1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facMul.cc |
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5 | * |
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6 | * This file implements functions for fast multiplication and division with |
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7 | * remainder |
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8 | * |
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9 | * @author Martin Lee |
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10 | * |
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11 | **/ |
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12 | /*****************************************************************************/ |
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13 | |
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14 | #include "debug.h" |
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15 | |
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16 | #include "canonicalform.h" |
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17 | #include "facMul.h" |
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18 | #include "algext.h" |
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19 | #include "cf_util.h" |
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20 | #include "templates/ftmpl_functions.h" |
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21 | |
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22 | #ifdef HAVE_NTL |
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23 | #include <NTL/lzz_pEX.h> |
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24 | #include "NTLconvert.h" |
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25 | |
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26 | #ifdef HAVE_FLINT |
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27 | #include "FLINTconvert.h" |
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28 | #endif |
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29 | |
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30 | // univariate polys |
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31 | |
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32 | #ifdef HAVE_FLINT |
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33 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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34 | { |
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35 | int degAy= degree (A); |
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36 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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37 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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38 | CFIterator j; |
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39 | for (CFIterator i= A; i.hasTerms(); i++) |
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40 | { |
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41 | if (i.coeff().inBaseDomain()) |
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42 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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43 | else |
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44 | for (j= i.coeff(); j.hasTerms(); j++) |
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45 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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46 | j.coeff()); |
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47 | } |
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48 | _fmpz_poly_normalise(result); |
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49 | } |
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50 | |
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51 | |
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52 | CanonicalForm |
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53 | reverseSubstQa (const fmpz_poly_t F, int d, const Variable& alpha, |
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54 | const CanonicalForm& den) |
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55 | { |
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56 | Variable x= Variable (1); |
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57 | |
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58 | CanonicalForm result= 0; |
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59 | int i= 0; |
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60 | int degf= fmpz_poly_degree (F); |
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61 | int k= 0; |
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62 | int degfSubK; |
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63 | int repLength, j; |
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64 | CanonicalForm coeff; |
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65 | fmpz* tmp; |
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66 | while (degf >= k) |
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67 | { |
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68 | coeff= 0; |
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69 | degfSubK= degf - k; |
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70 | if (degfSubK >= d) |
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71 | repLength= d; |
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72 | else |
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73 | repLength= degfSubK + 1; |
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74 | |
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75 | for (j= 0; j < repLength; j++) |
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76 | { |
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77 | tmp= fmpz_poly_get_coeff_ptr (F, j+k); |
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78 | if (!fmpz_is_zero (tmp)) |
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79 | { |
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80 | CanonicalForm ff= convertFmpz2CF (tmp)/den; |
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81 | coeff += ff*power (alpha, j); |
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82 | } |
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83 | } |
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84 | result += coeff*power (x, i); |
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85 | i++; |
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86 | k= d*i; |
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87 | } |
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88 | return result; |
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89 | } |
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90 | |
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91 | CanonicalForm |
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92 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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93 | const Variable& alpha) |
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94 | { |
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95 | CanonicalForm A= F; |
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96 | CanonicalForm B= G; |
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97 | |
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98 | CanonicalForm denA= bCommonDen (A); |
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99 | CanonicalForm denB= bCommonDen (B); |
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100 | |
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101 | A *= denA; |
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102 | B *= denB; |
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103 | int degAa= degree (A, alpha); |
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104 | int degBa= degree (B, alpha); |
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105 | int d= degAa + 1 + degBa; |
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106 | |
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107 | fmpz_poly_t FLINTA,FLINTB; |
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108 | fmpz_poly_init (FLINTA); |
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109 | fmpz_poly_init (FLINTB); |
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110 | kronSub (FLINTA, A, d); |
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111 | kronSub (FLINTB, B, d); |
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112 | |
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113 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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114 | |
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115 | denA *= denB; |
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116 | A= reverseSubstQa (FLINTA, d, alpha, denA); |
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117 | |
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118 | fmpz_poly_clear (FLINTA); |
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119 | fmpz_poly_clear (FLINTB); |
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120 | return A; |
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121 | } |
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122 | |
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123 | CanonicalForm |
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124 | mulFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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125 | { |
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126 | CanonicalForm A= F; |
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127 | CanonicalForm B= G; |
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128 | |
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129 | CanonicalForm denA= bCommonDen (A); |
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130 | CanonicalForm denB= bCommonDen (B); |
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131 | |
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132 | A *= denA; |
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133 | B *= denB; |
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134 | fmpz_poly_t FLINTA,FLINTB; |
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135 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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136 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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137 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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138 | denA *= denB; |
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139 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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140 | A /= denA; |
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141 | fmpz_poly_clear (FLINTA); |
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142 | fmpz_poly_clear (FLINTB); |
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143 | |
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144 | return A; |
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145 | } |
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146 | |
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147 | /*CanonicalForm |
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148 | mulFLINTQ2 (const CanonicalForm& F, const CanonicalForm& G) |
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149 | { |
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150 | CanonicalForm A= F; |
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151 | CanonicalForm B= G; |
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152 | |
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153 | fmpq_poly_t FLINTA,FLINTB; |
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154 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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155 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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156 | |
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157 | fmpq_poly_mul (FLINTA, FLINTA, FLINTB); |
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158 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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159 | fmpq_poly_clear (FLINTA); |
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160 | fmpq_poly_clear (FLINTB); |
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161 | return A; |
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162 | }*/ |
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163 | |
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164 | CanonicalForm |
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165 | divFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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166 | { |
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167 | CanonicalForm A= F; |
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168 | CanonicalForm B= G; |
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169 | |
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170 | fmpq_poly_t FLINTA,FLINTB; |
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171 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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172 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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173 | |
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174 | fmpq_poly_div (FLINTA, FLINTA, FLINTB); |
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175 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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176 | |
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177 | fmpq_poly_clear (FLINTA); |
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178 | fmpq_poly_clear (FLINTB); |
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179 | return A; |
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180 | } |
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181 | |
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182 | CanonicalForm |
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183 | modFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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184 | { |
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185 | CanonicalForm A= F; |
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186 | CanonicalForm B= G; |
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187 | |
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188 | fmpq_poly_t FLINTA,FLINTB; |
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189 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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190 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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191 | |
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192 | fmpq_poly_rem (FLINTA, FLINTA, FLINTB); |
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193 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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194 | |
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195 | fmpq_poly_clear (FLINTA); |
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196 | fmpq_poly_clear (FLINTB); |
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197 | return A; |
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198 | } |
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199 | |
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200 | CanonicalForm |
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201 | mulFLINTQaTrunc (const CanonicalForm& F, const CanonicalForm& G, |
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202 | const Variable& alpha, int m) |
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203 | { |
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204 | CanonicalForm A= F; |
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205 | CanonicalForm B= G; |
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206 | |
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207 | CanonicalForm denA= bCommonDen (A); |
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208 | CanonicalForm denB= bCommonDen (B); |
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209 | |
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210 | A *= denA; |
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211 | B *= denB; |
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212 | |
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213 | int degAa= degree (A, alpha); |
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214 | int degBa= degree (B, alpha); |
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215 | int d= degAa + 1 + degBa; |
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216 | |
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217 | fmpz_poly_t FLINTA,FLINTB; |
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218 | fmpz_poly_init (FLINTA); |
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219 | fmpz_poly_init (FLINTB); |
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220 | kronSub (FLINTA, A, d); |
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221 | kronSub (FLINTB, B, d); |
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222 | |
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223 | int k= d*m; |
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224 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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225 | |
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226 | denA *= denB; |
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227 | A= reverseSubstQa (FLINTA, d, alpha, denA); |
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228 | fmpz_poly_clear (FLINTA); |
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229 | fmpz_poly_clear (FLINTB); |
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230 | return A; |
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231 | } |
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232 | |
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233 | CanonicalForm |
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234 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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235 | { |
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236 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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237 | return mod (F*G, power (Variable (1), m)); |
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238 | Variable alpha; |
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239 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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240 | return mulFLINTQaTrunc (F, G, alpha, m); |
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241 | |
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242 | CanonicalForm A= F; |
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243 | CanonicalForm B= G; |
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244 | |
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245 | CanonicalForm denA= bCommonDen (A); |
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246 | CanonicalForm denB= bCommonDen (B); |
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247 | |
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248 | A *= denA; |
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249 | B *= denB; |
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250 | fmpz_poly_t FLINTA,FLINTB; |
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251 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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252 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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253 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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254 | denA *= denB; |
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255 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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256 | A /= denA; |
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257 | fmpz_poly_clear (FLINTA); |
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258 | fmpz_poly_clear (FLINTB); |
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259 | |
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260 | return A; |
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261 | } |
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262 | |
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263 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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264 | { |
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265 | if (d == 0) |
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266 | return F; |
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267 | if (F.inCoeffDomain()) |
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268 | return F*power (Variable (1),d); |
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269 | Variable x= Variable (1); |
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270 | CanonicalForm result= 0; |
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271 | CFIterator i= F; |
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272 | while (d - i.exp() < 0) |
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273 | i++; |
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274 | |
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275 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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276 | result += i.coeff()*power (x, d - i.exp()); |
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277 | return result; |
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278 | } |
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279 | |
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280 | CanonicalForm |
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281 | newtonInverse (const CanonicalForm& F, const int n) |
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282 | { |
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283 | int l= ilog2(n); |
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284 | |
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285 | CanonicalForm g= F [0]; |
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286 | |
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287 | ASSERT (!g.isZero(), "expected a unit"); |
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288 | |
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289 | if (!g.isOne()) |
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290 | g = 1/g; |
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291 | Variable x= Variable (1); |
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292 | CanonicalForm result; |
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293 | int exp= 0; |
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294 | if (n & 1) |
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295 | { |
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296 | result= g; |
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297 | exp= 1; |
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298 | } |
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299 | CanonicalForm h; |
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300 | |
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301 | for (int i= 1; i <= l; i++) |
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302 | { |
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303 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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304 | h= mod (h, power (x, (1 << i)) - 1); |
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305 | h= div (h, power (x, (1 << (i - 1)))); |
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306 | g -= power (x, (1 << (i - 1)))* |
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307 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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308 | |
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309 | if (n & (1 << i)) |
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310 | { |
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311 | if (exp) |
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312 | { |
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313 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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314 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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315 | h= div (h, power (x, exp)); |
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316 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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317 | exp += (1 << i); |
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318 | } |
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319 | else |
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320 | { |
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321 | exp= (1 << i); |
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322 | result= g; |
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323 | } |
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324 | } |
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325 | } |
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326 | |
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327 | return result; |
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328 | } |
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329 | |
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330 | void |
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331 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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332 | CanonicalForm& R) |
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333 | { |
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334 | CanonicalForm A= F; |
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335 | CanonicalForm B= G; |
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336 | Variable x= Variable (1); |
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337 | int degA= degree (A, x); |
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338 | int degB= degree (B, x); |
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339 | int m= degA - degB; |
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340 | |
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341 | if (m < 0) |
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342 | { |
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343 | R= A; |
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344 | Q= 0; |
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345 | return; |
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346 | } |
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347 | |
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348 | if (degB <= 1) |
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349 | divrem (A, B, Q, R); |
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350 | else |
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351 | { |
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352 | R= uniReverse (A, degA); |
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353 | |
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354 | CanonicalForm revB= uniReverse (B, degB); |
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355 | CanonicalForm buf= revB; |
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356 | revB= newtonInverse (revB, m + 1); |
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357 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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358 | Q= uniReverse (Q, m); |
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359 | |
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360 | R= A - mulNTL (Q, B); |
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361 | } |
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362 | } |
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363 | |
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364 | void |
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365 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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366 | { |
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367 | CanonicalForm A= F; |
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368 | CanonicalForm B= G; |
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369 | Variable x= Variable (1); |
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370 | int degA= degree (A, x); |
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371 | int degB= degree (B, x); |
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372 | int m= degA - degB; |
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373 | |
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374 | if (m < 0) |
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375 | { |
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376 | Q= 0; |
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377 | return; |
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378 | } |
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379 | |
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380 | if (degB <= 1) |
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381 | Q= div (A, B); |
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382 | else |
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383 | { |
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384 | CanonicalForm R= uniReverse (A, degA); |
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385 | |
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386 | CanonicalForm revB= uniReverse (B, degB); |
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387 | revB= newtonInverse (revB, m + 1); |
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388 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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389 | Q= uniReverse (Q, m); |
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390 | } |
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391 | } |
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392 | |
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393 | #endif |
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394 | |
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395 | CanonicalForm |
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396 | mulNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
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397 | { |
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398 | if (F.inCoeffDomain() || G.inCoeffDomain() || getCharacteristic() == 0) |
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399 | { |
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400 | Variable alpha; |
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401 | #ifdef HAVE_FLINT |
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402 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
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403 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
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404 | { |
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405 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
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406 | return result; |
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407 | } |
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408 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
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409 | { |
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410 | if (b.getp() != 0) |
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411 | { |
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412 | fmpz_t FLINTpk; |
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413 | fmpz_init_set_ui (FLINTpk, b.getp()); |
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414 | fmpz_pow_ui (FLINTpk, FLINTpk, b.getk()); |
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415 | fmpz_mod_poly_t FLINTF, FLINTG; |
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416 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
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417 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
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418 | fmpz_mod_poly_mul (FLINTF, FLINTF, FLINTG); |
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419 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF, F.mvar(), b); |
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420 | fmpz_mod_poly_clear (FLINTG); |
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421 | fmpz_mod_poly_clear (FLINTF); |
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422 | return result; |
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423 | } |
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424 | return mulFLINTQ (F, G); |
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425 | } |
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426 | #endif |
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427 | if (b.getp() != 0) |
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428 | return b (F*G); |
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429 | return F*G; |
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430 | } |
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431 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
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432 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
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433 | if (CFFactory::gettype() == GaloisFieldDomain) |
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434 | return F*G; |
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435 | zz_p::init (getCharacteristic()); |
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436 | Variable alpha; |
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437 | CanonicalForm result; |
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438 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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439 | { |
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440 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
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441 | zz_pE::init (NTLMipo); |
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442 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
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443 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
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444 | mul (NTLF, NTLF, NTLG); |
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445 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
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446 | } |
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447 | else |
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448 | { |
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449 | #ifdef HAVE_FLINT |
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450 | nmod_poly_t FLINTF, FLINTG; |
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451 | convertFacCF2nmod_poly_t (FLINTF, F); |
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452 | convertFacCF2nmod_poly_t (FLINTG, G); |
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453 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
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454 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
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455 | nmod_poly_clear (FLINTF); |
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456 | nmod_poly_clear (FLINTG); |
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457 | #else |
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458 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
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459 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
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460 | mul (NTLF, NTLF, NTLG); |
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461 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
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462 | #endif |
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463 | } |
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464 | return result; |
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465 | } |
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466 | |
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467 | CanonicalForm |
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468 | modNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
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469 | { |
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470 | if (F.inCoeffDomain() && G.isUnivariate()) |
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471 | { |
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472 | if (b.getp() != 0) |
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473 | return b(F); |
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474 | return F; |
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475 | } |
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476 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
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477 | { |
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478 | if (b.getp() != 0) |
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479 | return b(F%G); |
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480 | return mod (F, G); |
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481 | } |
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482 | else if (F.isUnivariate() && G.inCoeffDomain()) |
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483 | { |
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484 | if (b.getp() != 0) |
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485 | return b(F%G); |
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486 | return mod (F,G); |
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487 | } |
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488 | |
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489 | if (getCharacteristic() == 0) |
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490 | { |
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491 | #ifdef HAVE_FLINT |
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492 | Variable alpha; |
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493 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
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494 | { |
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495 | if (b.getp() != 0) |
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496 | { |
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497 | fmpz_t FLINTpk; |
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498 | fmpz_init_set_ui (FLINTpk, b.getp()); |
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499 | fmpz_pow_ui (FLINTpk, FLINTpk, b.getk()); |
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500 | fmpz_mod_poly_t FLINTF, FLINTG; |
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501 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
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502 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
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503 | fmpz_mod_poly_rem (FLINTF, FLINTF, FLINTG); |
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504 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
505 | fmpz_mod_poly_clear (FLINTG); |
---|
506 | fmpz_mod_poly_clear (FLINTF); |
---|
507 | return result; |
---|
508 | } |
---|
509 | return modFLINTQ (F, G); |
---|
510 | } |
---|
511 | else |
---|
512 | { |
---|
513 | CanonicalForm Q, R; |
---|
514 | newtonDivrem (F, G, Q, R); |
---|
515 | return R; |
---|
516 | } |
---|
517 | #else |
---|
518 | if (b.getp() != 0) |
---|
519 | { |
---|
520 | ZZ NTLpk= power_ZZ (b.getp(), b.getk()); |
---|
521 | ZZ_p::init (NTLpk); |
---|
522 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
523 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
524 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
525 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
526 | rem (NTLf, NTLf, NTLg); |
---|
527 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
528 | } |
---|
529 | return mod (F, G); |
---|
530 | #endif |
---|
531 | } |
---|
532 | |
---|
533 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
534 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
535 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
536 | return mod (F, G); |
---|
537 | zz_p::init (getCharacteristic()); |
---|
538 | Variable alpha; |
---|
539 | CanonicalForm result; |
---|
540 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
541 | { |
---|
542 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
543 | zz_pE::init (NTLMipo); |
---|
544 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
545 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
546 | rem (NTLF, NTLF, NTLG); |
---|
547 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
548 | } |
---|
549 | else |
---|
550 | { |
---|
551 | #ifdef HAVE_FLINT |
---|
552 | nmod_poly_t FLINTF, FLINTG; |
---|
553 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
554 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
555 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
556 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
557 | nmod_poly_clear (FLINTF); |
---|
558 | nmod_poly_clear (FLINTG); |
---|
559 | #else |
---|
560 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
561 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
562 | rem (NTLF, NTLF, NTLG); |
---|
563 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
564 | #endif |
---|
565 | } |
---|
566 | return result; |
---|
567 | } |
---|
568 | |
---|
569 | CanonicalForm |
---|
570 | divNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
571 | { |
---|
572 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
573 | { |
---|
574 | if (b.getp() != 0) |
---|
575 | return b(F); |
---|
576 | return F; |
---|
577 | } |
---|
578 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
579 | { |
---|
580 | if (b.getp() != 0) |
---|
581 | return b(div (F,G)); |
---|
582 | return div (F, G); |
---|
583 | } |
---|
584 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
585 | { |
---|
586 | if (b.getp() != 0) |
---|
587 | return b(div (F,G)); |
---|
588 | return div (F, G); |
---|
589 | } |
---|
590 | |
---|
591 | if (getCharacteristic() == 0) |
---|
592 | { |
---|
593 | #ifdef HAVE_FLINT |
---|
594 | Variable alpha; |
---|
595 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
596 | { |
---|
597 | if (b.getp() != 0) |
---|
598 | { |
---|
599 | fmpz_t FLINTpk; |
---|
600 | fmpz_init_set_ui (FLINTpk, b.getp()); |
---|
601 | fmpz_pow_ui (FLINTpk, FLINTpk, b.getk()); |
---|
602 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
603 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
604 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
605 | fmpz_mod_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG); |
---|
606 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
607 | fmpz_mod_poly_clear (FLINTG); |
---|
608 | fmpz_mod_poly_clear (FLINTF); |
---|
609 | return result; |
---|
610 | } |
---|
611 | return divFLINTQ (F,G); |
---|
612 | } |
---|
613 | else |
---|
614 | { |
---|
615 | CanonicalForm Q; |
---|
616 | newtonDiv (F, G, Q); |
---|
617 | return Q; |
---|
618 | } |
---|
619 | #else |
---|
620 | if (b.getp() != 0) |
---|
621 | { |
---|
622 | ZZ NTLpk= power_ZZ (b.getp(), b.getk()); |
---|
623 | ZZ_p::init (NTLpk); |
---|
624 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
625 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
626 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
627 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
628 | div (NTLf, NTLf, NTLg); |
---|
629 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
630 | } |
---|
631 | return div (F, G); |
---|
632 | #endif |
---|
633 | } |
---|
634 | |
---|
635 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
636 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
637 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
638 | return div (F, G); |
---|
639 | zz_p::init (getCharacteristic()); |
---|
640 | Variable alpha; |
---|
641 | CanonicalForm result; |
---|
642 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
643 | { |
---|
644 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
645 | zz_pE::init (NTLMipo); |
---|
646 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
647 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
648 | div (NTLF, NTLF, NTLG); |
---|
649 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
650 | } |
---|
651 | else |
---|
652 | { |
---|
653 | #ifdef HAVE_FLINT |
---|
654 | nmod_poly_t FLINTF, FLINTG; |
---|
655 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
656 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
657 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
658 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
659 | nmod_poly_clear (FLINTF); |
---|
660 | nmod_poly_clear (FLINTG); |
---|
661 | #else |
---|
662 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
663 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
664 | div (NTLF, NTLF, NTLG); |
---|
665 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
666 | #endif |
---|
667 | } |
---|
668 | return result; |
---|
669 | } |
---|
670 | |
---|
671 | // end univariate polys |
---|
672 | //************************* |
---|
673 | // bivariate polys |
---|
674 | |
---|
675 | #ifdef HAVE_FLINT |
---|
676 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
677 | { |
---|
678 | int degAy= degree (A); |
---|
679 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
680 | |
---|
681 | nmod_poly_t buf; |
---|
682 | |
---|
683 | int j, k, bufRepLength; |
---|
684 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
685 | { |
---|
686 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
687 | |
---|
688 | k= i.exp()*d; |
---|
689 | bufRepLength= (int) nmod_poly_length (buf); |
---|
690 | for (j= 0; j < bufRepLength; j++) |
---|
691 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
692 | nmod_poly_clear (buf); |
---|
693 | } |
---|
694 | _nmod_poly_normalise (result); |
---|
695 | } |
---|
696 | |
---|
697 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
698 | { |
---|
699 | int degAy= degree (A); |
---|
700 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
701 | |
---|
702 | fmpq_poly_t buf; |
---|
703 | fmpq_t coeff; |
---|
704 | |
---|
705 | int k, l, bufRepLength; |
---|
706 | CFIterator j; |
---|
707 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
708 | { |
---|
709 | if (i.coeff().inCoeffDomain()) |
---|
710 | { |
---|
711 | k= d1*i.exp(); |
---|
712 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
713 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
714 | for (l= 0; l < bufRepLength; l++) |
---|
715 | { |
---|
716 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
717 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
718 | } |
---|
719 | fmpq_poly_clear (buf); |
---|
720 | } |
---|
721 | else |
---|
722 | { |
---|
723 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
724 | { |
---|
725 | k= d1*i.exp(); |
---|
726 | k += d2*j.exp(); |
---|
727 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
728 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
729 | for (l= 0; l < bufRepLength; l++) |
---|
730 | { |
---|
731 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
732 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
733 | } |
---|
734 | fmpq_poly_clear (buf); |
---|
735 | } |
---|
736 | } |
---|
737 | } |
---|
738 | fmpq_clear (coeff); |
---|
739 | _fmpq_poly_normalise (result); |
---|
740 | } |
---|
741 | |
---|
742 | void |
---|
743 | kronSubReciproFp (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
744 | int d) |
---|
745 | { |
---|
746 | int degAy= degree (A); |
---|
747 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
748 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
749 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
750 | |
---|
751 | nmod_poly_t buf; |
---|
752 | |
---|
753 | int k, kk, j, bufRepLength; |
---|
754 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
755 | { |
---|
756 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
757 | |
---|
758 | k= i.exp()*d; |
---|
759 | kk= (degAy - i.exp())*d; |
---|
760 | bufRepLength= (int) nmod_poly_length (buf); |
---|
761 | for (j= 0; j < bufRepLength; j++) |
---|
762 | { |
---|
763 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
764 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
765 | nmod_poly_get_coeff_ui (buf, j), |
---|
766 | getCharacteristic() |
---|
767 | ) |
---|
768 | ); |
---|
769 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
770 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
771 | nmod_poly_get_coeff_ui (buf, j), |
---|
772 | getCharacteristic() |
---|
773 | ) |
---|
774 | ); |
---|
775 | } |
---|
776 | nmod_poly_clear (buf); |
---|
777 | } |
---|
778 | _nmod_poly_normalise (subA1); |
---|
779 | _nmod_poly_normalise (subA2); |
---|
780 | } |
---|
781 | |
---|
782 | void |
---|
783 | kronSubReciproQ (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
784 | int d) |
---|
785 | { |
---|
786 | int degAy= degree (A); |
---|
787 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
788 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
789 | |
---|
790 | fmpz_poly_t buf; |
---|
791 | fmpz_t coeff1, coeff2; |
---|
792 | |
---|
793 | int k, kk, j, bufRepLength; |
---|
794 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
795 | { |
---|
796 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
797 | |
---|
798 | k= i.exp()*d; |
---|
799 | kk= (degAy - i.exp())*d; |
---|
800 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
801 | for (j= 0; j < bufRepLength; j++) |
---|
802 | { |
---|
803 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
804 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
805 | fmpz_add (coeff1, coeff1, coeff2); |
---|
806 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
807 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
808 | fmpz_add (coeff1, coeff1, coeff2); |
---|
809 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
810 | } |
---|
811 | fmpz_poly_clear (buf); |
---|
812 | } |
---|
813 | fmpz_clear (coeff1); |
---|
814 | fmpz_clear (coeff2); |
---|
815 | _fmpz_poly_normalise (subA1); |
---|
816 | _fmpz_poly_normalise (subA2); |
---|
817 | } |
---|
818 | |
---|
819 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
820 | { |
---|
821 | Variable y= Variable (2); |
---|
822 | Variable x= Variable (1); |
---|
823 | |
---|
824 | fmpz_poly_t f; |
---|
825 | fmpz_poly_init (f); |
---|
826 | fmpz_poly_set (f, F); |
---|
827 | |
---|
828 | fmpz_poly_t buf; |
---|
829 | CanonicalForm result= 0; |
---|
830 | int i= 0; |
---|
831 | int degf= fmpz_poly_degree(f); |
---|
832 | int k= 0; |
---|
833 | int degfSubK, repLength, j; |
---|
834 | fmpz_t coeff; |
---|
835 | while (degf >= k) |
---|
836 | { |
---|
837 | degfSubK= degf - k; |
---|
838 | if (degfSubK >= d) |
---|
839 | repLength= d; |
---|
840 | else |
---|
841 | repLength= degfSubK + 1; |
---|
842 | |
---|
843 | fmpz_poly_init2 (buf, repLength); |
---|
844 | fmpz_init (coeff); |
---|
845 | for (j= 0; j < repLength; j++) |
---|
846 | { |
---|
847 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
848 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
849 | } |
---|
850 | _fmpz_poly_normalise (buf); |
---|
851 | |
---|
852 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
853 | i++; |
---|
854 | k= d*i; |
---|
855 | fmpz_poly_clear (buf); |
---|
856 | fmpz_clear (coeff); |
---|
857 | } |
---|
858 | fmpz_poly_clear (f); |
---|
859 | |
---|
860 | return result; |
---|
861 | } |
---|
862 | |
---|
863 | CanonicalForm |
---|
864 | reverseSubstReciproFp (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
865 | { |
---|
866 | Variable y= Variable (2); |
---|
867 | Variable x= Variable (1); |
---|
868 | |
---|
869 | nmod_poly_t f, g; |
---|
870 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
871 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
872 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
873 | nmod_poly_set (f, F); |
---|
874 | nmod_poly_set (g, G); |
---|
875 | int degf= nmod_poly_degree(f); |
---|
876 | int degg= nmod_poly_degree(g); |
---|
877 | |
---|
878 | |
---|
879 | nmod_poly_t buf1,buf2, buf3; |
---|
880 | |
---|
881 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
882 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
883 | |
---|
884 | CanonicalForm result= 0; |
---|
885 | int i= 0; |
---|
886 | int lf= 0; |
---|
887 | int lg= d*k; |
---|
888 | int degfSubLf= degf; |
---|
889 | int deggSubLg= degg-lg; |
---|
890 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
891 | while (degf >= lf || lg >= 0) |
---|
892 | { |
---|
893 | if (degfSubLf >= d) |
---|
894 | repLengthBuf1= d; |
---|
895 | else if (degfSubLf < 0) |
---|
896 | repLengthBuf1= 0; |
---|
897 | else |
---|
898 | repLengthBuf1= degfSubLf + 1; |
---|
899 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
900 | |
---|
901 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
902 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
903 | _nmod_poly_normalise (buf1); |
---|
904 | |
---|
905 | repLengthBuf1= nmod_poly_length (buf1); |
---|
906 | |
---|
907 | if (deggSubLg >= d - 1) |
---|
908 | repLengthBuf2= d - 1; |
---|
909 | else if (deggSubLg < 0) |
---|
910 | repLengthBuf2= 0; |
---|
911 | else |
---|
912 | repLengthBuf2= deggSubLg + 1; |
---|
913 | |
---|
914 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
915 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
916 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
917 | |
---|
918 | _nmod_poly_normalise (buf2); |
---|
919 | repLengthBuf2= nmod_poly_length (buf2); |
---|
920 | |
---|
921 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
922 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
923 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
924 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
925 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
926 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
927 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
928 | _nmod_poly_normalise (buf3); |
---|
929 | |
---|
930 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
931 | i++; |
---|
932 | |
---|
933 | |
---|
934 | lf= i*d; |
---|
935 | degfSubLf= degf - lf; |
---|
936 | |
---|
937 | lg= d*(k-i); |
---|
938 | deggSubLg= degg - lg; |
---|
939 | |
---|
940 | if (lg >= 0 && deggSubLg > 0) |
---|
941 | { |
---|
942 | if (repLengthBuf2 > degfSubLf + 1) |
---|
943 | degfSubLf= repLengthBuf2 - 1; |
---|
944 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
945 | for (ind= 0; ind < tmp; ind++) |
---|
946 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
947 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
948 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
949 | getCharacteristic() |
---|
950 | ) |
---|
951 | ); |
---|
952 | } |
---|
953 | if (lg < 0) |
---|
954 | { |
---|
955 | nmod_poly_clear (buf1); |
---|
956 | nmod_poly_clear (buf2); |
---|
957 | nmod_poly_clear (buf3); |
---|
958 | break; |
---|
959 | } |
---|
960 | if (degfSubLf >= 0) |
---|
961 | { |
---|
962 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
963 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
964 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
965 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
966 | getCharacteristic() |
---|
967 | ) |
---|
968 | ); |
---|
969 | } |
---|
970 | nmod_poly_clear (buf1); |
---|
971 | nmod_poly_clear (buf2); |
---|
972 | nmod_poly_clear (buf3); |
---|
973 | } |
---|
974 | |
---|
975 | nmod_poly_clear (f); |
---|
976 | nmod_poly_clear (g); |
---|
977 | |
---|
978 | return result; |
---|
979 | } |
---|
980 | |
---|
981 | CanonicalForm |
---|
982 | reverseSubstReciproQ (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
983 | { |
---|
984 | Variable y= Variable (2); |
---|
985 | Variable x= Variable (1); |
---|
986 | |
---|
987 | fmpz_poly_t f, g; |
---|
988 | fmpz_poly_init (f); |
---|
989 | fmpz_poly_init (g); |
---|
990 | fmpz_poly_set (f, F); |
---|
991 | fmpz_poly_set (g, G); |
---|
992 | int degf= fmpz_poly_degree(f); |
---|
993 | int degg= fmpz_poly_degree(g); |
---|
994 | |
---|
995 | |
---|
996 | fmpz_poly_t buf1,buf2, buf3; |
---|
997 | |
---|
998 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
999 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
1000 | |
---|
1001 | CanonicalForm result= 0; |
---|
1002 | int i= 0; |
---|
1003 | int lf= 0; |
---|
1004 | int lg= d*k; |
---|
1005 | int degfSubLf= degf; |
---|
1006 | int deggSubLg= degg-lg; |
---|
1007 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1008 | fmpz_t tmp1, tmp2; |
---|
1009 | while (degf >= lf || lg >= 0) |
---|
1010 | { |
---|
1011 | if (degfSubLf >= d) |
---|
1012 | repLengthBuf1= d; |
---|
1013 | else if (degfSubLf < 0) |
---|
1014 | repLengthBuf1= 0; |
---|
1015 | else |
---|
1016 | repLengthBuf1= degfSubLf + 1; |
---|
1017 | |
---|
1018 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
1019 | |
---|
1020 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1021 | { |
---|
1022 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1023 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
1024 | } |
---|
1025 | _fmpz_poly_normalise (buf1); |
---|
1026 | |
---|
1027 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
1028 | |
---|
1029 | if (deggSubLg >= d - 1) |
---|
1030 | repLengthBuf2= d - 1; |
---|
1031 | else if (deggSubLg < 0) |
---|
1032 | repLengthBuf2= 0; |
---|
1033 | else |
---|
1034 | repLengthBuf2= deggSubLg + 1; |
---|
1035 | |
---|
1036 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
1037 | |
---|
1038 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1039 | { |
---|
1040 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1041 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
1042 | } |
---|
1043 | |
---|
1044 | _fmpz_poly_normalise (buf2); |
---|
1045 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
1046 | |
---|
1047 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
1048 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1049 | { |
---|
1050 | fmpz_poly_get_coeff_fmpz (tmp1, buf1, ind); |
---|
1051 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
1052 | } |
---|
1053 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1054 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
1055 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1056 | { |
---|
1057 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
1058 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
1059 | } |
---|
1060 | _fmpz_poly_normalise (buf3); |
---|
1061 | |
---|
1062 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1063 | i++; |
---|
1064 | |
---|
1065 | |
---|
1066 | lf= i*d; |
---|
1067 | degfSubLf= degf - lf; |
---|
1068 | |
---|
1069 | lg= d*(k-i); |
---|
1070 | deggSubLg= degg - lg; |
---|
1071 | |
---|
1072 | if (lg >= 0 && deggSubLg > 0) |
---|
1073 | { |
---|
1074 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1075 | degfSubLf= repLengthBuf2 - 1; |
---|
1076 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1077 | for (ind= 0; ind < tmp; ind++) |
---|
1078 | { |
---|
1079 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1080 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
1081 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1082 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
1083 | } |
---|
1084 | } |
---|
1085 | if (lg < 0) |
---|
1086 | { |
---|
1087 | fmpz_poly_clear (buf1); |
---|
1088 | fmpz_poly_clear (buf2); |
---|
1089 | fmpz_poly_clear (buf3); |
---|
1090 | break; |
---|
1091 | } |
---|
1092 | if (degfSubLf >= 0) |
---|
1093 | { |
---|
1094 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1095 | { |
---|
1096 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1097 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
1098 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1099 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
1100 | } |
---|
1101 | } |
---|
1102 | fmpz_poly_clear (buf1); |
---|
1103 | fmpz_poly_clear (buf2); |
---|
1104 | fmpz_poly_clear (buf3); |
---|
1105 | } |
---|
1106 | |
---|
1107 | fmpz_poly_clear (f); |
---|
1108 | fmpz_poly_clear (g); |
---|
1109 | fmpz_clear (tmp1); |
---|
1110 | fmpz_clear (tmp2); |
---|
1111 | |
---|
1112 | return result; |
---|
1113 | } |
---|
1114 | |
---|
1115 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
1116 | { |
---|
1117 | Variable y= Variable (2); |
---|
1118 | Variable x= Variable (1); |
---|
1119 | |
---|
1120 | nmod_poly_t f; |
---|
1121 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1122 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1123 | nmod_poly_set (f, F); |
---|
1124 | |
---|
1125 | nmod_poly_t buf; |
---|
1126 | CanonicalForm result= 0; |
---|
1127 | int i= 0; |
---|
1128 | int degf= nmod_poly_degree(f); |
---|
1129 | int k= 0; |
---|
1130 | int degfSubK, repLength, j; |
---|
1131 | while (degf >= k) |
---|
1132 | { |
---|
1133 | degfSubK= degf - k; |
---|
1134 | if (degfSubK >= d) |
---|
1135 | repLength= d; |
---|
1136 | else |
---|
1137 | repLength= degfSubK + 1; |
---|
1138 | |
---|
1139 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
1140 | for (j= 0; j < repLength; j++) |
---|
1141 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
1142 | _nmod_poly_normalise (buf); |
---|
1143 | |
---|
1144 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
1145 | i++; |
---|
1146 | k= d*i; |
---|
1147 | nmod_poly_clear (buf); |
---|
1148 | } |
---|
1149 | nmod_poly_clear (f); |
---|
1150 | |
---|
1151 | return result; |
---|
1152 | } |
---|
1153 | |
---|
1154 | CanonicalForm |
---|
1155 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1156 | CanonicalForm& M) |
---|
1157 | { |
---|
1158 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
1159 | d1 /= 2; |
---|
1160 | d1 += 1; |
---|
1161 | |
---|
1162 | nmod_poly_t F1, F2; |
---|
1163 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1164 | nmod_poly_init_preinv (F1, getCharacteristic(), ninv); |
---|
1165 | nmod_poly_init_preinv (F2, getCharacteristic(), ninv); |
---|
1166 | kronSubReciproFp (F1, F2, F, d1); |
---|
1167 | |
---|
1168 | nmod_poly_t G1, G2; |
---|
1169 | nmod_poly_init_preinv (G1, getCharacteristic(), ninv); |
---|
1170 | nmod_poly_init_preinv (G2, getCharacteristic(), ninv); |
---|
1171 | kronSubReciproFp (G1, G2, G, d1); |
---|
1172 | |
---|
1173 | int k= d1*degree (M); |
---|
1174 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
1175 | |
---|
1176 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1177 | int degtailG= degree (tailcoeff (G), 1); |
---|
1178 | int taildegF= taildegree (F); |
---|
1179 | int taildegG= taildegree (G); |
---|
1180 | |
---|
1181 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
1182 | + d1*(2+taildegF + taildegG); |
---|
1183 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
1184 | nmod_poly_shift_right (F2, F2, b); |
---|
1185 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
1186 | |
---|
1187 | |
---|
1188 | CanonicalForm result= reverseSubstReciproFp (F1, F2, d1, d2); |
---|
1189 | |
---|
1190 | nmod_poly_clear (F1); |
---|
1191 | nmod_poly_clear (F2); |
---|
1192 | nmod_poly_clear (G1); |
---|
1193 | nmod_poly_clear (G2); |
---|
1194 | return result; |
---|
1195 | } |
---|
1196 | |
---|
1197 | CanonicalForm |
---|
1198 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1199 | CanonicalForm& M) |
---|
1200 | { |
---|
1201 | CanonicalForm A= F; |
---|
1202 | CanonicalForm B= G; |
---|
1203 | |
---|
1204 | int degAx= degree (A, 1); |
---|
1205 | int degAy= degree (A, 2); |
---|
1206 | int degBx= degree (B, 1); |
---|
1207 | int degBy= degree (B, 2); |
---|
1208 | int d1= degAx + 1 + degBx; |
---|
1209 | int d2= tmax (degAy, degBy); |
---|
1210 | |
---|
1211 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
1212 | return mulMod2FLINTFpReci (A, B, M); |
---|
1213 | |
---|
1214 | nmod_poly_t FLINTA, FLINTB; |
---|
1215 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1216 | nmod_poly_init_preinv (FLINTA, getCharacteristic(), ninv); |
---|
1217 | nmod_poly_init_preinv (FLINTB, getCharacteristic(), ninv); |
---|
1218 | kronSubFp (FLINTA, A, d1); |
---|
1219 | kronSubFp (FLINTB, B, d1); |
---|
1220 | |
---|
1221 | int k= d1*degree (M); |
---|
1222 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1223 | |
---|
1224 | A= reverseSubstFp (FLINTA, d1); |
---|
1225 | |
---|
1226 | nmod_poly_clear (FLINTA); |
---|
1227 | nmod_poly_clear (FLINTB); |
---|
1228 | return A; |
---|
1229 | } |
---|
1230 | |
---|
1231 | CanonicalForm |
---|
1232 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1233 | CanonicalForm& M) |
---|
1234 | { |
---|
1235 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
1236 | d1 /= 2; |
---|
1237 | d1 += 1; |
---|
1238 | |
---|
1239 | fmpz_poly_t F1, F2; |
---|
1240 | fmpz_poly_init (F1); |
---|
1241 | fmpz_poly_init (F2); |
---|
1242 | kronSubReciproQ (F1, F2, F, d1); |
---|
1243 | |
---|
1244 | fmpz_poly_t G1, G2; |
---|
1245 | fmpz_poly_init (G1); |
---|
1246 | fmpz_poly_init (G2); |
---|
1247 | kronSubReciproQ (G1, G2, G, d1); |
---|
1248 | |
---|
1249 | int k= d1*degree (M); |
---|
1250 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
1251 | |
---|
1252 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1253 | int degtailG= degree (tailcoeff (G), 1); |
---|
1254 | int taildegF= taildegree (F); |
---|
1255 | int taildegG= taildegree (G); |
---|
1256 | |
---|
1257 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
1258 | + d1*(2+taildegF + taildegG); |
---|
1259 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
1260 | fmpz_poly_shift_right (F2, F2, b); |
---|
1261 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
1262 | |
---|
1263 | CanonicalForm result= reverseSubstReciproQ (F1, F2, d1, d2); |
---|
1264 | |
---|
1265 | fmpz_poly_clear (F1); |
---|
1266 | fmpz_poly_clear (F2); |
---|
1267 | fmpz_poly_clear (G1); |
---|
1268 | fmpz_poly_clear (G2); |
---|
1269 | return result; |
---|
1270 | } |
---|
1271 | |
---|
1272 | CanonicalForm |
---|
1273 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1274 | CanonicalForm& M) |
---|
1275 | { |
---|
1276 | CanonicalForm A= F; |
---|
1277 | CanonicalForm B= G; |
---|
1278 | |
---|
1279 | int degAx= degree (A, 1); |
---|
1280 | int degBx= degree (B, 1); |
---|
1281 | int d1= degAx + 1 + degBx; |
---|
1282 | |
---|
1283 | CanonicalForm f= bCommonDen (F); |
---|
1284 | CanonicalForm g= bCommonDen (G); |
---|
1285 | A *= f; |
---|
1286 | B *= g; |
---|
1287 | |
---|
1288 | fmpz_poly_t FLINTA, FLINTB; |
---|
1289 | fmpz_poly_init (FLINTA); |
---|
1290 | fmpz_poly_init (FLINTB); |
---|
1291 | kronSub (FLINTA, A, d1); |
---|
1292 | kronSub (FLINTB, B, d1); |
---|
1293 | int k= d1*degree (M); |
---|
1294 | |
---|
1295 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1296 | A= reverseSubstQ (FLINTA, d1); |
---|
1297 | fmpz_poly_clear (FLINTA); |
---|
1298 | fmpz_poly_clear (FLINTB); |
---|
1299 | return A/(f*g); |
---|
1300 | } |
---|
1301 | |
---|
1302 | #endif |
---|
1303 | |
---|
1304 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
1305 | { |
---|
1306 | int degAy= degree (A); |
---|
1307 | zz_pX result; |
---|
1308 | result.rep.SetLength (d*(degAy + 1)); |
---|
1309 | |
---|
1310 | zz_p *resultp; |
---|
1311 | resultp= result.rep.elts(); |
---|
1312 | zz_pX buf; |
---|
1313 | zz_p *bufp; |
---|
1314 | int j, k, bufRepLength; |
---|
1315 | |
---|
1316 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1317 | { |
---|
1318 | if (i.coeff().inCoeffDomain()) |
---|
1319 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1320 | else |
---|
1321 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1322 | |
---|
1323 | k= i.exp()*d; |
---|
1324 | bufp= buf.rep.elts(); |
---|
1325 | bufRepLength= (int) buf.rep.length(); |
---|
1326 | for (j= 0; j < bufRepLength; j++) |
---|
1327 | resultp [j + k]= bufp [j]; |
---|
1328 | } |
---|
1329 | result.normalize(); |
---|
1330 | |
---|
1331 | return result; |
---|
1332 | } |
---|
1333 | |
---|
1334 | zz_pEX kronSubFq (const CanonicalForm& A, int d, const Variable& alpha) |
---|
1335 | { |
---|
1336 | int degAy= degree (A); |
---|
1337 | zz_pEX result; |
---|
1338 | result.rep.SetLength (d*(degAy + 1)); |
---|
1339 | |
---|
1340 | Variable v; |
---|
1341 | zz_pE *resultp; |
---|
1342 | resultp= result.rep.elts(); |
---|
1343 | zz_pEX buf1; |
---|
1344 | zz_pE *buf1p; |
---|
1345 | zz_pX buf2; |
---|
1346 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1347 | int j, k, buf1RepLength; |
---|
1348 | |
---|
1349 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1350 | { |
---|
1351 | if (i.coeff().inCoeffDomain()) |
---|
1352 | { |
---|
1353 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1354 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
1355 | } |
---|
1356 | else |
---|
1357 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1358 | |
---|
1359 | k= i.exp()*d; |
---|
1360 | buf1p= buf1.rep.elts(); |
---|
1361 | buf1RepLength= (int) buf1.rep.length(); |
---|
1362 | for (j= 0; j < buf1RepLength; j++) |
---|
1363 | resultp [j + k]= buf1p [j]; |
---|
1364 | } |
---|
1365 | result.normalize(); |
---|
1366 | |
---|
1367 | return result; |
---|
1368 | } |
---|
1369 | |
---|
1370 | void |
---|
1371 | kronSubReciproFq (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
1372 | const Variable& alpha) |
---|
1373 | { |
---|
1374 | int degAy= degree (A); |
---|
1375 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1376 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1377 | |
---|
1378 | Variable v; |
---|
1379 | zz_pE *subA1p; |
---|
1380 | zz_pE *subA2p; |
---|
1381 | subA1p= subA1.rep.elts(); |
---|
1382 | subA2p= subA2.rep.elts(); |
---|
1383 | zz_pEX buf; |
---|
1384 | zz_pE *bufp; |
---|
1385 | zz_pX buf2; |
---|
1386 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1387 | int j, k, kk, bufRepLength; |
---|
1388 | |
---|
1389 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1390 | { |
---|
1391 | if (i.coeff().inCoeffDomain()) |
---|
1392 | { |
---|
1393 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1394 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
1395 | } |
---|
1396 | else |
---|
1397 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1398 | |
---|
1399 | k= i.exp()*d; |
---|
1400 | kk= (degAy - i.exp())*d; |
---|
1401 | bufp= buf.rep.elts(); |
---|
1402 | bufRepLength= (int) buf.rep.length(); |
---|
1403 | for (j= 0; j < bufRepLength; j++) |
---|
1404 | { |
---|
1405 | subA1p [j + k] += bufp [j]; |
---|
1406 | subA2p [j + kk] += bufp [j]; |
---|
1407 | } |
---|
1408 | } |
---|
1409 | subA1.normalize(); |
---|
1410 | subA2.normalize(); |
---|
1411 | } |
---|
1412 | |
---|
1413 | void |
---|
1414 | kronSubReciproFp (zz_pX& subA1, zz_pX& subA2, const CanonicalForm& A, int d) |
---|
1415 | { |
---|
1416 | int degAy= degree (A); |
---|
1417 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1418 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1419 | |
---|
1420 | zz_p *subA1p; |
---|
1421 | zz_p *subA2p; |
---|
1422 | subA1p= subA1.rep.elts(); |
---|
1423 | subA2p= subA2.rep.elts(); |
---|
1424 | zz_pX buf; |
---|
1425 | zz_p *bufp; |
---|
1426 | int j, k, kk, bufRepLength; |
---|
1427 | |
---|
1428 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1429 | { |
---|
1430 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1431 | |
---|
1432 | k= i.exp()*d; |
---|
1433 | kk= (degAy - i.exp())*d; |
---|
1434 | bufp= buf.rep.elts(); |
---|
1435 | bufRepLength= (int) buf.rep.length(); |
---|
1436 | for (j= 0; j < bufRepLength; j++) |
---|
1437 | { |
---|
1438 | subA1p [j + k] += bufp [j]; |
---|
1439 | subA2p [j + kk] += bufp [j]; |
---|
1440 | } |
---|
1441 | } |
---|
1442 | subA1.normalize(); |
---|
1443 | subA2.normalize(); |
---|
1444 | } |
---|
1445 | |
---|
1446 | CanonicalForm |
---|
1447 | reverseSubstReciproFq (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
1448 | const Variable& alpha) |
---|
1449 | { |
---|
1450 | Variable y= Variable (2); |
---|
1451 | Variable x= Variable (1); |
---|
1452 | |
---|
1453 | zz_pEX f= F; |
---|
1454 | zz_pEX g= G; |
---|
1455 | int degf= deg(f); |
---|
1456 | int degg= deg(g); |
---|
1457 | |
---|
1458 | zz_pEX buf1; |
---|
1459 | zz_pEX buf2; |
---|
1460 | zz_pEX buf3; |
---|
1461 | |
---|
1462 | zz_pE *buf1p; |
---|
1463 | zz_pE *buf2p; |
---|
1464 | zz_pE *buf3p; |
---|
1465 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1466 | f.rep.SetLength ((long)d*(k+1)); |
---|
1467 | |
---|
1468 | zz_pE *gp= g.rep.elts(); |
---|
1469 | zz_pE *fp= f.rep.elts(); |
---|
1470 | CanonicalForm result= 0; |
---|
1471 | int i= 0; |
---|
1472 | int lf= 0; |
---|
1473 | int lg= d*k; |
---|
1474 | int degfSubLf= degf; |
---|
1475 | int deggSubLg= degg-lg; |
---|
1476 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1477 | zz_pE zzpEZero= zz_pE(); |
---|
1478 | |
---|
1479 | while (degf >= lf || lg >= 0) |
---|
1480 | { |
---|
1481 | if (degfSubLf >= d) |
---|
1482 | repLengthBuf1= d; |
---|
1483 | else if (degfSubLf < 0) |
---|
1484 | repLengthBuf1= 0; |
---|
1485 | else |
---|
1486 | repLengthBuf1= degfSubLf + 1; |
---|
1487 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1488 | |
---|
1489 | buf1p= buf1.rep.elts(); |
---|
1490 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1491 | buf1p [ind]= fp [ind + lf]; |
---|
1492 | buf1.normalize(); |
---|
1493 | |
---|
1494 | repLengthBuf1= buf1.rep.length(); |
---|
1495 | |
---|
1496 | if (deggSubLg >= d - 1) |
---|
1497 | repLengthBuf2= d - 1; |
---|
1498 | else if (deggSubLg < 0) |
---|
1499 | repLengthBuf2= 0; |
---|
1500 | else |
---|
1501 | repLengthBuf2= deggSubLg + 1; |
---|
1502 | |
---|
1503 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1504 | buf2p= buf2.rep.elts(); |
---|
1505 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1506 | buf2p [ind]= gp [ind + lg]; |
---|
1507 | buf2.normalize(); |
---|
1508 | |
---|
1509 | repLengthBuf2= buf2.rep.length(); |
---|
1510 | |
---|
1511 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1512 | buf3p= buf3.rep.elts(); |
---|
1513 | buf2p= buf2.rep.elts(); |
---|
1514 | buf1p= buf1.rep.elts(); |
---|
1515 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1516 | buf3p [ind]= buf1p [ind]; |
---|
1517 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1518 | buf3p [ind]= zzpEZero; |
---|
1519 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1520 | buf3p [ind + d]= buf2p [ind]; |
---|
1521 | buf3.normalize(); |
---|
1522 | |
---|
1523 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
1524 | i++; |
---|
1525 | |
---|
1526 | |
---|
1527 | lf= i*d; |
---|
1528 | degfSubLf= degf - lf; |
---|
1529 | |
---|
1530 | lg= d*(k-i); |
---|
1531 | deggSubLg= degg - lg; |
---|
1532 | |
---|
1533 | buf1p= buf1.rep.elts(); |
---|
1534 | |
---|
1535 | if (lg >= 0 && deggSubLg > 0) |
---|
1536 | { |
---|
1537 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1538 | degfSubLf= repLengthBuf2 - 1; |
---|
1539 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1540 | for (ind= 0; ind < tmp; ind++) |
---|
1541 | gp [ind + lg] -= buf1p [ind]; |
---|
1542 | } |
---|
1543 | |
---|
1544 | if (lg < 0) |
---|
1545 | break; |
---|
1546 | |
---|
1547 | buf2p= buf2.rep.elts(); |
---|
1548 | if (degfSubLf >= 0) |
---|
1549 | { |
---|
1550 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1551 | fp [ind + lf] -= buf2p [ind]; |
---|
1552 | } |
---|
1553 | } |
---|
1554 | |
---|
1555 | return result; |
---|
1556 | } |
---|
1557 | |
---|
1558 | CanonicalForm |
---|
1559 | reverseSubstReciproFp (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
1560 | { |
---|
1561 | Variable y= Variable (2); |
---|
1562 | Variable x= Variable (1); |
---|
1563 | |
---|
1564 | zz_pX f= F; |
---|
1565 | zz_pX g= G; |
---|
1566 | int degf= deg(f); |
---|
1567 | int degg= deg(g); |
---|
1568 | |
---|
1569 | zz_pX buf1; |
---|
1570 | zz_pX buf2; |
---|
1571 | zz_pX buf3; |
---|
1572 | |
---|
1573 | zz_p *buf1p; |
---|
1574 | zz_p *buf2p; |
---|
1575 | zz_p *buf3p; |
---|
1576 | |
---|
1577 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1578 | f.rep.SetLength ((long)d*(k+1)); |
---|
1579 | |
---|
1580 | zz_p *gp= g.rep.elts(); |
---|
1581 | zz_p *fp= f.rep.elts(); |
---|
1582 | CanonicalForm result= 0; |
---|
1583 | int i= 0; |
---|
1584 | int lf= 0; |
---|
1585 | int lg= d*k; |
---|
1586 | int degfSubLf= degf; |
---|
1587 | int deggSubLg= degg-lg; |
---|
1588 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1589 | zz_p zzpZero= zz_p(); |
---|
1590 | while (degf >= lf || lg >= 0) |
---|
1591 | { |
---|
1592 | if (degfSubLf >= d) |
---|
1593 | repLengthBuf1= d; |
---|
1594 | else if (degfSubLf < 0) |
---|
1595 | repLengthBuf1= 0; |
---|
1596 | else |
---|
1597 | repLengthBuf1= degfSubLf + 1; |
---|
1598 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1599 | |
---|
1600 | buf1p= buf1.rep.elts(); |
---|
1601 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1602 | buf1p [ind]= fp [ind + lf]; |
---|
1603 | buf1.normalize(); |
---|
1604 | |
---|
1605 | repLengthBuf1= buf1.rep.length(); |
---|
1606 | |
---|
1607 | if (deggSubLg >= d - 1) |
---|
1608 | repLengthBuf2= d - 1; |
---|
1609 | else if (deggSubLg < 0) |
---|
1610 | repLengthBuf2= 0; |
---|
1611 | else |
---|
1612 | repLengthBuf2= deggSubLg + 1; |
---|
1613 | |
---|
1614 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1615 | buf2p= buf2.rep.elts(); |
---|
1616 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1617 | buf2p [ind]= gp [ind + lg]; |
---|
1618 | |
---|
1619 | buf2.normalize(); |
---|
1620 | |
---|
1621 | repLengthBuf2= buf2.rep.length(); |
---|
1622 | |
---|
1623 | |
---|
1624 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1625 | buf3p= buf3.rep.elts(); |
---|
1626 | buf2p= buf2.rep.elts(); |
---|
1627 | buf1p= buf1.rep.elts(); |
---|
1628 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1629 | buf3p [ind]= buf1p [ind]; |
---|
1630 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1631 | buf3p [ind]= zzpZero; |
---|
1632 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1633 | buf3p [ind + d]= buf2p [ind]; |
---|
1634 | buf3.normalize(); |
---|
1635 | |
---|
1636 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
1637 | i++; |
---|
1638 | |
---|
1639 | |
---|
1640 | lf= i*d; |
---|
1641 | degfSubLf= degf - lf; |
---|
1642 | |
---|
1643 | lg= d*(k-i); |
---|
1644 | deggSubLg= degg - lg; |
---|
1645 | |
---|
1646 | buf1p= buf1.rep.elts(); |
---|
1647 | |
---|
1648 | if (lg >= 0 && deggSubLg > 0) |
---|
1649 | { |
---|
1650 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1651 | degfSubLf= repLengthBuf2 - 1; |
---|
1652 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1653 | for (ind= 0; ind < tmp; ind++) |
---|
1654 | gp [ind + lg] -= buf1p [ind]; |
---|
1655 | } |
---|
1656 | if (lg < 0) |
---|
1657 | break; |
---|
1658 | |
---|
1659 | buf2p= buf2.rep.elts(); |
---|
1660 | if (degfSubLf >= 0) |
---|
1661 | { |
---|
1662 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1663 | fp [ind + lf] -= buf2p [ind]; |
---|
1664 | } |
---|
1665 | } |
---|
1666 | |
---|
1667 | return result; |
---|
1668 | } |
---|
1669 | |
---|
1670 | CanonicalForm reverseSubstFq (const zz_pEX& F, int d, const Variable& alpha) |
---|
1671 | { |
---|
1672 | Variable y= Variable (2); |
---|
1673 | Variable x= Variable (1); |
---|
1674 | |
---|
1675 | zz_pEX f= F; |
---|
1676 | zz_pE *fp= f.rep.elts(); |
---|
1677 | |
---|
1678 | zz_pEX buf; |
---|
1679 | zz_pE *bufp; |
---|
1680 | CanonicalForm result= 0; |
---|
1681 | int i= 0; |
---|
1682 | int degf= deg(f); |
---|
1683 | int k= 0; |
---|
1684 | int degfSubK, repLength, j; |
---|
1685 | while (degf >= k) |
---|
1686 | { |
---|
1687 | degfSubK= degf - k; |
---|
1688 | if (degfSubK >= d) |
---|
1689 | repLength= d; |
---|
1690 | else |
---|
1691 | repLength= degfSubK + 1; |
---|
1692 | |
---|
1693 | buf.rep.SetLength ((long) repLength); |
---|
1694 | bufp= buf.rep.elts(); |
---|
1695 | for (j= 0; j < repLength; j++) |
---|
1696 | bufp [j]= fp [j + k]; |
---|
1697 | buf.normalize(); |
---|
1698 | |
---|
1699 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
1700 | i++; |
---|
1701 | k= d*i; |
---|
1702 | } |
---|
1703 | |
---|
1704 | return result; |
---|
1705 | } |
---|
1706 | |
---|
1707 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
1708 | { |
---|
1709 | Variable y= Variable (2); |
---|
1710 | Variable x= Variable (1); |
---|
1711 | |
---|
1712 | zz_pX f= F; |
---|
1713 | zz_p *fp= f.rep.elts(); |
---|
1714 | |
---|
1715 | zz_pX buf; |
---|
1716 | zz_p *bufp; |
---|
1717 | CanonicalForm result= 0; |
---|
1718 | int i= 0; |
---|
1719 | int degf= deg(f); |
---|
1720 | int k= 0; |
---|
1721 | int degfSubK, repLength, j; |
---|
1722 | while (degf >= k) |
---|
1723 | { |
---|
1724 | degfSubK= degf - k; |
---|
1725 | if (degfSubK >= d) |
---|
1726 | repLength= d; |
---|
1727 | else |
---|
1728 | repLength= degfSubK + 1; |
---|
1729 | |
---|
1730 | buf.rep.SetLength ((long) repLength); |
---|
1731 | bufp= buf.rep.elts(); |
---|
1732 | for (j= 0; j < repLength; j++) |
---|
1733 | bufp [j]= fp [j + k]; |
---|
1734 | buf.normalize(); |
---|
1735 | |
---|
1736 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
1737 | i++; |
---|
1738 | k= d*i; |
---|
1739 | } |
---|
1740 | |
---|
1741 | return result; |
---|
1742 | } |
---|
1743 | |
---|
1744 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
1745 | CanonicalForm |
---|
1746 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1747 | CanonicalForm& M) |
---|
1748 | { |
---|
1749 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1750 | d1 /= 2; |
---|
1751 | d1 += 1; |
---|
1752 | |
---|
1753 | zz_pX F1, F2; |
---|
1754 | kronSubReciproFp (F1, F2, F, d1); |
---|
1755 | zz_pX G1, G2; |
---|
1756 | kronSubReciproFp (G1, G2, G, d1); |
---|
1757 | |
---|
1758 | int k= d1*degree (M); |
---|
1759 | MulTrunc (F1, F1, G1, (long) k); |
---|
1760 | |
---|
1761 | int degtailF= degree (tailcoeff (F), 1); |
---|
1762 | int degtailG= degree (tailcoeff (G), 1); |
---|
1763 | int taildegF= taildegree (F); |
---|
1764 | int taildegG= taildegree (G); |
---|
1765 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
1766 | |
---|
1767 | reverse (F2, F2); |
---|
1768 | reverse (G2, G2); |
---|
1769 | MulTrunc (F2, F2, G2, b + 1); |
---|
1770 | reverse (F2, F2, b); |
---|
1771 | |
---|
1772 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
1773 | return reverseSubstReciproFp (F1, F2, d1, d2); |
---|
1774 | } |
---|
1775 | |
---|
1776 | //Kronecker substitution |
---|
1777 | CanonicalForm |
---|
1778 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1779 | CanonicalForm& M) |
---|
1780 | { |
---|
1781 | CanonicalForm A= F; |
---|
1782 | CanonicalForm B= G; |
---|
1783 | |
---|
1784 | int degAx= degree (A, 1); |
---|
1785 | int degAy= degree (A, 2); |
---|
1786 | int degBx= degree (B, 1); |
---|
1787 | int degBy= degree (B, 2); |
---|
1788 | int d1= degAx + 1 + degBx; |
---|
1789 | int d2= tmax (degAy, degBy); |
---|
1790 | |
---|
1791 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
1792 | return mulMod2NTLFpReci (A, B, M); |
---|
1793 | |
---|
1794 | zz_pX NTLA= kronSubFp (A, d1); |
---|
1795 | zz_pX NTLB= kronSubFp (B, d1); |
---|
1796 | |
---|
1797 | int k= d1*degree (M); |
---|
1798 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
1799 | |
---|
1800 | A= reverseSubstFp (NTLA, d1); |
---|
1801 | |
---|
1802 | return A; |
---|
1803 | } |
---|
1804 | |
---|
1805 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
1806 | CanonicalForm |
---|
1807 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1808 | CanonicalForm& M, const Variable& alpha) |
---|
1809 | { |
---|
1810 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1811 | d1 /= 2; |
---|
1812 | d1 += 1; |
---|
1813 | |
---|
1814 | zz_pEX F1, F2; |
---|
1815 | kronSubReciproFq (F1, F2, F, d1, alpha); |
---|
1816 | zz_pEX G1, G2; |
---|
1817 | kronSubReciproFq (G1, G2, G, d1, alpha); |
---|
1818 | |
---|
1819 | int k= d1*degree (M); |
---|
1820 | MulTrunc (F1, F1, G1, (long) k); |
---|
1821 | |
---|
1822 | int degtailF= degree (tailcoeff (F), 1); |
---|
1823 | int degtailG= degree (tailcoeff (G), 1); |
---|
1824 | int taildegF= taildegree (F); |
---|
1825 | int taildegG= taildegree (G); |
---|
1826 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
1827 | |
---|
1828 | reverse (F2, F2); |
---|
1829 | reverse (G2, G2); |
---|
1830 | MulTrunc (F2, F2, G2, b + 1); |
---|
1831 | reverse (F2, F2, b); |
---|
1832 | |
---|
1833 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
1834 | return reverseSubstReciproFq (F1, F2, d1, d2, alpha); |
---|
1835 | } |
---|
1836 | |
---|
1837 | #ifdef HAVE_FLINT |
---|
1838 | CanonicalForm |
---|
1839 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1840 | CanonicalForm& M); |
---|
1841 | #endif |
---|
1842 | |
---|
1843 | CanonicalForm |
---|
1844 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1845 | CanonicalForm& M) |
---|
1846 | { |
---|
1847 | Variable alpha; |
---|
1848 | CanonicalForm A= F; |
---|
1849 | CanonicalForm B= G; |
---|
1850 | |
---|
1851 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
1852 | { |
---|
1853 | int degAx= degree (A, 1); |
---|
1854 | int degAy= degree (A, 2); |
---|
1855 | int degBx= degree (B, 1); |
---|
1856 | int degBy= degree (B, 2); |
---|
1857 | int d1= degAx + degBx + 1; |
---|
1858 | int d2= tmax (degAy, degBy); |
---|
1859 | zz_p::init (getCharacteristic()); |
---|
1860 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1861 | zz_pE::init (NTLMipo); |
---|
1862 | |
---|
1863 | int degMipo= degree (getMipo (alpha)); |
---|
1864 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
1865 | (2*degAy > degree (M))) |
---|
1866 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
1867 | |
---|
1868 | zz_pEX NTLA= kronSubFq (A, d1, alpha); |
---|
1869 | zz_pEX NTLB= kronSubFq (B, d1, alpha); |
---|
1870 | |
---|
1871 | int k= d1*degree (M); |
---|
1872 | |
---|
1873 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
1874 | |
---|
1875 | A= reverseSubstFq (NTLA, d1, alpha); |
---|
1876 | |
---|
1877 | return A; |
---|
1878 | } |
---|
1879 | else |
---|
1880 | #ifdef HAVE_FLINT |
---|
1881 | return mulMod2FLINTFp (A, B, M); |
---|
1882 | #else |
---|
1883 | return mulMod2NTLFp (A, B, M); |
---|
1884 | #endif |
---|
1885 | } |
---|
1886 | |
---|
1887 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
1888 | const CanonicalForm& M) |
---|
1889 | { |
---|
1890 | if (A.isZero() || B.isZero()) |
---|
1891 | return 0; |
---|
1892 | |
---|
1893 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
1894 | |
---|
1895 | CanonicalForm F= mod (A, M); |
---|
1896 | CanonicalForm G= mod (B, M); |
---|
1897 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
1898 | return F*G; |
---|
1899 | Variable y= M.mvar(); |
---|
1900 | int degF= degree (F, y); |
---|
1901 | int degG= degree (G, y); |
---|
1902 | |
---|
1903 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
1904 | (F.level() == G.level())) |
---|
1905 | { |
---|
1906 | CanonicalForm result= mulNTL (F, G); |
---|
1907 | return mod (result, M); |
---|
1908 | } |
---|
1909 | else if (degF <= 1 && degG <= 1) |
---|
1910 | { |
---|
1911 | CanonicalForm result= F*G; |
---|
1912 | return mod (result, M); |
---|
1913 | } |
---|
1914 | |
---|
1915 | int sizeF= size (F); |
---|
1916 | int sizeG= size (G); |
---|
1917 | |
---|
1918 | int fallBackToNaive= 50; |
---|
1919 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
1920 | return mod (F*G, M); |
---|
1921 | |
---|
1922 | #ifdef HAVE_FLINT |
---|
1923 | Variable alpha; |
---|
1924 | if (getCharacteristic() == 0 && !hasFirstAlgVar (F, alpha) |
---|
1925 | && !hasFirstAlgVar (G, alpha)) |
---|
1926 | return mulMod2FLINTQ (F, G, M); |
---|
1927 | #endif |
---|
1928 | |
---|
1929 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
1930 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
1931 | return mulMod2NTLFq (F, G, M); |
---|
1932 | |
---|
1933 | int m= (int) ceil (degree (M)/2.0); |
---|
1934 | if (degF >= m || degG >= m) |
---|
1935 | { |
---|
1936 | CanonicalForm MLo= power (y, m); |
---|
1937 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
1938 | CanonicalForm F0= mod (F, MLo); |
---|
1939 | CanonicalForm F1= div (F, MLo); |
---|
1940 | CanonicalForm G0= mod (G, MLo); |
---|
1941 | CanonicalForm G1= div (G, MLo); |
---|
1942 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
1943 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
1944 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
1945 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
1946 | } |
---|
1947 | else |
---|
1948 | { |
---|
1949 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
1950 | CanonicalForm yToM= power (y, m); |
---|
1951 | CanonicalForm F0= mod (F, yToM); |
---|
1952 | CanonicalForm F1= div (F, yToM); |
---|
1953 | CanonicalForm G0= mod (G, yToM); |
---|
1954 | CanonicalForm G1= div (G, yToM); |
---|
1955 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
1956 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
1957 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
1958 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
1959 | } |
---|
1960 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
1961 | } |
---|
1962 | |
---|
1963 | // end bivariate polys |
---|
1964 | //********************** |
---|
1965 | // multivariate polys |
---|
1966 | |
---|
1967 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
1968 | { |
---|
1969 | CanonicalForm A= F; |
---|
1970 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
1971 | A= mod (A, i.getItem()); |
---|
1972 | return A; |
---|
1973 | } |
---|
1974 | |
---|
1975 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
1976 | const CFList& MOD) |
---|
1977 | { |
---|
1978 | if (A.isZero() || B.isZero()) |
---|
1979 | return 0; |
---|
1980 | |
---|
1981 | if (MOD.length() == 1) |
---|
1982 | return mulMod2 (A, B, MOD.getLast()); |
---|
1983 | |
---|
1984 | CanonicalForm M= MOD.getLast(); |
---|
1985 | CanonicalForm F= mod (A, M); |
---|
1986 | CanonicalForm G= mod (B, M); |
---|
1987 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
1988 | return F*G; |
---|
1989 | Variable y= M.mvar(); |
---|
1990 | int degF= degree (F, y); |
---|
1991 | int degG= degree (G, y); |
---|
1992 | |
---|
1993 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
1994 | (degG <= 1 && G.level() <= M.level())) |
---|
1995 | { |
---|
1996 | CFList buf= MOD; |
---|
1997 | buf.removeLast(); |
---|
1998 | if (degF == 1 && degG == 1) |
---|
1999 | { |
---|
2000 | CanonicalForm F0= mod (F, y); |
---|
2001 | CanonicalForm F1= div (F, y); |
---|
2002 | CanonicalForm G0= mod (G, y); |
---|
2003 | CanonicalForm G1= div (G, y); |
---|
2004 | if (degree (M) > 2) |
---|
2005 | { |
---|
2006 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
2007 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
2008 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
2009 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
2010 | } |
---|
2011 | else //here degree (M) == 2 |
---|
2012 | { |
---|
2013 | buf.append (y); |
---|
2014 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2015 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2016 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2017 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
2018 | return result; |
---|
2019 | } |
---|
2020 | } |
---|
2021 | else if (degF == 1 && degG == 0) |
---|
2022 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
2023 | else if (degF == 0 && degG == 1) |
---|
2024 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
2025 | else |
---|
2026 | return mulMod (F, G, buf); |
---|
2027 | } |
---|
2028 | int m= (int) ceil (degree (M)/2.0); |
---|
2029 | if (degF >= m || degG >= m) |
---|
2030 | { |
---|
2031 | CanonicalForm MLo= power (y, m); |
---|
2032 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2033 | CanonicalForm F0= mod (F, MLo); |
---|
2034 | CanonicalForm F1= div (F, MLo); |
---|
2035 | CanonicalForm G0= mod (G, MLo); |
---|
2036 | CanonicalForm G1= div (G, MLo); |
---|
2037 | CFList buf= MOD; |
---|
2038 | buf.removeLast(); |
---|
2039 | buf.append (MHi); |
---|
2040 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2041 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2042 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2043 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2044 | } |
---|
2045 | else |
---|
2046 | { |
---|
2047 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2048 | CanonicalForm yToM= power (y, m); |
---|
2049 | CanonicalForm F0= mod (F, yToM); |
---|
2050 | CanonicalForm F1= div (F, yToM); |
---|
2051 | CanonicalForm G0= mod (G, yToM); |
---|
2052 | CanonicalForm G1= div (G, yToM); |
---|
2053 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
2054 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
2055 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
2056 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2057 | } |
---|
2058 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
2059 | } |
---|
2060 | |
---|
2061 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
2062 | { |
---|
2063 | if (L.isEmpty()) |
---|
2064 | return 1; |
---|
2065 | int l= L.length(); |
---|
2066 | if (l == 1) |
---|
2067 | return mod (L.getFirst(), M); |
---|
2068 | else if (l == 2) { |
---|
2069 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
2070 | return result; |
---|
2071 | } |
---|
2072 | else |
---|
2073 | { |
---|
2074 | l /= 2; |
---|
2075 | CFList tmp1, tmp2; |
---|
2076 | CFListIterator i= L; |
---|
2077 | CanonicalForm buf1, buf2; |
---|
2078 | for (int j= 1; j <= l; j++, i++) |
---|
2079 | tmp1.append (i.getItem()); |
---|
2080 | tmp2= Difference (L, tmp1); |
---|
2081 | buf1= prodMod (tmp1, M); |
---|
2082 | buf2= prodMod (tmp2, M); |
---|
2083 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
2084 | return result; |
---|
2085 | } |
---|
2086 | } |
---|
2087 | |
---|
2088 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
2089 | { |
---|
2090 | if (L.isEmpty()) |
---|
2091 | return 1; |
---|
2092 | else if (L.length() == 1) |
---|
2093 | return L.getFirst(); |
---|
2094 | else if (L.length() == 2) |
---|
2095 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
2096 | else |
---|
2097 | { |
---|
2098 | int l= L.length()/2; |
---|
2099 | CFListIterator i= L; |
---|
2100 | CFList tmp1, tmp2; |
---|
2101 | CanonicalForm buf1, buf2; |
---|
2102 | for (int j= 1; j <= l; j++, i++) |
---|
2103 | tmp1.append (i.getItem()); |
---|
2104 | tmp2= Difference (L, tmp1); |
---|
2105 | buf1= prodMod (tmp1, M); |
---|
2106 | buf2= prodMod (tmp2, M); |
---|
2107 | return mulMod (buf1, buf2, M); |
---|
2108 | } |
---|
2109 | } |
---|
2110 | |
---|
2111 | // end multivariate polys |
---|
2112 | //*************************** |
---|
2113 | // division |
---|
2114 | |
---|
2115 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
2116 | { |
---|
2117 | if (d == 0) |
---|
2118 | return F; |
---|
2119 | CanonicalForm A= F; |
---|
2120 | Variable y= Variable (2); |
---|
2121 | Variable x= Variable (1); |
---|
2122 | if (degree (A, x) > 0) |
---|
2123 | { |
---|
2124 | A= swapvar (A, x, y); |
---|
2125 | CanonicalForm result= 0; |
---|
2126 | CFIterator i= A; |
---|
2127 | while (d - i.exp() < 0) |
---|
2128 | i++; |
---|
2129 | |
---|
2130 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
2131 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
2132 | return result; |
---|
2133 | } |
---|
2134 | else |
---|
2135 | return A*power (x, d); |
---|
2136 | } |
---|
2137 | |
---|
2138 | CanonicalForm |
---|
2139 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
2140 | { |
---|
2141 | int l= ilog2(n); |
---|
2142 | |
---|
2143 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
2144 | |
---|
2145 | ASSERT (!g.isZero(), "expected a unit"); |
---|
2146 | |
---|
2147 | Variable alpha; |
---|
2148 | |
---|
2149 | if (!g.isOne()) |
---|
2150 | g = 1/g; |
---|
2151 | Variable x= Variable (1); |
---|
2152 | CanonicalForm result; |
---|
2153 | int exp= 0; |
---|
2154 | if (n & 1) |
---|
2155 | { |
---|
2156 | result= g; |
---|
2157 | exp= 1; |
---|
2158 | } |
---|
2159 | CanonicalForm h; |
---|
2160 | |
---|
2161 | for (int i= 1; i <= l; i++) |
---|
2162 | { |
---|
2163 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
2164 | h= mod (h, power (x, (1 << i)) - 1); |
---|
2165 | h= div (h, power (x, (1 << (i - 1)))); |
---|
2166 | h= mod (h, M); |
---|
2167 | g -= power (x, (1 << (i - 1)))* |
---|
2168 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
2169 | |
---|
2170 | if (n & (1 << i)) |
---|
2171 | { |
---|
2172 | if (exp) |
---|
2173 | { |
---|
2174 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
2175 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
2176 | h= div (h, power (x, exp)); |
---|
2177 | h= mod (h, M); |
---|
2178 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
2179 | power (x, (1 << i))); |
---|
2180 | exp += (1 << i); |
---|
2181 | } |
---|
2182 | else |
---|
2183 | { |
---|
2184 | exp= (1 << i); |
---|
2185 | result= g; |
---|
2186 | } |
---|
2187 | } |
---|
2188 | } |
---|
2189 | |
---|
2190 | return result; |
---|
2191 | } |
---|
2192 | |
---|
2193 | CanonicalForm |
---|
2194 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
2195 | M) |
---|
2196 | { |
---|
2197 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
2198 | ASSERT (CFFactory::gettype() != GaloisFieldDomain, "no GF expected"); |
---|
2199 | |
---|
2200 | CanonicalForm A= mod (F, M); |
---|
2201 | CanonicalForm B= mod (G, M); |
---|
2202 | |
---|
2203 | Variable x= Variable (1); |
---|
2204 | int degA= degree (A, x); |
---|
2205 | int degB= degree (B, x); |
---|
2206 | int m= degA - degB; |
---|
2207 | if (m < 0) |
---|
2208 | return 0; |
---|
2209 | |
---|
2210 | Variable v; |
---|
2211 | CanonicalForm Q; |
---|
2212 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2213 | { |
---|
2214 | CanonicalForm R; |
---|
2215 | divrem2 (A, B, Q, R, M); |
---|
2216 | } |
---|
2217 | else |
---|
2218 | { |
---|
2219 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2220 | { |
---|
2221 | CanonicalForm R= reverse (A, degA); |
---|
2222 | CanonicalForm revB= reverse (B, degB); |
---|
2223 | revB= newtonInverse (revB, m + 1, M); |
---|
2224 | Q= mulMod2 (R, revB, M); |
---|
2225 | Q= mod (Q, power (x, m + 1)); |
---|
2226 | Q= reverse (Q, m); |
---|
2227 | } |
---|
2228 | else |
---|
2229 | { |
---|
2230 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2231 | Variable y= Variable (2); |
---|
2232 | zz_pEX NTLA, NTLB; |
---|
2233 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2234 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2235 | div (NTLA, NTLA, NTLB); |
---|
2236 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
2237 | } |
---|
2238 | } |
---|
2239 | |
---|
2240 | return Q; |
---|
2241 | } |
---|
2242 | |
---|
2243 | void |
---|
2244 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2245 | CanonicalForm& R, const CanonicalForm& M) |
---|
2246 | { |
---|
2247 | CanonicalForm A= mod (F, M); |
---|
2248 | CanonicalForm B= mod (G, M); |
---|
2249 | Variable x= Variable (1); |
---|
2250 | int degA= degree (A, x); |
---|
2251 | int degB= degree (B, x); |
---|
2252 | int m= degA - degB; |
---|
2253 | |
---|
2254 | if (m < 0) |
---|
2255 | { |
---|
2256 | R= A; |
---|
2257 | Q= 0; |
---|
2258 | return; |
---|
2259 | } |
---|
2260 | |
---|
2261 | Variable v; |
---|
2262 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2263 | { |
---|
2264 | divrem2 (A, B, Q, R, M); |
---|
2265 | } |
---|
2266 | else |
---|
2267 | { |
---|
2268 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2269 | { |
---|
2270 | R= reverse (A, degA); |
---|
2271 | |
---|
2272 | CanonicalForm revB= reverse (B, degB); |
---|
2273 | revB= newtonInverse (revB, m + 1, M); |
---|
2274 | Q= mulMod2 (R, revB, M); |
---|
2275 | |
---|
2276 | Q= mod (Q, power (x, m + 1)); |
---|
2277 | Q= reverse (Q, m); |
---|
2278 | |
---|
2279 | R= A - mulMod2 (Q, B, M); |
---|
2280 | } |
---|
2281 | else |
---|
2282 | { |
---|
2283 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2284 | Variable y= Variable (2); |
---|
2285 | zz_pEX NTLA, NTLB; |
---|
2286 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2287 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2288 | zz_pEX NTLQ, NTLR; |
---|
2289 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
2290 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
2291 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
2292 | } |
---|
2293 | } |
---|
2294 | } |
---|
2295 | |
---|
2296 | static inline |
---|
2297 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
2298 | { |
---|
2299 | CanonicalForm A= F; |
---|
2300 | CanonicalForm buf= 0; |
---|
2301 | bool swap= false; |
---|
2302 | if (degree (A, x) <= 0) |
---|
2303 | return CFList(A); |
---|
2304 | else if (x.level() != A.level()) |
---|
2305 | { |
---|
2306 | swap= true; |
---|
2307 | A= swapvar (A, x, A.mvar()); |
---|
2308 | } |
---|
2309 | |
---|
2310 | int j= (int) floor ((double) degree (A)/ m); |
---|
2311 | CFList result; |
---|
2312 | CFIterator i= A; |
---|
2313 | for (; j >= 0; j--) |
---|
2314 | { |
---|
2315 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
2316 | { |
---|
2317 | if (swap) |
---|
2318 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
2319 | else |
---|
2320 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
2321 | i++; |
---|
2322 | } |
---|
2323 | if (swap) |
---|
2324 | result.append (swapvar (buf, x, F.mvar())); |
---|
2325 | else |
---|
2326 | result.append (buf); |
---|
2327 | buf= 0; |
---|
2328 | } |
---|
2329 | return result; |
---|
2330 | } |
---|
2331 | |
---|
2332 | static inline |
---|
2333 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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2334 | CanonicalForm& R, const CFList& M); |
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2335 | |
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2336 | static inline |
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2337 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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2338 | CanonicalForm& R, const CFList& M) |
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2339 | { |
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2340 | CanonicalForm A= mod (F, M); |
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2341 | CanonicalForm B= mod (G, M); |
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2342 | Variable x= Variable (1); |
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2343 | int degB= degree (B, x); |
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2344 | int degA= degree (A, x); |
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2345 | if (degA < degB) |
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2346 | { |
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2347 | Q= 0; |
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2348 | R= A; |
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2349 | return; |
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2350 | } |
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2351 | ASSERT (2*degB > degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
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2352 | if (degB < 1) |
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2353 | { |
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2354 | divrem (A, B, Q, R); |
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2355 | Q= mod (Q, M); |
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2356 | R= mod (R, M); |
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2357 | return; |
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2358 | } |
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2359 | |
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2360 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
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2361 | CFList splitA= split (A, m, x); |
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2362 | if (splitA.length() == 3) |
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2363 | splitA.insert (0); |
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2364 | if (splitA.length() == 2) |
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2365 | { |
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2366 | splitA.insert (0); |
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2367 | splitA.insert (0); |
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2368 | } |
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2369 | if (splitA.length() == 1) |
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2370 | { |
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2371 | splitA.insert (0); |
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2372 | splitA.insert (0); |
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2373 | splitA.insert (0); |
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2374 | } |
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2375 | |
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2376 | CanonicalForm xToM= power (x, m); |
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2377 | |
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2378 | CFListIterator i= splitA; |
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2379 | CanonicalForm H= i.getItem(); |
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2380 | i++; |
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2381 | H *= xToM; |
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2382 | H += i.getItem(); |
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2383 | i++; |
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2384 | H *= xToM; |
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2385 | H += i.getItem(); |
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2386 | i++; |
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2387 | |
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2388 | divrem32 (H, B, Q, R, M); |
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2389 | |
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2390 | CFList splitR= split (R, m, x); |
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2391 | if (splitR.length() == 1) |
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2392 | splitR.insert (0); |
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2393 | |
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2394 | H= splitR.getFirst(); |
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2395 | H *= xToM; |
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2396 | H += splitR.getLast(); |
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2397 | H *= xToM; |
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2398 | H += i.getItem(); |
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2399 | |
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2400 | CanonicalForm bufQ; |
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2401 | divrem32 (H, B, bufQ, R, M); |
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2402 | |
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2403 | Q *= xToM; |
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2404 | Q += bufQ; |
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2405 | return; |
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2406 | } |
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2407 | |
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2408 | static inline |
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2409 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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2410 | CanonicalForm& R, const CFList& M) |
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2411 | { |
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2412 | CanonicalForm A= mod (F, M); |
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2413 | CanonicalForm B= mod (G, M); |
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2414 | Variable x= Variable (1); |
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2415 | int degB= degree (B, x); |
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2416 | int degA= degree (A, x); |
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2417 | if (degA < degB) |
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2418 | { |
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2419 | Q= 0; |
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2420 | R= A; |
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2421 | return; |
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2422 | } |
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2423 | ASSERT (3*(degB/2) > degA, "expected degree (F, 1) < 3*(degree (G, 1)/2)"); |
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2424 | if (degB < 1) |
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2425 | { |
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2426 | divrem (A, B, Q, R); |
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2427 | Q= mod (Q, M); |
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2428 | R= mod (R, M); |
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2429 | return; |
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2430 | } |
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2431 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
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2432 | |
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2433 | CFList splitA= split (A, m, x); |
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2434 | CFList splitB= split (B, m, x); |
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2435 | |
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2436 | if (splitA.length() == 2) |
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2437 | { |
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2438 | splitA.insert (0); |
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2439 | } |
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2440 | if (splitA.length() == 1) |
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2441 | { |
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2442 | splitA.insert (0); |
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2443 | splitA.insert (0); |
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2444 | } |
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2445 | CanonicalForm xToM= power (x, m); |
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2446 | |
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2447 | CanonicalForm H; |
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2448 | CFListIterator i= splitA; |
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2449 | i++; |
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2450 | |
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2451 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
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2452 | { |
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2453 | H= splitA.getFirst()*xToM + i.getItem(); |
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2454 | divrem21 (H, splitB.getFirst(), Q, R, M); |
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2455 | } |
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2456 | else |
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2457 | { |
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2458 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
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2459 | splitB.getFirst()*xToM; |
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2460 | Q= xToM - 1; |
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2461 | } |
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2462 | |
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2463 | H= mulMod (Q, splitB.getLast(), M); |
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2464 | |
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2465 | R= R*xToM + splitA.getLast() - H; |
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2466 | |
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2467 | while (degree (R, x) >= degB) |
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2468 | { |
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2469 | xToM= power (x, degree (R, x) - degB); |
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2470 | Q += LC (R, x)*xToM; |
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2471 | R -= mulMod (LC (R, x), B, M)*xToM; |
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2472 | Q= mod (Q, M); |
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2473 | R= mod (R, M); |
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2474 | } |
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2475 | |
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2476 | return; |
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2477 | } |
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2478 | |
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2479 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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2480 | CanonicalForm& R, const CanonicalForm& M) |
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2481 | { |
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2482 | CanonicalForm A= mod (F, M); |
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2483 | CanonicalForm B= mod (G, M); |
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2484 | |
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2485 | if (B.inCoeffDomain()) |
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2486 | { |
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2487 | divrem (A, B, Q, R); |
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2488 | return; |
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2489 | } |
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2490 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
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2491 | { |
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2492 | Q= 0; |
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2493 | R= A; |
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2494 | return; |
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2495 | } |
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2496 | |
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2497 | if (B.level() < A.level()) |
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2498 | { |
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2499 | divrem (A, B, Q, R); |
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2500 | return; |
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2501 | } |
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2502 | if (A.level() > B.level()) |
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2503 | { |
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2504 | R= A; |
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2505 | Q= 0; |
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2506 | return; |
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2507 | } |
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2508 | if (B.level() == 1 && B.isUnivariate()) |
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2509 | { |
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2510 | divrem (A, B, Q, R); |
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2511 | return; |
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2512 | } |
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2513 | if (!(B.level() == 1 && B.isUnivariate()) && |
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2514 | (A.level() == 1 && A.isUnivariate())) |
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2515 | { |
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2516 | Q= 0; |
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2517 | R= A; |
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2518 | return; |
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2519 | } |
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2520 | |
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2521 | Variable x= Variable (1); |
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2522 | int degB= degree (B, x); |
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2523 | if (degB > degree (A, x)) |
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2524 | { |
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2525 | Q= 0; |
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2526 | R= A; |
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2527 | return; |
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2528 | } |
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2529 | |
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2530 | CFList splitA= split (A, degB, x); |
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2531 | |
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2532 | CanonicalForm xToDegB= power (x, degB); |
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2533 | CanonicalForm H, bufQ; |
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2534 | Q= 0; |
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2535 | CFListIterator i= splitA; |
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2536 | H= i.getItem()*xToDegB; |
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2537 | i++; |
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2538 | H += i.getItem(); |
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2539 | CFList buf; |
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2540 | while (i.hasItem()) |
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2541 | { |
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2542 | buf= CFList (M); |
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2543 | divrem21 (H, B, bufQ, R, buf); |
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2544 | i++; |
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2545 | if (i.hasItem()) |
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2546 | H= R*xToDegB + i.getItem(); |
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2547 | Q *= xToDegB; |
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2548 | Q += bufQ; |
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2549 | } |
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2550 | return; |
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2551 | } |
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2552 | |
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2553 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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2554 | CanonicalForm& R, const CFList& MOD) |
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2555 | { |
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2556 | CanonicalForm A= mod (F, MOD); |
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2557 | CanonicalForm B= mod (G, MOD); |
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2558 | Variable x= Variable (1); |
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2559 | int degB= degree (B, x); |
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2560 | if (degB > degree (A, x)) |
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2561 | { |
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2562 | Q= 0; |
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2563 | R= A; |
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2564 | return; |
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2565 | } |
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2566 | |
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2567 | if (degB <= 0) |
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2568 | { |
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2569 | divrem (A, B, Q, R); |
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2570 | Q= mod (Q, MOD); |
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2571 | R= mod (R, MOD); |
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2572 | return; |
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2573 | } |
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2574 | CFList splitA= split (A, degB, x); |
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2575 | |
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2576 | CanonicalForm xToDegB= power (x, degB); |
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2577 | CanonicalForm H, bufQ; |
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2578 | Q= 0; |
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2579 | CFListIterator i= splitA; |
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2580 | H= i.getItem()*xToDegB; |
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2581 | i++; |
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2582 | H += i.getItem(); |
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2583 | while (i.hasItem()) |
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2584 | { |
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2585 | divrem21 (H, B, bufQ, R, MOD); |
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2586 | i++; |
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2587 | if (i.hasItem()) |
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2588 | H= R*xToDegB + i.getItem(); |
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2589 | Q *= xToDegB; |
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2590 | Q += bufQ; |
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2591 | } |
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2592 | return; |
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2593 | } |
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2594 | |
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2595 | bool |
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2596 | uniFdivides (const CanonicalForm& A, const CanonicalForm& B) |
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2597 | { |
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2598 | int p= getCharacteristic(); |
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2599 | if (p > 0) |
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2600 | { |
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2601 | zz_p::init (p); |
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2602 | Variable alpha; |
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2603 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
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2604 | { |
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2605 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
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2606 | zz_pE::init (NTLMipo); |
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2607 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
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2608 | zz_pEX NTLB= convertFacCF2NTLzz_pEX (B, NTLMipo); |
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2609 | return divide (NTLB, NTLA); |
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2610 | } |
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2611 | #ifdef HAVE_FLINT |
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2612 | nmod_poly_t FLINTA, FLINTB; |
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2613 | convertFacCF2nmod_poly_t (FLINTA, A); |
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2614 | convertFacCF2nmod_poly_t (FLINTB, B); |
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2615 | nmod_poly_rem (FLINTA, FLINTB, FLINTA); |
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2616 | bool result= nmod_poly_is_zero (FLINTA); |
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2617 | nmod_poly_clear (FLINTA); |
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2618 | nmod_poly_clear (FLINTB); |
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2619 | return result; |
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2620 | #else |
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2621 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
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2622 | zz_pX NTLB= convertFacCF2NTLzzpX (B); |
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2623 | return divide (NTLB, NTLA); |
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2624 | #endif |
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2625 | } |
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2626 | #ifdef HAVE_FLINT |
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2627 | fmpq_poly_t FLINTA,FLINTB; |
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2628 | fmpq_poly_init (FLINTA); |
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2629 | fmpq_poly_init (FLINTB); |
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2630 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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2631 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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2632 | fmpq_poly_rem (FLINTA, FLINTB, FLINTA); |
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2633 | bool result= fmpq_poly_is_zero (FLINTA); |
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2634 | fmpq_poly_clear (FLINTA); |
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2635 | fmpq_poly_clear (FLINTB); |
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2636 | return result; |
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2637 | #else |
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2638 | return fdivides (A, B); //maybe NTL? |
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2639 | #endif |
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2640 | } |
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2641 | |
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2642 | // end division |
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2643 | |
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2644 | #endif |
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