[a2dd9b2] | 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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[c1b9927] | 5 | * |
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[a2dd9b2] | 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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[e4fe2b] | 14 | #include "config.h" |
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[712a5a] | 15 | |
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| 16 | #include "cf_assert.h" |
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| 17 | |
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[a2dd9b2] | 18 | #include <stdlib.h> |
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| 19 | |
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| 20 | #include "canonicalform.h" |
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| 21 | #include "cf_iter.h" |
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| 22 | #include "cf_algorithm.h" |
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[b79b58] | 23 | #include "cf_primes.h" |
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| 24 | #include "cf_reval.h" |
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[712a5a] | 25 | #include "cf_factory.h" |
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| 26 | #include "gfops.h" |
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[a2dd9b2] | 27 | #include "cfNewtonPolygon.h" |
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| 28 | #include "templates/ftmpl_functions.h" |
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| 29 | #include "algext.h" |
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| 30 | |
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| 31 | static |
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| 32 | void translate (int** points, int* point, int sizePoints) //make point to 0 |
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| 33 | { |
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| 34 | for (int i= 0; i < sizePoints; i++) |
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| 35 | { |
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| 36 | points[i] [0] -= point [0]; |
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| 37 | points[i] [1] -= point [1]; |
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| 38 | } |
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| 39 | } |
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| 40 | |
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| 41 | static |
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| 42 | int smallestPointIndex (int** points, int sizePoints) |
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| 43 | { |
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| 44 | int min= 0; |
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| 45 | for (int i= 1; i < sizePoints; i++) |
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| 46 | { |
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[c1b9927] | 47 | if (points[i][0] < points[min][0] || |
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[a2dd9b2] | 48 | (points[i] [0] == points[min] [0] && points[i] [1] < points[min] [1])) |
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| 49 | min= i; |
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| 50 | } |
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| 51 | return min; |
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| 52 | } |
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| 53 | |
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| 54 | static |
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| 55 | void swap (int** points, int i, int j) |
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| 56 | { |
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| 57 | int* tmp= points[i]; |
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| 58 | points[i]= points[j]; |
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| 59 | points[j]= tmp; |
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| 60 | } |
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| 61 | |
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| 62 | static |
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| 63 | bool isLess (int* point1, int* point2) |
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| 64 | { |
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| 65 | int area= point1[0]*point2[1]- point1[1]*point2[0]; |
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| 66 | if (area > 0) return true; |
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| 67 | if (area == 0) |
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| 68 | { |
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[c1b9927] | 69 | return (abs (point1[0]) + abs (point1[1]) > |
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[a2dd9b2] | 70 | abs (point2[0]) + abs (point2[1])); |
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| 71 | } |
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| 72 | return false; |
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| 73 | } |
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| 74 | |
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| 75 | static |
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| 76 | void quickSort (int lo, int hi, int** points) |
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| 77 | { |
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| 78 | int i= lo, j= hi; |
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| 79 | int* point= new int [2]; |
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| 80 | point [0]= points [(lo+hi)/2] [0]; |
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| 81 | point [1]= points [(lo+hi)/2] [1]; |
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| 82 | while (i <= j) |
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| 83 | { |
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| 84 | while (isLess (points [i], point) && i < hi) i++; |
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| 85 | while (isLess (point, points[j]) && j > lo) j--; |
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| 86 | if (i <= j) |
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| 87 | { |
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| 88 | swap (points, i, j); |
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| 89 | i++; |
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| 90 | j--; |
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| 91 | } |
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| 92 | } |
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| 93 | delete [] point; |
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| 94 | if (lo < j) quickSort (lo, j, points); |
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| 95 | if (i < hi) quickSort (i, hi, points); |
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| 96 | } |
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| 97 | |
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| 98 | static |
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| 99 | void sort (int** points, int sizePoints) |
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| 100 | { |
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| 101 | quickSort (1, sizePoints - 1, points); |
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| 102 | } |
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| 103 | |
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| 104 | // check whether p2 is convex |
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| 105 | static |
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| 106 | bool isConvex (int* point1, int* point2, int* point3) |
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| 107 | { |
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| 108 | int relArea= (point1[0] - point2[0])*(point3[1] - point2[1]) - |
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| 109 | (point1[1] - point2[1])*(point3[0] - point2[0]); |
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| 110 | if (relArea < 0) |
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| 111 | return true; |
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| 112 | if (relArea == 0) |
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| 113 | { |
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| 114 | return !(abs (point1[0] - point3[0]) + abs (point1[1] - point3[1]) >= |
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| 115 | (abs (point2[0] - point1[0]) + abs (point2[1] - point1[1]) + |
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| 116 | abs (point2[0] - point3[0]) + abs (point2[1] - point3[1]))); |
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| 117 | } |
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| 118 | return false; |
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| 119 | } |
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| 120 | |
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| 121 | static |
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| 122 | bool isConvex (int** points, int i) |
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| 123 | { |
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| 124 | return isConvex (points[i - 1], points [i], points [i + 1]); |
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| 125 | } |
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| 126 | |
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| 127 | int grahamScan (int** points, int sizePoints) |
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| 128 | { |
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| 129 | swap (points, 0, smallestPointIndex (points, sizePoints)); |
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| 130 | int * minusPoint= new int [2]; |
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| 131 | minusPoint [0]= points[0] [0]; |
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| 132 | minusPoint [1]= points[0] [1]; |
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| 133 | translate (points, minusPoint, sizePoints); |
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| 134 | sort (points, sizePoints); |
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| 135 | minusPoint[0]= - minusPoint[0]; |
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| 136 | minusPoint[1]= - minusPoint[1]; |
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| 137 | translate (points, minusPoint, sizePoints); //reverse translation |
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| 138 | delete [] minusPoint; |
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| 139 | int i= 3, k= 3; |
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| 140 | while (k < sizePoints) |
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| 141 | { |
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| 142 | swap (points, i, k); |
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| 143 | while (!isConvex (points, i - 1)) |
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| 144 | { |
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| 145 | swap (points, i - 1, i); |
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| 146 | i--; |
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| 147 | } |
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| 148 | k++; |
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| 149 | i++; |
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| 150 | } |
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[6fd83c4] | 151 | if (i + 1 <= sizePoints || i == sizePoints) |
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[a2dd9b2] | 152 | { |
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| 153 | int relArea= |
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| 154 | (points [i-2][0] - points [i-1][0])*(points [0][1] - points [i-1][1])- |
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| 155 | (points [i-2][1] - points [i-1][1])*(points [0][0] - points [i-1][0]); |
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| 156 | if (relArea == 0) |
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| 157 | { |
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| 158 | if (abs (points [i-2][0] - points [0][0]) + |
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| 159 | abs (points [i-2][1] - points [0][1]) >= |
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| 160 | abs (points [i-1][0] - points [i-2][0]) + |
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| 161 | abs (points [i-1][1] - points [i-2][1]) + |
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| 162 | abs (points [i-1][0] - points [0][0]) + |
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| 163 | abs (points [i-1][1] - points [0][1])) |
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| 164 | i--; |
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| 165 | } |
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| 166 | } |
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| 167 | return i; |
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| 168 | } |
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| 169 | |
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| 170 | //points[i] [0] is x-coordinate, points [i] [1] is y-coordinate |
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| 171 | int polygon (int** points, int sizePoints) |
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| 172 | { |
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| 173 | if (sizePoints < 3) return sizePoints; |
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| 174 | return grahamScan (points, sizePoints); |
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| 175 | } |
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| 176 | |
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| 177 | static |
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| 178 | int* getDegrees (const CanonicalForm& F, int& sizeOfOutput) |
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| 179 | { |
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[96992c] | 180 | if (F.inCoeffDomain()) |
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| 181 | { |
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| 182 | int* result= new int [1]; |
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| 183 | result [0]= 0; |
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| 184 | sizeOfOutput= 1; |
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| 185 | return result; |
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| 186 | } |
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[a2dd9b2] | 187 | sizeOfOutput= size (F); |
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| 188 | int* result= new int [sizeOfOutput]; |
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| 189 | int j= 0; |
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| 190 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
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| 191 | result [j]= i.exp(); |
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| 192 | return result; |
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| 193 | } |
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| 194 | |
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| 195 | //get points in Z^2 whose convex hull is the Newton polygon |
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| 196 | int ** getPoints (const CanonicalForm& F, int& n) |
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| 197 | { |
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| 198 | n= size (F); |
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| 199 | int ** points= new int* [n]; |
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| 200 | for (int i= 0; i < n; i++) |
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| 201 | points [i]= new int [2]; |
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| 202 | |
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| 203 | int j= 0; |
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| 204 | int * buf; |
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| 205 | int bufSize; |
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| 206 | if (F.isUnivariate() && F.level() == 1) |
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| 207 | { |
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| 208 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
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| 209 | { |
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| 210 | points [j] [0]= i.exp(); |
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| 211 | points [j] [1]= 0; |
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| 212 | } |
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| 213 | return points; |
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| 214 | } |
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| 215 | for (CFIterator i= F; i.hasTerms(); i++) |
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| 216 | { |
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| 217 | buf= getDegrees (i.coeff(), bufSize); |
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| 218 | for (int k= 0; k < bufSize; k++, j++) |
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| 219 | { |
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| 220 | points [j] [0]= i.exp(); |
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| 221 | points [j] [1]= buf [k]; |
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| 222 | } |
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| 223 | delete [] buf; |
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| 224 | } |
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| 225 | return points; |
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| 226 | } |
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| 227 | |
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[16a0df] | 228 | int ** |
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| 229 | merge (int ** points1, int sizePoints1, int ** points2, int sizePoints2, |
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| 230 | int& sizeResult) |
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| 231 | { |
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| 232 | int i, j; |
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| 233 | sizeResult= sizePoints1+sizePoints2; |
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| 234 | for (i= 0; i < sizePoints1; i++) |
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| 235 | { |
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| 236 | for (j= 0; j < sizePoints2; j++) |
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| 237 | { |
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| 238 | if (points1[i][0] != points2[j][0]) |
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| 239 | continue; |
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| 240 | else |
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| 241 | { |
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| 242 | if (points1[i][1] != points2[j][1]) |
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| 243 | continue; |
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| 244 | else |
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| 245 | { |
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| 246 | points2[j][0]= -1; |
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| 247 | points2[j][1]= -1; |
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| 248 | sizeResult--; |
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| 249 | } |
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| 250 | } |
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| 251 | } |
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| 252 | } |
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| 253 | if (sizeResult == 0) |
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| 254 | return points1; |
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| 255 | |
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| 256 | int ** result= new int *[sizeResult]; |
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| 257 | for (i= 0; i < sizeResult; i++) |
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| 258 | result [i]= new int [2]; |
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| 259 | |
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| 260 | int k= 0; |
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| 261 | for (i= 0; i < sizePoints1; i++, k++) |
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| 262 | { |
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| 263 | result[k][0]= points1[i][0]; |
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| 264 | result[k][1]= points1[i][1]; |
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| 265 | } |
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| 266 | for (i= 0; i < sizePoints2; i++) |
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| 267 | { |
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| 268 | if (points2[i][0] < 0) |
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| 269 | continue; |
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| 270 | else |
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| 271 | { |
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| 272 | result[k][0]= points2[i][0]; |
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| 273 | result[k][1]= points2[i][1]; |
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| 274 | k++; |
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| 275 | } |
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| 276 | } |
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| 277 | return result; |
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| 278 | } |
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| 279 | |
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[a2dd9b2] | 280 | // assumes a bivariate poly as input |
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| 281 | int ** newtonPolygon (const CanonicalForm& F, int& sizeOfNewtonPoly) |
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| 282 | { |
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| 283 | int sizeF= size (F); |
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| 284 | int ** points= new int* [sizeF]; |
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| 285 | for (int i= 0; i < sizeF; i++) |
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| 286 | points [i]= new int [2]; |
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| 287 | int j= 0; |
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| 288 | int * buf; |
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| 289 | int bufSize; |
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| 290 | for (CFIterator i= F; i.hasTerms(); i++) |
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| 291 | { |
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| 292 | buf= getDegrees (i.coeff(), bufSize); |
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| 293 | for (int k= 0; k < bufSize; k++, j++) |
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| 294 | { |
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| 295 | points [j] [0]= i.exp(); |
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| 296 | points [j] [1]= buf [k]; |
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| 297 | } |
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| 298 | delete [] buf; |
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| 299 | } |
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| 300 | |
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| 301 | int n= polygon (points, sizeF); |
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| 302 | |
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| 303 | int ** result= new int* [n]; |
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| 304 | for (int i= 0; i < n; i++) |
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| 305 | { |
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| 306 | result [i]= new int [2]; |
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| 307 | result [i] [0]= points [i] [0]; |
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| 308 | result [i] [1]= points [i] [1]; |
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| 309 | } |
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| 310 | |
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| 311 | sizeOfNewtonPoly= n; |
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[eee11c] | 312 | for (int i= 0; i < sizeF; i++) |
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[a2dd9b2] | 313 | delete [] points[i]; |
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| 314 | delete [] points; |
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| 315 | |
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| 316 | return result; |
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| 317 | } |
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| 318 | |
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[16a0df] | 319 | // assumes a bivariate polys as input |
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| 320 | int ** newtonPolygon (const CanonicalForm& F, const CanonicalForm& G, |
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| 321 | int& sizeOfNewtonPoly) |
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| 322 | { |
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| 323 | int sizeF= size (F); |
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| 324 | int ** pointsF= new int* [sizeF]; |
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| 325 | for (int i= 0; i < sizeF; i++) |
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| 326 | pointsF [i]= new int [2]; |
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| 327 | int j= 0; |
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| 328 | int * buf; |
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| 329 | int bufSize; |
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| 330 | for (CFIterator i= F; i.hasTerms(); i++) |
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| 331 | { |
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| 332 | buf= getDegrees (i.coeff(), bufSize); |
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| 333 | for (int k= 0; k < bufSize; k++, j++) |
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| 334 | { |
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| 335 | pointsF [j] [0]= i.exp(); |
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| 336 | pointsF [j] [1]= buf [k]; |
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| 337 | } |
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| 338 | delete [] buf; |
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| 339 | } |
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| 340 | |
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| 341 | int sizeG= size (G); |
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| 342 | int ** pointsG= new int* [sizeG]; |
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| 343 | for (int i= 0; i < sizeG; i++) |
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| 344 | pointsG [i]= new int [2]; |
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| 345 | j= 0; |
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| 346 | for (CFIterator i= G; i.hasTerms(); i++) |
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| 347 | { |
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| 348 | buf= getDegrees (i.coeff(), bufSize); |
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| 349 | for (int k= 0; k < bufSize; k++, j++) |
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| 350 | { |
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| 351 | pointsG [j] [0]= i.exp(); |
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| 352 | pointsG [j] [1]= buf [k]; |
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| 353 | } |
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| 354 | delete [] buf; |
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| 355 | } |
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| 356 | |
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| 357 | int sizePoints; |
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| 358 | int ** points= merge (pointsF, sizeF, pointsG, sizeG, sizePoints); |
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| 359 | |
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| 360 | int n= polygon (points, sizePoints); |
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| 361 | |
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| 362 | int ** result= new int* [n]; |
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| 363 | for (int i= 0; i < n; i++) |
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| 364 | { |
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| 365 | result [i]= new int [2]; |
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| 366 | result [i] [0]= points [i] [0]; |
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| 367 | result [i] [1]= points [i] [1]; |
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| 368 | } |
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| 369 | |
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| 370 | sizeOfNewtonPoly= n; |
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| 371 | for (int i= 0; i < sizeF; i++) |
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| 372 | delete [] pointsF[i]; |
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| 373 | delete [] pointsF; |
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| 374 | for (int i= 0; i < sizeG; i++) |
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| 375 | delete [] pointsG[i]; |
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| 376 | delete [] pointsG; |
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| 377 | |
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| 378 | return result; |
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| 379 | } |
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| 380 | |
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[a2dd9b2] | 381 | // assumes first sizePoints entries of points form a Newton polygon |
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| 382 | bool isInPolygon (int ** points, int sizePoints, int* point) |
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| 383 | { |
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| 384 | int ** buf= new int* [sizePoints + 1]; |
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| 385 | for (int i= 0; i < sizePoints; i++) |
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| 386 | { |
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| 387 | buf [i]= new int [2]; |
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| 388 | buf [i] [0]= points [i] [0]; |
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| 389 | buf [i] [1]= points [i] [1]; |
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| 390 | } |
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| 391 | buf [sizePoints]= new int [2]; |
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| 392 | buf [sizePoints] [0]= point [0]; |
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| 393 | buf [sizePoints] [1]= point [1]; |
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| 394 | int sizeBuf= sizePoints + 1; |
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| 395 | |
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| 396 | swap (buf, 0, smallestPointIndex (buf, sizeBuf)); |
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| 397 | int * minusPoint= new int [2]; |
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| 398 | minusPoint [0]= buf[0] [0]; |
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| 399 | minusPoint [1]= buf[0] [1]; |
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| 400 | translate (buf, minusPoint, sizeBuf); |
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| 401 | sort (buf, sizeBuf); |
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| 402 | minusPoint[0]= - minusPoint[0]; |
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| 403 | minusPoint[1]= - minusPoint[1]; |
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| 404 | translate (buf, minusPoint, sizeBuf); //reverse translation |
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| 405 | delete [] minusPoint; |
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| 406 | |
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| 407 | if (buf [0] [0] == point [0] && buf [0] [1] == point [1]) |
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| 408 | { |
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| 409 | for (int i= 0; i < sizeBuf; i++) |
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| 410 | delete [] buf[i]; |
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| 411 | delete [] buf; |
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| 412 | return false; |
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| 413 | } |
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| 414 | |
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| 415 | for (int i= 1; i < sizeBuf-1; i++) |
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| 416 | { |
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| 417 | if (buf [i] [0] == point [0] && buf [i] [1] == point [1]) |
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| 418 | { |
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| 419 | bool result= !isConvex (buf, i); |
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| 420 | for (int i= 0; i < sizeBuf; i++) |
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| 421 | delete [] buf [i]; |
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| 422 | delete [] buf; |
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| 423 | return result; |
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| 424 | } |
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| 425 | } |
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[c1b9927] | 426 | |
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[a2dd9b2] | 427 | if (buf [sizeBuf - 1] [0] == point [0] && buf [sizeBuf-1] [1] == point [1]) |
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| 428 | { |
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| 429 | buf [1] [0]= point [0]; |
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| 430 | buf [1] [1]= point [1]; |
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| 431 | buf [2] [0]= buf [0] [0]; |
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| 432 | buf [2] [1]= buf [0] [1]; |
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| 433 | buf [0] [0]= buf [sizeBuf-2] [0]; |
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| 434 | buf [0] [1]= buf [sizeBuf-2] [1]; |
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| 435 | bool result= !isConvex (buf, 1); |
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| 436 | for (int i= 0; i < sizeBuf; i++) |
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| 437 | delete [] buf [i]; |
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| 438 | delete [] buf; |
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| 439 | return result; |
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| 440 | } |
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| 441 | for (int i= 0; i < sizeBuf; i++) |
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| 442 | delete [] buf [i]; |
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| 443 | delete [] buf; |
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| 444 | |
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| 445 | return false; |
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| 446 | } |
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| 447 | |
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| 448 | void lambda (int** points, int sizePoints) |
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| 449 | { |
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| 450 | for (int i= 0; i < sizePoints; i++) |
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| 451 | points [i] [1]= points [i] [1] - points [i] [0]; |
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| 452 | } |
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| 453 | |
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| 454 | void lambdaInverse (int** points, int sizePoints) |
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| 455 | { |
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| 456 | for (int i= 0; i < sizePoints; i++) |
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| 457 | points [i] [1]= points [i] [1] + points [i] [0]; |
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| 458 | } |
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| 459 | |
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| 460 | void tau (int** points, int sizePoints, int k) |
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| 461 | { |
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| 462 | for (int i= 0; i < sizePoints; i++) |
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| 463 | points [i] [1]= points [i] [1] + k; |
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| 464 | } |
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| 465 | |
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| 466 | void mu (int** points, int sizePoints) |
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| 467 | { |
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| 468 | int tmp; |
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| 469 | for (int i= 0; i < sizePoints; i++) |
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| 470 | { |
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| 471 | tmp= points [i] [0]; |
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| 472 | points [i] [0]= points [i] [1]; |
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| 473 | points [i] [1]= tmp; |
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| 474 | } |
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| 475 | } |
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| 476 | |
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| 477 | void getMaxMin (int** points, int sizePoints, int& minDiff, int& minSum, |
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| 478 | int& maxDiff, int& maxSum, int& maxX, int& maxY |
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| 479 | ) |
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| 480 | { |
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| 481 | minDiff= points [0] [1] - points [0] [0]; |
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| 482 | minSum= points [0] [1] + points [0] [0]; |
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| 483 | maxDiff= points [0] [1] - points [0] [0]; |
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| 484 | maxSum= points [0] [1] + points [0] [0]; |
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| 485 | maxX= points [0] [1]; |
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| 486 | maxY= points [0] [0]; |
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| 487 | int diff, sum; |
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| 488 | for (int i= 1; i < sizePoints; i++) |
---|
| 489 | { |
---|
| 490 | diff= points [i] [1] - points [i] [0]; |
---|
| 491 | sum= points [i] [1] + points [i] [0]; |
---|
| 492 | minDiff= tmin (minDiff, diff); |
---|
| 493 | minSum= tmin (minSum, sum); |
---|
| 494 | maxDiff= tmax (maxDiff, diff); |
---|
| 495 | maxSum= tmax (maxSum, sum); |
---|
| 496 | maxX= tmax (maxX, points [i] [1]); |
---|
| 497 | maxY= tmax (maxY, points [i] [0]); |
---|
| 498 | } |
---|
| 499 | } |
---|
| 500 | |
---|
[2072126] | 501 | #ifdef HAVE_NTL |
---|
[a2dd9b2] | 502 | void convexDense(int** points, int sizePoints, mat_ZZ& M, vec_ZZ& A) |
---|
| 503 | { |
---|
| 504 | if (sizePoints < 3) |
---|
| 505 | { |
---|
| 506 | if (sizePoints == 2) |
---|
| 507 | { |
---|
| 508 | int maxX= (points [1] [1] < points [0] [1])?points [0] [1]:points [1] [1]; |
---|
| 509 | int maxY= (points [1] [0] < points [0] [0])?points [0] [0]:points [1] [0]; |
---|
| 510 | long u,v,g; |
---|
| 511 | XGCD (g, u, v, maxX, maxY); |
---|
| 512 | M.SetDims (2,2); |
---|
| 513 | A.SetLength (2); |
---|
| 514 | if (points [0] [1] != points [0] [0] && points [1] [0] != points [1] [1]) |
---|
| 515 | { |
---|
| 516 | M (1,1)= -u; |
---|
| 517 | M (1,2)= v; |
---|
| 518 | M (2,1)= maxY/g; |
---|
| 519 | M (2,2)= maxX/g; |
---|
| 520 | A (1)= u*maxX; |
---|
| 521 | A (2)= -(maxY/g)*maxX; |
---|
| 522 | } |
---|
| 523 | else |
---|
| 524 | { |
---|
| 525 | M (1,1)= u; |
---|
| 526 | M (1,2)= v; |
---|
| 527 | M (2,1)= -maxY/g; |
---|
| 528 | M (2,2)= maxX/g; |
---|
| 529 | A (1)= to_ZZ (0); |
---|
| 530 | A (2)= to_ZZ (0); |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | else if (sizePoints == 1) |
---|
| 534 | { |
---|
| 535 | ident (M, 2); |
---|
| 536 | A.SetLength (2); |
---|
| 537 | A (1)= to_ZZ (0); |
---|
| 538 | A (2)= to_ZZ (0); |
---|
| 539 | } |
---|
| 540 | return; |
---|
| 541 | } |
---|
| 542 | A.SetLength (2); |
---|
| 543 | A (1)= to_ZZ (0); |
---|
| 544 | A (2)= to_ZZ (0); |
---|
| 545 | ident (M, 2); |
---|
| 546 | mat_ZZ Mu; |
---|
| 547 | Mu.SetDims (2, 2); |
---|
| 548 | Mu (2,1)= to_ZZ (1); |
---|
| 549 | Mu (1,2)= to_ZZ (1); |
---|
| 550 | Mu (1,1)= to_ZZ (0); |
---|
| 551 | Mu (2,2)= to_ZZ (0); |
---|
| 552 | mat_ZZ Lambda; |
---|
| 553 | Lambda.SetDims (2, 2); |
---|
| 554 | Lambda (1,1)= to_ZZ (1); |
---|
| 555 | Lambda (1,2)= to_ZZ (-1); |
---|
| 556 | Lambda (2,2)= to_ZZ (1); |
---|
| 557 | Lambda (2,1)= to_ZZ (0); |
---|
| 558 | mat_ZZ InverseLambda; |
---|
| 559 | InverseLambda.SetDims (2,2); |
---|
| 560 | InverseLambda (1,1)= to_ZZ (1); |
---|
| 561 | InverseLambda (1,2)= to_ZZ (1); |
---|
| 562 | InverseLambda (2,2)= to_ZZ (1); |
---|
| 563 | InverseLambda (2,1)= to_ZZ (0); |
---|
| 564 | ZZ tmp; |
---|
| 565 | int minDiff, minSum, maxDiff, maxSum, maxX, maxY, b, d, f, h; |
---|
| 566 | getMaxMin (points, sizePoints, minDiff, minSum, maxDiff, maxSum, maxX, maxY); |
---|
| 567 | do |
---|
| 568 | { |
---|
| 569 | if (maxX < maxY) |
---|
| 570 | { |
---|
| 571 | mu (points, sizePoints); |
---|
| 572 | M= Mu*M; |
---|
| 573 | tmp= A (1); |
---|
| 574 | A (1)= A (2); |
---|
| 575 | A (2)= tmp; |
---|
| 576 | } |
---|
| 577 | getMaxMin (points, sizePoints, minDiff, minSum, maxDiff, maxSum, maxX, maxY); |
---|
| 578 | b= maxX - maxDiff; |
---|
| 579 | d= maxX + maxY - maxSum; |
---|
| 580 | f= maxY + minDiff; |
---|
| 581 | h= minSum; |
---|
| 582 | if (b + f > maxY) |
---|
| 583 | { |
---|
| 584 | lambda (points, sizePoints); |
---|
| 585 | tau (points, sizePoints, maxY - f); |
---|
| 586 | M= Lambda*M; |
---|
| 587 | A [0] += (maxY-f); |
---|
| 588 | maxX= maxX + maxY - b - f; |
---|
| 589 | } |
---|
| 590 | else if (d + h > maxY) |
---|
| 591 | { |
---|
| 592 | lambdaInverse (points, sizePoints); |
---|
| 593 | tau (points, sizePoints, -h); |
---|
| 594 | M= InverseLambda*M; |
---|
| 595 | A [0] += (-h); |
---|
| 596 | maxX= maxX + maxY - d - h; |
---|
| 597 | } |
---|
| 598 | else |
---|
| 599 | return; |
---|
| 600 | } while (1); |
---|
| 601 | } |
---|
| 602 | |
---|
| 603 | CanonicalForm |
---|
[e243418] | 604 | compress (const CanonicalForm& F, mat_ZZ& M, vec_ZZ& A, bool computeMA) |
---|
[a2dd9b2] | 605 | { |
---|
| 606 | int n; |
---|
[7a1151] | 607 | int ** newtonPolyg= NULL; |
---|
[e243418] | 608 | if (computeMA) |
---|
| 609 | { |
---|
| 610 | newtonPolyg= newtonPolygon (F, n); |
---|
| 611 | convexDense (newtonPolyg, n, M, A); |
---|
| 612 | } |
---|
[a2dd9b2] | 613 | CanonicalForm result= 0; |
---|
| 614 | ZZ expX, expY; |
---|
| 615 | Variable x= Variable (1); |
---|
| 616 | Variable y= Variable (2); |
---|
| 617 | |
---|
| 618 | ZZ minExpX, minExpY; |
---|
| 619 | |
---|
| 620 | int k= 0; |
---|
| 621 | Variable alpha; |
---|
| 622 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 623 | { |
---|
| 624 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
| 625 | { |
---|
| 626 | expX= i.exp()*M (1,2) + A (1); |
---|
| 627 | expY= i.exp()*M (2,2) + A (2); |
---|
| 628 | if (k == 0) |
---|
| 629 | { |
---|
| 630 | minExpY= expY; |
---|
| 631 | minExpX= expX; |
---|
| 632 | k= 1; |
---|
| 633 | } |
---|
| 634 | else |
---|
| 635 | { |
---|
| 636 | minExpY= (minExpY > expY) ? expY : minExpY; |
---|
| 637 | minExpX= (minExpX > expX) ? expX : minExpX; |
---|
| 638 | } |
---|
| 639 | result += i.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 640 | continue; |
---|
| 641 | } |
---|
| 642 | CFIterator j= i.coeff(); |
---|
| 643 | if (k == 0) |
---|
| 644 | { |
---|
| 645 | expX= j.exp()*M (1,1) + i.exp()*M (1,2) + A (1); |
---|
| 646 | expY= j.exp()*M (2,1) + i.exp()*M (2,2) + A (2); |
---|
| 647 | minExpX= expX; |
---|
| 648 | minExpY= expY; |
---|
| 649 | result += j.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 650 | j++; |
---|
| 651 | k= 1; |
---|
| 652 | } |
---|
| 653 | |
---|
| 654 | for (; j.hasTerms(); j++) |
---|
| 655 | { |
---|
| 656 | expX= j.exp()*M (1,1) + i.exp()*M (1,2) + A (1); |
---|
| 657 | expY= j.exp()*M (2,1) + i.exp()*M (2,2) + A (2); |
---|
| 658 | result += j.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 659 | minExpY= (minExpY > expY) ? expY : minExpY; |
---|
| 660 | minExpX= (minExpX > expX) ? expX : minExpX; |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | |
---|
| 664 | if (to_long (minExpX) < 0) |
---|
| 665 | { |
---|
| 666 | result *= power (x,-to_long(minExpX)); |
---|
| 667 | result /= CanonicalForm (x, 0); |
---|
| 668 | } |
---|
| 669 | else |
---|
| 670 | result /= power (x,to_long(minExpX)); |
---|
| 671 | |
---|
| 672 | if (to_long (minExpY) < 0) |
---|
| 673 | { |
---|
| 674 | result *= power (y,-to_long(minExpY)); |
---|
| 675 | result /= CanonicalForm (y, 0); |
---|
| 676 | } |
---|
| 677 | else |
---|
| 678 | result /= power (y,to_long(minExpY)); |
---|
| 679 | |
---|
| 680 | CanonicalForm tmp= LC (result); |
---|
| 681 | if (tmp.inPolyDomain() && degree (tmp) <= 0) |
---|
| 682 | { |
---|
| 683 | int d= degree (result); |
---|
| 684 | Variable x= result.mvar(); |
---|
| 685 | result -= tmp*power (x, d); |
---|
| 686 | result += Lc (tmp)*power (x, d); |
---|
| 687 | } |
---|
| 688 | |
---|
[e243418] | 689 | if (computeMA) |
---|
| 690 | { |
---|
| 691 | for (int i= 0; i < n; i++) |
---|
| 692 | delete [] newtonPolyg [i]; |
---|
| 693 | delete [] newtonPolyg; |
---|
| 694 | M= inv (M); |
---|
| 695 | } |
---|
[a2dd9b2] | 696 | |
---|
| 697 | return result; |
---|
| 698 | } |
---|
| 699 | |
---|
| 700 | CanonicalForm |
---|
| 701 | decompress (const CanonicalForm& F, const mat_ZZ& inverseM, const vec_ZZ& A) |
---|
| 702 | { |
---|
| 703 | CanonicalForm result= 0; |
---|
| 704 | ZZ expX, expY; |
---|
| 705 | Variable x= Variable (1); |
---|
| 706 | Variable y= Variable (2); |
---|
| 707 | ZZ minExpX, minExpY; |
---|
| 708 | if (F.isUnivariate() && F.level() == 1) |
---|
| 709 | { |
---|
| 710 | CFIterator i= F; |
---|
| 711 | expX= (i.exp() - A (1))*inverseM (1,1) + (-A (2))*inverseM (1,2); |
---|
| 712 | expY= (i.exp() - A (1))*inverseM (2,1) + (-A (2))*inverseM (2,2); |
---|
| 713 | minExpX= expX; |
---|
| 714 | minExpY= expY; |
---|
| 715 | result += i.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 716 | i++; |
---|
| 717 | for (; i.hasTerms(); i++) |
---|
| 718 | { |
---|
| 719 | expX= (i.exp() - A (1))*inverseM (1,1) + (-A (2))*inverseM (1,2); |
---|
| 720 | expY= (i.exp() - A (1))*inverseM (2,1) + (-A (2))*inverseM (2,2); |
---|
| 721 | result += i.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 722 | minExpY= (minExpY > expY) ? expY : minExpY; |
---|
| 723 | minExpX= (minExpX > expX) ? expX : minExpX; |
---|
| 724 | } |
---|
| 725 | |
---|
| 726 | if (to_long (minExpX) < 0) |
---|
| 727 | { |
---|
| 728 | result *= power (x,-to_long(minExpX)); |
---|
| 729 | result /= CanonicalForm (x, 0); |
---|
| 730 | } |
---|
| 731 | else |
---|
| 732 | result /= power (x,to_long(minExpX)); |
---|
| 733 | |
---|
| 734 | if (to_long (minExpY) < 0) |
---|
| 735 | { |
---|
| 736 | result *= power (y,-to_long(minExpY)); |
---|
| 737 | result /= CanonicalForm (y, 0); |
---|
| 738 | } |
---|
| 739 | else |
---|
| 740 | result /= power (y,to_long(minExpY)); |
---|
| 741 | |
---|
| 742 | return result/ Lc (result); //normalize |
---|
| 743 | } |
---|
| 744 | |
---|
| 745 | int k= 0; |
---|
| 746 | Variable alpha; |
---|
| 747 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 748 | { |
---|
| 749 | if (i.coeff().inCoeffDomain() && hasFirstAlgVar (i.coeff(), alpha)) |
---|
| 750 | { |
---|
| 751 | expX= -A(1)*inverseM (1,1) + (i.exp() - A (2))*inverseM (1,2); |
---|
| 752 | expY= -A(1)*inverseM (2,1) + (i.exp() - A (2))*inverseM (2,2); |
---|
| 753 | if (k == 0) |
---|
| 754 | { |
---|
| 755 | minExpY= expY; |
---|
| 756 | minExpX= expX; |
---|
| 757 | k= 1; |
---|
| 758 | } |
---|
| 759 | else |
---|
| 760 | { |
---|
| 761 | minExpY= (minExpY > expY) ? expY : minExpY; |
---|
| 762 | minExpX= (minExpX > expX) ? expX : minExpX; |
---|
| 763 | } |
---|
| 764 | result += i.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 765 | continue; |
---|
| 766 | } |
---|
| 767 | CFIterator j= i.coeff(); |
---|
| 768 | if (k == 0) |
---|
| 769 | { |
---|
| 770 | expX= (j.exp() - A (1))*inverseM (1,1) + (i.exp() - A (2))*inverseM (1,2); |
---|
| 771 | expY= (j.exp() - A (1))*inverseM (2,1) + (i.exp() - A (2))*inverseM (2,2); |
---|
| 772 | minExpX= expX; |
---|
| 773 | minExpY= expY; |
---|
| 774 | result += j.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 775 | j++; |
---|
| 776 | k= 1; |
---|
| 777 | } |
---|
| 778 | |
---|
| 779 | for (; j.hasTerms(); j++) |
---|
| 780 | { |
---|
| 781 | expX= (j.exp() - A (1))*inverseM (1,1) + (i.exp() - A (2))*inverseM (1,2); |
---|
| 782 | expY= (j.exp() - A (1))*inverseM (2,1) + (i.exp() - A (2))*inverseM (2,2); |
---|
| 783 | result += j.coeff()*power (x, to_long (expX))*power (y, to_long (expY)); |
---|
| 784 | minExpY= (minExpY > expY) ? expY : minExpY; |
---|
| 785 | minExpX= (minExpX > expX) ? expX : minExpX; |
---|
| 786 | } |
---|
| 787 | } |
---|
| 788 | |
---|
| 789 | if (to_long (minExpX) < 0) |
---|
| 790 | { |
---|
| 791 | result *= power (x,-to_long(minExpX)); |
---|
| 792 | result /= CanonicalForm (x, 0); |
---|
| 793 | } |
---|
| 794 | else |
---|
| 795 | result /= power (x,to_long(minExpX)); |
---|
| 796 | |
---|
| 797 | if (to_long (minExpY) < 0) |
---|
| 798 | { |
---|
| 799 | result *= power (y,-to_long(minExpY)); |
---|
| 800 | result /= CanonicalForm (y, 0); |
---|
| 801 | } |
---|
| 802 | else |
---|
| 803 | result /= power (y,to_long(minExpY)); |
---|
| 804 | |
---|
| 805 | return result/Lc (result); //normalize |
---|
| 806 | } |
---|
[2072126] | 807 | #endif |
---|
[6fd83c4] | 808 | |
---|
| 809 | //assumes the input is a Newton polygon of a bivariate polynomial which is |
---|
| 810 | //primitive wrt. x and y, i.e. there is at least one point of the polygon lying |
---|
| 811 | //on the x-axis and one lying on the y-axis |
---|
| 812 | int* getRightSide (int** polygon, int sizeOfPolygon, int& sizeOfOutput) |
---|
| 813 | { |
---|
| 814 | int maxY= polygon [0][0]; |
---|
| 815 | int indexY= 0; |
---|
| 816 | for (int i= 1; i < sizeOfPolygon; i++) |
---|
| 817 | { |
---|
| 818 | if (maxY < polygon [i][0]) |
---|
| 819 | { |
---|
| 820 | maxY= polygon [i][0]; |
---|
| 821 | indexY= i; |
---|
| 822 | } |
---|
| 823 | else if (maxY == polygon [i][0]) |
---|
| 824 | { |
---|
| 825 | if (polygon [indexY][1] < polygon[i][1]) |
---|
| 826 | indexY= i; |
---|
| 827 | } |
---|
| 828 | if (maxY > polygon [i][0]) |
---|
| 829 | break; |
---|
| 830 | } |
---|
| 831 | |
---|
| 832 | int count= -1; |
---|
| 833 | for (int i= indexY; i < sizeOfPolygon; i++) |
---|
| 834 | { |
---|
| 835 | if (polygon[i][0] == 0) |
---|
| 836 | { |
---|
| 837 | count= i - indexY; |
---|
| 838 | break; |
---|
| 839 | } |
---|
| 840 | } |
---|
| 841 | |
---|
| 842 | int * result; |
---|
| 843 | int index= 0; |
---|
| 844 | if (count < 0) |
---|
| 845 | { |
---|
| 846 | result= new int [sizeOfPolygon - indexY]; |
---|
| 847 | sizeOfOutput= sizeOfPolygon - indexY; |
---|
| 848 | count= sizeOfPolygon - indexY - 1; |
---|
| 849 | result [0]= polygon[sizeOfPolygon - 1][0] - polygon [0] [0]; |
---|
| 850 | index= 1; |
---|
| 851 | } |
---|
| 852 | else |
---|
| 853 | { |
---|
| 854 | sizeOfOutput= count; |
---|
| 855 | result= new int [count]; |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | for (int i= indexY + count; i > indexY; i--, index++) |
---|
| 859 | result [index]= polygon [i - 1] [0] - polygon [i] [0]; |
---|
| 860 | |
---|
| 861 | return result; |
---|
| 862 | } |
---|
[9752db] | 863 | |
---|
| 864 | bool irreducibilityTest (const CanonicalForm& F) |
---|
| 865 | { |
---|
[36ef97a] | 866 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
| 867 | ASSERT (getCharacteristic() == 0, "expected polynomial over integers or rationals"); |
---|
| 868 | |
---|
[9752db] | 869 | int sizeOfNewtonPolygon; |
---|
| 870 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
| 871 | if (sizeOfNewtonPolygon == 3) |
---|
| 872 | { |
---|
| 873 | bool check1= |
---|
| 874 | (newtonPolyg[0][0]==0 || newtonPolyg[1][0]==0 || newtonPolyg[2][0]==0); |
---|
| 875 | if (check1) |
---|
| 876 | { |
---|
| 877 | bool check2= |
---|
| 878 | (newtonPolyg[0][1]==0 || newtonPolyg[1][1]==0 || newtonPolyg[2][0]==0); |
---|
| 879 | if (check2) |
---|
| 880 | { |
---|
| 881 | bool isRat= isOn (SW_RATIONAL); |
---|
| 882 | if (isRat) |
---|
| 883 | Off (SW_RATIONAL); |
---|
[36ef97a] | 884 | CanonicalForm tmp= gcd (newtonPolyg[0][0],newtonPolyg[0][1]); // maybe it's better to use plain intgcd |
---|
[9752db] | 885 | tmp= gcd (tmp, newtonPolyg[1][0]); |
---|
| 886 | tmp= gcd (tmp, newtonPolyg[1][1]); |
---|
| 887 | tmp= gcd (tmp, newtonPolyg[2][0]); |
---|
| 888 | tmp= gcd (tmp, newtonPolyg[2][1]); |
---|
| 889 | if (isRat) |
---|
| 890 | On (SW_RATIONAL); |
---|
[7c118d] | 891 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
| 892 | delete [] newtonPolyg [i]; |
---|
| 893 | delete [] newtonPolyg; |
---|
[9752db] | 894 | return (tmp==1); |
---|
| 895 | } |
---|
| 896 | } |
---|
| 897 | } |
---|
| 898 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
| 899 | delete [] newtonPolyg [i]; |
---|
| 900 | delete [] newtonPolyg; |
---|
| 901 | return false; |
---|
| 902 | } |
---|
[36ef97a] | 903 | |
---|
| 904 | bool absIrredTest (const CanonicalForm& F) |
---|
| 905 | { |
---|
| 906 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
| 907 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
| 908 | |
---|
| 909 | int sizeOfNewtonPolygon; |
---|
| 910 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
| 911 | bool isRat= isOn (SW_RATIONAL); |
---|
| 912 | if (isRat) |
---|
| 913 | Off (SW_RATIONAL); |
---|
| 914 | int p=getCharacteristic(); |
---|
| 915 | int d=1; |
---|
| 916 | char bufGFName='Z'; |
---|
| 917 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 918 | if (GF) |
---|
| 919 | { |
---|
| 920 | d= getGFDegree(); |
---|
| 921 | bufGFName=gf_name; |
---|
| 922 | } |
---|
| 923 | |
---|
| 924 | setCharacteristic(0); |
---|
| 925 | |
---|
| 926 | CanonicalForm g= gcd (newtonPolyg[0][0], newtonPolyg[0][1]); //maybe it's better to use plain intgcd |
---|
| 927 | |
---|
| 928 | int i= 1; |
---|
| 929 | while (!g.isOne() && i < sizeOfNewtonPolygon) |
---|
| 930 | { |
---|
| 931 | g= gcd (g, newtonPolyg[i][0]); |
---|
| 932 | g= gcd (g, newtonPolyg[i][1]); |
---|
| 933 | i++; |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | bool result= g.isOne(); |
---|
| 937 | |
---|
| 938 | if (GF) |
---|
| 939 | setCharacteristic (p, d, bufGFName); |
---|
| 940 | else |
---|
| 941 | setCharacteristic(p); |
---|
| 942 | |
---|
| 943 | if (isRat) |
---|
| 944 | On (SW_RATIONAL); |
---|
| 945 | |
---|
[b79b58] | 946 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
| 947 | delete [] newtonPolyg[i]; |
---|
| 948 | |
---|
| 949 | delete [] newtonPolyg; |
---|
| 950 | |
---|
[36ef97a] | 951 | return result; |
---|
| 952 | } |
---|
| 953 | |
---|
[b79b58] | 954 | bool modularIrredTest (const CanonicalForm& F) |
---|
| 955 | { |
---|
| 956 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
| 957 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
| 958 | |
---|
| 959 | bool isRat= isOn (SW_RATIONAL); |
---|
| 960 | if (isRat) |
---|
| 961 | Off (SW_RATIONAL); |
---|
| 962 | |
---|
| 963 | if (isRat) |
---|
| 964 | ASSERT (bCommonDen (F).isOne(), "poly over Z expected"); |
---|
| 965 | |
---|
| 966 | CanonicalForm Fp, N= maxNorm (F); |
---|
| 967 | int tdeg= totaldegree (F); |
---|
| 968 | |
---|
| 969 | int i= 0; |
---|
| 970 | //TODO: maybe it's better to choose the characteristic as large as possible |
---|
| 971 | // as factorization over large finite field will be faster |
---|
| 972 | //TODO: handle those cases where our factory primes are not enough |
---|
| 973 | //TODO: factorize coefficients corresponding to the vertices of the Newton |
---|
| 974 | // polygon and only try the obtained factors |
---|
| 975 | if (N < cf_getSmallPrime (cf_getNumSmallPrimes()-1)) |
---|
| 976 | { |
---|
| 977 | while (i < cf_getNumSmallPrimes() && N > cf_getSmallPrime(i)) |
---|
| 978 | { |
---|
| 979 | setCharacteristic (cf_getSmallPrime (i)); |
---|
| 980 | Fp= F.mapinto(); |
---|
| 981 | i++; |
---|
| 982 | if (totaldegree (Fp) == tdeg) |
---|
| 983 | { |
---|
| 984 | if (absIrredTest (Fp)) |
---|
| 985 | { |
---|
| 986 | CFFList factors= factorize (Fp); |
---|
| 987 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
| 988 | { |
---|
| 989 | if (isRat) |
---|
| 990 | On (SW_RATIONAL); |
---|
| 991 | setCharacteristic (0); |
---|
| 992 | return true; |
---|
| 993 | } |
---|
| 994 | } |
---|
| 995 | } |
---|
| 996 | setCharacteristic (0); |
---|
| 997 | } |
---|
| 998 | } |
---|
| 999 | else |
---|
| 1000 | { |
---|
| 1001 | while (i < cf_getNumPrimes() && N > cf_getPrime (i)) |
---|
| 1002 | { |
---|
| 1003 | setCharacteristic (cf_getPrime (i)); |
---|
| 1004 | Fp= F.mapinto(); |
---|
| 1005 | i++; |
---|
| 1006 | if (totaldegree (Fp) == tdeg) |
---|
| 1007 | { |
---|
| 1008 | if (absIrredTest (Fp)) |
---|
| 1009 | { |
---|
| 1010 | CFFList factors= factorize (Fp); |
---|
| 1011 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
| 1012 | { |
---|
| 1013 | if (isRat) |
---|
| 1014 | On (SW_RATIONAL); |
---|
| 1015 | setCharacteristic (0); |
---|
| 1016 | return true; |
---|
| 1017 | } |
---|
| 1018 | } |
---|
| 1019 | } |
---|
| 1020 | setCharacteristic (0); |
---|
| 1021 | } |
---|
| 1022 | } |
---|
| 1023 | |
---|
| 1024 | if (isRat) |
---|
| 1025 | On (SW_RATIONAL); |
---|
| 1026 | |
---|
| 1027 | return false; |
---|
| 1028 | } |
---|
| 1029 | |
---|
| 1030 | bool |
---|
| 1031 | modularIrredTestWithShift (const CanonicalForm& F) |
---|
| 1032 | { |
---|
| 1033 | ASSERT (getNumVars (F) == 2, "expected bivariate polynomial"); |
---|
| 1034 | ASSERT (factorize (F).length() <= 2, " expected irreducible polynomial"); |
---|
| 1035 | |
---|
| 1036 | bool isRat= isOn (SW_RATIONAL); |
---|
| 1037 | if (isRat) |
---|
| 1038 | Off (SW_RATIONAL); |
---|
| 1039 | |
---|
| 1040 | if (isRat) |
---|
| 1041 | ASSERT (bCommonDen (F).isOne(), "poly over Z expected"); |
---|
| 1042 | |
---|
| 1043 | Variable x= Variable (1); |
---|
| 1044 | Variable y= Variable (2); |
---|
| 1045 | CanonicalForm Fp; |
---|
| 1046 | int tdeg= totaldegree (F); |
---|
| 1047 | |
---|
| 1048 | REvaluation E; |
---|
| 1049 | |
---|
| 1050 | setCharacteristic (2); |
---|
| 1051 | Fp= F.mapinto(); |
---|
| 1052 | |
---|
| 1053 | E= REvaluation (1,2, FFRandom()); |
---|
| 1054 | |
---|
| 1055 | E.nextpoint(); |
---|
| 1056 | |
---|
| 1057 | Fp= Fp (x+E[1], x); |
---|
| 1058 | Fp= Fp (y+E[2], y); |
---|
| 1059 | |
---|
| 1060 | if (tdeg == totaldegree (Fp)) |
---|
| 1061 | { |
---|
| 1062 | if (absIrredTest (Fp)) |
---|
| 1063 | { |
---|
| 1064 | CFFList factors= factorize (Fp); |
---|
| 1065 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
| 1066 | { |
---|
| 1067 | if (isRat) |
---|
| 1068 | On (SW_RATIONAL); |
---|
| 1069 | setCharacteristic (0); |
---|
| 1070 | return true; |
---|
| 1071 | } |
---|
| 1072 | } |
---|
| 1073 | } |
---|
| 1074 | |
---|
| 1075 | E.nextpoint(); |
---|
| 1076 | |
---|
| 1077 | Fp= Fp (x+E[1], x); |
---|
| 1078 | Fp= Fp (y+E[2], y); |
---|
| 1079 | |
---|
| 1080 | if (tdeg == totaldegree (Fp)) |
---|
| 1081 | { |
---|
| 1082 | if (absIrredTest (Fp)) |
---|
| 1083 | { |
---|
| 1084 | CFFList factors= factorize (Fp); |
---|
| 1085 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
| 1086 | { |
---|
| 1087 | if (isRat) |
---|
| 1088 | On (SW_RATIONAL); |
---|
| 1089 | setCharacteristic (0); |
---|
| 1090 | return true; |
---|
| 1091 | } |
---|
| 1092 | } |
---|
| 1093 | } |
---|
| 1094 | |
---|
| 1095 | int i= 0; |
---|
| 1096 | while (cf_getSmallPrime (i) < 102) |
---|
| 1097 | { |
---|
| 1098 | setCharacteristic (cf_getSmallPrime (i)); |
---|
| 1099 | i++; |
---|
| 1100 | E= REvaluation (1, 2, FFRandom()); |
---|
| 1101 | |
---|
| 1102 | for (int j= 0; j < 3; j++) |
---|
| 1103 | { |
---|
| 1104 | Fp= F.mapinto(); |
---|
| 1105 | E.nextpoint(); |
---|
| 1106 | Fp= Fp (x+E[1], x); |
---|
| 1107 | Fp= Fp (y+E[2], y); |
---|
| 1108 | |
---|
| 1109 | if (tdeg == totaldegree (Fp)) |
---|
| 1110 | { |
---|
| 1111 | if (absIrredTest (Fp)) |
---|
| 1112 | { |
---|
| 1113 | CFFList factors= factorize (Fp); |
---|
| 1114 | if (factors.length() == 2 && factors.getLast().exp() == 1) |
---|
| 1115 | { |
---|
| 1116 | if (isRat) |
---|
| 1117 | On (SW_RATIONAL); |
---|
| 1118 | setCharacteristic (0); |
---|
| 1119 | return true; |
---|
| 1120 | } |
---|
| 1121 | } |
---|
| 1122 | } |
---|
| 1123 | } |
---|
| 1124 | } |
---|
| 1125 | |
---|
| 1126 | setCharacteristic (0); |
---|
| 1127 | if (isRat) |
---|
| 1128 | On (SW_RATIONAL); |
---|
| 1129 | |
---|
| 1130 | return false; |
---|
| 1131 | } |
---|
| 1132 | |
---|
| 1133 | |
---|