps;tt>=0;tt--) mpz_clear(exps[tt]); |
---|
933 | delete [] exps; |
---|
934 | return result/ Lc (result); //normalize |
---|
935 | } |
---|
936 | |
---|
937 | mpz_t tmp; |
---|
938 | mpz_init (tmp); |
---|
939 | int k= 0; |
---|
940 | Variable alpha; |
---|
941 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
942 | { |
---|
943 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
944 | { |
---|
945 | mpz_set_si (expX, i.exp()); |
---|
946 | mpz_sub (expX, expX, A[1]); |
---|
947 | mpz_mul (expX, expX, inverseM[1]); |
---|
948 | mpz_submul (expX, A[0], inverseM[0]); |
---|
949 | |
---|
950 | mpz_set_si (expY, i.exp()); |
---|
951 | mpz_sub (expY, expY, A[1]); |
---|
952 | mpz_mul (expY, expY, inverseM[3]); |
---|
953 | mpz_submul (expY, A[0], inverseM[2]); |
---|
954 | |
---|
955 | if (k == 0) |
---|
956 | { |
---|
957 | mpz_set (minExpX, expX); |
---|
958 | mpz_set (minExpY, expY); |
---|
959 | k= 1; |
---|
960 | } |
---|
961 | else |
---|
962 | { |
---|
963 | if (mpz_cmp (minExpY, expY) > 0) |
---|
964 | mpz_set (minExpY, expY); |
---|
965 | if (mpz_cmp (minExpX, expX) > 0) |
---|
966 | mpz_set (minExpX, expX); |
---|
967 | } |
---|
968 | mpz_init_set (exps[count], expX); |
---|
969 | count++; |
---|
970 | mpz_init_set (exps[count], expY); |
---|
971 | max_exps=count; |
---|
972 | count++; |
---|
973 | continue; |
---|
974 | } |
---|
975 | CFIterator j= i.coeff(); |
---|
976 | if (k == 0) |
---|
977 | { |
---|
978 | mpz_set_si (expX, j.exp()); |
---|
979 | mpz_sub (expX, expX, A[0]); |
---|
980 | mpz_mul (expX, expX, inverseM[0]); |
---|
981 | mpz_set_si (tmp, i.exp()); |
---|
982 | mpz_sub (tmp, tmp, A[1]); |
---|
983 | mpz_addmul (expX, tmp, inverseM[1]); |
---|
984 | |
---|
985 | mpz_set_si (expY, j.exp()); |
---|
986 | mpz_sub (expY, expY, A[0]); |
---|
987 | mpz_mul (expY, expY, inverseM[2]); |
---|
988 | mpz_set_si (tmp, i.exp()); |
---|
989 | mpz_sub (tmp, tmp, A[1]); |
---|
990 | mpz_addmul (expY, tmp, inverseM[3]); |
---|
991 | |
---|
992 | mpz_set (minExpX, expX); |
---|
993 | mpz_set (minExpY, expY); |
---|
994 | |
---|
995 | mpz_init_set (exps[count], expX); |
---|
996 | count++; |
---|
997 | mpz_init_set (exps[count], expY); |
---|
998 | max_exps=count; |
---|
999 | count++; |
---|
1000 | |
---|
1001 | j++; |
---|
1002 | k= 1; |
---|
1003 | } |
---|
1004 | |
---|
1005 | for (; j.hasTerms(); j++) |
---|
1006 | { |
---|
1007 | mpz_set_si (expX, j.exp()); |
---|
1008 | mpz_sub (expX, expX, A[0]); |
---|
1009 | mpz_mul (expX, expX, inverseM[0]); |
---|
1010 | mpz_set_si (tmp, i.exp()); |
---|
1011 | mpz_sub (tmp, tmp, A[1]); |
---|
1012 | mpz_addmul (expX, tmp, inverseM[1]); |
---|
1013 | |
---|
1014 | mpz_set_si (expY, j.exp()); |
---|
1015 | mpz_sub (expY, expY, A[0]); |
---|
1016 | mpz_mul (expY, expY, inverseM[2]); |
---|
1017 | mpz_set_si (tmp, i.exp()); |
---|
1018 | mpz_sub (tmp, tmp, A[1]); |
---|
1019 | mpz_addmul (expY, tmp, inverseM[3]); |
---|
1020 | |
---|
1021 | mpz_init_set (exps[count], expX); |
---|
1022 | count++; |
---|
1023 | mpz_init_set (exps[count], expY); |
---|
1024 | max_exps=count; |
---|
1025 | count++; |
---|
1026 | |
---|
1027 | if (mpz_cmp (minExpY, expY) > 0) |
---|
1028 | mpz_set (minExpY, expY); |
---|
1029 | if (mpz_cmp (minExpX, expX) > 0) |
---|
1030 | mpz_set (minExpX, expX); |
---|
1031 | } |
---|
1032 | } |
---|
1033 | |
---|
1034 | int mExpX= mpz_get_si (minExpX); |
---|
1035 | int mExpY= mpz_get_si (minExpY); |
---|
1036 | count= 0; |
---|
1037 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
1038 | { |
---|
1039 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
1040 | { |
---|
1041 | result += i.coeff()*power (x, mpz_get_si (exps[count])-mExpX)* |
---|
1042 | power (y, mpz_get_si (exps[count+1])-mExpY); |
---|
1043 | max_exps=count+1; |
---|
1044 | count += 2; |
---|
1045 | continue; |
---|
1046 | } |
---|
1047 | for (CFIterator j= i.coeff(); j.hasTerms(); j++) |
---|
1048 | { |
---|
1049 | result += j.coeff()*power (x, mpz_get_si (exps[count])-mExpX)* |
---|
1050 | power (y, mpz_get_si (exps[count+1])-mExpY); |
---|
1051 | max_exps=count+1; |
---|
1052 | count += 2; |
---|
1053 | } |
---|
1054 | } |
---|
1055 | |
---|
1056 | mpz_clear (expX); |
---|
1057 | mpz_clear (expY); |
---|
1058 | mpz_clear (minExpX); |
---|
1059 | mpz_clear (minExpY); |
---|
1060 | mpz_clear (tmp); |
---|
1061 | |
---|
1062 | for(int tt=max_exps;tt>=0;tt--) mpz_clear(exps[tt]); |
---|
1063 | delete [] exps; |
---|
1064 | |
---|
1065 | return result/Lc (result); //normalize |
---|
1066 | } |
---|
1067 | |
---|
1068 | //assumes the input is a Newton polygon of a bivariate polynomial which is |
---|
1069 | //primitive wrt. x and y, i.e. there is at least one point of the polygon lying |
---|
1070 | //on the x-axis and one lying on the y-axis |
---|
1071 | int* getRightSide (int** polygon, int sizeOfPolygon, int& sizeOfOutput) |
---|
1072 | { |
---|
1073 | int maxY= polygon [0][0]; |
---|
1074 | int indexY= 0; |
---|
1075 | for (int i= 1; i < sizeOfPolygon; i++) |
---|
1076 | { |
---|
1077 | if (maxY < polygon [i][0]) |
---|
1078 | { |
---|
1079 | maxY= polygon [i][0]; |
---|
1080 | indexY= i; |
---|
1081 | } |
---|
1082 | else if (maxY == polygon [i][0]) |
---|
1083 | { |
---|
1084 | if (polygon [indexY][1] < polygon[i][1]) |
---|
1085 | indexY= i; |
---|
1086 | } |
---|
1087 | if (maxY > polygon [i][0]) |
---|
1088 | break; |
---|
1089 | } |
---|
1090 | |
---|
1091 | int count= -1; |
---|
1092 | for (int i= indexY; i < sizeOfPolygon; i++) |
---|
1093 | { |
---|
1094 | if (polygon[i][0] == 0) |
---|
1095 | { |
---|
1096 | count= i - indexY; |
---|
1097 | break; |
---|
1098 | } |
---|
1099 | } |
---|
1100 | |
---|
1101 | int * result; |
---|
1102 | int index= 0; |
---|
1103 | if (count < 0) |
---|
1104 | { |
---|
1105 | result= new int [sizeOfPolygon - indexY]; |
---|
1106 | sizeOfOutput= sizeOfPolygon - indexY; |
---|
1107 | count= sizeOfPolygon - indexY - 1; |
---|
1108 | result [0]= polygon[sizeOfPolygon - 1][0] - polygon [0] [0]; |
---|
1109 | index= 1; |
---|
1110 | } |
---|
1111 | else |
---|
1112 | { |
---|
1113 | sizeOfOutput= count; |
---|
1114 | result= new int [count]; |
---|
1115 | } |
---|
1116 | |
---|
1117 | for (int i= indexY + count; i > indexY; i--, index++) |
---|
1118 | result [index]= polygon [i - 1] [0] - polygon [i] [0]; |
---|
1119 | |
---|
1120 | return result; |
---|
1121 | } |
---|
1122 | |
---|
1123 | bool irreducibilityTest (const CanonicalForm& F) |
---|
1124 | { |
---|
1125 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
1126 | ASSERT (getCharacteristic() == 0, "expected polynomial over integers or rationals"); |
---|
1127 | |
---|
1128 | int sizeOfNewtonPolygon; |
---|
1129 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
1130 | if (sizeOfNewtonPolygon == 3) |
---|
1131 | { |
---|
1132 | bool check1= |
---|
1133 | (newtonPolyg[0][0]==0 || newtonPolyg[1][0]==0 || newtonPolyg[2][0]==0); |
---|
1134 | if (check1) |
---|
1135 | { |
---|
1136 | bool check2= |
---|
1137 | (newtonPolyg[0][1]==0 || newtonPolyg[1][1]==0 || newtonPolyg[2][0]==0); |
---|
1138 | if (check2) |
---|
1139 | { |
---|
1140 | bool isRat= isOn (SW_RATIONAL); |
---|
1141 | if (isRat) |
---|
1142 | Off (SW_RATIONAL); |
---|
1143 | CanonicalForm tmp= gcd (newtonPolyg[0][0],newtonPolyg[0][1]); // maybe it's better to use plain intgcd |
---|
1144 | tmp= gcd (tmp, newtonPolyg[1][0]); |
---|
1145 | tmp= gcd (tmp, newtonPolyg[1][1]); |
---|
1146 | tmp= gcd (tmp, newtonPolyg[2][0]); |
---|
1147 | tmp= gcd (tmp, newtonPolyg[2][1]); |
---|
1148 | if (isRat) |
---|
1149 | On (SW_RATIONAL); |
---|
1150 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
1151 | delete [] newtonPolyg [i]; |
---|
1152 | delete [] newtonPolyg; |
---|
1153 | return (tmp==1); |
---|
1154 | } |
---|
1155 | } |
---|
1156 | } |
---|
1157 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
1158 | delete [] newtonPolyg [i]; |
---|
1159 | delete [] newtonPolyg; |
---|
1160 | return false; |
---|
1161 | } |
---|
1162 | |
---|
1163 | bool absIrredTest (const CanonicalForm& F) |
---|
1164 | { |
---|
1165 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
1166 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
1167 | |
---|
1168 | int sizeOfNewtonPolygon; |
---|
1169 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
1170 | bool isRat= isOn (SW_RATIONAL); |
---|
1171 | if (isRat) |
---|
1172 | Off (SW_RATIONAL); |
---|
1173 | int p=getCharacteristic(); |
---|
1174 | int d=1; |
---|
1175 | char bufGFName='Z'; |
---|
1176 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
1177 | if (GF) |
---|
1178 | { |
---|
1179 | d= getGFDegree(); |
---|
1180 | bufGFName=gf_name; |
---|
1181 | } |
---|
1182 | |
---|
1183 | setCharacteristic(0); |
---|
1184 | |
---|
1185 | CanonicalForm g= gcd (newtonPolyg[0][0], newtonPolyg[0][1]); //maybe it's better to use plain intgcd |
---|
1186 | |
---|
1187 | int i= 1; |
---|
1188 | while (!g.isOne() && i < sizeOfNewtonPolygon) |
---|
1189 | { |
---|
1190 | g= gcd (g, newtonPolyg[i][0]); |
---|
1191 | g= gcd (g, newtonPolyg[i][1]); |
---|
1192 | i++; |
---|
1193 | } |
---|
1194 | |
---|
1195 | bool result= g.isOne(); |
---|
1196 | |
---|
1197 | if (GF) |
---|
1198 | setCharacteristic (p, d, bufGFName); |
---|
1199 | else |
---|
1200 | setCharacteristic(p); |
---|
1201 | |
---|
1202 | if (isRat) |
---|
1203 | On (SW_RATIONAL); |
---|
1204 | |
---|
1205 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
1206 | delete [] newtonPolyg[i]; |
---|
1207 | |
---|
1208 | delete [] newtonPolyg; |
---|
1209 | |
---|
1210 | return result; |
---|
1211 | } |
---|
1212 | |
---|
1213 | bool modularIrredTest (const CanonicalForm& F) |
---|
1214 | { |
---|
1215 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
1216 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
1217 | |
---|
1218 | bool isRat= isOn (SW_RATIONAL); |
---|
1219 | if (isRat) |
---|
1220 | Off (SW_RATIONAL); |
---|
1221 | |
---|
1222 | if (isRat) |
---|
1223 | { |
---|
1224 | ASSERT (bCommonDen (F).isOne(), "poly over Z expected"); |
---|
1225 | } |
---|
1226 | |
---|
1227 | CanonicalForm Fp, N= maxNorm (F); |
---|
1228 | int tdeg= totaldegree (F); |
---|
1229 | |
---|
1230 | int i= 0; |
---|
1231 | //TODO: maybe it's better to choose the characteristic as large as possible |
---|
1232 | // as factorization over large finite field will be faster |
---|
1233 | //TODO: handle those cases where our factory primes are not enough |
---|
1234 | //TODO: factorize coefficients corresponding to the vertices of the Newton |
---|
1235 | // polygon and only try the obtained factors |
---|
1236 | if (N < cf_getSmallPrime (cf_getNumSmallPrimes()-1)) |
---|
1237 | { |
---|
1238 | while (i < cf_getNumSmallPrimes() && N > cf_getSmallPrime(i)) |
---|
1239 | { |
---|
1240 | setCharacteristic (cf_getSmallPrime (i)); |
---|
1241 | Fp= F.mapinto(); |
---|
1242 | i++; |
---|
1243 | if (totaldegree (Fp) == tdeg) |
---|
1244 | { |
---|
1245 | if (absIrredTest (Fp)) |
---|
1246 | { |
---|
1247 | CFFList factors= factorize (Fp); |
---|
1248 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
1249 | { |
---|
1250 | if (isRat) |
---|
1251 | On (SW_RATIONAL); |
---|
1252 | setCharacteristic (0); |
---|
1253 | return true; |
---|
1254 | } |
---|
1255 | } |
---|
1256 | } |
---|
1257 | setCharacteristic (0); |
---|
1258 | } |
---|
1259 | } |
---|
1260 | else |
---|
1261 | { |
---|
1262 | while (i < cf_getNumPrimes() && N > cf_getPrime (i)) |
---|
1263 | { |
---|
1264 | setCharacteristic (cf_getPrime (i)); |
---|
1265 | Fp= F.mapinto(); |
---|
1266 | i++; |
---|
1267 | if (totaldegree (Fp) == tdeg) |
---|
1268 | { |
---|
1269 | if (absIrredTest (Fp)) |
---|
1270 | { |
---|
1271 | CFFList factors= factorize (Fp); |
---|
1272 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
1273 | { |
---|
1274 | if (isRat) |
---|
1275 | On (SW_RATIONAL); |
---|
1276 | setCharacteristic (0); |
---|
1277 | return true; |
---|
1278 | } |
---|
1279 | } |
---|
1280 | } |
---|
1281 | setCharacteristic (0); |
---|
1282 | } |
---|
1283 | } |
---|
1284 | |
---|
1285 | if (isRat) |
---|
1286 | On (SW_RATIONAL); |
---|
1287 | |
---|
1288 | return false; |
---|
1289 | } |
---|
1290 | |
---|
1291 | bool |
---|
1292 | modularIrredTestWithShift (const CanonicalForm& F) |
---|
1293 | { |
---|
1294 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
1295 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
1296 | |
---|
1297 | bool isRat= isOn (SW_RATIONAL); |
---|
1298 | if (isRat) |
---|
1299 | Off (SW_RATIONAL); |
---|
1300 | |
---|
1301 | if (isRat) |
---|
1302 | { |
---|
1303 | ASSERT (bCommonDen (F).isOne(), "poly over Z expected"); |
---|
1304 | } |
---|
1305 | |
---|
1306 | Variable x= Variable (1); |
---|
1307 | Variable y= Variable (2); |
---|
1308 | CanonicalForm Fp; |
---|
1309 | int tdeg= totaldegree (F); |
---|
1310 | |
---|
1311 | REvaluation E; |
---|
1312 | |
---|
1313 | setCharacteristic (2); |
---|
1314 | Fp= F.mapinto(); |
---|
1315 | |
---|
1316 | E= REvaluation (1,2, FFRandom()); |
---|
1317 | |
---|
1318 | E.nextpoint(); |
---|
1319 | |
---|
1320 | Fp= Fp (x+E[1], x); |
---|
1321 | Fp= Fp (y+E[2], y); |
---|
1322 | |
---|
1323 | if (tdeg == totaldegree (Fp)) |
---|
1324 | { |
---|
1325 | if (absIrredTest (Fp)) |
---|
1326 | { |
---|
1327 | CFFList factors= factorize (Fp); |
---|
1328 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
1329 | { |
---|
1330 | if (isRat) |
---|
1331 | On (SW_RATIONAL); |
---|
1332 | setCharacteristic (0); |
---|
1333 | return true; |
---|
1334 | } |
---|
1335 | } |
---|
1336 | } |
---|
1337 | |
---|
1338 | E.nextpoint(); |
---|
1339 | |
---|
1340 | Fp= Fp (x+E[1], x); |
---|
1341 | Fp= Fp (y+E[2], y); |
---|
1342 | |
---|
1343 | if (tdeg == totaldegree (Fp)) |
---|
1344 | { |
---|
1345 | if (absIrredTest (Fp)) |
---|
1346 | { |
---|
1347 | CFFList factors= factorize (Fp); |
---|
1348 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
1349 | { |
---|
1350 | if (isRat) |
---|
1351 | On (SW_RATIONAL); |
---|
1352 | setCharacteristic (0); |
---|
1353 | return true; |
---|
1354 | } |
---|
1355 | } |
---|
1356 | } |
---|
1357 | |
---|
1358 | int i= 0; |
---|
1359 | while (cf_getSmallPrime (i) < 102) |
---|
1360 | { |
---|
1361 | setCharacteristic (cf_getSmallPrime (i)); |
---|
1362 | i++; |
---|
1363 | E= REvaluation (1, 2, FFRandom()); |
---|
1364 | |
---|
1365 | for (int j= 0; j < 3; j++) |
---|
1366 | { |
---|
1367 | Fp= F.mapinto(); |
---|
1368 | E.nextpoint(); |
---|
1369 | Fp= Fp (x+E[1], x); |
---|
1370 | Fp= Fp (y+E[2], y); |
---|
1371 | |
---|
1372 | if (tdeg == totaldegree (Fp)) |
---|
1373 | { |
---|
1374 | if (absIrredTest (Fp)) |
---|
1375 | { |
---|
1376 | CFFList factors= factorize (Fp); |
---|
1377 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
1378 | { |
---|
1379 | if (isRat) |
---|
1380 | On (SW_RATIONAL); |
---|
1381 | setCharacteristic (0); |
---|
1382 | return true; |
---|
1383 | } |
---|
1384 | } |
---|
1385 | } |
---|
1386 | } |
---|
1387 | } |
---|
1388 | |
---|
1389 | setCharacteristic (0); |
---|
1390 | if (isRat) |
---|
1391 | On (SW_RATIONAL); |
---|
1392 | |
---|
1393 | return false; |
---|
1394 | } |
---|
1395 | |
---|
1396 | |
---|