1 | /***************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | *****************************************/ |
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4 | /* |
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5 | * * ABSTRACT: class bigintmat: matrices of numbers. |
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6 | * * a few functinos might be limited to bigint or euclidean rings. |
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7 | * */ |
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8 | |
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9 | |
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10 | #include <misc/auxiliary.h> |
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11 | |
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12 | |
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13 | |
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14 | #include "bigintmat.h" |
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15 | #include <misc/intvec.h> |
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16 | #include <coeffs/longrat.h> |
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17 | |
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18 | |
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19 | #include <math.h> |
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20 | #include <string.h> |
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21 | |
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22 | |
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23 | //#define BIMATELEM(M,I,J) (M)[ (M).index(I,J) ] |
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24 | |
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25 | bigintmat * bigintmat::transpose() |
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26 | { |
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27 | bigintmat * t = new bigintmat(col, row, basecoeffs()); |
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28 | for (int i=1; i<=row; i++) |
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29 | { |
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30 | for (int j=1; j<=col; j++) |
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31 | { |
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32 | t->set(j, i, BIMATELEM(*this,i,j)); |
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33 | } |
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34 | } |
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35 | return t; |
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36 | } |
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37 | |
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38 | void bigintmat::inpTranspose() |
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39 | { |
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40 | int n = row, |
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41 | m = col, |
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42 | nm = n<m?n : m; // the min, describing the square part of the matrix |
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43 | //CF: this is not optimal, but so far, it seems to work |
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44 | |
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45 | #define swap(_i, _j) \ |
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46 | int __i = (_i), __j=(_j); \ |
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47 | number c = v[__i]; \ |
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48 | v[__i] = v[__j]; \ |
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49 | v[__j] = c \ |
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50 | |
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51 | for (int i=0; i< nm; i++) |
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52 | for (int j=i+1; j< nm; j++) { |
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53 | swap(i*m+j, j*n+i); |
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54 | } |
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55 | if (n<m) |
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56 | for (int i=nm; i<m; i++) |
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57 | for(int j=0; j<n; j++) { |
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58 | swap(j*n+i, i*m+j); |
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59 | } |
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60 | if (n>m) |
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61 | for (int i=nm; i<n; i++) |
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62 | for(int j=0; j<m; j++) { |
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63 | swap(i*m+j, j*n+i); |
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64 | } |
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65 | #undef swap |
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66 | row = m; |
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67 | col = n; |
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68 | } |
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69 | |
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70 | |
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71 | // Beginnt bei [0] |
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72 | void bigintmat::set(int i, number n, const coeffs C) |
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73 | { |
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74 | assume (C == NULL || C == basecoeffs()); |
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75 | |
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76 | rawset(i, n_Copy(n, basecoeffs()), basecoeffs()); |
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77 | } |
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78 | |
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79 | // Beginnt bei [1,1] |
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80 | void bigintmat::set(int i, int j, number n, const coeffs C) |
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81 | { |
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82 | assume (C == NULL || C == basecoeffs()); |
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83 | assume (i > 0 && j > 0); |
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84 | assume (i <= rows() && j <= cols()); |
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85 | set(index(i, j), n, C); |
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86 | } |
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87 | |
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88 | number bigintmat::get(int i) const |
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89 | { |
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90 | assume (i >= 0); |
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91 | assume (i<rows()*cols()); |
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92 | |
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93 | return n_Copy(v[i], basecoeffs()); |
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94 | } |
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95 | |
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96 | number bigintmat::view(int i) const |
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97 | { |
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98 | assume (i >= 0); |
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99 | assume (i<rows()*cols()); |
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100 | |
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101 | return v[i]; |
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102 | } |
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103 | |
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104 | number bigintmat::get(int i, int j) const |
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105 | { |
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106 | assume (i > 0 && j > 0); |
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107 | assume (i <= rows() && j <= cols()); |
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108 | |
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109 | return get(index(i, j)); |
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110 | } |
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111 | |
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112 | number bigintmat::view(int i, int j) const |
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113 | { |
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114 | assume (i >= 0 && j >= 0); |
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115 | assume (i <= rows() && j <= cols()); |
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116 | |
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117 | return view(index(i, j)); |
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118 | } |
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119 | // Ueberladener *=-Operator (fÃŒr int und bigint) |
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120 | // Frage hier: *= verwenden oder lieber = und * einzeln? |
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121 | void bigintmat::operator*=(int intop) |
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122 | { |
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123 | number iop = n_Init(intop, basecoeffs()); |
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124 | |
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125 | inpMult(iop, basecoeffs()); |
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126 | |
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127 | n_Delete(&iop, basecoeffs()); |
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128 | } |
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129 | |
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130 | void bigintmat::inpMult(number bintop, const coeffs C) |
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131 | { |
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132 | assume (C == NULL || C == basecoeffs()); |
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133 | |
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134 | const int l = rows() * cols(); |
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135 | |
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136 | for (int i=0; i < l; i++) |
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137 | n_InpMult(v[i], bintop, basecoeffs()); |
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138 | } |
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139 | |
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140 | // Stimmen Parameter? |
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141 | // Welche der beiden Methoden? |
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142 | // Oder lieber eine comp-Funktion? |
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143 | |
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144 | bool operator==(const bigintmat & lhr, const bigintmat & rhr) |
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145 | { |
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146 | if (&lhr == &rhr) { return true; } |
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147 | if (lhr.cols() != rhr.cols()) { return false; } |
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148 | if (lhr.rows() != rhr.rows()) { return false; } |
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149 | if (lhr.basecoeffs() != rhr.basecoeffs()) { return false; } |
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150 | |
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151 | const int l = (lhr.rows())*(lhr.cols()); |
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152 | |
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153 | for (int i=0; i < l; i++) |
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154 | { |
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155 | if (!n_Equal(lhr[i], rhr[i], lhr.basecoeffs())) { return false; } |
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156 | } |
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157 | |
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158 | return true; |
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159 | } |
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160 | |
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161 | bool operator!=(const bigintmat & lhr, const bigintmat & rhr) |
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162 | { |
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163 | return !(lhr==rhr); |
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164 | } |
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165 | |
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166 | // Matrix-Add/-Sub/-Mult so oder mit operator+/-/* ? |
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167 | bigintmat * bimAdd(bigintmat * a, bigintmat * b) |
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168 | { |
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169 | if (a->cols() != b->cols()) return NULL; |
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170 | if (a->rows() != b->rows()) return NULL; |
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171 | if (a->basecoeffs() != b->basecoeffs()) { return NULL; } |
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172 | |
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173 | const coeffs basecoeffs = a->basecoeffs(); |
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174 | |
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175 | int i; |
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176 | |
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177 | bigintmat * bim = new bigintmat(a->rows(), a->cols(), basecoeffs); |
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178 | |
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179 | for (i=a->rows()*a->cols()-1;i>=0; i--) |
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180 | bim->rawset(i, n_Add((*a)[i], (*b)[i], basecoeffs), basecoeffs); |
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181 | |
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182 | return bim; |
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183 | } |
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184 | bigintmat * bimAdd(bigintmat * a, int b) |
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185 | { |
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186 | |
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187 | const int mn = a->rows()*a->cols(); |
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188 | |
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189 | const coeffs basecoeffs = a->basecoeffs(); |
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190 | number bb=n_Init(b,basecoeffs); |
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191 | |
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192 | int i; |
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193 | |
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194 | bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs); |
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195 | |
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196 | for (i=0; i<mn; i++) |
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197 | bim->rawset(i, n_Add((*a)[i], bb, basecoeffs), basecoeffs); |
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198 | |
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199 | n_Delete(&bb,basecoeffs); |
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200 | return bim; |
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201 | } |
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202 | |
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203 | bigintmat * bimSub(bigintmat * a, bigintmat * b) |
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204 | { |
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205 | if (a->cols() != b->cols()) return NULL; |
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206 | if (a->rows() != b->rows()) return NULL; |
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207 | if (a->basecoeffs() != b->basecoeffs()) { return NULL; } |
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208 | |
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209 | const coeffs basecoeffs = a->basecoeffs(); |
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210 | |
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211 | int i; |
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212 | |
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213 | bigintmat * bim = new bigintmat(a->rows(), a->cols(), basecoeffs); |
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214 | |
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215 | for (i=a->rows()*a->cols()-1;i>=0; i--) |
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216 | bim->rawset(i, n_Sub((*a)[i], (*b)[i], basecoeffs), basecoeffs); |
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217 | |
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218 | return bim; |
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219 | } |
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220 | |
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221 | bigintmat * bimSub(bigintmat * a, int b) |
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222 | { |
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223 | const int mn = a->rows()*a->cols(); |
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224 | |
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225 | const coeffs basecoeffs = a->basecoeffs(); |
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226 | number bb=n_Init(b,basecoeffs); |
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227 | |
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228 | int i; |
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229 | |
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230 | bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs); |
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231 | |
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232 | for (i=0; i<mn; i++) |
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233 | bim->rawset(i, n_Sub((*a)[i], bb, basecoeffs), basecoeffs); |
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234 | |
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235 | n_Delete(&bb,basecoeffs); |
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236 | return bim; |
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237 | } |
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238 | |
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239 | //TODO: make special versions for certain rings! |
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240 | bigintmat * bimMult(bigintmat * a, bigintmat * b) |
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241 | { |
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242 | const int ca = a->cols(); |
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243 | const int cb = b->cols(); |
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244 | |
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245 | const int ra = a->rows(); |
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246 | const int rb = b->rows(); |
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247 | |
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248 | if (ca != rb) |
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249 | { |
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250 | #ifndef SING_NDEBUG |
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251 | Werror("wrong bigintmat sizes at multiplication a * b: acols: %d != brows: %d\n", ca, rb); |
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252 | #endif |
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253 | return NULL; |
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254 | } |
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255 | |
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256 | assume (ca == rb); |
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257 | |
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258 | if (a->basecoeffs() != b->basecoeffs()) { return NULL; } |
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259 | |
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260 | const coeffs basecoeffs = a->basecoeffs(); |
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261 | |
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262 | int i, j, k; |
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263 | |
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264 | number sum; |
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265 | |
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266 | bigintmat * bim = new bigintmat(ra, cb, basecoeffs); |
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267 | |
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268 | for (i=1; i<=ra; i++) |
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269 | for (j=1; j<=cb; j++) |
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270 | { |
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271 | sum = n_Init(0, basecoeffs); |
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272 | |
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273 | for (k=1; k<=ca; k++) |
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274 | { |
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275 | number prod = n_Mult( BIMATELEM(*a, i, k), BIMATELEM(*b, k, j), basecoeffs); |
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276 | |
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277 | number sum2 = n_Add(sum, prod, basecoeffs); // no inplace add :( |
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278 | |
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279 | n_Delete(&sum, basecoeffs); n_Delete(&prod, basecoeffs); |
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280 | |
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281 | sum = sum2; |
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282 | } |
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283 | bim->rawset(i, j, sum, basecoeffs); |
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284 | } |
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285 | return bim; |
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286 | } |
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287 | |
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288 | bigintmat * bimMult(bigintmat * a, int b) |
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289 | { |
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290 | |
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291 | const int mn = a->rows()*a->cols(); |
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292 | |
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293 | const coeffs basecoeffs = a->basecoeffs(); |
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294 | number bb=n_Init(b,basecoeffs); |
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295 | |
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296 | int i; |
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297 | |
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298 | bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs); |
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299 | |
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300 | for (i=0; i<mn; i++) |
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301 | bim->rawset(i, n_Mult((*a)[i], bb, basecoeffs), basecoeffs); |
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302 | |
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303 | n_Delete(&bb,basecoeffs); |
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304 | return bim; |
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305 | } |
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306 | |
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307 | bigintmat * bimMult(bigintmat * a, number b, const coeffs cf) |
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308 | { |
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309 | if (cf!=a->basecoeffs()) return NULL; |
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310 | |
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311 | const int mn = a->rows()*a->cols(); |
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312 | |
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313 | const coeffs basecoeffs = a->basecoeffs(); |
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314 | |
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315 | int i; |
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316 | |
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317 | bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs); |
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318 | |
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319 | for (i=0; i<mn; i++) |
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320 | bim->rawset(i, n_Mult((*a)[i], b, basecoeffs), basecoeffs); |
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321 | |
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322 | return bim; |
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323 | } |
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324 | |
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325 | // ----------------------------------------------------------------- // |
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326 | // Korrekt? |
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327 | |
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328 | intvec * bim2iv(bigintmat * b) |
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329 | { |
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330 | intvec * iv = new intvec(b->rows(), b->cols(), 0); |
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331 | for (int i=0; i<(b->rows())*(b->cols()); i++) |
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332 | (*iv)[i] = n_Int((*b)[i], b->basecoeffs()); // Geht das so? |
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333 | return iv; |
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334 | } |
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335 | |
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336 | bigintmat * iv2bim(intvec * b, const coeffs C) |
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337 | { |
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338 | const int l = (b->rows())*(b->cols()); |
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339 | bigintmat * bim = new bigintmat(b->rows(), b->cols(), C); |
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340 | |
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341 | for (int i=0; i < l; i++) |
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342 | bim->rawset(i, n_Init((*b)[i], C), C); |
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343 | |
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344 | return bim; |
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345 | } |
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346 | |
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347 | // ----------------------------------------------------------------- // |
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348 | |
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349 | int bigintmat::compare(const bigintmat* op) const |
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350 | { |
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351 | assume (basecoeffs() == op->basecoeffs() ); |
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352 | |
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353 | #ifndef SING_NDEBUG |
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354 | if (basecoeffs() != op->basecoeffs() ) |
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355 | WerrorS("wrong bigintmat comparison: different basecoeffs!\n"); |
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356 | #endif |
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357 | |
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358 | if ((col!=1) ||(op->cols()!=1)) |
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359 | { |
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360 | if((col!=op->cols()) |
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361 | || (row!=op->rows())) |
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362 | return -2; |
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363 | } |
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364 | |
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365 | int i; |
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366 | for (i=0; i<si_min(row*col,op->rows()*op->cols()); i++) |
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367 | { |
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368 | if ( n_Greater(v[i], (*op)[i], basecoeffs()) ) |
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369 | return 1; |
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370 | else if (! n_Equal(v[i], (*op)[i], basecoeffs())) |
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371 | return -1; |
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372 | } |
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373 | |
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374 | for (; i<row; i++) |
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375 | { |
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376 | if ( n_GreaterZero(v[i], basecoeffs()) ) |
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377 | return 1; |
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378 | else if (! n_IsZero(v[i], basecoeffs()) ) |
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379 | return -1; |
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380 | } |
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381 | for (; i<op->rows(); i++) |
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382 | { |
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383 | if ( n_GreaterZero((*op)[i], basecoeffs()) ) |
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384 | return -1; |
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385 | else if (! n_IsZero((*op)[i], basecoeffs()) ) |
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386 | return 1; |
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387 | } |
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388 | return 0; |
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389 | } |
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390 | |
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391 | |
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392 | bigintmat * bimCopy(const bigintmat * b) |
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393 | { |
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394 | if (b == NULL) |
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395 | return NULL; |
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396 | |
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397 | return new bigintmat(b); |
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398 | } |
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399 | |
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400 | void bigintmat::Write() |
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401 | { |
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402 | int n = cols(), m=rows(); |
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403 | |
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404 | StringAppendS("[ "); |
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405 | for(int i=1; i<= m; i++) { |
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406 | StringAppendS("[ "); |
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407 | for(int j=1; j< n; j++) { |
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408 | n_Write(v[(i-1)*n+j-1], basecoeffs()); |
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409 | StringAppendS(", "); |
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410 | } |
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411 | if (n) n_Write(v[i*n-1], basecoeffs()); |
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412 | StringAppendS(" ]"); |
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413 | if (i<m) { |
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414 | StringAppendS(", "); |
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415 | } |
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416 | } |
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417 | StringAppendS(" ] "); |
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418 | } |
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419 | |
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420 | char* bigintmat::String() |
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421 | { |
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422 | StringSetS(""); |
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423 | Write(); |
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424 | return StringEndS(); |
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425 | } |
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426 | |
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427 | void bigintmat::Print() |
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428 | { |
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429 | char * s = String(); |
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430 | PrintS(s); |
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431 | omFree(s); |
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432 | } |
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433 | |
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434 | |
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435 | char* bigintmat::StringAsPrinted() |
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436 | { |
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437 | if ((col==0) || (row==0)) |
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438 | return NULL; |
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439 | else |
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440 | { |
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441 | int * colwid = getwid(80); |
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442 | if (colwid == NULL) |
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443 | { |
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444 | WerrorS("not enough space to print bigintmat"); |
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445 | WerrorS("try string(...) for a unformatted output"); |
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446 | return NULL; |
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447 | } |
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448 | char * ps; |
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449 | int slength = 0; |
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450 | for (int j=0; j<col; j++) |
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451 | slength += colwid[j]*row; |
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452 | slength += col*row+row; |
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453 | ps = (char*) omAlloc0(sizeof(char)*(slength)); |
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454 | int pos = 0; |
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455 | for (int i=0; i<col*row; i++) |
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456 | { |
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457 | StringSetS(""); |
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458 | n_Write(v[i], basecoeffs()); |
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459 | char * ts = StringEndS(); |
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460 | const int _nl = strlen(ts); |
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461 | int cj = i%col; |
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462 | if (_nl > colwid[cj]) |
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463 | { |
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464 | StringSetS(""); |
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465 | int ci = i/col; |
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466 | StringAppend("[%d,%d]", ci+1, cj+1); |
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467 | char * ph = StringEndS(); |
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468 | int phl = strlen(ph); |
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469 | if (phl > colwid[cj]) |
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470 | { |
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471 | for (int j=0; j<colwid[cj]-1; j++) |
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472 | ps[pos+j] = ' '; |
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473 | ps[pos+colwid[cj]-1] = '*'; |
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474 | } |
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475 | else |
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476 | { |
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477 | for (int j=0; j<colwid[cj]-phl; j++) |
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478 | ps[pos+j] = ' '; |
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479 | for (int j=0; j<phl; j++) |
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480 | ps[pos+colwid[cj]-phl+j] = ph[j]; |
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481 | } |
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482 | omFree(ph); |
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483 | } |
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484 | else // Mit Leerzeichen auffÃŒllen und zahl reinschreiben |
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485 | { |
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486 | for (int j=0; j<colwid[cj]-_nl; j++) |
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487 | ps[pos+j] = ' '; |
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488 | for (int j=0; j<_nl; j++) |
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489 | ps[pos+colwid[cj]-_nl+j] = ts[j]; |
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490 | } |
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491 | // ", " und (evtl) "\n" einfÃŒgen |
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492 | if ((i+1)%col == 0) |
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493 | { |
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494 | if (i != col*row-1) |
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495 | { |
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496 | ps[pos+colwid[cj]] = ','; |
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497 | ps[pos+colwid[cj]+1] = '\n'; |
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498 | pos += colwid[cj]+2; |
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499 | } |
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500 | } |
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501 | else |
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502 | { |
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503 | ps[pos+colwid[cj]] = ','; |
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504 | pos += colwid[cj]+1; |
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505 | } |
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506 | |
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507 | omFree(ts); // Hier ts zerstören |
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508 | } |
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509 | return(ps); |
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510 | // omFree(ps); |
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511 | } |
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512 | } |
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513 | |
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514 | static int intArrSum(int * a, int length) |
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515 | { |
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516 | int sum = 0; |
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517 | for (int i=0; i<length; i++) |
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518 | sum += a[i]; |
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519 | return sum; |
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520 | } |
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521 | |
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522 | static int findLongest(int * a, int length) |
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523 | { |
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524 | int l = 0; |
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525 | int index; |
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526 | for (int i=0; i<length; i++) |
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527 | { |
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528 | if (a[i] > l) |
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529 | { |
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530 | l = a[i]; |
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531 | index = i; |
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532 | } |
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533 | } |
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534 | return index; |
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535 | } |
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536 | |
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537 | static int getShorter (int * a, int l, int j, int cols, int rows) |
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538 | { |
---|
539 | int sndlong = 0; |
---|
540 | int min; |
---|
541 | for (int i=0; i<rows; i++) |
---|
542 | { |
---|
543 | int index = cols*i+j; |
---|
544 | if ((a[index] > sndlong) && (a[index] < l)) |
---|
545 | { |
---|
546 | min = floor(log10((double)cols))+floor(log10((double)rows))+5; |
---|
547 | if ((a[index] < min) && (min < l)) |
---|
548 | sndlong = min; |
---|
549 | else |
---|
550 | sndlong = a[index]; |
---|
551 | } |
---|
552 | } |
---|
553 | if (sndlong == 0) |
---|
554 | { |
---|
555 | min = floor(log10((double)cols))+floor(log10((double)rows))+5; |
---|
556 | if (min < l) |
---|
557 | sndlong = min; |
---|
558 | else |
---|
559 | sndlong = 1; |
---|
560 | } |
---|
561 | return sndlong; |
---|
562 | } |
---|
563 | |
---|
564 | |
---|
565 | int * bigintmat::getwid(int maxwid) |
---|
566 | { |
---|
567 | int const c = /*2**/(col-1)+1; |
---|
568 | if (col + c > maxwid-1) return NULL; |
---|
569 | int * wv = (int*)omAlloc(sizeof(int)*col*row); |
---|
570 | int * cwv = (int*)omAlloc(sizeof(int)*col); |
---|
571 | for (int j=0; j<col; j++) |
---|
572 | { |
---|
573 | cwv[j] = 0; |
---|
574 | for (int i=0; i<row; i++) |
---|
575 | { |
---|
576 | StringSetS(""); |
---|
577 | n_Write(v[col*i+j], basecoeffs()); |
---|
578 | char * tmp = StringEndS(); |
---|
579 | const int _nl = strlen(tmp); |
---|
580 | wv[col*i+j] = _nl; |
---|
581 | if (_nl > cwv[j]) |
---|
582 | cwv[j]=_nl; |
---|
583 | omFree(tmp); |
---|
584 | } |
---|
585 | } |
---|
586 | |
---|
587 | // Groesse verkleinern, bis < maxwid |
---|
588 | while (intArrSum(cwv, col)+c > maxwid) |
---|
589 | { |
---|
590 | int j = findLongest(cwv, col); |
---|
591 | cwv[j] = getShorter(wv, cwv[j], j, col, row); |
---|
592 | } |
---|
593 | omFree(wv); |
---|
594 | return cwv; |
---|
595 | } |
---|
596 | |
---|
597 | void bigintmat::pprint(int maxwid) |
---|
598 | { |
---|
599 | if ((col==0) || (row==0)) |
---|
600 | PrintS(""); |
---|
601 | else |
---|
602 | { |
---|
603 | int * colwid = getwid(maxwid); |
---|
604 | if (colwid == NULL) |
---|
605 | { |
---|
606 | WerrorS("not enough space to print bigintmat"); |
---|
607 | return; |
---|
608 | } |
---|
609 | char * ps; |
---|
610 | int slength = 0; |
---|
611 | for (int j=0; j<col; j++) |
---|
612 | slength += colwid[j]*row; |
---|
613 | slength += col*row+row; |
---|
614 | ps = (char*) omAlloc0(sizeof(char)*(slength)); |
---|
615 | int pos = 0; |
---|
616 | for (int i=0; i<col*row; i++) |
---|
617 | { |
---|
618 | StringSetS(""); |
---|
619 | n_Write(v[i], basecoeffs()); |
---|
620 | char * ts = StringEndS(); |
---|
621 | const int _nl = strlen(ts); |
---|
622 | int cj = i%col; |
---|
623 | if (_nl > colwid[cj]) |
---|
624 | { |
---|
625 | StringSetS(""); |
---|
626 | int ci = i/col; |
---|
627 | StringAppend("[%d,%d]", ci+1, cj+1); |
---|
628 | char * ph = StringEndS(); |
---|
629 | int phl = strlen(ph); |
---|
630 | if (phl > colwid[cj]) |
---|
631 | { |
---|
632 | for (int j=0; j<colwid[cj]-1; j++) |
---|
633 | ps[pos+j] = ' '; |
---|
634 | ps[pos+colwid[cj]-1] = '*'; |
---|
635 | } |
---|
636 | else |
---|
637 | { |
---|
638 | for (int j=0; j<colwid[cj]-phl; j++) |
---|
639 | ps[pos+j] = ' '; |
---|
640 | for (int j=0; j<phl; j++) |
---|
641 | ps[pos+colwid[cj]-phl+j] = ph[j]; |
---|
642 | } |
---|
643 | omFree(ph); |
---|
644 | } |
---|
645 | else // Mit Leerzeichen auffÃŒllen und zahl reinschreiben |
---|
646 | { |
---|
647 | for (int j=0; j<colwid[cj]-_nl; j++) |
---|
648 | ps[pos+j] = ' '; |
---|
649 | for (int j=0; j<_nl; j++) |
---|
650 | ps[pos+colwid[cj]-_nl+j] = ts[j]; |
---|
651 | } |
---|
652 | // ", " und (evtl) "\n" einfÃŒgen |
---|
653 | if ((i+1)%col == 0) |
---|
654 | { |
---|
655 | if (i != col*row-1) |
---|
656 | { |
---|
657 | ps[pos+colwid[cj]] = ','; |
---|
658 | ps[pos+colwid[cj]+1] = '\n'; |
---|
659 | pos += colwid[cj]+2; |
---|
660 | } |
---|
661 | } |
---|
662 | else |
---|
663 | { |
---|
664 | ps[pos+colwid[cj]] = ','; |
---|
665 | pos += colwid[cj]+1; |
---|
666 | } |
---|
667 | |
---|
668 | omFree(ts); // Hier ts zerstören |
---|
669 | } |
---|
670 | PrintS(ps); |
---|
671 | omFree(ps); |
---|
672 | } |
---|
673 | } |
---|
674 | |
---|
675 | |
---|
676 | //swaps columns i and j |
---|
677 | void bigintmat::swap(int i, int j) { |
---|
678 | if ((i <= col) && (j <= col) && (i>0) && (j>0)) { |
---|
679 | number tmp; |
---|
680 | number t; |
---|
681 | for (int k=1; k<=row; k++) { |
---|
682 | tmp = get(k, i); |
---|
683 | t = view(k, j); |
---|
684 | set(k, i, t); |
---|
685 | set(k, j, tmp); |
---|
686 | n_Delete(&tmp, basecoeffs()); |
---|
687 | } |
---|
688 | } else |
---|
689 | Werror("Error in swap"); |
---|
690 | } |
---|
691 | |
---|
692 | void bigintmat::swaprow(int i, int j) { |
---|
693 | if ((i <= row) && (j <= row) && (i>0) && (j>0)) { |
---|
694 | number tmp; |
---|
695 | number t; |
---|
696 | for (int k=1; k<=col; k++) { |
---|
697 | tmp = get(i, k); |
---|
698 | t = view(j, k); |
---|
699 | set(i, k, t); |
---|
700 | set(j, k, tmp); |
---|
701 | n_Delete(&tmp, basecoeffs()); |
---|
702 | } |
---|
703 | } |
---|
704 | else |
---|
705 | Werror("Error in swaprow"); |
---|
706 | } |
---|
707 | |
---|
708 | int bigintmat::findnonzero(int i) |
---|
709 | { |
---|
710 | for (int j=1; j<=col; j++) { |
---|
711 | if (!n_IsZero(view(i,j), basecoeffs())) |
---|
712 | { |
---|
713 | return j; |
---|
714 | } |
---|
715 | } |
---|
716 | return 0; |
---|
717 | } |
---|
718 | |
---|
719 | int bigintmat::findcolnonzero(int j) |
---|
720 | { |
---|
721 | for (int i=row; i>=1; i--) { |
---|
722 | if (!n_IsZero(view(i,j), basecoeffs())) |
---|
723 | { |
---|
724 | return i; |
---|
725 | } |
---|
726 | } |
---|
727 | return 0; |
---|
728 | } |
---|
729 | |
---|
730 | void bigintmat::getcol(int j, bigintmat *a) |
---|
731 | { |
---|
732 | assume((j<=col) && (j>=1)); |
---|
733 | if (((a->rows() != row) || (a->cols() != 1)) && ((a->rows() != 1) || (a->cols() != row))) { |
---|
734 | assume(0); |
---|
735 | Werror("Error in getcol. Dimensions must agree!"); |
---|
736 | return; |
---|
737 | } |
---|
738 | if (!nCoeffs_are_equal(basecoeffs(), a->basecoeffs())) { |
---|
739 | nMapFunc f = n_SetMap(basecoeffs(), a->basecoeffs()); |
---|
740 | number t1, t2; |
---|
741 | for (int i=1; i<=row;i++) { |
---|
742 | t1 = get(i,j); |
---|
743 | t2 = f(t1, basecoeffs(), a->basecoeffs()); |
---|
744 | a->set(i-1,t1); |
---|
745 | n_Delete(&t1, basecoeffs()); |
---|
746 | n_Delete(&t2, a->basecoeffs()); |
---|
747 | } |
---|
748 | return; |
---|
749 | } |
---|
750 | number t1; |
---|
751 | for (int i=1; i<=row;i++) { |
---|
752 | t1 = view(i,j); |
---|
753 | a->set(i-1,t1); |
---|
754 | } |
---|
755 | } |
---|
756 | |
---|
757 | void bigintmat::getColRange(int j, int no, bigintmat *a) |
---|
758 | { |
---|
759 | number t1; |
---|
760 | for(int ii=0; ii< no; ii++) { |
---|
761 | for (int i=1; i<=row;i++) { |
---|
762 | t1 = view(i, ii+j); |
---|
763 | a->set(i, ii+1, t1); |
---|
764 | } |
---|
765 | } |
---|
766 | } |
---|
767 | |
---|
768 | void bigintmat::getrow(int i, bigintmat *a) |
---|
769 | { |
---|
770 | if ((i>row) || (i<1)) { |
---|
771 | Werror("Error in getrow: Index out of range!"); |
---|
772 | return; |
---|
773 | } |
---|
774 | if (((a->rows() != 1) || (a->cols() != col)) && ((a->rows() != col) || (a->cols() != 1))) { |
---|
775 | Werror("Error in getrow. Dimensions must agree!"); |
---|
776 | return; |
---|
777 | } |
---|
778 | if (!nCoeffs_are_equal(basecoeffs(), a->basecoeffs())) { |
---|
779 | nMapFunc f = n_SetMap(basecoeffs(), a->basecoeffs()); |
---|
780 | number t1, t2; |
---|
781 | for (int j=1; j<=col;j++) { |
---|
782 | t1 = get(i,j); |
---|
783 | t2 = f(t1, basecoeffs(), a->basecoeffs()); |
---|
784 | a->set(j-1,t2); |
---|
785 | n_Delete(&t1, basecoeffs()); |
---|
786 | n_Delete(&t2, a->basecoeffs()); |
---|
787 | } |
---|
788 | return; |
---|
789 | } |
---|
790 | number t1; |
---|
791 | for (int j=1; j<=col;j++) { |
---|
792 | t1 = get(i,j); |
---|
793 | a->set(j-1,t1); |
---|
794 | n_Delete(&t1, basecoeffs()); |
---|
795 | } |
---|
796 | } |
---|
797 | |
---|
798 | |
---|
799 | void bigintmat::setcol(int j, bigintmat *m) |
---|
800 | { |
---|
801 | if ((j>col) || (j<1)) { |
---|
802 | Werror("Error in setcol: Index out of range!"); |
---|
803 | return; |
---|
804 | } |
---|
805 | if (((m->rows() != row) || (m->cols() != 1)) && ((m->rows() != 1) || (m->cols() != row))) { |
---|
806 | Werror("Error in setcol. Dimensions must agree!"); |
---|
807 | return; |
---|
808 | } |
---|
809 | if (!nCoeffs_are_equal(basecoeffs(), m->basecoeffs())) { |
---|
810 | nMapFunc f = n_SetMap(m->basecoeffs(), basecoeffs()); |
---|
811 | number t1,t2; |
---|
812 | for (int i=1; i<=row; i++) { |
---|
813 | t1 = m->get(i-1); |
---|
814 | t2 = f(t1, m->basecoeffs(),basecoeffs()); |
---|
815 | set(i, j, t2); |
---|
816 | n_Delete(&t2, basecoeffs()); |
---|
817 | n_Delete(&t1, m->basecoeffs()); |
---|
818 | } |
---|
819 | return; |
---|
820 | } |
---|
821 | number t1; |
---|
822 | for (int i=1; i<=row; i++) { |
---|
823 | t1 = m->view(i-1); |
---|
824 | set(i, j, t1); |
---|
825 | } |
---|
826 | } |
---|
827 | |
---|
828 | void bigintmat::setrow(int j, bigintmat *m) { |
---|
829 | if ((j>row) || (j<1)) { |
---|
830 | Werror("Error in setrow: Index out of range!"); |
---|
831 | return; |
---|
832 | } |
---|
833 | if (((m->rows() != 1) || (m->cols() != col)) && ((m->rows() != col) || (m->cols() != 1))) { |
---|
834 | Werror("Error in setrow. Dimensions must agree!"); |
---|
835 | return; |
---|
836 | } |
---|
837 | if (!nCoeffs_are_equal(basecoeffs(), m->basecoeffs())) { |
---|
838 | nMapFunc f = n_SetMap(m->basecoeffs(), basecoeffs()); |
---|
839 | number tmp1,tmp2; |
---|
840 | for (int i=1; i<=col; i++) { |
---|
841 | tmp1 = m->get(i-1); |
---|
842 | tmp2 = f(tmp1, m->basecoeffs(),basecoeffs()); |
---|
843 | set(j, i, tmp2); |
---|
844 | n_Delete(&tmp2, basecoeffs()); |
---|
845 | n_Delete(&tmp1, m->basecoeffs()); |
---|
846 | } |
---|
847 | return; |
---|
848 | } |
---|
849 | number tmp; |
---|
850 | for (int i=1; i<=col; i++) { |
---|
851 | tmp = m->view(i-1); |
---|
852 | set(j, i, tmp); |
---|
853 | } |
---|
854 | |
---|
855 | } |
---|
856 | |
---|
857 | bool bigintmat::add(bigintmat *b) |
---|
858 | { |
---|
859 | if ((b->rows() != row) || (b->cols() != col)) { |
---|
860 | Werror("Error in bigintmat::add. Dimensions do not agree!"); |
---|
861 | return false; |
---|
862 | } |
---|
863 | if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs())) { |
---|
864 | Werror("Error in bigintmat::add. coeffs do not agree!"); |
---|
865 | return false; |
---|
866 | } |
---|
867 | for (int i=1; i<=row; i++) { |
---|
868 | for (int j=1; j<=col; j++) { |
---|
869 | rawset(i, j, n_Add(b->view(i,j), view(i,j), basecoeffs())); |
---|
870 | } |
---|
871 | } |
---|
872 | return true; |
---|
873 | } |
---|
874 | |
---|
875 | bool bigintmat::sub(bigintmat *b) |
---|
876 | { |
---|
877 | if ((b->rows() != row) || (b->cols() != col)) { |
---|
878 | Werror("Error in bigintmat::sub. Dimensions do not agree!"); |
---|
879 | return false; |
---|
880 | } |
---|
881 | if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs())) { |
---|
882 | Werror("Error in bigintmat::sub. coeffs do not agree!"); |
---|
883 | return false; |
---|
884 | } |
---|
885 | for (int i=1; i<=row; i++) { |
---|
886 | for (int j=1; j<=col; j++) { |
---|
887 | rawset(i, j, n_Sub(view(i,j), b->view(i,j), basecoeffs())); |
---|
888 | } |
---|
889 | } |
---|
890 | return true; |
---|
891 | } |
---|
892 | |
---|
893 | bool bigintmat::skalmult(number b, coeffs c) |
---|
894 | { |
---|
895 | if (!nCoeffs_are_equal(c, basecoeffs())) |
---|
896 | { |
---|
897 | Werror("Wrong coeffs\n"); |
---|
898 | return false; |
---|
899 | } |
---|
900 | number t1, t2; |
---|
901 | if ( n_IsOne(b,c)) return true; |
---|
902 | for (int i=1; i<=row; i++) |
---|
903 | { |
---|
904 | for (int j=1; j<=col; j++) |
---|
905 | { |
---|
906 | t1 = view(i, j); |
---|
907 | t2 = n_Mult(t1, b, basecoeffs()); |
---|
908 | rawset(i, j, t2); |
---|
909 | } |
---|
910 | } |
---|
911 | return true; |
---|
912 | } |
---|
913 | |
---|
914 | bool bigintmat::addcol(int i, int j, number a, coeffs c) |
---|
915 | { |
---|
916 | if ((i>col) || (j>col) || (i<1) || (j<1)) { |
---|
917 | Werror("Error in addcol: Index out of range!"); |
---|
918 | return false; |
---|
919 | } |
---|
920 | if (!nCoeffs_are_equal(c, basecoeffs())) { |
---|
921 | Werror("Error in addcol: coeffs do not agree!"); |
---|
922 | return false; |
---|
923 | } |
---|
924 | number t1, t2, t3, t4; |
---|
925 | for (int k=1; k<=row; k++) |
---|
926 | { |
---|
927 | t1 = view(k, j); |
---|
928 | t2 = view(k, i); |
---|
929 | t3 = n_Mult(t1, a, basecoeffs()); |
---|
930 | t4 = n_Add(t3, t2, basecoeffs()); |
---|
931 | rawset(k, i, t4); |
---|
932 | n_Delete(&t3, basecoeffs()); |
---|
933 | } |
---|
934 | return true; |
---|
935 | } |
---|
936 | |
---|
937 | bool bigintmat::addrow(int i, int j, number a, coeffs c) |
---|
938 | { |
---|
939 | if ((i>row) || (j>row) || (i<1) || (j<1)) { |
---|
940 | Werror("Error in addrow: Index out of range!"); |
---|
941 | return false; |
---|
942 | } |
---|
943 | if (!nCoeffs_are_equal(c, basecoeffs())) { |
---|
944 | Werror("Error in addrow: coeffs do not agree!"); |
---|
945 | return false; |
---|
946 | } |
---|
947 | number t1, t2, t3, t4; |
---|
948 | for (int k=1; k<=col; k++) |
---|
949 | { |
---|
950 | t1 = view(j, k); |
---|
951 | t2 = view(i, k); |
---|
952 | t3 = n_Mult(t1, a, basecoeffs()); |
---|
953 | t4 = n_Add(t3, t2, basecoeffs()); |
---|
954 | rawset(i, k, t4); |
---|
955 | n_Delete(&t3, basecoeffs()); |
---|
956 | } |
---|
957 | return true; |
---|
958 | } |
---|
959 | |
---|
960 | void bigintmat::colskalmult(int i, number a, coeffs c) { |
---|
961 | if ((i>=1) && (i<=col) && (nCoeffs_are_equal(c, basecoeffs()))) { |
---|
962 | number t, tmult; |
---|
963 | for (int j=1; j<=row; j++) { |
---|
964 | t = view(j, i); |
---|
965 | tmult = n_Mult(a, t, basecoeffs()); |
---|
966 | rawset(j, i, tmult); |
---|
967 | } |
---|
968 | } |
---|
969 | else |
---|
970 | Werror("Error in colskalmult"); |
---|
971 | } |
---|
972 | |
---|
973 | void bigintmat::rowskalmult(int i, number a, coeffs c) { |
---|
974 | if ((i>=1) && (i<=row) && (nCoeffs_are_equal(c, basecoeffs()))) { |
---|
975 | number t, tmult; |
---|
976 | for (int j=1; j<=col; j++) { |
---|
977 | t = view(i, j); |
---|
978 | tmult = n_Mult(a, t, basecoeffs()); |
---|
979 | rawset(i, j, tmult); |
---|
980 | } |
---|
981 | } |
---|
982 | else |
---|
983 | Werror("Error in rowskalmult"); |
---|
984 | } |
---|
985 | |
---|
986 | void bigintmat::concatrow(bigintmat *a, bigintmat *b) { |
---|
987 | int ay = a->cols(); |
---|
988 | int ax = a->rows(); |
---|
989 | int by = b->cols(); |
---|
990 | int bx = b->rows(); |
---|
991 | number tmp; |
---|
992 | if (!((col == ay) && (col == by) && (ax+bx == row))) { |
---|
993 | Werror("Error in concatrow. Dimensions must agree!"); |
---|
994 | return; |
---|
995 | } |
---|
996 | if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs()))) { |
---|
997 | Werror("Error in concatrow. coeffs do not agree!"); |
---|
998 | return; |
---|
999 | } |
---|
1000 | for (int i=1; i<=ax; i++) { |
---|
1001 | for (int j=1; j<=ay; j++) { |
---|
1002 | tmp = a->get(i,j); |
---|
1003 | set(i, j, tmp); |
---|
1004 | n_Delete(&tmp, basecoeffs()); |
---|
1005 | } |
---|
1006 | } |
---|
1007 | for (int i=1; i<=bx; i++) { |
---|
1008 | for (int j=1; j<=by; j++) { |
---|
1009 | tmp = b->get(i,j); |
---|
1010 | set(i+ax, j, tmp); |
---|
1011 | n_Delete(&tmp, basecoeffs()); |
---|
1012 | } |
---|
1013 | } |
---|
1014 | } |
---|
1015 | |
---|
1016 | void bigintmat::extendCols(int i) { |
---|
1017 | bigintmat * tmp = new bigintmat(rows(), i, basecoeffs()); |
---|
1018 | appendCol(tmp); |
---|
1019 | delete tmp; |
---|
1020 | } |
---|
1021 | void bigintmat::appendCol (bigintmat *a) { |
---|
1022 | coeffs R = basecoeffs(); |
---|
1023 | int ay = a->cols(); |
---|
1024 | int ax = a->rows(); |
---|
1025 | assume(row == ax); |
---|
1026 | |
---|
1027 | assume(nCoeffs_are_equal(a->basecoeffs(), R)); |
---|
1028 | |
---|
1029 | bigintmat * tmp = new bigintmat(rows(), cols() + ay, R); |
---|
1030 | tmp->concatcol(this, a); |
---|
1031 | this->swapMatrix(tmp); |
---|
1032 | delete tmp; |
---|
1033 | } |
---|
1034 | |
---|
1035 | |
---|
1036 | void bigintmat::concatcol (bigintmat *a, bigintmat *b) { |
---|
1037 | int ay = a->cols(); |
---|
1038 | int ax = a->rows(); |
---|
1039 | int by = b->cols(); |
---|
1040 | int bx = b->rows(); |
---|
1041 | number tmp; |
---|
1042 | |
---|
1043 | assume(row==ax && row == bx && ay+by ==col); |
---|
1044 | |
---|
1045 | assume(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs())); |
---|
1046 | |
---|
1047 | for (int i=1; i<=ax; i++) { |
---|
1048 | for (int j=1; j<=ay; j++) { |
---|
1049 | tmp = a->view(i,j); |
---|
1050 | set(i, j, tmp); |
---|
1051 | } |
---|
1052 | } |
---|
1053 | for (int i=1; i<=bx; i++) { |
---|
1054 | for (int j=1; j<=by; j++) { |
---|
1055 | tmp = b->view(i,j); |
---|
1056 | set(i, j+ay, tmp); |
---|
1057 | } |
---|
1058 | } |
---|
1059 | } |
---|
1060 | |
---|
1061 | void bigintmat::splitrow(bigintmat *a, bigintmat *b) { |
---|
1062 | int ay = a->cols(); |
---|
1063 | int ax = a->rows(); |
---|
1064 | int by = b->cols(); |
---|
1065 | int bx = b->rows(); |
---|
1066 | number tmp; |
---|
1067 | if (!(ax + bx == row)) { |
---|
1068 | Werror("Error in splitrow. Dimensions must agree!"); |
---|
1069 | } |
---|
1070 | else if (!((col == ay) && (col == by))) { |
---|
1071 | Werror("Error in splitrow. Dimensions must agree!"); |
---|
1072 | } |
---|
1073 | else if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs()))) { |
---|
1074 | Werror("Error in splitrow. coeffs do not agree!"); |
---|
1075 | } |
---|
1076 | else { |
---|
1077 | for(int i = 1; i<=ax; i++) { |
---|
1078 | for(int j = 1; j<=ay;j++) { |
---|
1079 | tmp = get(i,j); |
---|
1080 | a->set(i,j,tmp); |
---|
1081 | n_Delete(&tmp, basecoeffs()); |
---|
1082 | } |
---|
1083 | } |
---|
1084 | for (int i =1; i<=bx; i++) { |
---|
1085 | for (int j=1;j<=col;j++) { |
---|
1086 | tmp = get(i+ax, j); |
---|
1087 | b->set(i,j,tmp); |
---|
1088 | n_Delete(&tmp, basecoeffs()); |
---|
1089 | } |
---|
1090 | } |
---|
1091 | } |
---|
1092 | } |
---|
1093 | |
---|
1094 | void bigintmat::splitcol(bigintmat *a, bigintmat *b) { |
---|
1095 | int ay = a->cols(); |
---|
1096 | int ax = a->rows(); |
---|
1097 | int by = b->cols(); |
---|
1098 | int bx = b->rows(); |
---|
1099 | number tmp; |
---|
1100 | if (!((row == ax) && (row == bx))) { |
---|
1101 | Werror("Error in splitcol. Dimensions must agree!"); |
---|
1102 | } |
---|
1103 | else if (!(ay+by == col)) { |
---|
1104 | Werror("Error in splitcol. Dimensions must agree!"); |
---|
1105 | } |
---|
1106 | else if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()) && nCoeffs_are_equal(b->basecoeffs(), basecoeffs()))) { |
---|
1107 | Werror("Error in splitcol. coeffs do not agree!"); |
---|
1108 | } |
---|
1109 | else { |
---|
1110 | for (int i=1; i<=ax; i++) { |
---|
1111 | for (int j=1; j<=ay; j++) { |
---|
1112 | tmp = view(i,j); |
---|
1113 | a->set(i,j,tmp); |
---|
1114 | } |
---|
1115 | } |
---|
1116 | for (int i=1; i<=bx; i++) { |
---|
1117 | for (int j=1; j<=by; j++) { |
---|
1118 | tmp = view(i,j+ay); |
---|
1119 | b->set(i,j,tmp); |
---|
1120 | } |
---|
1121 | } |
---|
1122 | } |
---|
1123 | } |
---|
1124 | |
---|
1125 | void bigintmat::splitcol(bigintmat *a, int i) { |
---|
1126 | number tmp; |
---|
1127 | if ((a->rows() != row) || (a->cols()+i-1 > col) || (i<1)) { |
---|
1128 | Werror("Error in splitcol. Dimensions must agree!"); |
---|
1129 | return; |
---|
1130 | } |
---|
1131 | if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()))) { |
---|
1132 | Werror("Error in splitcol. coeffs do not agree!"); |
---|
1133 | return; |
---|
1134 | } |
---|
1135 | int width = a->cols(); |
---|
1136 | for (int j=1; j<=width; j++) { |
---|
1137 | for (int k=1; k<=row; k++) { |
---|
1138 | tmp = get(k, j+i-1); |
---|
1139 | a->set(k, j, tmp); |
---|
1140 | n_Delete(&tmp, basecoeffs()); |
---|
1141 | } |
---|
1142 | } |
---|
1143 | } |
---|
1144 | |
---|
1145 | void bigintmat::splitrow(bigintmat *a, int i) { |
---|
1146 | number tmp; |
---|
1147 | if ((a->cols() != col) || (a->rows()+i-1 > row) || (i<1)) { |
---|
1148 | Werror("Error in Marco-splitrow"); |
---|
1149 | return; |
---|
1150 | } |
---|
1151 | |
---|
1152 | if (!(nCoeffs_are_equal(a->basecoeffs(), basecoeffs()))) { |
---|
1153 | Werror("Error in splitrow. coeffs do not agree!"); |
---|
1154 | return; |
---|
1155 | } |
---|
1156 | int height = a->rows(); |
---|
1157 | for (int j=1; j<=height; j++) { |
---|
1158 | for (int k=1; k<=col; k++) { |
---|
1159 | tmp = view(j+i-1, k); |
---|
1160 | a->set(j, k, tmp); |
---|
1161 | } |
---|
1162 | } |
---|
1163 | } |
---|
1164 | |
---|
1165 | bool bigintmat::copy(bigintmat *b) |
---|
1166 | { |
---|
1167 | if ((b->rows() != row) || (b->cols() != col)) { |
---|
1168 | Werror("Error in bigintmat::copy. Dimensions do not agree!"); |
---|
1169 | return false; |
---|
1170 | } |
---|
1171 | if (!nCoeffs_are_equal(basecoeffs(), b->basecoeffs())) { |
---|
1172 | Werror("Error in bigintmat::copy. coeffs do not agree!"); |
---|
1173 | return false; |
---|
1174 | } |
---|
1175 | number t1; |
---|
1176 | for (int i=1; i<=row; i++) |
---|
1177 | { |
---|
1178 | for (int j=1; j<=col; j++) |
---|
1179 | { |
---|
1180 | t1 = b->view(i, j); |
---|
1181 | set(i, j, t1); |
---|
1182 | } |
---|
1183 | } |
---|
1184 | return true; |
---|
1185 | } |
---|
1186 | |
---|
1187 | // copy the submatrix of b, staring at (a,b) having n rows, m cols into |
---|
1188 | // the given matrix at pos. (c,d) |
---|
1189 | // needs c+n, d+m <= rows, cols |
---|
1190 | // a+n, b+m <= b.rows(), b.cols() |
---|
1191 | void bigintmat::copySubmatInto(bigintmat *B, int a, int b, int n, int m, int c, int d) |
---|
1192 | { |
---|
1193 | number t1; |
---|
1194 | for (int i=1; i<=n; i++) |
---|
1195 | { |
---|
1196 | for (int j=1; j<=m; j++) |
---|
1197 | { |
---|
1198 | t1 = B->view(a+i-1, b+j-1); |
---|
1199 | set(c+i-1, d+j-1, t1); |
---|
1200 | } |
---|
1201 | } |
---|
1202 | } |
---|
1203 | |
---|
1204 | |
---|
1205 | int bigintmat::isOne() { |
---|
1206 | coeffs r = basecoeffs(); |
---|
1207 | if (row==col) { |
---|
1208 | for (int i=1; i<=row; i++) { |
---|
1209 | for (int j=1; j<=col; j++) { |
---|
1210 | if (i==j) { |
---|
1211 | if (!n_IsOne(view(i, j), r)) |
---|
1212 | return 0; |
---|
1213 | } |
---|
1214 | else { |
---|
1215 | if (!n_IsZero(view(i,j), r)) |
---|
1216 | return 0; |
---|
1217 | } |
---|
1218 | } |
---|
1219 | } |
---|
1220 | } |
---|
1221 | return 1; |
---|
1222 | } |
---|
1223 | |
---|
1224 | |
---|
1225 | void bigintmat::one() { |
---|
1226 | if (row==col) { |
---|
1227 | number one = n_Init(1, basecoeffs()), |
---|
1228 | zero = n_Init(0, basecoeffs()); |
---|
1229 | for (int i=1; i<=row; i++) { |
---|
1230 | for (int j=1; j<=col; j++) { |
---|
1231 | if (i==j) { |
---|
1232 | set(i, j, one); |
---|
1233 | } else { |
---|
1234 | set(i, j, zero); |
---|
1235 | } |
---|
1236 | } |
---|
1237 | } |
---|
1238 | n_Delete(&one, basecoeffs()); |
---|
1239 | n_Delete(&zero, basecoeffs()); |
---|
1240 | } |
---|
1241 | } |
---|
1242 | |
---|
1243 | void bigintmat::zero() { |
---|
1244 | number tmp = n_Init(0, basecoeffs()); |
---|
1245 | for (int i=1; i<=row; i++) { |
---|
1246 | for (int j=1; j<=col; j++) { |
---|
1247 | set(i, j, tmp); |
---|
1248 | } |
---|
1249 | } |
---|
1250 | n_Delete(&tmp,basecoeffs()); |
---|
1251 | } |
---|
1252 | |
---|
1253 | int bigintmat::isZero() { |
---|
1254 | for (int i=1; i<=row; i++) { |
---|
1255 | for (int j=1; j<=col; j++) { |
---|
1256 | if (!n_IsZero(view(i,j), basecoeffs())) |
---|
1257 | return FALSE; |
---|
1258 | } |
---|
1259 | } |
---|
1260 | return TRUE; |
---|
1261 | } |
---|
1262 | //**************************************************************************** |
---|
1263 | // |
---|
1264 | //**************************************************************************** |
---|
1265 | |
---|
1266 | //used in the det function. No idea what it does. |
---|
1267 | //looks like it return the submatrix where the i-th row |
---|
1268 | //and j-th column has been removed in the LaPlace generic |
---|
1269 | //determinant algorithm |
---|
1270 | bigintmat *bigintmat::elim(int i, int j) |
---|
1271 | { |
---|
1272 | if ((i<=0) || (i>row) || (j<=0) || (j>col)) |
---|
1273 | return NULL; |
---|
1274 | int cx, cy; |
---|
1275 | cx=1; |
---|
1276 | cy=1; |
---|
1277 | number t; |
---|
1278 | bigintmat *b = new bigintmat(row-1, col-1, basecoeffs()); |
---|
1279 | for (int k=1; k<=row; k++) { |
---|
1280 | if (k!=i) |
---|
1281 | { |
---|
1282 | cy=1; |
---|
1283 | for (int l=1; l<=col; l++) |
---|
1284 | { |
---|
1285 | if (l!=j) |
---|
1286 | { |
---|
1287 | t = get(k, l); |
---|
1288 | b->set(cx, cy, t); |
---|
1289 | n_Delete(&t, basecoeffs()); |
---|
1290 | cy++; |
---|
1291 | } |
---|
1292 | } |
---|
1293 | cx++; |
---|
1294 | } |
---|
1295 | } |
---|
1296 | return b; |
---|
1297 | } |
---|
1298 | |
---|
1299 | |
---|
1300 | //returns d such that a/d is the inverse of the input |
---|
1301 | //TODO: make work for p not prime using the euc stuff. |
---|
1302 | //long term: rewrite for Z using p-adic lifting |
---|
1303 | //and Dixon. Possibly even the sparse recent Storjohann stuff |
---|
1304 | number bigintmat::pseudoinv(bigintmat *a) { |
---|
1305 | |
---|
1306 | // Falls Matrix ÃŒber reellen Zahlen nicht invertierbar, breche ab |
---|
1307 | assume((a->rows() == row) && (a->rows() == a->cols()) && (row == col)); |
---|
1308 | |
---|
1309 | number det = this->det(); //computes the HNF, so should e reused. |
---|
1310 | if ((n_IsZero(det, basecoeffs()))) |
---|
1311 | return det; |
---|
1312 | |
---|
1313 | // HÀnge Einheitsmatrix Ìber Matrix und wendet HNF an. An Stelle der Einheitsmatrix steht im Ergebnis die Transformationsmatrix dazu |
---|
1314 | a->one(); |
---|
1315 | bigintmat *m = new bigintmat(2*row, col, basecoeffs()); |
---|
1316 | m->concatrow(a,this); |
---|
1317 | m->hnf(); |
---|
1318 | // Arbeite weiterhin mit der zusammengehÀngten Matrix |
---|
1319 | // Laufe durch die Diagonalelemente, und multipliziere jede Spalte rechts davon damit, speichere aber den alten Eintrag der Spalte, temp, der in der Zeile des Diagonalelements liegt, zwischen. Dann addiere das -temp-Fache der Diagonalspalte zur entsprechenenden Spalte rechts davon. Dadurch entsteht ÃŒberall rechts der Diagonalen eine 0 |
---|
1320 | number diag; |
---|
1321 | number temp, ttemp; |
---|
1322 | for (int i=1; i<=col; i++) { |
---|
1323 | diag = m->get(row+i, i); |
---|
1324 | for (int j=i+1; j<=col; j++) { |
---|
1325 | temp = m->get(row+i, j); |
---|
1326 | m->colskalmult(j, diag, basecoeffs()); |
---|
1327 | temp = n_InpNeg(temp, basecoeffs()); |
---|
1328 | m->addcol(j, i, temp, basecoeffs()); |
---|
1329 | n_Delete(&temp, basecoeffs()); |
---|
1330 | } |
---|
1331 | n_Delete(&diag, basecoeffs()); |
---|
1332 | } |
---|
1333 | // Falls wir nicht modulo n arbeiten, können wir die Spalten durch den ggT teilen, um die EintrÀge kleiner zu bekommen |
---|
1334 | // Bei Z/n sparen wir uns das, da es hier sinnlos ist |
---|
1335 | number g; |
---|
1336 | number gcd; |
---|
1337 | for (int j=1; j<=col; j++) { |
---|
1338 | g = n_Init(0, basecoeffs()); |
---|
1339 | for (int i=1; i<=2*row; i++) { |
---|
1340 | temp = m->get(i,j); |
---|
1341 | gcd = n_Gcd(g, temp, basecoeffs()); |
---|
1342 | n_Delete(&g, basecoeffs()); |
---|
1343 | n_Delete(&temp, basecoeffs()); |
---|
1344 | g = n_Copy(gcd, basecoeffs()); |
---|
1345 | n_Delete(&gcd, basecoeffs()); |
---|
1346 | } |
---|
1347 | if (!(n_IsOne(g, basecoeffs()))) |
---|
1348 | m->colskaldiv(j, g); |
---|
1349 | n_Delete(&g, basecoeffs()); |
---|
1350 | } |
---|
1351 | |
---|
1352 | // Nun mÌssen die Diagonalelemente durch Spaltenmultiplikation gleich gesett werden. Bei Z können wir mit dem kgV arbeiten, bei Z/n bringen wir jedes Diagonalelement auf 1 (wir arbeiten immer mit n = Primzahl. FÌr n != Primzahl muss noch an anderen Stellen etwas geÀndert werden) |
---|
1353 | |
---|
1354 | g = n_Init(0, basecoeffs()); |
---|
1355 | number prod = n_Init(1, basecoeffs()); |
---|
1356 | for (int i=1; i<=col; i++) { |
---|
1357 | gcd = n_Gcd(g, m->get(row+i, i), basecoeffs()); |
---|
1358 | n_Delete(&g, basecoeffs()); |
---|
1359 | g = n_Copy(gcd, basecoeffs()); |
---|
1360 | n_Delete(&gcd, basecoeffs()); |
---|
1361 | ttemp = n_Copy(prod, basecoeffs()); |
---|
1362 | temp = m->get(row+i, i); |
---|
1363 | n_Delete(&prod, basecoeffs()); |
---|
1364 | prod = n_Mult(ttemp, temp, basecoeffs()); |
---|
1365 | n_Delete(&ttemp, basecoeffs()); |
---|
1366 | n_Delete(&temp, basecoeffs()); |
---|
1367 | } |
---|
1368 | number lcm; |
---|
1369 | lcm = n_Div(prod, g, basecoeffs()); |
---|
1370 | for (int j=1; j<=col; j++) { |
---|
1371 | ttemp = m->get(row+j,j); |
---|
1372 | temp = n_QuotRem(lcm, ttemp, NULL, basecoeffs()); |
---|
1373 | m->colskalmult(j, temp, basecoeffs()); |
---|
1374 | n_Delete(&ttemp, basecoeffs()); |
---|
1375 | n_Delete(&temp, basecoeffs()); |
---|
1376 | } |
---|
1377 | n_Delete(&lcm, basecoeffs()); |
---|
1378 | n_Delete(&prod, basecoeffs()); |
---|
1379 | |
---|
1380 | number divisor = m->get(row+1, 1); |
---|
1381 | m->splitrow(a, 1); |
---|
1382 | delete m; |
---|
1383 | n_Delete(&det, basecoeffs()); |
---|
1384 | return divisor; |
---|
1385 | } |
---|
1386 | |
---|
1387 | number bigintmat::trace() |
---|
1388 | { |
---|
1389 | assume (col == row); |
---|
1390 | number t = get(1,1), |
---|
1391 | h; |
---|
1392 | coeffs r = basecoeffs(); |
---|
1393 | for(int i=2; i<= col; i++) { |
---|
1394 | h = n_Add(t, view(i,i), r); |
---|
1395 | n_Delete(&t, r); |
---|
1396 | t = h; |
---|
1397 | } |
---|
1398 | return t; |
---|
1399 | } |
---|
1400 | |
---|
1401 | number bigintmat::det() |
---|
1402 | { |
---|
1403 | assume (row==col); |
---|
1404 | |
---|
1405 | if (col == 1) |
---|
1406 | return get(1, 1); |
---|
1407 | // should work as well in Z/pZ of type n_Zp? |
---|
1408 | // relies on XExtGcd and the other euc. functinos. |
---|
1409 | if ( getCoeffType(basecoeffs())== n_Z || getCoeffType(basecoeffs() )== n_Zn) { |
---|
1410 | return hnfdet(); |
---|
1411 | } |
---|
1412 | number sum = n_Init(0, basecoeffs()); |
---|
1413 | number t1, t2, t3, t4; |
---|
1414 | bigintmat *b; |
---|
1415 | for (int i=1; i<=row; i++) { |
---|
1416 | b = elim(i, 1); |
---|
1417 | t1 = get(i, 1); |
---|
1418 | t2 = b->det(); |
---|
1419 | t3 = n_Mult(t1, t2, basecoeffs()); |
---|
1420 | t4 = n_Copy(sum, basecoeffs()); |
---|
1421 | n_Delete(&sum, basecoeffs()); |
---|
1422 | if ((i+1)>>1<<1==(i+1)) |
---|
1423 | sum = n_Add(t4, t3, basecoeffs()); |
---|
1424 | else |
---|
1425 | sum = n_Sub(t4, t3, basecoeffs()); |
---|
1426 | n_Delete(&t1, basecoeffs()); |
---|
1427 | n_Delete(&t2, basecoeffs()); |
---|
1428 | n_Delete(&t3, basecoeffs()); |
---|
1429 | n_Delete(&t4, basecoeffs()); |
---|
1430 | } |
---|
1431 | return sum; |
---|
1432 | } |
---|
1433 | |
---|
1434 | number bigintmat::hnfdet() |
---|
1435 | { |
---|
1436 | assume (col == row); |
---|
1437 | |
---|
1438 | if (col == 1) |
---|
1439 | return get(1, 1); |
---|
1440 | bigintmat *m = new bigintmat(this); |
---|
1441 | m->hnf(); |
---|
1442 | number prod = n_Init(1, basecoeffs()); |
---|
1443 | number temp, temp2; |
---|
1444 | for (int i=1; i<=col; i++) { |
---|
1445 | temp = m->get(i, i); |
---|
1446 | temp2 = n_Mult(temp, prod, basecoeffs()); |
---|
1447 | n_Delete(&prod, basecoeffs()); |
---|
1448 | prod = temp2; |
---|
1449 | n_Delete(&temp, basecoeffs()); |
---|
1450 | } |
---|
1451 | delete m; |
---|
1452 | return prod; |
---|
1453 | } |
---|
1454 | |
---|
1455 | void bigintmat::swapMatrix(bigintmat *a) |
---|
1456 | { |
---|
1457 | int n = rows(), m = cols(); |
---|
1458 | row = a->rows(); |
---|
1459 | col = a->cols(); |
---|
1460 | number * V = v; |
---|
1461 | v = a->v; |
---|
1462 | a->v = V; |
---|
1463 | a->row = n; |
---|
1464 | a->col = m; |
---|
1465 | } |
---|
1466 | int bigintmat::colIsZero(int j) |
---|
1467 | { |
---|
1468 | coeffs R = basecoeffs(); |
---|
1469 | for(int i=1; i<=rows(); i++) |
---|
1470 | if (!n_IsZero(view(i, j), R)) return FALSE; |
---|
1471 | return TRUE; |
---|
1472 | } |
---|
1473 | |
---|
1474 | void bigintmat::howell() |
---|
1475 | { |
---|
1476 | coeffs R = basecoeffs(); |
---|
1477 | hnf(); // as a starting point... |
---|
1478 | if (getCoeffType(R)== n_Z) return; //wrong, need to prune! |
---|
1479 | |
---|
1480 | int n = cols(), m = rows(), i, j, k; |
---|
1481 | |
---|
1482 | //make sure, the matrix has enough space. We need no rows+1 columns. |
---|
1483 | //The resulting Howell form will be pruned to be at most square. |
---|
1484 | bigintmat * t = new bigintmat(m, m+1, R); |
---|
1485 | t->copySubmatInto(this, 1, n>m ? n-m+1 : 1, m, n>m ? m : n, 1, n>m ? 2 : m+2-n ); |
---|
1486 | swapMatrix(t); |
---|
1487 | delete t; |
---|
1488 | for(i=1; i<= cols(); i++) { |
---|
1489 | if (!colIsZero(i)) break; |
---|
1490 | } |
---|
1491 | assume (i>1); |
---|
1492 | if (i>cols()) { |
---|
1493 | t = new bigintmat(rows(), 0, R); |
---|
1494 | swapMatrix(t); |
---|
1495 | delete t; |
---|
1496 | return; // zero matrix found, clearly normal. |
---|
1497 | } |
---|
1498 | |
---|
1499 | int last_zero_col = i-1; |
---|
1500 | for (int c = cols(); c>0; c--) { |
---|
1501 | for(i=rows(); i>0; i--) { |
---|
1502 | if (!n_IsZero(view(i, c), R)) break; |
---|
1503 | } |
---|
1504 | if (i==0) break; // matrix SHOULD be zero from here on |
---|
1505 | number a = n_Ann(view(i, c), R); |
---|
1506 | addcol(last_zero_col, c, a, R); |
---|
1507 | n_Delete(&a, R); |
---|
1508 | for(j = c-1; j>last_zero_col; j--) { |
---|
1509 | for(k=rows(); k>0; k--) { |
---|
1510 | if (!n_IsZero(view(k, j), R)) break; |
---|
1511 | if (!n_IsZero(view(k, last_zero_col), R)) break; |
---|
1512 | } |
---|
1513 | if (k==0) break; |
---|
1514 | if (!n_IsZero(view(k, last_zero_col), R)) { |
---|
1515 | number gcd, co1, co2, co3, co4; |
---|
1516 | gcd = n_XExtGcd(view(k, last_zero_col), view(k, j), &co1, &co2, &co3, &co4, R); |
---|
1517 | if (n_Equal(gcd, view(k, j), R)) { |
---|
1518 | number q = n_Div(view(k, last_zero_col), gcd, R); |
---|
1519 | q = n_InpNeg(q, R); |
---|
1520 | addcol(last_zero_col, j, q, R); |
---|
1521 | n_Delete(&q, R); |
---|
1522 | } else if (n_Equal(gcd, view(k, last_zero_col), R)) { |
---|
1523 | swap(last_zero_col, k); |
---|
1524 | number q = n_Div(view(k, last_zero_col), gcd, R); |
---|
1525 | q = n_InpNeg(q, R); |
---|
1526 | addcol(last_zero_col, j, q, R); |
---|
1527 | n_Delete(&q, R); |
---|
1528 | } else { |
---|
1529 | coltransform(last_zero_col, j, co3, co4, co1, co2); |
---|
1530 | } |
---|
1531 | n_Delete(&gcd, R); |
---|
1532 | n_Delete(&co1, R); |
---|
1533 | n_Delete(&co2, R); |
---|
1534 | n_Delete(&co3, R); |
---|
1535 | n_Delete(&co4, R); |
---|
1536 | } |
---|
1537 | } |
---|
1538 | for(k=rows(); k>0; k--) { |
---|
1539 | if (!n_IsZero(view(k, last_zero_col), R)) break; |
---|
1540 | } |
---|
1541 | if (k) last_zero_col--; |
---|
1542 | } |
---|
1543 | t = new bigintmat(rows(), cols()-last_zero_col, R); |
---|
1544 | t->copySubmatInto(this, 1, last_zero_col+1, rows(), cols()-last_zero_col, 1, 1); |
---|
1545 | swapMatrix(t); |
---|
1546 | delete t; |
---|
1547 | } |
---|
1548 | |
---|
1549 | void bigintmat::hnf() |
---|
1550 | { |
---|
1551 | // Laufen von unten nach oben und von links nach rechts |
---|
1552 | // CF: TODO: for n_Z: write a recursive version. This one will |
---|
1553 | // have exponential blow-up. Look at Michianchio |
---|
1554 | // Alternatively, do p-adic det and modular method |
---|
1555 | |
---|
1556 | #if 0 |
---|
1557 | char * s; |
---|
1558 | ::Print("mat over Z is \n"); |
---|
1559 | ::Print("%s\n", s = basecoeffs()->cfCoeffString(basecoeffs())); |
---|
1560 | omFree(s); |
---|
1561 | Print(); |
---|
1562 | ::Print("\n(%d x %d)\n", rows(), cols()); |
---|
1563 | #endif |
---|
1564 | |
---|
1565 | int i = rows(); |
---|
1566 | int j = cols(); |
---|
1567 | number q = n_Init(0, basecoeffs()); |
---|
1568 | number one = n_Init(1, basecoeffs()); |
---|
1569 | number minusone = n_Init(-1, basecoeffs()); |
---|
1570 | number tmp1 = n_Init(0, basecoeffs()); |
---|
1571 | number tmp2 = n_Init(0, basecoeffs()); |
---|
1572 | number co1, co2, co3, co4; |
---|
1573 | number ggt = n_Init(0, basecoeffs()); |
---|
1574 | |
---|
1575 | while ((i>0) && (j>0)) { |
---|
1576 | // Falls erstes Nicht-Null-Element in Zeile i nicht existiert, oder hinter Spalte j vorkommt, gehe in nÀchste Zeile |
---|
1577 | if ((findnonzero(i)==0) || (findnonzero(i)>j)) { |
---|
1578 | i--; |
---|
1579 | } else { |
---|
1580 | // Laufe von links nach rechts durch die Zeile: |
---|
1581 | for (int l=1; l<=j-1; l++) { |
---|
1582 | n_Delete(&tmp1, basecoeffs()); |
---|
1583 | tmp1 = get(i, l); |
---|
1584 | // Falls Eintrag (im folgenden x genannt) gleich 0, gehe eine Spalte weiter. Ansonsten... |
---|
1585 | if (!n_IsZero(tmp1, basecoeffs())) { |
---|
1586 | n_Delete(&tmp2, basecoeffs()); |
---|
1587 | tmp2 = get(i, l+1); |
---|
1588 | // Falls Eintrag (i.f. y g.) rechts daneben gleich 0, tausche beide Spalten, sonst... |
---|
1589 | if (!n_IsZero(tmp2, basecoeffs())) { |
---|
1590 | n_Delete(&ggt, basecoeffs()); |
---|
1591 | ggt = n_XExtGcd(tmp1, tmp2, &co1, &co2, &co3, &co4, basecoeffs()); |
---|
1592 | // Falls x=ggT(x, y), tausche die beiden Spalten und ziehe die (neue) rechte Spalte so hÀufig von der linken ab, dass an der ehemaligen Stelle von x nun eine 0 steht. Dazu: |
---|
1593 | if (n_Equal(tmp1, ggt, basecoeffs())) { |
---|
1594 | swap(l, l+1); |
---|
1595 | n_Delete(&q, basecoeffs()); |
---|
1596 | q = n_Div(tmp2, ggt, basecoeffs()); |
---|
1597 | q = n_InpNeg(q, basecoeffs()); |
---|
1598 | // Dann addiere das -q-fache der (neuen) rechten Spalte zur linken dazu. Damit erhalten wir die gewÃŒnschte 0 |
---|
1599 | |
---|
1600 | addcol(l, l+1, q, basecoeffs()); |
---|
1601 | n_Delete(&q, basecoeffs()); |
---|
1602 | } |
---|
1603 | else if (n_Equal(tmp1, minusone, basecoeffs())) { |
---|
1604 | // Falls x=-1, so ist x=-ggt(x, y). Dann gehe wie oben vor, multipliziere aber zuerst die neue rechte Spalte (die mit x) mit -1 |
---|
1605 | // Die Berechnung von q (=y/ggt) entfÀllt, da ggt=1 |
---|
1606 | swap(l, l+1); |
---|
1607 | colskalmult(l+1, minusone, basecoeffs()); |
---|
1608 | tmp2 = n_InpNeg(tmp2, basecoeffs()); |
---|
1609 | addcol(l, l+1, tmp2, basecoeffs()); |
---|
1610 | } |
---|
1611 | else { |
---|
1612 | // CF: use the 2x2 matrix (co1, co2)(co3, co4) to |
---|
1613 | // get the gcd in position and the 0 in the other: |
---|
1614 | #ifdef CF_DEB |
---|
1615 | ::Print("applying trafo\n"); |
---|
1616 | StringSetS(""); |
---|
1617 | n_Write(co1, basecoeffs()); StringAppendS("\t"); |
---|
1618 | n_Write(co2, basecoeffs()); StringAppendS("\t"); |
---|
1619 | n_Write(co3, basecoeffs()); StringAppendS("\t"); |
---|
1620 | n_Write(co4, basecoeffs()); StringAppendS("\t"); |
---|
1621 | ::Print("%s\nfor l=%d\n", StringEndS(), l); |
---|
1622 | {char * s = String(); |
---|
1623 | ::Print("to %s\n", s);omFree(s);}; |
---|
1624 | #endif |
---|
1625 | coltransform(l, l+1, co3, co4, co1, co2); |
---|
1626 | #ifdef CF_DEB |
---|
1627 | {char * s = String(); |
---|
1628 | ::Print("gives %s\n", s);} |
---|
1629 | #endif |
---|
1630 | } |
---|
1631 | n_Delete(&co1, basecoeffs()); |
---|
1632 | n_Delete(&co2, basecoeffs()); |
---|
1633 | n_Delete(&co3, basecoeffs()); |
---|
1634 | n_Delete(&co4, basecoeffs()); |
---|
1635 | } |
---|
1636 | else { |
---|
1637 | swap(l, l+1); |
---|
1638 | } |
---|
1639 | // Dann betrachte die vormals rechte Spalte als neue linke, und die rechts daneben als neue rechte. |
---|
1640 | } |
---|
1641 | } |
---|
1642 | |
---|
1643 | // normalize by units: |
---|
1644 | if (!n_IsZero(view(i, j), basecoeffs())) { |
---|
1645 | number u = n_GetUnit(view(i, j), basecoeffs()); |
---|
1646 | if (!n_IsOne(u, basecoeffs())) { |
---|
1647 | colskaldiv(j, u); |
---|
1648 | } |
---|
1649 | n_Delete(&u, basecoeffs()); |
---|
1650 | } |
---|
1651 | // Zum Schluss mache alle EintrÀge rechts vom Diagonalelement betragsmÀÃig kleiner als dieses |
---|
1652 | for (int l=j+1; l<=col; l++) { |
---|
1653 | n_Delete(&q, basecoeffs()); |
---|
1654 | q = n_QuotRem(view(i, l), view(i, j), NULL, basecoeffs()); |
---|
1655 | q = n_InpNeg(q, basecoeffs()); |
---|
1656 | addcol(l, j, q, basecoeffs()); |
---|
1657 | } |
---|
1658 | i--; |
---|
1659 | j--; |
---|
1660 | // Dann betrachte die Zeile darÃŒber und gehe dort wie vorher vor |
---|
1661 | } |
---|
1662 | } |
---|
1663 | n_Delete(&q, basecoeffs()); |
---|
1664 | n_Delete(&tmp1, basecoeffs()); |
---|
1665 | n_Delete(&tmp2, basecoeffs()); |
---|
1666 | n_Delete(&ggt, basecoeffs()); |
---|
1667 | n_Delete(&one, basecoeffs()); |
---|
1668 | n_Delete(&minusone, basecoeffs()); |
---|
1669 | |
---|
1670 | #if 0 |
---|
1671 | ::Print("hnf over Z is \n"); |
---|
1672 | Print(); |
---|
1673 | ::Print("\n(%d x %d)\n", rows(), cols()); |
---|
1674 | #endif |
---|
1675 | } |
---|
1676 | |
---|
1677 | bigintmat * bimChangeCoeff(bigintmat *a, coeffs cnew) |
---|
1678 | { |
---|
1679 | coeffs cold = a->basecoeffs(); |
---|
1680 | bigintmat *b = new bigintmat(a->rows(), a->cols(), cnew); |
---|
1681 | // Erzeugt Karte von alten coeffs nach neuen |
---|
1682 | nMapFunc f = n_SetMap(cold, cnew); |
---|
1683 | number t1; |
---|
1684 | number t2; |
---|
1685 | // apply map to all entries. |
---|
1686 | for (int i=1; i<=a->rows(); i++) |
---|
1687 | { |
---|
1688 | for (int j=1; j<=a->cols(); j++) |
---|
1689 | { |
---|
1690 | t1 = a->get(i, j); |
---|
1691 | t2 = f(t1, cold, cnew); |
---|
1692 | b->set(i, j, t2); |
---|
1693 | n_Delete(&t1, cold); |
---|
1694 | n_Delete(&t2, cnew); |
---|
1695 | } |
---|
1696 | } |
---|
1697 | return b; |
---|
1698 | } |
---|
1699 | |
---|
1700 | //OK: a HNF of (this | p*I) |
---|
1701 | //so the result will always have FULL rank!!!! |
---|
1702 | //(This is different form a lift of the HNF mod p: consider the matrix (p) |
---|
1703 | //to see the difference. It CAN be computed as HNF mod p^2 usually..) |
---|
1704 | bigintmat * bigintmat::modhnf(number p, coeffs R) |
---|
1705 | { |
---|
1706 | coeffs Rp = numbercoeffs(p, R); // R/pR |
---|
1707 | bigintmat *m = bimChangeCoeff(this, Rp); |
---|
1708 | m->howell(); |
---|
1709 | bigintmat *a = bimChangeCoeff(m, R); |
---|
1710 | delete m; |
---|
1711 | bigintmat *C = new bigintmat(rows(), rows(), R); |
---|
1712 | int piv = rows(), i = a->cols(); |
---|
1713 | while (piv) { |
---|
1714 | if (!i || n_IsZero(a->view(piv, i), R)) { |
---|
1715 | C->set(piv, piv, p, R); |
---|
1716 | } else { |
---|
1717 | C->copySubmatInto(a, 1, i, rows(), 1, 1, piv); |
---|
1718 | i--; |
---|
1719 | } |
---|
1720 | piv--; |
---|
1721 | } |
---|
1722 | delete a; |
---|
1723 | return C; |
---|
1724 | } |
---|
1725 | |
---|
1726 | |
---|
1727 | //exactly divide matrix by b |
---|
1728 | void bigintmat::skaldiv(number b) |
---|
1729 | { |
---|
1730 | number tmp1, tmp2; |
---|
1731 | for (int i=1; i<=row; i++) |
---|
1732 | { |
---|
1733 | for (int j=1; j<=col; j++) |
---|
1734 | { |
---|
1735 | tmp1 = view(i, j); |
---|
1736 | tmp2 = n_Div(tmp1, b, basecoeffs()); |
---|
1737 | rawset(i, j, tmp2); |
---|
1738 | } |
---|
1739 | } |
---|
1740 | } |
---|
1741 | |
---|
1742 | //exactly divide col j by b |
---|
1743 | void bigintmat::colskaldiv(int j, number b) |
---|
1744 | { |
---|
1745 | number tmp1, tmp2; |
---|
1746 | for (int i=1; i<=row; i++) |
---|
1747 | { |
---|
1748 | tmp1 = view(i, j); |
---|
1749 | tmp2 = n_Div(tmp1, b, basecoeffs()); |
---|
1750 | rawset(i, j, tmp2); |
---|
1751 | } |
---|
1752 | } |
---|
1753 | |
---|
1754 | // col(j, k) <- col(j,k)*matrix((a, c)(b, d)) |
---|
1755 | // mostly used internally in the hnf and Howell stuff |
---|
1756 | void bigintmat::coltransform(int j, int k, number a, number b, number c, number d) |
---|
1757 | { |
---|
1758 | number tmp1, tmp2, tmp3, tmp4; |
---|
1759 | for (int i=1; i<=row; i++) |
---|
1760 | { |
---|
1761 | tmp1 = get(i, j); |
---|
1762 | tmp2 = get(i, k); |
---|
1763 | tmp3 = n_Mult(tmp1, a, basecoeffs()); |
---|
1764 | tmp4 = n_Mult(tmp2, b, basecoeffs()); |
---|
1765 | n_InpAdd(tmp3, tmp4, basecoeffs()); |
---|
1766 | n_Delete(&tmp4, basecoeffs()); |
---|
1767 | |
---|
1768 | n_InpMult(tmp1, c, basecoeffs()); |
---|
1769 | n_InpMult(tmp2, d, basecoeffs()); |
---|
1770 | n_InpAdd(tmp1, tmp2, basecoeffs()); |
---|
1771 | n_Delete(&tmp2, basecoeffs()); |
---|
1772 | |
---|
1773 | set(i, j, tmp3); |
---|
1774 | set(i, k, tmp1); |
---|
1775 | n_Delete(&tmp1, basecoeffs()); |
---|
1776 | n_Delete(&tmp3, basecoeffs()); |
---|
1777 | } |
---|
1778 | } |
---|
1779 | |
---|
1780 | |
---|
1781 | |
---|
1782 | //reduce all entries mod p. Does NOT change the coeffs type |
---|
1783 | void bigintmat::mod(number p, coeffs c) |
---|
1784 | { |
---|
1785 | // produce the matrix in Z/pZ |
---|
1786 | // CF: TODO rewrite using QuotRem and not the map |
---|
1787 | coeffs coe = numbercoeffs(p, c); |
---|
1788 | nMapFunc f1 = n_SetMap(basecoeffs(), coe); |
---|
1789 | nMapFunc f2 = n_SetMap(coe, basecoeffs()); |
---|
1790 | number tmp1, tmp2; |
---|
1791 | for (int i=1; i<=row; i++) |
---|
1792 | { |
---|
1793 | for (int j=1; j<=col; j++) |
---|
1794 | { |
---|
1795 | tmp1 = get(i, j); |
---|
1796 | tmp2 = f1(tmp1, basecoeffs(), coe); |
---|
1797 | n_Delete(&tmp1, basecoeffs()); |
---|
1798 | tmp1 = f2(tmp2, coe, basecoeffs()); |
---|
1799 | set(i, j, tmp1); |
---|
1800 | n_Delete(&tmp1, basecoeffs()); |
---|
1801 | n_Delete(&tmp2, coe); |
---|
1802 | } |
---|
1803 | } |
---|
1804 | nKillChar(coe); |
---|
1805 | } |
---|
1806 | |
---|
1807 | void bimMult(bigintmat *a, bigintmat *b, bigintmat *c) |
---|
1808 | { |
---|
1809 | if (!nCoeffs_are_equal(a->basecoeffs(), b->basecoeffs())) { |
---|
1810 | Werror("Error in bimMult. Coeffs do not agree!"); |
---|
1811 | return; |
---|
1812 | } |
---|
1813 | if ((a->rows() != c->rows()) || (b->cols() != c->cols()) || (a->cols() != b->rows())) { |
---|
1814 | Werror("Error in bimMult. Dimensions do not agree!"); |
---|
1815 | return; |
---|
1816 | } |
---|
1817 | bigintmat *tmp = bimMult(a, b); |
---|
1818 | c->copy(tmp); |
---|
1819 | |
---|
1820 | delete tmp; |
---|
1821 | } |
---|
1822 | |
---|
1823 | static void reduce_mod_howell(bigintmat *A, bigintmat *b, bigintmat * eps, bigintmat *x) { |
---|
1824 | //write b = Ax + eps where eps is "small" in the sense of bounded by the |
---|
1825 | //pivot entries in H. H does not need to be Howell (or HNF) but need |
---|
1826 | //to be triagonal in the same direction. |
---|
1827 | //b can have multiple columns. |
---|
1828 | #if 0 |
---|
1829 | Print("reduce_mod_howell: A:\n"); |
---|
1830 | A->Print(); |
---|
1831 | Print("\nb:\n"); |
---|
1832 | b->Print(); |
---|
1833 | #endif |
---|
1834 | |
---|
1835 | coeffs R = A->basecoeffs(); |
---|
1836 | assume(x->basecoeffs() == R); |
---|
1837 | assume(b->basecoeffs() == R); |
---|
1838 | assume(eps->basecoeffs() == R); |
---|
1839 | if (!A->cols()) { |
---|
1840 | x->zero(); |
---|
1841 | eps->copy(b); |
---|
1842 | |
---|
1843 | #if 0 |
---|
1844 | Print("\nx:\n"); |
---|
1845 | x->Print(); |
---|
1846 | Print("\neps:\n"); |
---|
1847 | eps->Print(); |
---|
1848 | Print("\n****************************************\n"); |
---|
1849 | #endif |
---|
1850 | return; |
---|
1851 | } |
---|
1852 | |
---|
1853 | bigintmat * B = new bigintmat(b->rows(), 1, R); |
---|
1854 | for(int i=1; i<= b->cols(); i++) { |
---|
1855 | int A_col = A->cols(); |
---|
1856 | b->getcol(i, B); |
---|
1857 | for(int j = B->rows(); j>0; j--) { |
---|
1858 | number Ai = A->view(A->rows() - B->rows() + j, A_col); |
---|
1859 | if (n_IsZero(Ai, R) && |
---|
1860 | n_IsZero(B->view(j, 1), R)) { |
---|
1861 | continue; //all is fine: 0*x = 0 |
---|
1862 | } else if (n_IsZero(B->view(j, 1), R)) { |
---|
1863 | x->rawset(x->rows() - B->rows() + j, i, n_Init(0, R)); |
---|
1864 | A_col--; |
---|
1865 | } else if (n_IsZero(Ai, R)) { |
---|
1866 | A_col--; |
---|
1867 | } else { |
---|
1868 | // "solve" ax=b, possibly enlarging d |
---|
1869 | number Bj = B->view(j, 1); |
---|
1870 | number q = n_Div(Bj, Ai, R); |
---|
1871 | x->rawset(x->rows() - B->rows() + j, i, q); |
---|
1872 | for(int k=j; k>B->rows() - A->rows(); k--) { |
---|
1873 | //B[k] = B[k] - x[k]A[k][j] |
---|
1874 | number s = n_Mult(q, A->view(A->rows() - B->rows() + k, A_col), R); |
---|
1875 | B->rawset(k, 1, n_Sub(B->view(k, 1), s, R)); |
---|
1876 | n_Delete(&s, R); |
---|
1877 | } |
---|
1878 | A_col--; |
---|
1879 | } |
---|
1880 | if (!A_col) { |
---|
1881 | break; |
---|
1882 | } |
---|
1883 | } |
---|
1884 | eps->setcol(i, B); |
---|
1885 | } |
---|
1886 | delete B; |
---|
1887 | #if 0 |
---|
1888 | Print("\nx:\n"); |
---|
1889 | x->Print(); |
---|
1890 | Print("\neps:\n"); |
---|
1891 | eps->Print(); |
---|
1892 | Print("\n****************************************\n"); |
---|
1893 | #endif |
---|
1894 | } |
---|
1895 | |
---|
1896 | static bigintmat * prependIdentity(bigintmat *A) |
---|
1897 | { |
---|
1898 | coeffs R = A->basecoeffs(); |
---|
1899 | bigintmat *m = new bigintmat(A->rows()+A->cols(), A->cols(), R); |
---|
1900 | m->copySubmatInto(A, 1, 1, A->rows(), A->cols(), A->cols()+1, 1); |
---|
1901 | number one = n_Init(1, R); |
---|
1902 | for(int i=1; i<= A->cols(); i++) |
---|
1903 | m->set(i,i,one); |
---|
1904 | n_Delete(&one, R); |
---|
1905 | return m; |
---|
1906 | } |
---|
1907 | |
---|
1908 | static number bimFarey(bigintmat *A, number N, bigintmat *L) { |
---|
1909 | coeffs Z = A->basecoeffs(), |
---|
1910 | Q = nInitChar(n_Q, 0); |
---|
1911 | number den = n_Init(1, Z); |
---|
1912 | nMapFunc f = n_SetMap(Q, Z); |
---|
1913 | |
---|
1914 | for(int i=1; i<= A->rows(); i++) { |
---|
1915 | for(int j=1; j<= A->cols(); j++) { |
---|
1916 | number ad = n_Mult(den, A->view(i, j), Z); |
---|
1917 | number re = n_IntMod(ad, N, Z); |
---|
1918 | n_Delete(&ad, Z); |
---|
1919 | number q = n_Farey(re, N, Z); |
---|
1920 | n_Delete(&re, Z); |
---|
1921 | if (!q) { |
---|
1922 | n_Delete(&ad, Z); |
---|
1923 | n_Delete(&den, Z); |
---|
1924 | return NULL; |
---|
1925 | } |
---|
1926 | |
---|
1927 | number d = nlGetDenom(q, Q), |
---|
1928 | n = nlGetNumerator(q, Q); |
---|
1929 | |
---|
1930 | n_Delete(&q, Q); |
---|
1931 | n_Delete(&ad, Z); |
---|
1932 | number dz = f(d, Q, Z), |
---|
1933 | nz = f(n, Q, Z); |
---|
1934 | n_Delete(&d, Q); |
---|
1935 | n_Delete(&n, Q); |
---|
1936 | |
---|
1937 | if (!n_IsOne(dz, Z)) { |
---|
1938 | L->skalmult(dz, Z); |
---|
1939 | n_InpMult(den, dz, Z); |
---|
1940 | #if 0 |
---|
1941 | Print("den increasing to "); |
---|
1942 | n_Print(den, Z); |
---|
1943 | Print("\n"); |
---|
1944 | #endif |
---|
1945 | } |
---|
1946 | n_Delete(&dz, Z); |
---|
1947 | L->rawset(i, j, nz); |
---|
1948 | } |
---|
1949 | } |
---|
1950 | |
---|
1951 | nKillChar(Q); |
---|
1952 | Print("bimFarey worked\n"); |
---|
1953 | #if 0 |
---|
1954 | L->Print(); |
---|
1955 | Print("\n * 1/"); |
---|
1956 | n_Print(den, Z); |
---|
1957 | Print("\n"); |
---|
1958 | #endif |
---|
1959 | return den; |
---|
1960 | } |
---|
1961 | |
---|
1962 | static number solveAx_dixon(bigintmat *A, bigintmat *B, bigintmat *x, bigintmat *kern) { |
---|
1963 | coeffs R = A->basecoeffs(); |
---|
1964 | |
---|
1965 | assume(getCoeffType(R) == n_Z); |
---|
1966 | |
---|
1967 | number p = n_Init(536870909, R); // PreviousPrime(2^29); not clever |
---|
1968 | coeffs Rp = numbercoeffs(p, R); // R/pR |
---|
1969 | bigintmat *Ap = bimChangeCoeff(A, Rp), |
---|
1970 | *m = prependIdentity(Ap), |
---|
1971 | *Tp, *Hp; |
---|
1972 | delete Ap; |
---|
1973 | |
---|
1974 | m->howell(); |
---|
1975 | Hp = new bigintmat(A->rows(), A->cols(), Rp); |
---|
1976 | Hp->copySubmatInto(m, A->cols()+1, 1, A->rows(), A->cols(), 1, 1); |
---|
1977 | Tp = new bigintmat(A->cols(), A->cols(), Rp); |
---|
1978 | Tp->copySubmatInto(m, 1, 1, A->cols(), A->cols(), 1, 1); |
---|
1979 | |
---|
1980 | int i, j; |
---|
1981 | |
---|
1982 | for(i=1; i<= A->cols(); i++) { |
---|
1983 | for(j=m->rows(); j>A->cols(); j--) { |
---|
1984 | if (!n_IsZero(m->view(j, i), Rp)) break; |
---|
1985 | } |
---|
1986 | if (j>A->cols()) break; |
---|
1987 | } |
---|
1988 | // Print("Found nullity (kern dim) of %d\n", i-1); |
---|
1989 | bigintmat * kp = new bigintmat(A->cols(), i-1, Rp); |
---|
1990 | kp->copySubmatInto(Tp, 1, 1, A->cols(), i-1, 1, 1); |
---|
1991 | kp->howell(); |
---|
1992 | |
---|
1993 | delete m; |
---|
1994 | |
---|
1995 | //Hp is the mod-p howell form |
---|
1996 | //Tp the transformation, mod p |
---|
1997 | //kp a basis for the kernel, in howell form, mod p |
---|
1998 | |
---|
1999 | bigintmat * eps_p = new bigintmat(B->rows(), B->cols(), Rp), |
---|
2000 | * x_p = new bigintmat(A->cols(), B->cols(), Rp), |
---|
2001 | * fps_p = new bigintmat(kp->cols(), B->cols(), Rp); |
---|
2002 | |
---|
2003 | //initial solution |
---|
2004 | |
---|
2005 | number zero = n_Init(0, R); |
---|
2006 | x->skalmult(zero, R); |
---|
2007 | n_Delete(&zero, R); |
---|
2008 | |
---|
2009 | bigintmat * b = new bigintmat(B); |
---|
2010 | number pp = n_Init(1, R); |
---|
2011 | i = 1; |
---|
2012 | do { |
---|
2013 | bigintmat * b_p = bimChangeCoeff(b, Rp), * s; |
---|
2014 | bigintmat * t1, *t2; |
---|
2015 | reduce_mod_howell(Hp, b_p, eps_p, x_p); |
---|
2016 | delete b_p; |
---|
2017 | if (!eps_p->isZero()) { |
---|
2018 | Print("no solution, since no modular solution\n"); |
---|
2019 | |
---|
2020 | delete eps_p; |
---|
2021 | delete x_p; |
---|
2022 | delete Hp; |
---|
2023 | delete kp; |
---|
2024 | delete Tp; |
---|
2025 | delete b; |
---|
2026 | n_Delete(&pp, R); |
---|
2027 | n_Delete(&p, R); |
---|
2028 | nKillChar(Rp); |
---|
2029 | |
---|
2030 | return NULL; |
---|
2031 | } |
---|
2032 | t1 = bimMult(Tp, x_p); |
---|
2033 | delete x_p; |
---|
2034 | x_p = t1; |
---|
2035 | reduce_mod_howell(kp, x_p, x_p, fps_p); //we're not all interested in fps_p |
---|
2036 | s = bimChangeCoeff(x_p, R); |
---|
2037 | t1 = bimMult(A, s); |
---|
2038 | t2 = bimSub(b, t1); |
---|
2039 | t2->skaldiv(p); |
---|
2040 | delete b; |
---|
2041 | delete t1; |
---|
2042 | b = t2; |
---|
2043 | s->skalmult(pp, R); |
---|
2044 | t1 = bimAdd(x, s); |
---|
2045 | delete s; |
---|
2046 | x->swapMatrix(t1); |
---|
2047 | delete t1; |
---|
2048 | |
---|
2049 | if(kern && i==1) { |
---|
2050 | bigintmat * ker = bimChangeCoeff(kp, R); |
---|
2051 | t1 = bimMult(A, ker); |
---|
2052 | t1->skaldiv(p); |
---|
2053 | t1->skalmult(n_Init(-1, R), R); |
---|
2054 | b->appendCol(t1); |
---|
2055 | delete t1; |
---|
2056 | x->appendCol(ker); |
---|
2057 | delete ker; |
---|
2058 | x_p->extendCols(kp->cols()); |
---|
2059 | eps_p->extendCols(kp->cols()); |
---|
2060 | fps_p->extendCols(kp->cols()); |
---|
2061 | } |
---|
2062 | |
---|
2063 | n_InpMult(pp, p, R); |
---|
2064 | |
---|
2065 | if (b->isZero()) { |
---|
2066 | //exact solution found, stop |
---|
2067 | delete eps_p; |
---|
2068 | delete fps_p; |
---|
2069 | delete x_p; |
---|
2070 | delete Hp; |
---|
2071 | delete kp; |
---|
2072 | delete Tp; |
---|
2073 | delete b; |
---|
2074 | n_Delete(&pp, R); |
---|
2075 | n_Delete(&p, R); |
---|
2076 | nKillChar(Rp); |
---|
2077 | |
---|
2078 | return n_Init(1, R); |
---|
2079 | } else { |
---|
2080 | bigintmat *y = new bigintmat(x->rows(), x->cols(), R); |
---|
2081 | number d = bimFarey(x, pp, y); |
---|
2082 | if (d) { |
---|
2083 | bigintmat *c = bimMult(A, y); |
---|
2084 | bigintmat *bd = new bigintmat(B); |
---|
2085 | bd->skalmult(d, R); |
---|
2086 | if (kern) { |
---|
2087 | bd->extendCols(kp->cols()); |
---|
2088 | } |
---|
2089 | if (*c == *bd) { |
---|
2090 | x->swapMatrix(y); |
---|
2091 | delete y; |
---|
2092 | delete c; |
---|
2093 | if (kern) { |
---|
2094 | y = new bigintmat(x->rows(), B->cols(), R); |
---|
2095 | c = new bigintmat(x->rows(), kp->cols(), R); |
---|
2096 | x->splitcol(y, c); |
---|
2097 | x->swapMatrix(y); |
---|
2098 | delete y; |
---|
2099 | kern->swapMatrix(c); |
---|
2100 | delete c; |
---|
2101 | } |
---|
2102 | |
---|
2103 | delete bd; |
---|
2104 | |
---|
2105 | delete eps_p; |
---|
2106 | delete fps_p; |
---|
2107 | delete x_p; |
---|
2108 | delete Hp; |
---|
2109 | delete kp; |
---|
2110 | delete Tp; |
---|
2111 | delete b; |
---|
2112 | n_Delete(&pp, R); |
---|
2113 | n_Delete(&p, R); |
---|
2114 | nKillChar(Rp); |
---|
2115 | |
---|
2116 | return d; |
---|
2117 | } |
---|
2118 | delete c; |
---|
2119 | delete bd; |
---|
2120 | n_Delete(&d, R); |
---|
2121 | } |
---|
2122 | delete y; |
---|
2123 | } |
---|
2124 | i++; |
---|
2125 | } while (1); |
---|
2126 | delete eps_p; |
---|
2127 | delete fps_p; |
---|
2128 | delete x_p; |
---|
2129 | delete Hp; |
---|
2130 | delete kp; |
---|
2131 | delete Tp; |
---|
2132 | n_Delete(&pp, R); |
---|
2133 | n_Delete(&p, R); |
---|
2134 | nKillChar(Rp); |
---|
2135 | return NULL; |
---|
2136 | } |
---|
2137 | |
---|
2138 | //TODO: re-write using reduce_mod_howell |
---|
2139 | static number solveAx_howell(bigintmat *A, bigintmat *b, bigintmat *x, bigintmat *kern) { |
---|
2140 | // try to solve Ax=b, more precisely, find |
---|
2141 | // number d |
---|
2142 | // bigintmat x |
---|
2143 | // sth. Ax=db |
---|
2144 | // where d is small-ish (divides the determinant of A if this makes sense) |
---|
2145 | // return 0 if there is no solution. |
---|
2146 | // |
---|
2147 | // if kern is non-NULL, return a basis for the kernel |
---|
2148 | |
---|
2149 | //Algo: we do row-howell (triangular matrix). The idea is |
---|
2150 | // Ax = b <=> AT T^-1x = b |
---|
2151 | // y := T^-1 x, solve AT y = b |
---|
2152 | // and return Ty. |
---|
2153 | //Howell does not compute the trafo, hence we need to cheat: |
---|
2154 | //B := (I_n | A^t)^t, then the top part of the Howell form of |
---|
2155 | //B will give a useful trafo |
---|
2156 | //Then we can find x by back-substitution and lcm/gcd to find the denominator |
---|
2157 | //The defining property of Howell makes this work. |
---|
2158 | |
---|
2159 | coeffs R = A->basecoeffs(); |
---|
2160 | bigintmat *m = prependIdentity(A); |
---|
2161 | m->howell(); // since m contains the identity, we'll have A->cols() |
---|
2162 | // many cols. |
---|
2163 | number den = n_Init(1, R); |
---|
2164 | |
---|
2165 | bigintmat * B = new bigintmat(A->rows(), 1, R); |
---|
2166 | for(int i=1; i<= b->cols(); i++) { |
---|
2167 | int A_col = A->cols(); |
---|
2168 | b->getcol(i, B); |
---|
2169 | B->skalmult(den, R); |
---|
2170 | for(int j = B->rows(); j>0; j--) { |
---|
2171 | number Ai = m->view(m->rows()-B->rows() + j, A_col); |
---|
2172 | if (n_IsZero(Ai, R) && |
---|
2173 | n_IsZero(B->view(j, 1), R)) { |
---|
2174 | continue; //all is fine: 0*x = 0 |
---|
2175 | } else if (n_IsZero(B->view(j, 1), R)) { |
---|
2176 | x->rawset(x->rows() - B->rows() + j, i, n_Init(0, R)); |
---|
2177 | A_col--; |
---|
2178 | } else if (n_IsZero(Ai, R)) { |
---|
2179 | delete m; |
---|
2180 | delete B; |
---|
2181 | n_Delete(&den, R); |
---|
2182 | return 0; |
---|
2183 | } else { |
---|
2184 | // solve ax=db, possibly enlarging d |
---|
2185 | // so x = db/a |
---|
2186 | number Bj = B->view(j, 1); |
---|
2187 | number g = n_Gcd(Bj, Ai, R); |
---|
2188 | number xi; |
---|
2189 | if (n_Equal(Ai, g, R)) { //good: den stable! |
---|
2190 | xi = n_Div(Bj, Ai, R); |
---|
2191 | } else { //den <- den * (a/g), so old sol. needs to be adjusted |
---|
2192 | number inc_d = n_Div(Ai, g, R); |
---|
2193 | n_InpMult(den, inc_d, R); |
---|
2194 | x->skalmult(inc_d, R); |
---|
2195 | B->skalmult(inc_d, R); |
---|
2196 | xi = n_Div(Bj, g, R); |
---|
2197 | n_Delete(&inc_d, R); |
---|
2198 | } //now for the back-substitution: |
---|
2199 | x->rawset(x->rows() - B->rows() + j, i, xi); |
---|
2200 | for(int k=j; k>0; k--) { |
---|
2201 | //B[k] = B[k] - x[k]A[k][j] |
---|
2202 | number s = n_Mult(xi, m->view(m->rows()-B->rows() + k, A_col), R); |
---|
2203 | B->rawset(k, 1, n_Sub(B->view(k, 1), s, R)); |
---|
2204 | n_Delete(&s, R); |
---|
2205 | } |
---|
2206 | n_Delete(&g, R); |
---|
2207 | A_col--; |
---|
2208 | } |
---|
2209 | if (!A_col) { |
---|
2210 | if (B->isZero()) break; |
---|
2211 | else { |
---|
2212 | delete m; |
---|
2213 | delete B; |
---|
2214 | n_Delete(&den, R); |
---|
2215 | return 0; |
---|
2216 | } |
---|
2217 | } |
---|
2218 | } |
---|
2219 | } |
---|
2220 | delete B; |
---|
2221 | bigintmat *T = new bigintmat(A->cols(), A->cols(), R); |
---|
2222 | T->copySubmatInto(m, 1, 1, A->cols(), A->cols(), 1, 1); |
---|
2223 | if (kern) { |
---|
2224 | int i, j; |
---|
2225 | for(i=1; i<= A->cols(); i++) { |
---|
2226 | for(j=m->rows(); j>A->cols(); j--) { |
---|
2227 | if (!n_IsZero(m->view(j, i), R)) break; |
---|
2228 | } |
---|
2229 | if (j>A->cols()) break; |
---|
2230 | } |
---|
2231 | Print("Found nullity (kern dim) of %d\n", i-1); |
---|
2232 | bigintmat * ker = new bigintmat(A->rows(), i-1, R); |
---|
2233 | ker->copySubmatInto(T, 1, 1, A->rows(), i-1, 1, 1); |
---|
2234 | kern->swapMatrix(ker); |
---|
2235 | delete ker; |
---|
2236 | } |
---|
2237 | delete m; |
---|
2238 | bigintmat * y = bimMult(T, x); |
---|
2239 | x->swapMatrix(y); |
---|
2240 | delete y; |
---|
2241 | x->simplifyContentDen(&den); |
---|
2242 | #if 0 |
---|
2243 | Print("sol = 1/"); |
---|
2244 | n_Print(den, R); |
---|
2245 | Print(" *\n"); |
---|
2246 | x->Print(); |
---|
2247 | Print("\n"); |
---|
2248 | #endif |
---|
2249 | return den; |
---|
2250 | } |
---|
2251 | |
---|
2252 | number solveAx(bigintmat *A, bigintmat *b, bigintmat *x) { |
---|
2253 | #if 0 |
---|
2254 | Print("Solve Ax=b for A=\n"); |
---|
2255 | A->Print(); |
---|
2256 | Print("\nb = \n"); |
---|
2257 | b->Print(); |
---|
2258 | Print("\nx = \n"); |
---|
2259 | x->Print(); |
---|
2260 | Print("\n"); |
---|
2261 | #endif |
---|
2262 | |
---|
2263 | coeffs R = A->basecoeffs(); |
---|
2264 | assume (R == b->basecoeffs()); |
---|
2265 | assume (R == x->basecoeffs()); |
---|
2266 | assume ((x->cols() == b->cols()) && (x->rows() == A->cols()) && (A->rows() == b->rows())); |
---|
2267 | |
---|
2268 | switch (getCoeffType(R)) { |
---|
2269 | case n_Z: |
---|
2270 | return solveAx_dixon(A, b, x, NULL); |
---|
2271 | case n_Zn: |
---|
2272 | case n_Znm: |
---|
2273 | case n_Z2m: |
---|
2274 | return solveAx_howell(A, b, x, NULL); |
---|
2275 | case n_Zp: |
---|
2276 | case n_Q: |
---|
2277 | case n_GF: |
---|
2278 | case n_algExt: |
---|
2279 | case n_transExt: |
---|
2280 | Warn("have field, should use Gauss or better"); |
---|
2281 | default: |
---|
2282 | if (R->cfXExtGcd && R->cfAnn) { //assume it's Euclidean |
---|
2283 | return solveAx_howell(A, b, x, NULL); |
---|
2284 | } |
---|
2285 | Werror("have no solve algorithm"); |
---|
2286 | } |
---|
2287 | return NULL; |
---|
2288 | } |
---|
2289 | |
---|
2290 | void diagonalForm(bigintmat *A, bigintmat ** S, bigintmat ** T) |
---|
2291 | { |
---|
2292 | bigintmat * t, *s, *a=A; |
---|
2293 | coeffs R = a->basecoeffs(); |
---|
2294 | if (T) { |
---|
2295 | *T = new bigintmat(a->cols(), a->cols(), R), |
---|
2296 | (*T)->one(); |
---|
2297 | t = new bigintmat(*T); |
---|
2298 | } else { |
---|
2299 | t = *T; |
---|
2300 | } |
---|
2301 | |
---|
2302 | if (S) { |
---|
2303 | *S = new bigintmat(a->rows(), a->rows(), R); |
---|
2304 | (*S)->one(); |
---|
2305 | s = new bigintmat(*S); |
---|
2306 | } else { |
---|
2307 | s = *S; |
---|
2308 | } |
---|
2309 | |
---|
2310 | int flip=0; |
---|
2311 | do { |
---|
2312 | bigintmat * x, *X; |
---|
2313 | if (flip) { |
---|
2314 | x = s; |
---|
2315 | X = *S; |
---|
2316 | } else { |
---|
2317 | x = t; |
---|
2318 | X = *T; |
---|
2319 | } |
---|
2320 | |
---|
2321 | if (x) { |
---|
2322 | x->one(); |
---|
2323 | bigintmat * r = new bigintmat(a->rows()+a->cols(), a->cols(), R); |
---|
2324 | bigintmat * rw = new bigintmat(1, a->cols(), R); |
---|
2325 | for(int i=0; i<a->cols(); i++) { |
---|
2326 | x->getrow(i+1, rw); |
---|
2327 | r->setrow(i+1, rw); |
---|
2328 | } |
---|
2329 | for (int i=0; i<a->rows(); i++) { |
---|
2330 | a->getrow(i+1, rw); |
---|
2331 | r->setrow(i+a->cols()+1, rw); |
---|
2332 | } |
---|
2333 | r->hnf(); |
---|
2334 | for(int i=0; i<a->cols(); i++) { |
---|
2335 | r->getrow(i+1, rw); |
---|
2336 | x->setrow(i+1, rw); |
---|
2337 | } |
---|
2338 | for(int i=0; i<a->rows(); i++) { |
---|
2339 | r->getrow(i+a->cols()+1, rw); |
---|
2340 | a->setrow(i+1, rw); |
---|
2341 | } |
---|
2342 | delete rw; |
---|
2343 | delete r; |
---|
2344 | |
---|
2345 | #if 0 |
---|
2346 | Print("X: %ld\n", X); |
---|
2347 | X->Print(); |
---|
2348 | Print("\nx: %ld\n", x); |
---|
2349 | x->Print(); |
---|
2350 | #endif |
---|
2351 | bimMult(X, x, X); |
---|
2352 | #if 0 |
---|
2353 | Print("\n2:X: %ld %ld %ld\n", X, *S, *T); |
---|
2354 | X->Print(); |
---|
2355 | Print("\n2:x: %ld\n", x); |
---|
2356 | x->Print(); |
---|
2357 | Print("\n"); |
---|
2358 | #endif |
---|
2359 | } else { |
---|
2360 | a->hnf(); |
---|
2361 | } |
---|
2362 | |
---|
2363 | int diag = 1; |
---|
2364 | for(int i=a->rows(); diag && i>0; i--) { |
---|
2365 | for(int j=a->cols(); j>0; j--) { |
---|
2366 | if ((a->rows()-i)!=(a->cols()-j) && !n_IsZero(a->view(i, j), R)) { |
---|
2367 | diag = 0; |
---|
2368 | break; |
---|
2369 | } |
---|
2370 | } |
---|
2371 | } |
---|
2372 | #if 0 |
---|
2373 | Print("Diag ? %d\n", diag); |
---|
2374 | a->Print(); |
---|
2375 | Print("\n"); |
---|
2376 | #endif |
---|
2377 | if (diag) break; |
---|
2378 | |
---|
2379 | a = a->transpose(); // leaks - I need to write inpTranspose |
---|
2380 | flip = 1-flip; |
---|
2381 | } while (1); |
---|
2382 | if (flip) |
---|
2383 | a = a->transpose(); |
---|
2384 | |
---|
2385 | if (S) *S = (*S)->transpose(); |
---|
2386 | if (s) delete s; |
---|
2387 | if (t) delete t; |
---|
2388 | A->copy(a); |
---|
2389 | } |
---|
2390 | |
---|
2391 | //a "q-base" for the kernel of a. |
---|
2392 | //Should be re-done to use Howell rather than smith. |
---|
2393 | //can be done using solveAx now. |
---|
2394 | int kernbase (bigintmat *a, bigintmat *c, number p, coeffs q) { |
---|
2395 | #if 0 |
---|
2396 | Print("Kernel of "); |
---|
2397 | a->Print(); |
---|
2398 | Print(" modulo "); |
---|
2399 | n_Print(p, q); |
---|
2400 | Print("\n"); |
---|
2401 | #endif |
---|
2402 | |
---|
2403 | coeffs coe = numbercoeffs(p, q); |
---|
2404 | bigintmat *m = bimChangeCoeff(a, coe), *U, *V; |
---|
2405 | diagonalForm(m, &U, &V); |
---|
2406 | #if 0 |
---|
2407 | Print("\ndiag form: "); |
---|
2408 | m->Print(); |
---|
2409 | Print("\nU:\n"); |
---|
2410 | U->Print(); |
---|
2411 | Print("\nV:\n"); |
---|
2412 | V->Print(); |
---|
2413 | Print("\n"); |
---|
2414 | #endif |
---|
2415 | |
---|
2416 | int rg = 0; |
---|
2417 | #undef MIN |
---|
2418 | #define MIN(a,b) (a < b ? a : b) |
---|
2419 | for(rg=0; rg<MIN(m->rows(), m->cols()) && !n_IsZero(m->view(m->rows()-rg,m->cols()-rg), coe); rg++); |
---|
2420 | |
---|
2421 | #undef MAX |
---|
2422 | #define MAX(a,b) (a > b ? a : b) |
---|
2423 | bigintmat * k = new bigintmat(m->cols(), m->rows(), coe); |
---|
2424 | for(int i=0; i<rg; i++) { |
---|
2425 | number A = n_Ann(m->view(m->rows()-i, m->cols()-i), coe); |
---|
2426 | k->set(m->cols()-i, i+1, A); |
---|
2427 | n_Delete(&A, coe); |
---|
2428 | } |
---|
2429 | for(int i=rg; i<m->cols(); i++) { |
---|
2430 | k->set(m->cols()-i, i+1-rg, n_Init(1, coe)); |
---|
2431 | } |
---|
2432 | bimMult(V, k, k); |
---|
2433 | c->copy(bimChangeCoeff(k, q)); |
---|
2434 | return c->cols(); |
---|
2435 | } |
---|
2436 | |
---|
2437 | |
---|
2438 | //create Z/nA of type n_Zn |
---|
2439 | coeffs numbercoeffs(number n, coeffs c) { |
---|
2440 | mpz_t p; |
---|
2441 | number2mpz(n, c, p); |
---|
2442 | ZnmInfo *pp = new ZnmInfo; |
---|
2443 | pp->base = p; |
---|
2444 | pp->exp = 1; |
---|
2445 | coeffs nc = nInitChar(n_Zn, (void*)pp); |
---|
2446 | mpz_clear(p); |
---|
2447 | delete pp; |
---|
2448 | return nc; |
---|
2449 | } |
---|
2450 | |
---|
2451 | bool nCoeffs_are_equal(coeffs r, coeffs s) { |
---|
2452 | if ((r == NULL) || (s == NULL)) |
---|
2453 | return false; |
---|
2454 | if ((getCoeffType(r)==n_Z) && (getCoeffType(s)==n_Z)) |
---|
2455 | return true; |
---|
2456 | if ((getCoeffType(r)==n_Zp) && (getCoeffType(s)==n_Zp)) { |
---|
2457 | if (r->ch == s->ch) |
---|
2458 | return true; |
---|
2459 | else |
---|
2460 | return false; |
---|
2461 | } |
---|
2462 | // n_Zn stimmt wahrscheinlich noch nicht |
---|
2463 | if ((getCoeffType(r)==n_Zn) && (getCoeffType(s)==n_Zn)) { |
---|
2464 | if (r->ch == s->ch) |
---|
2465 | return true; |
---|
2466 | else |
---|
2467 | return false; |
---|
2468 | } |
---|
2469 | if ((getCoeffType(r)==n_Q) && (getCoeffType(s)==n_Q)) |
---|
2470 | return true; |
---|
2471 | // FALL n_Zn FEHLT NOCH! |
---|
2472 | //if ((getCoeffType(r)==n_Zn) && (getCoeffType(s)==n_Zn)) |
---|
2473 | return false; |
---|
2474 | } |
---|
2475 | |
---|
2476 | number bigintmat::content() |
---|
2477 | { |
---|
2478 | coeffs r = basecoeffs(); |
---|
2479 | number g = get(1,1), h; |
---|
2480 | int n=rows()*cols(); |
---|
2481 | for(int i=1; i<n && !n_IsOne(g, r); i++) { |
---|
2482 | h = n_Gcd(g, view(i), r); |
---|
2483 | n_Delete(&g, r); |
---|
2484 | g=h; |
---|
2485 | } |
---|
2486 | return g; |
---|
2487 | } |
---|
2488 | void bigintmat::simplifyContentDen(number *d) |
---|
2489 | { |
---|
2490 | coeffs r = basecoeffs(); |
---|
2491 | number g = n_Copy(*d, r), h; |
---|
2492 | int n=rows()*cols(); |
---|
2493 | for(int i=0; i<n && !n_IsOne(g, r); i++) { |
---|
2494 | h = n_Gcd(g, view(i), r); |
---|
2495 | n_Delete(&g, r); |
---|
2496 | g=h; |
---|
2497 | } |
---|
2498 | *d = n_Div(*d, g, r); |
---|
2499 | if (!n_IsOne(g, r)) |
---|
2500 | skaldiv(g); |
---|
2501 | } |
---|