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 | #include "config.h" |
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16 | |
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17 | #include "canonicalform.h" |
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18 | #include "facMul.h" |
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19 | #include "algext.h" |
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20 | #include "cf_util.h" |
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21 | #include "templates/ftmpl_functions.h" |
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22 | |
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23 | #ifdef HAVE_NTL |
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24 | #include <NTL/lzz_pEX.h> |
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25 | #include "NTLconvert.h" |
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26 | |
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27 | #ifdef HAVE_FLINT |
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28 | #include "FLINTconvert.h" |
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29 | #endif |
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30 | |
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31 | // univariate polys |
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32 | |
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33 | #ifdef HAVE_FLINT |
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34 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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35 | { |
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36 | int degAy= degree (A); |
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37 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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38 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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39 | CFIterator j; |
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40 | for (CFIterator i= A; i.hasTerms(); i++) |
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41 | { |
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42 | if (i.coeff().inBaseDomain()) |
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43 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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44 | else |
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45 | for (j= i.coeff(); j.hasTerms(); j++) |
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46 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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47 | j.coeff()); |
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48 | } |
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49 | _fmpz_poly_normalise(result); |
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50 | } |
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51 | |
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52 | |
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53 | CanonicalForm |
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54 | reverseSubstQa (const fmpz_poly_t F, int d, const Variable& x, |
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55 | const Variable& alpha, const CanonicalForm& den) |
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56 | { |
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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, ff; |
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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 | ff= convertFmpz2CF (tmp); |
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81 | coeff += ff*power (alpha, j); //TODO faster reduction mod alpha |
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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 | result /= den; |
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89 | return result; |
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90 | } |
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91 | |
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92 | CanonicalForm |
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93 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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94 | const Variable& alpha) |
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95 | { |
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96 | CanonicalForm A= F; |
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97 | CanonicalForm B= G; |
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98 | |
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99 | CanonicalForm denA= bCommonDen (A); |
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100 | CanonicalForm denB= bCommonDen (B); |
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101 | |
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102 | A *= denA; |
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103 | B *= denB; |
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104 | int degAa= degree (A, alpha); |
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105 | int degBa= degree (B, alpha); |
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106 | int d= degAa + 1 + degBa; |
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107 | |
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108 | fmpz_poly_t FLINTA,FLINTB; |
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109 | fmpz_poly_init (FLINTA); |
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110 | fmpz_poly_init (FLINTB); |
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111 | kronSub (FLINTA, A, d); |
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112 | kronSub (FLINTB, B, d); |
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113 | |
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114 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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115 | |
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116 | denA *= denB; |
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117 | A= reverseSubstQa (FLINTA, d, F.mvar(), alpha, denA); |
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118 | |
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119 | fmpz_poly_clear (FLINTA); |
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120 | fmpz_poly_clear (FLINTB); |
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121 | return A; |
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122 | } |
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123 | |
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124 | CanonicalForm |
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125 | mulFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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126 | { |
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127 | CanonicalForm A= F; |
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128 | CanonicalForm B= G; |
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129 | |
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130 | CanonicalForm denA= bCommonDen (A); |
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131 | CanonicalForm denB= bCommonDen (B); |
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132 | |
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133 | A *= denA; |
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134 | B *= denB; |
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135 | fmpz_poly_t FLINTA,FLINTB; |
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136 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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137 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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138 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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139 | denA *= denB; |
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140 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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141 | A /= denA; |
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142 | fmpz_poly_clear (FLINTA); |
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143 | fmpz_poly_clear (FLINTB); |
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144 | |
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145 | return A; |
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146 | } |
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147 | |
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148 | /*CanonicalForm |
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149 | mulFLINTQ2 (const CanonicalForm& F, const CanonicalForm& G) |
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150 | { |
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151 | CanonicalForm A= F; |
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152 | CanonicalForm B= G; |
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153 | |
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154 | fmpq_poly_t FLINTA,FLINTB; |
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155 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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156 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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157 | |
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158 | fmpq_poly_mul (FLINTA, FLINTA, FLINTB); |
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159 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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160 | fmpq_poly_clear (FLINTA); |
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161 | fmpq_poly_clear (FLINTB); |
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162 | return A; |
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163 | }*/ |
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164 | |
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165 | CanonicalForm |
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166 | divFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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167 | { |
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168 | CanonicalForm A= F; |
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169 | CanonicalForm B= G; |
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170 | |
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171 | fmpq_poly_t FLINTA,FLINTB; |
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172 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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173 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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174 | |
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175 | fmpq_poly_div (FLINTA, FLINTA, FLINTB); |
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176 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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177 | |
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178 | fmpq_poly_clear (FLINTA); |
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179 | fmpq_poly_clear (FLINTB); |
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180 | return A; |
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181 | } |
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182 | |
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183 | CanonicalForm |
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184 | modFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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185 | { |
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186 | CanonicalForm A= F; |
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187 | CanonicalForm B= G; |
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188 | |
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189 | fmpq_poly_t FLINTA,FLINTB; |
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190 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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191 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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192 | |
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193 | fmpq_poly_rem (FLINTA, FLINTA, FLINTB); |
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194 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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195 | |
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196 | fmpq_poly_clear (FLINTA); |
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197 | fmpq_poly_clear (FLINTB); |
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198 | return A; |
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199 | } |
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200 | |
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201 | CanonicalForm |
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202 | mulFLINTQaTrunc (const CanonicalForm& F, const CanonicalForm& G, |
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203 | const Variable& alpha, int m) |
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204 | { |
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205 | CanonicalForm A= F; |
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206 | CanonicalForm B= G; |
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207 | |
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208 | CanonicalForm denA= bCommonDen (A); |
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209 | CanonicalForm denB= bCommonDen (B); |
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210 | |
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211 | A *= denA; |
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212 | B *= denB; |
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213 | |
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214 | int degAa= degree (A, alpha); |
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215 | int degBa= degree (B, alpha); |
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216 | int d= degAa + 1 + degBa; |
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217 | |
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218 | fmpz_poly_t FLINTA,FLINTB; |
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219 | fmpz_poly_init (FLINTA); |
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220 | fmpz_poly_init (FLINTB); |
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221 | kronSub (FLINTA, A, d); |
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222 | kronSub (FLINTB, B, d); |
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223 | |
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224 | int k= d*m; |
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225 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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226 | |
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227 | denA *= denB; |
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228 | A= reverseSubstQa (FLINTA, d, F.mvar(), alpha, denA); |
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229 | fmpz_poly_clear (FLINTA); |
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230 | fmpz_poly_clear (FLINTB); |
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231 | return A; |
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232 | } |
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233 | |
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234 | CanonicalForm |
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235 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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236 | { |
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237 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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238 | return mod (F*G, power (Variable (1), m)); |
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239 | Variable alpha; |
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240 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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241 | return mulFLINTQaTrunc (F, G, alpha, m); |
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242 | |
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243 | CanonicalForm A= F; |
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244 | CanonicalForm B= G; |
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245 | |
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246 | CanonicalForm denA= bCommonDen (A); |
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247 | CanonicalForm denB= bCommonDen (B); |
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248 | |
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249 | A *= denA; |
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250 | B *= denB; |
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251 | fmpz_poly_t FLINTA,FLINTB; |
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252 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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253 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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254 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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255 | denA *= denB; |
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256 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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257 | A /= denA; |
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258 | fmpz_poly_clear (FLINTA); |
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259 | fmpz_poly_clear (FLINTB); |
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260 | |
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261 | return A; |
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262 | } |
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263 | |
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264 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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265 | { |
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266 | if (d == 0) |
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267 | return F; |
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268 | if (F.inCoeffDomain()) |
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269 | return F*power (Variable (1),d); |
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270 | Variable x= Variable (1); |
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271 | CanonicalForm result= 0; |
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272 | CFIterator i= F; |
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273 | while (d - i.exp() < 0) |
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274 | i++; |
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275 | |
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276 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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277 | result += i.coeff()*power (x, d - i.exp()); |
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278 | return result; |
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279 | } |
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280 | |
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281 | CanonicalForm |
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282 | newtonInverse (const CanonicalForm& F, const int n) |
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283 | { |
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284 | int l= ilog2(n); |
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285 | |
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286 | CanonicalForm g= F [0]; |
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287 | |
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288 | ASSERT (!g.isZero(), "expected a unit"); |
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289 | |
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290 | if (!g.isOne()) |
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291 | g = 1/g; |
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292 | Variable x= Variable (1); |
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293 | CanonicalForm result; |
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294 | int exp= 0; |
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295 | if (n & 1) |
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296 | { |
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297 | result= g; |
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298 | exp= 1; |
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299 | } |
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300 | CanonicalForm h; |
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301 | |
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302 | for (int i= 1; i <= l; i++) |
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303 | { |
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304 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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305 | h= mod (h, power (x, (1 << i)) - 1); |
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306 | h= div (h, power (x, (1 << (i - 1)))); |
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307 | g -= power (x, (1 << (i - 1)))* |
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308 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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309 | |
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310 | if (n & (1 << i)) |
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311 | { |
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312 | if (exp) |
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313 | { |
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314 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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315 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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316 | h= div (h, power (x, exp)); |
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317 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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318 | exp += (1 << i); |
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319 | } |
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320 | else |
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321 | { |
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322 | exp= (1 << i); |
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323 | result= g; |
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324 | } |
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325 | } |
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326 | } |
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327 | |
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328 | return result; |
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329 | } |
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330 | |
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331 | void |
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332 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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333 | CanonicalForm& R) |
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334 | { |
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335 | CanonicalForm A= F; |
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336 | CanonicalForm B= G; |
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337 | Variable x= Variable (1); |
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338 | int degA= degree (A, x); |
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339 | int degB= degree (B, x); |
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340 | int m= degA - degB; |
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341 | |
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342 | if (m < 0) |
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343 | { |
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344 | R= A; |
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345 | Q= 0; |
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346 | return; |
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347 | } |
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348 | |
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349 | if (degB <= 1) |
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350 | divrem (A, B, Q, R); |
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351 | else |
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352 | { |
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353 | R= uniReverse (A, degA); |
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354 | |
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355 | CanonicalForm revB= uniReverse (B, degB); |
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356 | CanonicalForm buf= revB; |
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357 | revB= newtonInverse (revB, m + 1); |
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358 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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359 | Q= uniReverse (Q, m); |
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360 | |
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361 | R= A - mulNTL (Q, B); |
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362 | } |
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363 | } |
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364 | |
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365 | void |
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366 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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367 | { |
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368 | CanonicalForm A= F; |
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369 | CanonicalForm B= G; |
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370 | Variable x= Variable (1); |
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371 | int degA= degree (A, x); |
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372 | int degB= degree (B, x); |
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373 | int m= degA - degB; |
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374 | |
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375 | if (m < 0) |
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376 | { |
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377 | Q= 0; |
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378 | return; |
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379 | } |
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380 | |
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381 | if (degB <= 1) |
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382 | Q= div (A, B); |
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383 | else |
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384 | { |
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385 | CanonicalForm R= uniReverse (A, degA); |
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386 | |
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387 | CanonicalForm revB= uniReverse (B, degB); |
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388 | revB= newtonInverse (revB, m + 1); |
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389 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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390 | Q= uniReverse (Q, m); |
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391 | } |
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392 | } |
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393 | |
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394 | #endif |
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395 | |
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396 | CanonicalForm |
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397 | mulNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
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398 | { |
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399 | if (CFFactory::gettype() == GaloisFieldDomain) |
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400 | return F*G; |
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401 | if (getCharacteristic() == 0) |
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402 | { |
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403 | Variable alpha; |
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404 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
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405 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
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406 | { |
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407 | if (b.getp() != 0) |
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408 | { |
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409 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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410 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
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411 | ZZ_pE::init (NTLmipo); |
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412 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
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413 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
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414 | mul (NTLf, NTLf, NTLg); |
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415 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
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416 | } |
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417 | #ifdef HAVE_FLINT |
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418 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
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419 | return result; |
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420 | #else |
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421 | return F*G; |
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422 | #endif |
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423 | } |
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424 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
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425 | { |
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426 | #ifdef HAVE_FLINT |
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427 | if (b.getp() != 0) |
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428 | { |
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429 | fmpz_t FLINTpk; |
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430 | fmpz_init (FLINTpk); |
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431 | convertCF2Fmpz (FLINTpk, b.getpk()); |
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432 | fmpz_mod_poly_t FLINTF, FLINTG; |
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433 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
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434 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
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435 | fmpz_mod_poly_mul (FLINTF, FLINTF, FLINTG); |
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436 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF, F.mvar(), b); |
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437 | fmpz_mod_poly_clear (FLINTG); |
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438 | fmpz_mod_poly_clear (FLINTF); |
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439 | fmpz_clear (FLINTpk); |
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440 | return result; |
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441 | } |
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442 | return mulFLINTQ (F, G); |
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443 | #else |
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444 | if (b.getp() != 0) |
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445 | { |
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446 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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447 | ZZX ZZf= convertFacCF2NTLZZX (F); |
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448 | ZZX ZZg= convertFacCF2NTLZZX (G); |
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449 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
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450 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
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451 | mul (NTLf, NTLf, NTLg); |
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452 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
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453 | } |
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454 | return F*G; |
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455 | #endif |
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456 | } |
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457 | if (b.getp() != 0) |
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458 | { |
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459 | if (!F.inBaseDomain() && !G.inBaseDomain()) |
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460 | { |
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461 | if (hasFirstAlgVar (G, alpha) || hasFirstAlgVar (F, alpha)) |
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462 | { |
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463 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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464 | if (F.inCoeffDomain() && !G.inCoeffDomain()) |
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465 | { |
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466 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
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467 | ZZ_pE::init (NTLmipo); |
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468 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
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469 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
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470 | mul (NTLg, to_ZZ_pE (NTLf), NTLg); |
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471 | return b (convertNTLZZ_pEX2CF (NTLg, G.mvar(), alpha)); |
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472 | } |
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473 | else if (!F.inCoeffDomain() && G.inCoeffDomain()) |
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474 | { |
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475 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
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476 | ZZ_pE::init (NTLmipo); |
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477 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
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478 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
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479 | mul (NTLf, NTLf, to_ZZ_pE (NTLg)); |
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480 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
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481 | } |
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482 | else |
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483 | { |
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484 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
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485 | ZZ_pE::init (NTLmipo); |
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486 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
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487 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
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488 | ZZ_pE result; |
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489 | mul (result, to_ZZ_pE (NTLg), to_ZZ_pE (NTLf)); |
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490 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
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491 | } |
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492 | } |
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493 | } |
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494 | return b (F*G); |
---|
495 | } |
---|
496 | return F*G; |
---|
497 | } |
---|
498 | else if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
499 | return F*G; |
---|
500 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
501 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
502 | zz_p::init (getCharacteristic()); |
---|
503 | Variable alpha; |
---|
504 | CanonicalForm result; |
---|
505 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
506 | { |
---|
507 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
508 | zz_pE::init (NTLMipo); |
---|
509 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
510 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
511 | mul (NTLF, NTLF, NTLG); |
---|
512 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
513 | } |
---|
514 | else |
---|
515 | { |
---|
516 | #ifdef HAVE_FLINT |
---|
517 | nmod_poly_t FLINTF, FLINTG; |
---|
518 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
519 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
520 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
---|
521 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
522 | nmod_poly_clear (FLINTF); |
---|
523 | nmod_poly_clear (FLINTG); |
---|
524 | #else |
---|
525 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
526 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
527 | mul (NTLF, NTLF, NTLG); |
---|
528 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
529 | #endif |
---|
530 | } |
---|
531 | return result; |
---|
532 | } |
---|
533 | |
---|
534 | CanonicalForm |
---|
535 | modNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
536 | { |
---|
537 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
538 | return mod (F, G); |
---|
539 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
540 | { |
---|
541 | if (b.getp() != 0) |
---|
542 | return b(F); |
---|
543 | return F; |
---|
544 | } |
---|
545 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
546 | { |
---|
547 | if (b.getp() != 0) |
---|
548 | return b(F%G); |
---|
549 | return mod (F, G); |
---|
550 | } |
---|
551 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
552 | { |
---|
553 | if (b.getp() != 0) |
---|
554 | return b(F%G); |
---|
555 | return mod (F,G); |
---|
556 | } |
---|
557 | |
---|
558 | if (getCharacteristic() == 0) |
---|
559 | { |
---|
560 | Variable alpha; |
---|
561 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
562 | { |
---|
563 | #ifdef HAVE_FLINT |
---|
564 | if (b.getp() != 0) |
---|
565 | { |
---|
566 | fmpz_t FLINTpk; |
---|
567 | fmpz_init (FLINTpk); |
---|
568 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
569 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
570 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
571 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
572 | fmpz_mod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
573 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
574 | fmpz_mod_poly_clear (FLINTG); |
---|
575 | fmpz_mod_poly_clear (FLINTF); |
---|
576 | fmpz_clear (FLINTpk); |
---|
577 | return result; |
---|
578 | } |
---|
579 | return modFLINTQ (F, G); |
---|
580 | #else |
---|
581 | if (b.getp() != 0) |
---|
582 | { |
---|
583 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
584 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
585 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
586 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
587 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
588 | rem (NTLf, NTLf, NTLg); |
---|
589 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
590 | } |
---|
591 | return mod (F, G); |
---|
592 | #endif |
---|
593 | } |
---|
594 | else |
---|
595 | { |
---|
596 | if (b.getp() != 0) |
---|
597 | { |
---|
598 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
599 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
600 | ZZ_pE::init (NTLmipo); |
---|
601 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
602 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
603 | rem (NTLf, NTLf, NTLg); |
---|
604 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
605 | } |
---|
606 | #ifdef HAVE_FLINT |
---|
607 | CanonicalForm Q, R; |
---|
608 | newtonDivrem (F, G, Q, R); |
---|
609 | return R; |
---|
610 | #else |
---|
611 | return mod (F,G); |
---|
612 | #endif |
---|
613 | } |
---|
614 | } |
---|
615 | |
---|
616 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
617 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
618 | zz_p::init (getCharacteristic()); |
---|
619 | Variable alpha; |
---|
620 | CanonicalForm result; |
---|
621 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
622 | { |
---|
623 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
624 | zz_pE::init (NTLMipo); |
---|
625 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
626 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
627 | rem (NTLF, NTLF, NTLG); |
---|
628 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
629 | } |
---|
630 | else |
---|
631 | { |
---|
632 | #ifdef HAVE_FLINT |
---|
633 | nmod_poly_t FLINTF, FLINTG; |
---|
634 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
635 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
636 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
637 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
638 | nmod_poly_clear (FLINTF); |
---|
639 | nmod_poly_clear (FLINTG); |
---|
640 | #else |
---|
641 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
642 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
643 | rem (NTLF, NTLF, NTLG); |
---|
644 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
645 | #endif |
---|
646 | } |
---|
647 | return result; |
---|
648 | } |
---|
649 | |
---|
650 | CanonicalForm |
---|
651 | divNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
652 | { |
---|
653 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
654 | return div (F, G); |
---|
655 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
656 | { |
---|
657 | return 0; |
---|
658 | } |
---|
659 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
660 | { |
---|
661 | if (b.getp() != 0) |
---|
662 | { |
---|
663 | if (!F.inBaseDomain() || !G.inBaseDomain()) |
---|
664 | { |
---|
665 | Variable alpha; |
---|
666 | hasFirstAlgVar (F, alpha); |
---|
667 | hasFirstAlgVar (G, alpha); |
---|
668 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
669 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
670 | ZZ_pE::init (NTLmipo); |
---|
671 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
672 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
673 | ZZ_pE result; |
---|
674 | div (result, to_ZZ_pE (NTLf), to_ZZ_pE (NTLg)); |
---|
675 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
---|
676 | } |
---|
677 | return b(div (F,G)); |
---|
678 | } |
---|
679 | return div (F, G); |
---|
680 | } |
---|
681 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
682 | { |
---|
683 | if (b.getp() != 0) |
---|
684 | { |
---|
685 | if (!G.inBaseDomain()) |
---|
686 | { |
---|
687 | Variable alpha; |
---|
688 | hasFirstAlgVar (G, alpha); |
---|
689 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
690 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
691 | ZZ_pE::init (NTLmipo); |
---|
692 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
693 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
694 | div (NTLf, NTLf, to_ZZ_pE (NTLg)); |
---|
695 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
696 | } |
---|
697 | return b(div (F,G)); |
---|
698 | } |
---|
699 | return div (F, G); |
---|
700 | } |
---|
701 | |
---|
702 | if (getCharacteristic() == 0) |
---|
703 | { |
---|
704 | |
---|
705 | Variable alpha; |
---|
706 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
707 | { |
---|
708 | #ifdef HAVE_FLINT |
---|
709 | if (b.getp() != 0) |
---|
710 | { |
---|
711 | fmpz_t FLINTpk; |
---|
712 | fmpz_init (FLINTpk); |
---|
713 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
714 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
715 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
716 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
717 | fmpz_mod_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG); |
---|
718 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
719 | fmpz_mod_poly_clear (FLINTG); |
---|
720 | fmpz_mod_poly_clear (FLINTF); |
---|
721 | fmpz_clear (FLINTpk); |
---|
722 | return result; |
---|
723 | } |
---|
724 | return divFLINTQ (F,G); |
---|
725 | #else |
---|
726 | if (b.getp() != 0) |
---|
727 | { |
---|
728 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
729 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
730 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
731 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
732 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
733 | div (NTLf, NTLf, NTLg); |
---|
734 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
735 | } |
---|
736 | return div (F, G); |
---|
737 | #endif |
---|
738 | } |
---|
739 | else |
---|
740 | { |
---|
741 | if (b.getp() != 0) |
---|
742 | { |
---|
743 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
744 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
745 | ZZ_pE::init (NTLmipo); |
---|
746 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
747 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
748 | div (NTLf, NTLf, NTLg); |
---|
749 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
750 | } |
---|
751 | #ifdef HAVE_FLINT |
---|
752 | CanonicalForm Q; |
---|
753 | newtonDiv (F, G, Q); |
---|
754 | return Q; |
---|
755 | #else |
---|
756 | return div (F,G); |
---|
757 | #endif |
---|
758 | } |
---|
759 | } |
---|
760 | |
---|
761 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
762 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
763 | zz_p::init (getCharacteristic()); |
---|
764 | Variable alpha; |
---|
765 | CanonicalForm result; |
---|
766 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
767 | { |
---|
768 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
769 | zz_pE::init (NTLMipo); |
---|
770 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
771 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
772 | div (NTLF, NTLF, NTLG); |
---|
773 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
774 | } |
---|
775 | else |
---|
776 | { |
---|
777 | #ifdef HAVE_FLINT |
---|
778 | nmod_poly_t FLINTF, FLINTG; |
---|
779 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
780 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
781 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
782 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
783 | nmod_poly_clear (FLINTF); |
---|
784 | nmod_poly_clear (FLINTG); |
---|
785 | #else |
---|
786 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
787 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
788 | div (NTLF, NTLF, NTLG); |
---|
789 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
790 | #endif |
---|
791 | } |
---|
792 | return result; |
---|
793 | } |
---|
794 | |
---|
795 | // end univariate polys |
---|
796 | //************************* |
---|
797 | // bivariate polys |
---|
798 | |
---|
799 | #ifdef HAVE_FLINT |
---|
800 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
801 | { |
---|
802 | int degAy= degree (A); |
---|
803 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
804 | |
---|
805 | nmod_poly_t buf; |
---|
806 | |
---|
807 | int j, k, bufRepLength; |
---|
808 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
809 | { |
---|
810 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
811 | |
---|
812 | k= i.exp()*d; |
---|
813 | bufRepLength= (int) nmod_poly_length (buf); |
---|
814 | for (j= 0; j < bufRepLength; j++) |
---|
815 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
816 | nmod_poly_clear (buf); |
---|
817 | } |
---|
818 | _nmod_poly_normalise (result); |
---|
819 | } |
---|
820 | |
---|
821 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
822 | { |
---|
823 | int degAy= degree (A); |
---|
824 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
825 | |
---|
826 | fmpq_poly_t buf; |
---|
827 | fmpq_t coeff; |
---|
828 | |
---|
829 | int k, l, bufRepLength; |
---|
830 | CFIterator j; |
---|
831 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
832 | { |
---|
833 | if (i.coeff().inCoeffDomain()) |
---|
834 | { |
---|
835 | k= d1*i.exp(); |
---|
836 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
837 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
838 | for (l= 0; l < bufRepLength; l++) |
---|
839 | { |
---|
840 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
841 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
842 | } |
---|
843 | fmpq_poly_clear (buf); |
---|
844 | } |
---|
845 | else |
---|
846 | { |
---|
847 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
848 | { |
---|
849 | k= d1*i.exp(); |
---|
850 | k += d2*j.exp(); |
---|
851 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
852 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
853 | for (l= 0; l < bufRepLength; l++) |
---|
854 | { |
---|
855 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
856 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
857 | } |
---|
858 | fmpq_poly_clear (buf); |
---|
859 | } |
---|
860 | } |
---|
861 | } |
---|
862 | fmpq_clear (coeff); |
---|
863 | _fmpq_poly_normalise (result); |
---|
864 | } |
---|
865 | |
---|
866 | void |
---|
867 | kronSubReciproFp (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
868 | int d) |
---|
869 | { |
---|
870 | int degAy= degree (A); |
---|
871 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
872 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
873 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
874 | |
---|
875 | nmod_poly_t buf; |
---|
876 | |
---|
877 | int k, kk, j, bufRepLength; |
---|
878 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
879 | { |
---|
880 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
881 | |
---|
882 | k= i.exp()*d; |
---|
883 | kk= (degAy - i.exp())*d; |
---|
884 | bufRepLength= (int) nmod_poly_length (buf); |
---|
885 | for (j= 0; j < bufRepLength; j++) |
---|
886 | { |
---|
887 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
888 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
889 | nmod_poly_get_coeff_ui (buf, j), |
---|
890 | getCharacteristic() |
---|
891 | ) |
---|
892 | ); |
---|
893 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
894 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
895 | nmod_poly_get_coeff_ui (buf, j), |
---|
896 | getCharacteristic() |
---|
897 | ) |
---|
898 | ); |
---|
899 | } |
---|
900 | nmod_poly_clear (buf); |
---|
901 | } |
---|
902 | _nmod_poly_normalise (subA1); |
---|
903 | _nmod_poly_normalise (subA2); |
---|
904 | } |
---|
905 | |
---|
906 | void |
---|
907 | kronSubReciproQ (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
908 | int d) |
---|
909 | { |
---|
910 | int degAy= degree (A); |
---|
911 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
912 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
913 | |
---|
914 | fmpz_poly_t buf; |
---|
915 | fmpz_t coeff1, coeff2; |
---|
916 | |
---|
917 | int k, kk, j, bufRepLength; |
---|
918 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
919 | { |
---|
920 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
921 | |
---|
922 | k= i.exp()*d; |
---|
923 | kk= (degAy - i.exp())*d; |
---|
924 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
925 | for (j= 0; j < bufRepLength; j++) |
---|
926 | { |
---|
927 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
928 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
929 | fmpz_add (coeff1, coeff1, coeff2); |
---|
930 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
931 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
932 | fmpz_add (coeff1, coeff1, coeff2); |
---|
933 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
934 | } |
---|
935 | fmpz_poly_clear (buf); |
---|
936 | } |
---|
937 | fmpz_clear (coeff1); |
---|
938 | fmpz_clear (coeff2); |
---|
939 | _fmpz_poly_normalise (subA1); |
---|
940 | _fmpz_poly_normalise (subA2); |
---|
941 | } |
---|
942 | |
---|
943 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
944 | { |
---|
945 | Variable y= Variable (2); |
---|
946 | Variable x= Variable (1); |
---|
947 | |
---|
948 | fmpz_poly_t f; |
---|
949 | fmpz_poly_init (f); |
---|
950 | fmpz_poly_set (f, F); |
---|
951 | |
---|
952 | fmpz_poly_t buf; |
---|
953 | CanonicalForm result= 0; |
---|
954 | int i= 0; |
---|
955 | int degf= fmpz_poly_degree(f); |
---|
956 | int k= 0; |
---|
957 | int degfSubK, repLength, j; |
---|
958 | fmpz_t coeff; |
---|
959 | while (degf >= k) |
---|
960 | { |
---|
961 | degfSubK= degf - k; |
---|
962 | if (degfSubK >= d) |
---|
963 | repLength= d; |
---|
964 | else |
---|
965 | repLength= degfSubK + 1; |
---|
966 | |
---|
967 | fmpz_poly_init2 (buf, repLength); |
---|
968 | fmpz_init (coeff); |
---|
969 | for (j= 0; j < repLength; j++) |
---|
970 | { |
---|
971 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
972 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
973 | } |
---|
974 | _fmpz_poly_normalise (buf); |
---|
975 | |
---|
976 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
977 | i++; |
---|
978 | k= d*i; |
---|
979 | fmpz_poly_clear (buf); |
---|
980 | fmpz_clear (coeff); |
---|
981 | } |
---|
982 | fmpz_poly_clear (f); |
---|
983 | |
---|
984 | return result; |
---|
985 | } |
---|
986 | |
---|
987 | CanonicalForm |
---|
988 | reverseSubstQa (const fmpq_poly_t F, int d1, int d2, const Variable& alpha, |
---|
989 | const fmpq_poly_t mipo) |
---|
990 | { |
---|
991 | Variable y= Variable (2); |
---|
992 | Variable x= Variable (1); |
---|
993 | |
---|
994 | fmpq_poly_t f; |
---|
995 | fmpq_poly_init (f); |
---|
996 | fmpq_poly_set (f, F); |
---|
997 | |
---|
998 | fmpq_poly_t buf; |
---|
999 | CanonicalForm result= 0, result2; |
---|
1000 | int i= 0; |
---|
1001 | int degf= fmpq_poly_degree(f); |
---|
1002 | int k= 0; |
---|
1003 | int degfSubK; |
---|
1004 | int repLength; |
---|
1005 | fmpq_t coeff; |
---|
1006 | while (degf >= k) |
---|
1007 | { |
---|
1008 | degfSubK= degf - k; |
---|
1009 | if (degfSubK >= d1) |
---|
1010 | repLength= d1; |
---|
1011 | else |
---|
1012 | repLength= degfSubK + 1; |
---|
1013 | |
---|
1014 | fmpq_init (coeff); |
---|
1015 | int j= 0; |
---|
1016 | int l; |
---|
1017 | result2= 0; |
---|
1018 | while (j*d2 < repLength) |
---|
1019 | { |
---|
1020 | fmpq_poly_init2 (buf, d2); |
---|
1021 | for (l= 0; l < d2; l++) |
---|
1022 | { |
---|
1023 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
1024 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
1025 | } |
---|
1026 | _fmpq_poly_normalise (buf); |
---|
1027 | fmpq_poly_rem (buf, buf, mipo); |
---|
1028 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
1029 | j++; |
---|
1030 | fmpq_poly_clear (buf); |
---|
1031 | } |
---|
1032 | if (repLength - j*d2 != 0 && j*d2 - repLength < d2) |
---|
1033 | { |
---|
1034 | j--; |
---|
1035 | repLength -= j*d2; |
---|
1036 | fmpq_poly_init2 (buf, repLength); |
---|
1037 | j++; |
---|
1038 | for (l= 0; l < repLength; l++) |
---|
1039 | { |
---|
1040 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
1041 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
1042 | } |
---|
1043 | _fmpq_poly_normalise (buf); |
---|
1044 | fmpq_poly_rem (buf, buf, mipo); |
---|
1045 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
1046 | fmpq_poly_clear (buf); |
---|
1047 | } |
---|
1048 | fmpq_clear (coeff); |
---|
1049 | |
---|
1050 | result += result2*power (y, i); |
---|
1051 | i++; |
---|
1052 | k= d1*i; |
---|
1053 | } |
---|
1054 | |
---|
1055 | fmpq_poly_clear (f); |
---|
1056 | return result; |
---|
1057 | } |
---|
1058 | |
---|
1059 | CanonicalForm |
---|
1060 | reverseSubstReciproFp (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
1061 | { |
---|
1062 | Variable y= Variable (2); |
---|
1063 | Variable x= Variable (1); |
---|
1064 | |
---|
1065 | nmod_poly_t f, g; |
---|
1066 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1067 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1068 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
1069 | nmod_poly_set (f, F); |
---|
1070 | nmod_poly_set (g, G); |
---|
1071 | int degf= nmod_poly_degree(f); |
---|
1072 | int degg= nmod_poly_degree(g); |
---|
1073 | |
---|
1074 | |
---|
1075 | nmod_poly_t buf1,buf2, buf3; |
---|
1076 | |
---|
1077 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1078 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
1079 | |
---|
1080 | CanonicalForm result= 0; |
---|
1081 | int i= 0; |
---|
1082 | int lf= 0; |
---|
1083 | int lg= d*k; |
---|
1084 | int degfSubLf= degf; |
---|
1085 | int deggSubLg= degg-lg; |
---|
1086 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1087 | while (degf >= lf || lg >= 0) |
---|
1088 | { |
---|
1089 | if (degfSubLf >= d) |
---|
1090 | repLengthBuf1= d; |
---|
1091 | else if (degfSubLf < 0) |
---|
1092 | repLengthBuf1= 0; |
---|
1093 | else |
---|
1094 | repLengthBuf1= degfSubLf + 1; |
---|
1095 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
1096 | |
---|
1097 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1098 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
1099 | _nmod_poly_normalise (buf1); |
---|
1100 | |
---|
1101 | repLengthBuf1= nmod_poly_length (buf1); |
---|
1102 | |
---|
1103 | if (deggSubLg >= d - 1) |
---|
1104 | repLengthBuf2= d - 1; |
---|
1105 | else if (deggSubLg < 0) |
---|
1106 | repLengthBuf2= 0; |
---|
1107 | else |
---|
1108 | repLengthBuf2= deggSubLg + 1; |
---|
1109 | |
---|
1110 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
1111 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1112 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
1113 | |
---|
1114 | _nmod_poly_normalise (buf2); |
---|
1115 | repLengthBuf2= nmod_poly_length (buf2); |
---|
1116 | |
---|
1117 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
1118 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1119 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
1120 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1121 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
1122 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1123 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
1124 | _nmod_poly_normalise (buf3); |
---|
1125 | |
---|
1126 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1127 | i++; |
---|
1128 | |
---|
1129 | |
---|
1130 | lf= i*d; |
---|
1131 | degfSubLf= degf - lf; |
---|
1132 | |
---|
1133 | lg= d*(k-i); |
---|
1134 | deggSubLg= degg - lg; |
---|
1135 | |
---|
1136 | if (lg >= 0 && deggSubLg > 0) |
---|
1137 | { |
---|
1138 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1139 | degfSubLf= repLengthBuf2 - 1; |
---|
1140 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1141 | for (ind= 0; ind < tmp; ind++) |
---|
1142 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
1143 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
1144 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
1145 | getCharacteristic() |
---|
1146 | ) |
---|
1147 | ); |
---|
1148 | } |
---|
1149 | if (lg < 0) |
---|
1150 | { |
---|
1151 | nmod_poly_clear (buf1); |
---|
1152 | nmod_poly_clear (buf2); |
---|
1153 | nmod_poly_clear (buf3); |
---|
1154 | break; |
---|
1155 | } |
---|
1156 | if (degfSubLf >= 0) |
---|
1157 | { |
---|
1158 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1159 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
1160 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
1161 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
1162 | getCharacteristic() |
---|
1163 | ) |
---|
1164 | ); |
---|
1165 | } |
---|
1166 | nmod_poly_clear (buf1); |
---|
1167 | nmod_poly_clear (buf2); |
---|
1168 | nmod_poly_clear (buf3); |
---|
1169 | } |
---|
1170 | |
---|
1171 | nmod_poly_clear (f); |
---|
1172 | nmod_poly_clear (g); |
---|
1173 | |
---|
1174 | return result; |
---|
1175 | } |
---|
1176 | |
---|
1177 | CanonicalForm |
---|
1178 | reverseSubstReciproQ (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
1179 | { |
---|
1180 | Variable y= Variable (2); |
---|
1181 | Variable x= Variable (1); |
---|
1182 | |
---|
1183 | fmpz_poly_t f, g; |
---|
1184 | fmpz_poly_init (f); |
---|
1185 | fmpz_poly_init (g); |
---|
1186 | fmpz_poly_set (f, F); |
---|
1187 | fmpz_poly_set (g, G); |
---|
1188 | int degf= fmpz_poly_degree(f); |
---|
1189 | int degg= fmpz_poly_degree(g); |
---|
1190 | |
---|
1191 | |
---|
1192 | fmpz_poly_t buf1,buf2, buf3; |
---|
1193 | |
---|
1194 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1195 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
1196 | |
---|
1197 | CanonicalForm result= 0; |
---|
1198 | int i= 0; |
---|
1199 | int lf= 0; |
---|
1200 | int lg= d*k; |
---|
1201 | int degfSubLf= degf; |
---|
1202 | int deggSubLg= degg-lg; |
---|
1203 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1204 | fmpz_t tmp1, tmp2; |
---|
1205 | while (degf >= lf || lg >= 0) |
---|
1206 | { |
---|
1207 | if (degfSubLf >= d) |
---|
1208 | repLengthBuf1= d; |
---|
1209 | else if (degfSubLf < 0) |
---|
1210 | repLengthBuf1= 0; |
---|
1211 | else |
---|
1212 | repLengthBuf1= degfSubLf + 1; |
---|
1213 | |
---|
1214 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
1215 | |
---|
1216 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1217 | { |
---|
1218 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1219 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
1220 | } |
---|
1221 | _fmpz_poly_normalise (buf1); |
---|
1222 | |
---|
1223 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
1224 | |
---|
1225 | if (deggSubLg >= d - 1) |
---|
1226 | repLengthBuf2= d - 1; |
---|
1227 | else if (deggSubLg < 0) |
---|
1228 | repLengthBuf2= 0; |
---|
1229 | else |
---|
1230 | repLengthBuf2= deggSubLg + 1; |
---|
1231 | |
---|
1232 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
1233 | |
---|
1234 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1235 | { |
---|
1236 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1237 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
1238 | } |
---|
1239 | |
---|
1240 | _fmpz_poly_normalise (buf2); |
---|
1241 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
1242 | |
---|
1243 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
1244 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1245 | { |
---|
1246 | fmpz_poly_get_coeff_fmpz (tmp1, buf1, ind); |
---|
1247 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
1248 | } |
---|
1249 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1250 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
1251 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1252 | { |
---|
1253 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
1254 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
1255 | } |
---|
1256 | _fmpz_poly_normalise (buf3); |
---|
1257 | |
---|
1258 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1259 | i++; |
---|
1260 | |
---|
1261 | |
---|
1262 | lf= i*d; |
---|
1263 | degfSubLf= degf - lf; |
---|
1264 | |
---|
1265 | lg= d*(k-i); |
---|
1266 | deggSubLg= degg - lg; |
---|
1267 | |
---|
1268 | if (lg >= 0 && deggSubLg > 0) |
---|
1269 | { |
---|
1270 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1271 | degfSubLf= repLengthBuf2 - 1; |
---|
1272 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1273 | for (ind= 0; ind < tmp; ind++) |
---|
1274 | { |
---|
1275 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1276 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
1277 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1278 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
1279 | } |
---|
1280 | } |
---|
1281 | if (lg < 0) |
---|
1282 | { |
---|
1283 | fmpz_poly_clear (buf1); |
---|
1284 | fmpz_poly_clear (buf2); |
---|
1285 | fmpz_poly_clear (buf3); |
---|
1286 | break; |
---|
1287 | } |
---|
1288 | if (degfSubLf >= 0) |
---|
1289 | { |
---|
1290 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1291 | { |
---|
1292 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1293 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
1294 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1295 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
1296 | } |
---|
1297 | } |
---|
1298 | fmpz_poly_clear (buf1); |
---|
1299 | fmpz_poly_clear (buf2); |
---|
1300 | fmpz_poly_clear (buf3); |
---|
1301 | } |
---|
1302 | |
---|
1303 | fmpz_poly_clear (f); |
---|
1304 | fmpz_poly_clear (g); |
---|
1305 | fmpz_clear (tmp1); |
---|
1306 | fmpz_clear (tmp2); |
---|
1307 | |
---|
1308 | return result; |
---|
1309 | } |
---|
1310 | |
---|
1311 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
1312 | { |
---|
1313 | Variable y= Variable (2); |
---|
1314 | Variable x= Variable (1); |
---|
1315 | |
---|
1316 | nmod_poly_t f; |
---|
1317 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1318 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1319 | nmod_poly_set (f, F); |
---|
1320 | |
---|
1321 | nmod_poly_t buf; |
---|
1322 | CanonicalForm result= 0; |
---|
1323 | int i= 0; |
---|
1324 | int degf= nmod_poly_degree(f); |
---|
1325 | int k= 0; |
---|
1326 | int degfSubK, repLength, j; |
---|
1327 | while (degf >= k) |
---|
1328 | { |
---|
1329 | degfSubK= degf - k; |
---|
1330 | if (degfSubK >= d) |
---|
1331 | repLength= d; |
---|
1332 | else |
---|
1333 | repLength= degfSubK + 1; |
---|
1334 | |
---|
1335 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
1336 | for (j= 0; j < repLength; j++) |
---|
1337 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
1338 | _nmod_poly_normalise (buf); |
---|
1339 | |
---|
1340 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
1341 | i++; |
---|
1342 | k= d*i; |
---|
1343 | nmod_poly_clear (buf); |
---|
1344 | } |
---|
1345 | nmod_poly_clear (f); |
---|
1346 | |
---|
1347 | return result; |
---|
1348 | } |
---|
1349 | |
---|
1350 | CanonicalForm |
---|
1351 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1352 | CanonicalForm& M) |
---|
1353 | { |
---|
1354 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
1355 | d1 /= 2; |
---|
1356 | d1 += 1; |
---|
1357 | |
---|
1358 | nmod_poly_t F1, F2; |
---|
1359 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1360 | nmod_poly_init_preinv (F1, getCharacteristic(), ninv); |
---|
1361 | nmod_poly_init_preinv (F2, getCharacteristic(), ninv); |
---|
1362 | kronSubReciproFp (F1, F2, F, d1); |
---|
1363 | |
---|
1364 | nmod_poly_t G1, G2; |
---|
1365 | nmod_poly_init_preinv (G1, getCharacteristic(), ninv); |
---|
1366 | nmod_poly_init_preinv (G2, getCharacteristic(), ninv); |
---|
1367 | kronSubReciproFp (G1, G2, G, d1); |
---|
1368 | |
---|
1369 | int k= d1*degree (M); |
---|
1370 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
1371 | |
---|
1372 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1373 | int degtailG= degree (tailcoeff (G), 1); |
---|
1374 | int taildegF= taildegree (F); |
---|
1375 | int taildegG= taildegree (G); |
---|
1376 | |
---|
1377 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
1378 | + d1*(2+taildegF + taildegG); |
---|
1379 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
1380 | nmod_poly_shift_right (F2, F2, b); |
---|
1381 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
1382 | |
---|
1383 | |
---|
1384 | CanonicalForm result= reverseSubstReciproFp (F1, F2, d1, d2); |
---|
1385 | |
---|
1386 | nmod_poly_clear (F1); |
---|
1387 | nmod_poly_clear (F2); |
---|
1388 | nmod_poly_clear (G1); |
---|
1389 | nmod_poly_clear (G2); |
---|
1390 | return result; |
---|
1391 | } |
---|
1392 | |
---|
1393 | CanonicalForm |
---|
1394 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1395 | CanonicalForm& M) |
---|
1396 | { |
---|
1397 | CanonicalForm A= F; |
---|
1398 | CanonicalForm B= G; |
---|
1399 | |
---|
1400 | int degAx= degree (A, 1); |
---|
1401 | int degAy= degree (A, 2); |
---|
1402 | int degBx= degree (B, 1); |
---|
1403 | int degBy= degree (B, 2); |
---|
1404 | int d1= degAx + 1 + degBx; |
---|
1405 | int d2= tmax (degAy, degBy); |
---|
1406 | |
---|
1407 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
1408 | return mulMod2FLINTFpReci (A, B, M); |
---|
1409 | |
---|
1410 | nmod_poly_t FLINTA, FLINTB; |
---|
1411 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1412 | nmod_poly_init_preinv (FLINTA, getCharacteristic(), ninv); |
---|
1413 | nmod_poly_init_preinv (FLINTB, getCharacteristic(), ninv); |
---|
1414 | kronSubFp (FLINTA, A, d1); |
---|
1415 | kronSubFp (FLINTB, B, d1); |
---|
1416 | |
---|
1417 | int k= d1*degree (M); |
---|
1418 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1419 | |
---|
1420 | A= reverseSubstFp (FLINTA, d1); |
---|
1421 | |
---|
1422 | nmod_poly_clear (FLINTA); |
---|
1423 | nmod_poly_clear (FLINTB); |
---|
1424 | return A; |
---|
1425 | } |
---|
1426 | |
---|
1427 | CanonicalForm |
---|
1428 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1429 | CanonicalForm& M) |
---|
1430 | { |
---|
1431 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
1432 | d1 /= 2; |
---|
1433 | d1 += 1; |
---|
1434 | |
---|
1435 | fmpz_poly_t F1, F2; |
---|
1436 | fmpz_poly_init (F1); |
---|
1437 | fmpz_poly_init (F2); |
---|
1438 | kronSubReciproQ (F1, F2, F, d1); |
---|
1439 | |
---|
1440 | fmpz_poly_t G1, G2; |
---|
1441 | fmpz_poly_init (G1); |
---|
1442 | fmpz_poly_init (G2); |
---|
1443 | kronSubReciproQ (G1, G2, G, d1); |
---|
1444 | |
---|
1445 | int k= d1*degree (M); |
---|
1446 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
1447 | |
---|
1448 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1449 | int degtailG= degree (tailcoeff (G), 1); |
---|
1450 | int taildegF= taildegree (F); |
---|
1451 | int taildegG= taildegree (G); |
---|
1452 | |
---|
1453 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
1454 | + d1*(2+taildegF + taildegG); |
---|
1455 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
1456 | fmpz_poly_shift_right (F2, F2, b); |
---|
1457 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
1458 | |
---|
1459 | CanonicalForm result= reverseSubstReciproQ (F1, F2, d1, d2); |
---|
1460 | |
---|
1461 | fmpz_poly_clear (F1); |
---|
1462 | fmpz_poly_clear (F2); |
---|
1463 | fmpz_poly_clear (G1); |
---|
1464 | fmpz_poly_clear (G2); |
---|
1465 | return result; |
---|
1466 | } |
---|
1467 | |
---|
1468 | CanonicalForm |
---|
1469 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1470 | CanonicalForm& M) |
---|
1471 | { |
---|
1472 | CanonicalForm A= F; |
---|
1473 | CanonicalForm B= G; |
---|
1474 | |
---|
1475 | int degAx= degree (A, 1); |
---|
1476 | int degBx= degree (B, 1); |
---|
1477 | int d1= degAx + 1 + degBx; |
---|
1478 | |
---|
1479 | CanonicalForm f= bCommonDen (F); |
---|
1480 | CanonicalForm g= bCommonDen (G); |
---|
1481 | A *= f; |
---|
1482 | B *= g; |
---|
1483 | |
---|
1484 | fmpz_poly_t FLINTA, FLINTB; |
---|
1485 | fmpz_poly_init (FLINTA); |
---|
1486 | fmpz_poly_init (FLINTB); |
---|
1487 | kronSub (FLINTA, A, d1); |
---|
1488 | kronSub (FLINTB, B, d1); |
---|
1489 | int k= d1*degree (M); |
---|
1490 | |
---|
1491 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1492 | A= reverseSubstQ (FLINTA, d1); |
---|
1493 | fmpz_poly_clear (FLINTA); |
---|
1494 | fmpz_poly_clear (FLINTB); |
---|
1495 | return A/(f*g); |
---|
1496 | } |
---|
1497 | |
---|
1498 | CanonicalForm |
---|
1499 | mulMod2FLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
---|
1500 | const CanonicalForm& M) |
---|
1501 | { |
---|
1502 | Variable a; |
---|
1503 | if (!hasFirstAlgVar (F,a) && !hasFirstAlgVar (G, a)) |
---|
1504 | return mulMod2FLINTQ (F, G, M); |
---|
1505 | CanonicalForm A= F; |
---|
1506 | |
---|
1507 | int degFx= degree (F, 1); |
---|
1508 | int degFa= degree (F, a); |
---|
1509 | int degGx= degree (G, 1); |
---|
1510 | int degGa= degree (G, a); |
---|
1511 | |
---|
1512 | int d2= degFa+degGa+1; |
---|
1513 | int d1= degFx + 1 + degGx; |
---|
1514 | d1 *= d2; |
---|
1515 | |
---|
1516 | fmpq_poly_t FLINTF, FLINTG; |
---|
1517 | kronSubQa (FLINTF, F, d1, d2); |
---|
1518 | kronSubQa (FLINTG, G, d1, d2); |
---|
1519 | |
---|
1520 | fmpq_poly_mullow (FLINTF, FLINTF, FLINTG, d1*degree (M)); |
---|
1521 | |
---|
1522 | fmpq_poly_t mipo; |
---|
1523 | convertFacCF2Fmpq_poly_t (mipo, getMipo (a)); |
---|
1524 | CanonicalForm result= reverseSubstQa (FLINTF, d1, d2, a, mipo); |
---|
1525 | fmpq_poly_clear (FLINTF); |
---|
1526 | fmpq_poly_clear (FLINTG); |
---|
1527 | return result; |
---|
1528 | } |
---|
1529 | |
---|
1530 | #endif |
---|
1531 | |
---|
1532 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
1533 | { |
---|
1534 | int degAy= degree (A); |
---|
1535 | zz_pX result; |
---|
1536 | result.rep.SetLength (d*(degAy + 1)); |
---|
1537 | |
---|
1538 | zz_p *resultp; |
---|
1539 | resultp= result.rep.elts(); |
---|
1540 | zz_pX buf; |
---|
1541 | zz_p *bufp; |
---|
1542 | int j, k, bufRepLength; |
---|
1543 | |
---|
1544 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1545 | { |
---|
1546 | if (i.coeff().inCoeffDomain()) |
---|
1547 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1548 | else |
---|
1549 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1550 | |
---|
1551 | k= i.exp()*d; |
---|
1552 | bufp= buf.rep.elts(); |
---|
1553 | bufRepLength= (int) buf.rep.length(); |
---|
1554 | for (j= 0; j < bufRepLength; j++) |
---|
1555 | resultp [j + k]= bufp [j]; |
---|
1556 | } |
---|
1557 | result.normalize(); |
---|
1558 | |
---|
1559 | return result; |
---|
1560 | } |
---|
1561 | |
---|
1562 | zz_pEX kronSubFq (const CanonicalForm& A, int d, const Variable& alpha) |
---|
1563 | { |
---|
1564 | int degAy= degree (A); |
---|
1565 | zz_pEX result; |
---|
1566 | result.rep.SetLength (d*(degAy + 1)); |
---|
1567 | |
---|
1568 | Variable v; |
---|
1569 | zz_pE *resultp; |
---|
1570 | resultp= result.rep.elts(); |
---|
1571 | zz_pEX buf1; |
---|
1572 | zz_pE *buf1p; |
---|
1573 | zz_pX buf2; |
---|
1574 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1575 | int j, k, buf1RepLength; |
---|
1576 | |
---|
1577 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1578 | { |
---|
1579 | if (i.coeff().inCoeffDomain()) |
---|
1580 | { |
---|
1581 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1582 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
1583 | } |
---|
1584 | else |
---|
1585 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1586 | |
---|
1587 | k= i.exp()*d; |
---|
1588 | buf1p= buf1.rep.elts(); |
---|
1589 | buf1RepLength= (int) buf1.rep.length(); |
---|
1590 | for (j= 0; j < buf1RepLength; j++) |
---|
1591 | resultp [j + k]= buf1p [j]; |
---|
1592 | } |
---|
1593 | result.normalize(); |
---|
1594 | |
---|
1595 | return result; |
---|
1596 | } |
---|
1597 | |
---|
1598 | void |
---|
1599 | kronSubReciproFq (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
1600 | const Variable& alpha) |
---|
1601 | { |
---|
1602 | int degAy= degree (A); |
---|
1603 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1604 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1605 | |
---|
1606 | Variable v; |
---|
1607 | zz_pE *subA1p; |
---|
1608 | zz_pE *subA2p; |
---|
1609 | subA1p= subA1.rep.elts(); |
---|
1610 | subA2p= subA2.rep.elts(); |
---|
1611 | zz_pEX buf; |
---|
1612 | zz_pE *bufp; |
---|
1613 | zz_pX buf2; |
---|
1614 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1615 | int j, k, kk, bufRepLength; |
---|
1616 | |
---|
1617 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1618 | { |
---|
1619 | if (i.coeff().inCoeffDomain()) |
---|
1620 | { |
---|
1621 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1622 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
1623 | } |
---|
1624 | else |
---|
1625 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1626 | |
---|
1627 | k= i.exp()*d; |
---|
1628 | kk= (degAy - i.exp())*d; |
---|
1629 | bufp= buf.rep.elts(); |
---|
1630 | bufRepLength= (int) buf.rep.length(); |
---|
1631 | for (j= 0; j < bufRepLength; j++) |
---|
1632 | { |
---|
1633 | subA1p [j + k] += bufp [j]; |
---|
1634 | subA2p [j + kk] += bufp [j]; |
---|
1635 | } |
---|
1636 | } |
---|
1637 | subA1.normalize(); |
---|
1638 | subA2.normalize(); |
---|
1639 | } |
---|
1640 | |
---|
1641 | void |
---|
1642 | kronSubReciproFp (zz_pX& subA1, zz_pX& subA2, const CanonicalForm& A, int d) |
---|
1643 | { |
---|
1644 | int degAy= degree (A); |
---|
1645 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1646 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1647 | |
---|
1648 | zz_p *subA1p; |
---|
1649 | zz_p *subA2p; |
---|
1650 | subA1p= subA1.rep.elts(); |
---|
1651 | subA2p= subA2.rep.elts(); |
---|
1652 | zz_pX buf; |
---|
1653 | zz_p *bufp; |
---|
1654 | int j, k, kk, bufRepLength; |
---|
1655 | |
---|
1656 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1657 | { |
---|
1658 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1659 | |
---|
1660 | k= i.exp()*d; |
---|
1661 | kk= (degAy - i.exp())*d; |
---|
1662 | bufp= buf.rep.elts(); |
---|
1663 | bufRepLength= (int) buf.rep.length(); |
---|
1664 | for (j= 0; j < bufRepLength; j++) |
---|
1665 | { |
---|
1666 | subA1p [j + k] += bufp [j]; |
---|
1667 | subA2p [j + kk] += bufp [j]; |
---|
1668 | } |
---|
1669 | } |
---|
1670 | subA1.normalize(); |
---|
1671 | subA2.normalize(); |
---|
1672 | } |
---|
1673 | |
---|
1674 | CanonicalForm |
---|
1675 | reverseSubstReciproFq (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
1676 | const Variable& alpha) |
---|
1677 | { |
---|
1678 | Variable y= Variable (2); |
---|
1679 | Variable x= Variable (1); |
---|
1680 | |
---|
1681 | zz_pEX f= F; |
---|
1682 | zz_pEX g= G; |
---|
1683 | int degf= deg(f); |
---|
1684 | int degg= deg(g); |
---|
1685 | |
---|
1686 | zz_pEX buf1; |
---|
1687 | zz_pEX buf2; |
---|
1688 | zz_pEX buf3; |
---|
1689 | |
---|
1690 | zz_pE *buf1p; |
---|
1691 | zz_pE *buf2p; |
---|
1692 | zz_pE *buf3p; |
---|
1693 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1694 | f.rep.SetLength ((long)d*(k+1)); |
---|
1695 | |
---|
1696 | zz_pE *gp= g.rep.elts(); |
---|
1697 | zz_pE *fp= f.rep.elts(); |
---|
1698 | CanonicalForm result= 0; |
---|
1699 | int i= 0; |
---|
1700 | int lf= 0; |
---|
1701 | int lg= d*k; |
---|
1702 | int degfSubLf= degf; |
---|
1703 | int deggSubLg= degg-lg; |
---|
1704 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1705 | zz_pE zzpEZero= zz_pE(); |
---|
1706 | |
---|
1707 | while (degf >= lf || lg >= 0) |
---|
1708 | { |
---|
1709 | if (degfSubLf >= d) |
---|
1710 | repLengthBuf1= d; |
---|
1711 | else if (degfSubLf < 0) |
---|
1712 | repLengthBuf1= 0; |
---|
1713 | else |
---|
1714 | repLengthBuf1= degfSubLf + 1; |
---|
1715 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1716 | |
---|
1717 | buf1p= buf1.rep.elts(); |
---|
1718 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1719 | buf1p [ind]= fp [ind + lf]; |
---|
1720 | buf1.normalize(); |
---|
1721 | |
---|
1722 | repLengthBuf1= buf1.rep.length(); |
---|
1723 | |
---|
1724 | if (deggSubLg >= d - 1) |
---|
1725 | repLengthBuf2= d - 1; |
---|
1726 | else if (deggSubLg < 0) |
---|
1727 | repLengthBuf2= 0; |
---|
1728 | else |
---|
1729 | repLengthBuf2= deggSubLg + 1; |
---|
1730 | |
---|
1731 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1732 | buf2p= buf2.rep.elts(); |
---|
1733 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1734 | buf2p [ind]= gp [ind + lg]; |
---|
1735 | buf2.normalize(); |
---|
1736 | |
---|
1737 | repLengthBuf2= buf2.rep.length(); |
---|
1738 | |
---|
1739 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1740 | buf3p= buf3.rep.elts(); |
---|
1741 | buf2p= buf2.rep.elts(); |
---|
1742 | buf1p= buf1.rep.elts(); |
---|
1743 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1744 | buf3p [ind]= buf1p [ind]; |
---|
1745 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1746 | buf3p [ind]= zzpEZero; |
---|
1747 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1748 | buf3p [ind + d]= buf2p [ind]; |
---|
1749 | buf3.normalize(); |
---|
1750 | |
---|
1751 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
1752 | i++; |
---|
1753 | |
---|
1754 | |
---|
1755 | lf= i*d; |
---|
1756 | degfSubLf= degf - lf; |
---|
1757 | |
---|
1758 | lg= d*(k-i); |
---|
1759 | deggSubLg= degg - lg; |
---|
1760 | |
---|
1761 | buf1p= buf1.rep.elts(); |
---|
1762 | |
---|
1763 | if (lg >= 0 && deggSubLg > 0) |
---|
1764 | { |
---|
1765 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1766 | degfSubLf= repLengthBuf2 - 1; |
---|
1767 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1768 | for (ind= 0; ind < tmp; ind++) |
---|
1769 | gp [ind + lg] -= buf1p [ind]; |
---|
1770 | } |
---|
1771 | |
---|
1772 | if (lg < 0) |
---|
1773 | break; |
---|
1774 | |
---|
1775 | buf2p= buf2.rep.elts(); |
---|
1776 | if (degfSubLf >= 0) |
---|
1777 | { |
---|
1778 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1779 | fp [ind + lf] -= buf2p [ind]; |
---|
1780 | } |
---|
1781 | } |
---|
1782 | |
---|
1783 | return result; |
---|
1784 | } |
---|
1785 | |
---|
1786 | CanonicalForm |
---|
1787 | reverseSubstReciproFp (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
1788 | { |
---|
1789 | Variable y= Variable (2); |
---|
1790 | Variable x= Variable (1); |
---|
1791 | |
---|
1792 | zz_pX f= F; |
---|
1793 | zz_pX g= G; |
---|
1794 | int degf= deg(f); |
---|
1795 | int degg= deg(g); |
---|
1796 | |
---|
1797 | zz_pX buf1; |
---|
1798 | zz_pX buf2; |
---|
1799 | zz_pX buf3; |
---|
1800 | |
---|
1801 | zz_p *buf1p; |
---|
1802 | zz_p *buf2p; |
---|
1803 | zz_p *buf3p; |
---|
1804 | |
---|
1805 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1806 | f.rep.SetLength ((long)d*(k+1)); |
---|
1807 | |
---|
1808 | zz_p *gp= g.rep.elts(); |
---|
1809 | zz_p *fp= f.rep.elts(); |
---|
1810 | CanonicalForm result= 0; |
---|
1811 | int i= 0; |
---|
1812 | int lf= 0; |
---|
1813 | int lg= d*k; |
---|
1814 | int degfSubLf= degf; |
---|
1815 | int deggSubLg= degg-lg; |
---|
1816 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1817 | zz_p zzpZero= zz_p(); |
---|
1818 | while (degf >= lf || lg >= 0) |
---|
1819 | { |
---|
1820 | if (degfSubLf >= d) |
---|
1821 | repLengthBuf1= d; |
---|
1822 | else if (degfSubLf < 0) |
---|
1823 | repLengthBuf1= 0; |
---|
1824 | else |
---|
1825 | repLengthBuf1= degfSubLf + 1; |
---|
1826 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1827 | |
---|
1828 | buf1p= buf1.rep.elts(); |
---|
1829 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1830 | buf1p [ind]= fp [ind + lf]; |
---|
1831 | buf1.normalize(); |
---|
1832 | |
---|
1833 | repLengthBuf1= buf1.rep.length(); |
---|
1834 | |
---|
1835 | if (deggSubLg >= d - 1) |
---|
1836 | repLengthBuf2= d - 1; |
---|
1837 | else if (deggSubLg < 0) |
---|
1838 | repLengthBuf2= 0; |
---|
1839 | else |
---|
1840 | repLengthBuf2= deggSubLg + 1; |
---|
1841 | |
---|
1842 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1843 | buf2p= buf2.rep.elts(); |
---|
1844 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1845 | buf2p [ind]= gp [ind + lg]; |
---|
1846 | |
---|
1847 | buf2.normalize(); |
---|
1848 | |
---|
1849 | repLengthBuf2= buf2.rep.length(); |
---|
1850 | |
---|
1851 | |
---|
1852 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1853 | buf3p= buf3.rep.elts(); |
---|
1854 | buf2p= buf2.rep.elts(); |
---|
1855 | buf1p= buf1.rep.elts(); |
---|
1856 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1857 | buf3p [ind]= buf1p [ind]; |
---|
1858 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1859 | buf3p [ind]= zzpZero; |
---|
1860 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1861 | buf3p [ind + d]= buf2p [ind]; |
---|
1862 | buf3.normalize(); |
---|
1863 | |
---|
1864 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
1865 | i++; |
---|
1866 | |
---|
1867 | |
---|
1868 | lf= i*d; |
---|
1869 | degfSubLf= degf - lf; |
---|
1870 | |
---|
1871 | lg= d*(k-i); |
---|
1872 | deggSubLg= degg - lg; |
---|
1873 | |
---|
1874 | buf1p= buf1.rep.elts(); |
---|
1875 | |
---|
1876 | if (lg >= 0 && deggSubLg > 0) |
---|
1877 | { |
---|
1878 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1879 | degfSubLf= repLengthBuf2 - 1; |
---|
1880 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1881 | for (ind= 0; ind < tmp; ind++) |
---|
1882 | gp [ind + lg] -= buf1p [ind]; |
---|
1883 | } |
---|
1884 | if (lg < 0) |
---|
1885 | break; |
---|
1886 | |
---|
1887 | buf2p= buf2.rep.elts(); |
---|
1888 | if (degfSubLf >= 0) |
---|
1889 | { |
---|
1890 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1891 | fp [ind + lf] -= buf2p [ind]; |
---|
1892 | } |
---|
1893 | } |
---|
1894 | |
---|
1895 | return result; |
---|
1896 | } |
---|
1897 | |
---|
1898 | CanonicalForm reverseSubstFq (const zz_pEX& F, int d, const Variable& alpha) |
---|
1899 | { |
---|
1900 | Variable y= Variable (2); |
---|
1901 | Variable x= Variable (1); |
---|
1902 | |
---|
1903 | zz_pEX f= F; |
---|
1904 | zz_pE *fp= f.rep.elts(); |
---|
1905 | |
---|
1906 | zz_pEX buf; |
---|
1907 | zz_pE *bufp; |
---|
1908 | CanonicalForm result= 0; |
---|
1909 | int i= 0; |
---|
1910 | int degf= deg(f); |
---|
1911 | int k= 0; |
---|
1912 | int degfSubK, repLength, j; |
---|
1913 | while (degf >= k) |
---|
1914 | { |
---|
1915 | degfSubK= degf - k; |
---|
1916 | if (degfSubK >= d) |
---|
1917 | repLength= d; |
---|
1918 | else |
---|
1919 | repLength= degfSubK + 1; |
---|
1920 | |
---|
1921 | buf.rep.SetLength ((long) repLength); |
---|
1922 | bufp= buf.rep.elts(); |
---|
1923 | for (j= 0; j < repLength; j++) |
---|
1924 | bufp [j]= fp [j + k]; |
---|
1925 | buf.normalize(); |
---|
1926 | |
---|
1927 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
1928 | i++; |
---|
1929 | k= d*i; |
---|
1930 | } |
---|
1931 | |
---|
1932 | return result; |
---|
1933 | } |
---|
1934 | |
---|
1935 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
1936 | { |
---|
1937 | Variable y= Variable (2); |
---|
1938 | Variable x= Variable (1); |
---|
1939 | |
---|
1940 | zz_pX f= F; |
---|
1941 | zz_p *fp= f.rep.elts(); |
---|
1942 | |
---|
1943 | zz_pX buf; |
---|
1944 | zz_p *bufp; |
---|
1945 | CanonicalForm result= 0; |
---|
1946 | int i= 0; |
---|
1947 | int degf= deg(f); |
---|
1948 | int k= 0; |
---|
1949 | int degfSubK, repLength, j; |
---|
1950 | while (degf >= k) |
---|
1951 | { |
---|
1952 | degfSubK= degf - k; |
---|
1953 | if (degfSubK >= d) |
---|
1954 | repLength= d; |
---|
1955 | else |
---|
1956 | repLength= degfSubK + 1; |
---|
1957 | |
---|
1958 | buf.rep.SetLength ((long) repLength); |
---|
1959 | bufp= buf.rep.elts(); |
---|
1960 | for (j= 0; j < repLength; j++) |
---|
1961 | bufp [j]= fp [j + k]; |
---|
1962 | buf.normalize(); |
---|
1963 | |
---|
1964 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
1965 | i++; |
---|
1966 | k= d*i; |
---|
1967 | } |
---|
1968 | |
---|
1969 | return result; |
---|
1970 | } |
---|
1971 | |
---|
1972 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
1973 | CanonicalForm |
---|
1974 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1975 | CanonicalForm& M) |
---|
1976 | { |
---|
1977 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1978 | d1 /= 2; |
---|
1979 | d1 += 1; |
---|
1980 | |
---|
1981 | zz_pX F1, F2; |
---|
1982 | kronSubReciproFp (F1, F2, F, d1); |
---|
1983 | zz_pX G1, G2; |
---|
1984 | kronSubReciproFp (G1, G2, G, d1); |
---|
1985 | |
---|
1986 | int k= d1*degree (M); |
---|
1987 | MulTrunc (F1, F1, G1, (long) k); |
---|
1988 | |
---|
1989 | int degtailF= degree (tailcoeff (F), 1); |
---|
1990 | int degtailG= degree (tailcoeff (G), 1); |
---|
1991 | int taildegF= taildegree (F); |
---|
1992 | int taildegG= taildegree (G); |
---|
1993 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
1994 | |
---|
1995 | reverse (F2, F2); |
---|
1996 | reverse (G2, G2); |
---|
1997 | MulTrunc (F2, F2, G2, b + 1); |
---|
1998 | reverse (F2, F2, b); |
---|
1999 | |
---|
2000 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
2001 | return reverseSubstReciproFp (F1, F2, d1, d2); |
---|
2002 | } |
---|
2003 | |
---|
2004 | //Kronecker substitution |
---|
2005 | CanonicalForm |
---|
2006 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2007 | CanonicalForm& M) |
---|
2008 | { |
---|
2009 | CanonicalForm A= F; |
---|
2010 | CanonicalForm B= G; |
---|
2011 | |
---|
2012 | int degAx= degree (A, 1); |
---|
2013 | int degAy= degree (A, 2); |
---|
2014 | int degBx= degree (B, 1); |
---|
2015 | int degBy= degree (B, 2); |
---|
2016 | int d1= degAx + 1 + degBx; |
---|
2017 | int d2= tmax (degAy, degBy); |
---|
2018 | |
---|
2019 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
2020 | return mulMod2NTLFpReci (A, B, M); |
---|
2021 | |
---|
2022 | zz_pX NTLA= kronSubFp (A, d1); |
---|
2023 | zz_pX NTLB= kronSubFp (B, d1); |
---|
2024 | |
---|
2025 | int k= d1*degree (M); |
---|
2026 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
2027 | |
---|
2028 | A= reverseSubstFp (NTLA, d1); |
---|
2029 | |
---|
2030 | return A; |
---|
2031 | } |
---|
2032 | |
---|
2033 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
2034 | CanonicalForm |
---|
2035 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2036 | CanonicalForm& M, const Variable& alpha) |
---|
2037 | { |
---|
2038 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
2039 | d1 /= 2; |
---|
2040 | d1 += 1; |
---|
2041 | |
---|
2042 | zz_pEX F1, F2; |
---|
2043 | kronSubReciproFq (F1, F2, F, d1, alpha); |
---|
2044 | zz_pEX G1, G2; |
---|
2045 | kronSubReciproFq (G1, G2, G, d1, alpha); |
---|
2046 | |
---|
2047 | int k= d1*degree (M); |
---|
2048 | MulTrunc (F1, F1, G1, (long) k); |
---|
2049 | |
---|
2050 | int degtailF= degree (tailcoeff (F), 1); |
---|
2051 | int degtailG= degree (tailcoeff (G), 1); |
---|
2052 | int taildegF= taildegree (F); |
---|
2053 | int taildegG= taildegree (G); |
---|
2054 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
2055 | |
---|
2056 | reverse (F2, F2); |
---|
2057 | reverse (G2, G2); |
---|
2058 | MulTrunc (F2, F2, G2, b + 1); |
---|
2059 | reverse (F2, F2, b); |
---|
2060 | |
---|
2061 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
2062 | return reverseSubstReciproFq (F1, F2, d1, d2, alpha); |
---|
2063 | } |
---|
2064 | |
---|
2065 | #ifdef HAVE_FLINT |
---|
2066 | CanonicalForm |
---|
2067 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2068 | CanonicalForm& M); |
---|
2069 | #endif |
---|
2070 | |
---|
2071 | CanonicalForm |
---|
2072 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2073 | CanonicalForm& M) |
---|
2074 | { |
---|
2075 | Variable alpha; |
---|
2076 | CanonicalForm A= F; |
---|
2077 | CanonicalForm B= G; |
---|
2078 | |
---|
2079 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
2080 | { |
---|
2081 | int degAx= degree (A, 1); |
---|
2082 | int degAy= degree (A, 2); |
---|
2083 | int degBx= degree (B, 1); |
---|
2084 | int degBy= degree (B, 2); |
---|
2085 | int d1= degAx + degBx + 1; |
---|
2086 | int d2= tmax (degAy, degBy); |
---|
2087 | zz_p::init (getCharacteristic()); |
---|
2088 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2089 | zz_pE::init (NTLMipo); |
---|
2090 | |
---|
2091 | int degMipo= degree (getMipo (alpha)); |
---|
2092 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
2093 | (2*degAy > degree (M))) |
---|
2094 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
2095 | |
---|
2096 | zz_pEX NTLA= kronSubFq (A, d1, alpha); |
---|
2097 | zz_pEX NTLB= kronSubFq (B, d1, alpha); |
---|
2098 | |
---|
2099 | int k= d1*degree (M); |
---|
2100 | |
---|
2101 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
2102 | |
---|
2103 | A= reverseSubstFq (NTLA, d1, alpha); |
---|
2104 | |
---|
2105 | return A; |
---|
2106 | } |
---|
2107 | else |
---|
2108 | #ifdef HAVE_FLINT |
---|
2109 | return mulMod2FLINTFp (A, B, M); |
---|
2110 | #else |
---|
2111 | return mulMod2NTLFp (A, B, M); |
---|
2112 | #endif |
---|
2113 | } |
---|
2114 | |
---|
2115 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
2116 | const CanonicalForm& M) |
---|
2117 | { |
---|
2118 | if (A.isZero() || B.isZero()) |
---|
2119 | return 0; |
---|
2120 | |
---|
2121 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
2122 | |
---|
2123 | CanonicalForm F= mod (A, M); |
---|
2124 | CanonicalForm G= mod (B, M); |
---|
2125 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
2126 | return F*G; |
---|
2127 | Variable y= M.mvar(); |
---|
2128 | int degF= degree (F, y); |
---|
2129 | int degG= degree (G, y); |
---|
2130 | |
---|
2131 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
2132 | (F.level() == G.level())) |
---|
2133 | { |
---|
2134 | CanonicalForm result= mulNTL (F, G); |
---|
2135 | return mod (result, M); |
---|
2136 | } |
---|
2137 | else if (degF <= 1 && degG <= 1) |
---|
2138 | { |
---|
2139 | CanonicalForm result= F*G; |
---|
2140 | return mod (result, M); |
---|
2141 | } |
---|
2142 | |
---|
2143 | int sizeF= size (F); |
---|
2144 | int sizeG= size (G); |
---|
2145 | |
---|
2146 | int fallBackToNaive= 50; |
---|
2147 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
2148 | return mod (F*G, M); |
---|
2149 | |
---|
2150 | #ifdef HAVE_FLINT |
---|
2151 | if (getCharacteristic() == 0) |
---|
2152 | return mulMod2FLINTQa (F, G, M); |
---|
2153 | #endif |
---|
2154 | |
---|
2155 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
2156 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
2157 | return mulMod2NTLFq (F, G, M); |
---|
2158 | |
---|
2159 | int m= (int) ceil (degree (M)/2.0); |
---|
2160 | if (degF >= m || degG >= m) |
---|
2161 | { |
---|
2162 | CanonicalForm MLo= power (y, m); |
---|
2163 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2164 | CanonicalForm F0= mod (F, MLo); |
---|
2165 | CanonicalForm F1= div (F, MLo); |
---|
2166 | CanonicalForm G0= mod (G, MLo); |
---|
2167 | CanonicalForm G1= div (G, MLo); |
---|
2168 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
2169 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
2170 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
2171 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2172 | } |
---|
2173 | else |
---|
2174 | { |
---|
2175 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2176 | CanonicalForm yToM= power (y, m); |
---|
2177 | CanonicalForm F0= mod (F, yToM); |
---|
2178 | CanonicalForm F1= div (F, yToM); |
---|
2179 | CanonicalForm G0= mod (G, yToM); |
---|
2180 | CanonicalForm G1= div (G, yToM); |
---|
2181 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
2182 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
2183 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
2184 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2185 | } |
---|
2186 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
2187 | } |
---|
2188 | |
---|
2189 | // end bivariate polys |
---|
2190 | //********************** |
---|
2191 | // multivariate polys |
---|
2192 | |
---|
2193 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
2194 | { |
---|
2195 | CanonicalForm A= F; |
---|
2196 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
2197 | A= mod (A, i.getItem()); |
---|
2198 | return A; |
---|
2199 | } |
---|
2200 | |
---|
2201 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
2202 | const CFList& MOD) |
---|
2203 | { |
---|
2204 | if (A.isZero() || B.isZero()) |
---|
2205 | return 0; |
---|
2206 | |
---|
2207 | if (MOD.length() == 1) |
---|
2208 | return mulMod2 (A, B, MOD.getLast()); |
---|
2209 | |
---|
2210 | CanonicalForm M= MOD.getLast(); |
---|
2211 | CanonicalForm F= mod (A, M); |
---|
2212 | CanonicalForm G= mod (B, M); |
---|
2213 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
2214 | return F*G; |
---|
2215 | Variable y= M.mvar(); |
---|
2216 | int degF= degree (F, y); |
---|
2217 | int degG= degree (G, y); |
---|
2218 | |
---|
2219 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
2220 | (degG <= 1 && G.level() <= M.level())) |
---|
2221 | { |
---|
2222 | CFList buf= MOD; |
---|
2223 | buf.removeLast(); |
---|
2224 | if (degF == 1 && degG == 1) |
---|
2225 | { |
---|
2226 | CanonicalForm F0= mod (F, y); |
---|
2227 | CanonicalForm F1= div (F, y); |
---|
2228 | CanonicalForm G0= mod (G, y); |
---|
2229 | CanonicalForm G1= div (G, y); |
---|
2230 | if (degree (M) > 2) |
---|
2231 | { |
---|
2232 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
2233 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
2234 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
2235 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
2236 | } |
---|
2237 | else //here degree (M) == 2 |
---|
2238 | { |
---|
2239 | buf.append (y); |
---|
2240 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2241 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2242 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2243 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
2244 | return result; |
---|
2245 | } |
---|
2246 | } |
---|
2247 | else if (degF == 1 && degG == 0) |
---|
2248 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
2249 | else if (degF == 0 && degG == 1) |
---|
2250 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
2251 | else |
---|
2252 | return mulMod (F, G, buf); |
---|
2253 | } |
---|
2254 | int m= (int) ceil (degree (M)/2.0); |
---|
2255 | if (degF >= m || degG >= m) |
---|
2256 | { |
---|
2257 | CanonicalForm MLo= power (y, m); |
---|
2258 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2259 | CanonicalForm F0= mod (F, MLo); |
---|
2260 | CanonicalForm F1= div (F, MLo); |
---|
2261 | CanonicalForm G0= mod (G, MLo); |
---|
2262 | CanonicalForm G1= div (G, MLo); |
---|
2263 | CFList buf= MOD; |
---|
2264 | buf.removeLast(); |
---|
2265 | buf.append (MHi); |
---|
2266 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2267 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2268 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2269 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2270 | } |
---|
2271 | else |
---|
2272 | { |
---|
2273 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2274 | CanonicalForm yToM= power (y, m); |
---|
2275 | CanonicalForm F0= mod (F, yToM); |
---|
2276 | CanonicalForm F1= div (F, yToM); |
---|
2277 | CanonicalForm G0= mod (G, yToM); |
---|
2278 | CanonicalForm G1= div (G, yToM); |
---|
2279 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
2280 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
2281 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
2282 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2283 | } |
---|
2284 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
2285 | } |
---|
2286 | |
---|
2287 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
2288 | { |
---|
2289 | if (L.isEmpty()) |
---|
2290 | return 1; |
---|
2291 | int l= L.length(); |
---|
2292 | if (l == 1) |
---|
2293 | return mod (L.getFirst(), M); |
---|
2294 | else if (l == 2) { |
---|
2295 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
2296 | return result; |
---|
2297 | } |
---|
2298 | else |
---|
2299 | { |
---|
2300 | l /= 2; |
---|
2301 | CFList tmp1, tmp2; |
---|
2302 | CFListIterator i= L; |
---|
2303 | CanonicalForm buf1, buf2; |
---|
2304 | for (int j= 1; j <= l; j++, i++) |
---|
2305 | tmp1.append (i.getItem()); |
---|
2306 | tmp2= Difference (L, tmp1); |
---|
2307 | buf1= prodMod (tmp1, M); |
---|
2308 | buf2= prodMod (tmp2, M); |
---|
2309 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
2310 | return result; |
---|
2311 | } |
---|
2312 | } |
---|
2313 | |
---|
2314 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
2315 | { |
---|
2316 | if (L.isEmpty()) |
---|
2317 | return 1; |
---|
2318 | else if (L.length() == 1) |
---|
2319 | return L.getFirst(); |
---|
2320 | else if (L.length() == 2) |
---|
2321 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
2322 | else |
---|
2323 | { |
---|
2324 | int l= L.length()/2; |
---|
2325 | CFListIterator i= L; |
---|
2326 | CFList tmp1, tmp2; |
---|
2327 | CanonicalForm buf1, buf2; |
---|
2328 | for (int j= 1; j <= l; j++, i++) |
---|
2329 | tmp1.append (i.getItem()); |
---|
2330 | tmp2= Difference (L, tmp1); |
---|
2331 | buf1= prodMod (tmp1, M); |
---|
2332 | buf2= prodMod (tmp2, M); |
---|
2333 | return mulMod (buf1, buf2, M); |
---|
2334 | } |
---|
2335 | } |
---|
2336 | |
---|
2337 | // end multivariate polys |
---|
2338 | //*************************** |
---|
2339 | // division |
---|
2340 | |
---|
2341 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
2342 | { |
---|
2343 | if (d == 0) |
---|
2344 | return F; |
---|
2345 | CanonicalForm A= F; |
---|
2346 | Variable y= Variable (2); |
---|
2347 | Variable x= Variable (1); |
---|
2348 | if (degree (A, x) > 0) |
---|
2349 | { |
---|
2350 | A= swapvar (A, x, y); |
---|
2351 | CanonicalForm result= 0; |
---|
2352 | CFIterator i= A; |
---|
2353 | while (d - i.exp() < 0) |
---|
2354 | i++; |
---|
2355 | |
---|
2356 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
2357 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
2358 | return result; |
---|
2359 | } |
---|
2360 | else |
---|
2361 | return A*power (x, d); |
---|
2362 | } |
---|
2363 | |
---|
2364 | CanonicalForm |
---|
2365 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
2366 | { |
---|
2367 | int l= ilog2(n); |
---|
2368 | |
---|
2369 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
2370 | |
---|
2371 | ASSERT (!g.isZero(), "expected a unit"); |
---|
2372 | |
---|
2373 | Variable alpha; |
---|
2374 | |
---|
2375 | if (!g.isOne()) |
---|
2376 | g = 1/g; |
---|
2377 | Variable x= Variable (1); |
---|
2378 | CanonicalForm result; |
---|
2379 | int exp= 0; |
---|
2380 | if (n & 1) |
---|
2381 | { |
---|
2382 | result= g; |
---|
2383 | exp= 1; |
---|
2384 | } |
---|
2385 | CanonicalForm h; |
---|
2386 | |
---|
2387 | for (int i= 1; i <= l; i++) |
---|
2388 | { |
---|
2389 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
2390 | h= mod (h, power (x, (1 << i)) - 1); |
---|
2391 | h= div (h, power (x, (1 << (i - 1)))); |
---|
2392 | h= mod (h, M); |
---|
2393 | g -= power (x, (1 << (i - 1)))* |
---|
2394 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
2395 | |
---|
2396 | if (n & (1 << i)) |
---|
2397 | { |
---|
2398 | if (exp) |
---|
2399 | { |
---|
2400 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
2401 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
2402 | h= div (h, power (x, exp)); |
---|
2403 | h= mod (h, M); |
---|
2404 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
2405 | power (x, (1 << i))); |
---|
2406 | exp += (1 << i); |
---|
2407 | } |
---|
2408 | else |
---|
2409 | { |
---|
2410 | exp= (1 << i); |
---|
2411 | result= g; |
---|
2412 | } |
---|
2413 | } |
---|
2414 | } |
---|
2415 | |
---|
2416 | return result; |
---|
2417 | } |
---|
2418 | |
---|
2419 | CanonicalForm |
---|
2420 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
2421 | M) |
---|
2422 | { |
---|
2423 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
2424 | |
---|
2425 | CanonicalForm A= mod (F, M); |
---|
2426 | CanonicalForm B= mod (G, M); |
---|
2427 | |
---|
2428 | Variable x= Variable (1); |
---|
2429 | int degA= degree (A, x); |
---|
2430 | int degB= degree (B, x); |
---|
2431 | int m= degA - degB; |
---|
2432 | if (m < 0) |
---|
2433 | return 0; |
---|
2434 | |
---|
2435 | Variable v; |
---|
2436 | CanonicalForm Q; |
---|
2437 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2438 | { |
---|
2439 | CanonicalForm R; |
---|
2440 | divrem2 (A, B, Q, R, M); |
---|
2441 | } |
---|
2442 | else |
---|
2443 | { |
---|
2444 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2445 | { |
---|
2446 | CanonicalForm R= reverse (A, degA); |
---|
2447 | CanonicalForm revB= reverse (B, degB); |
---|
2448 | revB= newtonInverse (revB, m + 1, M); |
---|
2449 | Q= mulMod2 (R, revB, M); |
---|
2450 | Q= mod (Q, power (x, m + 1)); |
---|
2451 | Q= reverse (Q, m); |
---|
2452 | } |
---|
2453 | else |
---|
2454 | { |
---|
2455 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2456 | Variable y= Variable (2); |
---|
2457 | zz_pEX NTLA, NTLB; |
---|
2458 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2459 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2460 | div (NTLA, NTLA, NTLB); |
---|
2461 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
2462 | } |
---|
2463 | } |
---|
2464 | |
---|
2465 | return Q; |
---|
2466 | } |
---|
2467 | |
---|
2468 | void |
---|
2469 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2470 | CanonicalForm& R, const CanonicalForm& M) |
---|
2471 | { |
---|
2472 | CanonicalForm A= mod (F, M); |
---|
2473 | CanonicalForm B= mod (G, M); |
---|
2474 | Variable x= Variable (1); |
---|
2475 | int degA= degree (A, x); |
---|
2476 | int degB= degree (B, x); |
---|
2477 | int m= degA - degB; |
---|
2478 | |
---|
2479 | if (m < 0) |
---|
2480 | { |
---|
2481 | R= A; |
---|
2482 | Q= 0; |
---|
2483 | return; |
---|
2484 | } |
---|
2485 | |
---|
2486 | Variable v; |
---|
2487 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2488 | { |
---|
2489 | divrem2 (A, B, Q, R, M); |
---|
2490 | } |
---|
2491 | else |
---|
2492 | { |
---|
2493 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2494 | { |
---|
2495 | R= reverse (A, degA); |
---|
2496 | |
---|
2497 | CanonicalForm revB= reverse (B, degB); |
---|
2498 | revB= newtonInverse (revB, m + 1, M); |
---|
2499 | Q= mulMod2 (R, revB, M); |
---|
2500 | |
---|
2501 | Q= mod (Q, power (x, m + 1)); |
---|
2502 | Q= reverse (Q, m); |
---|
2503 | |
---|
2504 | R= A - mulMod2 (Q, B, M); |
---|
2505 | } |
---|
2506 | else |
---|
2507 | { |
---|
2508 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2509 | Variable y= Variable (2); |
---|
2510 | zz_pEX NTLA, NTLB; |
---|
2511 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2512 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2513 | zz_pEX NTLQ, NTLR; |
---|
2514 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
2515 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
2516 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
2517 | } |
---|
2518 | } |
---|
2519 | } |
---|
2520 | |
---|
2521 | static inline |
---|
2522 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
2523 | { |
---|
2524 | CanonicalForm A= F; |
---|
2525 | CanonicalForm buf= 0; |
---|
2526 | bool swap= false; |
---|
2527 | if (degree (A, x) <= 0) |
---|
2528 | return CFList(A); |
---|
2529 | else if (x.level() != A.level()) |
---|
2530 | { |
---|
2531 | swap= true; |
---|
2532 | A= swapvar (A, x, A.mvar()); |
---|
2533 | } |
---|
2534 | |
---|
2535 | int j= (int) floor ((double) degree (A)/ m); |
---|
2536 | CFList result; |
---|
2537 | CFIterator i= A; |
---|
2538 | for (; j >= 0; j--) |
---|
2539 | { |
---|
2540 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
2541 | { |
---|
2542 | if (swap) |
---|
2543 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
2544 | else |
---|
2545 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
2546 | i++; |
---|
2547 | } |
---|
2548 | if (swap) |
---|
2549 | result.append (swapvar (buf, x, F.mvar())); |
---|
2550 | else |
---|
2551 | result.append (buf); |
---|
2552 | buf= 0; |
---|
2553 | } |
---|
2554 | return result; |
---|
2555 | } |
---|
2556 | |
---|
2557 | static inline |
---|
2558 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2559 | CanonicalForm& R, const CFList& M); |
---|
2560 | |
---|
2561 | static inline |
---|
2562 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2563 | CanonicalForm& R, const CFList& M) |
---|
2564 | { |
---|
2565 | CanonicalForm A= mod (F, M); |
---|
2566 | CanonicalForm B= mod (G, M); |
---|
2567 | Variable x= Variable (1); |
---|
2568 | int degB= degree (B, x); |
---|
2569 | int degA= degree (A, x); |
---|
2570 | if (degA < degB) |
---|
2571 | { |
---|
2572 | Q= 0; |
---|
2573 | R= A; |
---|
2574 | return; |
---|
2575 | } |
---|
2576 | if (degB < 1) |
---|
2577 | { |
---|
2578 | divrem (A, B, Q, R); |
---|
2579 | Q= mod (Q, M); |
---|
2580 | R= mod (R, M); |
---|
2581 | return; |
---|
2582 | } |
---|
2583 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
2584 | ASSERT (4*m >= degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
2585 | CFList splitA= split (A, m, x); |
---|
2586 | if (splitA.length() == 3) |
---|
2587 | splitA.insert (0); |
---|
2588 | if (splitA.length() == 2) |
---|
2589 | { |
---|
2590 | splitA.insert (0); |
---|
2591 | splitA.insert (0); |
---|
2592 | } |
---|
2593 | if (splitA.length() == 1) |
---|
2594 | { |
---|
2595 | splitA.insert (0); |
---|
2596 | splitA.insert (0); |
---|
2597 | splitA.insert (0); |
---|
2598 | } |
---|
2599 | |
---|
2600 | CanonicalForm xToM= power (x, m); |
---|
2601 | |
---|
2602 | CFListIterator i= splitA; |
---|
2603 | CanonicalForm H= i.getItem(); |
---|
2604 | i++; |
---|
2605 | H *= xToM; |
---|
2606 | H += i.getItem(); |
---|
2607 | i++; |
---|
2608 | H *= xToM; |
---|
2609 | H += i.getItem(); |
---|
2610 | i++; |
---|
2611 | |
---|
2612 | divrem32 (H, B, Q, R, M); |
---|
2613 | |
---|
2614 | CFList splitR= split (R, m, x); |
---|
2615 | if (splitR.length() == 1) |
---|
2616 | splitR.insert (0); |
---|
2617 | |
---|
2618 | H= splitR.getFirst(); |
---|
2619 | H *= xToM; |
---|
2620 | H += splitR.getLast(); |
---|
2621 | H *= xToM; |
---|
2622 | H += i.getItem(); |
---|
2623 | |
---|
2624 | CanonicalForm bufQ; |
---|
2625 | divrem32 (H, B, bufQ, R, M); |
---|
2626 | |
---|
2627 | Q *= xToM; |
---|
2628 | Q += bufQ; |
---|
2629 | return; |
---|
2630 | } |
---|
2631 | |
---|
2632 | static inline |
---|
2633 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2634 | CanonicalForm& R, const CFList& M) |
---|
2635 | { |
---|
2636 | CanonicalForm A= mod (F, M); |
---|
2637 | CanonicalForm B= mod (G, M); |
---|
2638 | Variable x= Variable (1); |
---|
2639 | int degB= degree (B, x); |
---|
2640 | int degA= degree (A, x); |
---|
2641 | if (degA < degB) |
---|
2642 | { |
---|
2643 | Q= 0; |
---|
2644 | R= A; |
---|
2645 | return; |
---|
2646 | } |
---|
2647 | if (degB < 1) |
---|
2648 | { |
---|
2649 | divrem (A, B, Q, R); |
---|
2650 | Q= mod (Q, M); |
---|
2651 | R= mod (R, M); |
---|
2652 | return; |
---|
2653 | } |
---|
2654 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
2655 | ASSERT (3*m > degA, "expected degree (F, 1) < 3*degree (G, 1)"); |
---|
2656 | CFList splitA= split (A, m, x); |
---|
2657 | CFList splitB= split (B, m, x); |
---|
2658 | |
---|
2659 | if (splitA.length() == 2) |
---|
2660 | { |
---|
2661 | splitA.insert (0); |
---|
2662 | } |
---|
2663 | if (splitA.length() == 1) |
---|
2664 | { |
---|
2665 | splitA.insert (0); |
---|
2666 | splitA.insert (0); |
---|
2667 | } |
---|
2668 | CanonicalForm xToM= power (x, m); |
---|
2669 | |
---|
2670 | CanonicalForm H; |
---|
2671 | CFListIterator i= splitA; |
---|
2672 | i++; |
---|
2673 | |
---|
2674 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
2675 | { |
---|
2676 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
2677 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
2678 | } |
---|
2679 | else |
---|
2680 | { |
---|
2681 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
2682 | splitB.getFirst()*xToM; |
---|
2683 | Q= xToM - 1; |
---|
2684 | } |
---|
2685 | |
---|
2686 | H= mulMod (Q, splitB.getLast(), M); |
---|
2687 | |
---|
2688 | R= R*xToM + splitA.getLast() - H; |
---|
2689 | |
---|
2690 | while (degree (R, x) >= degB) |
---|
2691 | { |
---|
2692 | xToM= power (x, degree (R, x) - degB); |
---|
2693 | Q += LC (R, x)*xToM; |
---|
2694 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
2695 | Q= mod (Q, M); |
---|
2696 | R= mod (R, M); |
---|
2697 | } |
---|
2698 | |
---|
2699 | return; |
---|
2700 | } |
---|
2701 | |
---|
2702 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2703 | CanonicalForm& R, const CanonicalForm& M) |
---|
2704 | { |
---|
2705 | CanonicalForm A= mod (F, M); |
---|
2706 | CanonicalForm B= mod (G, M); |
---|
2707 | |
---|
2708 | if (B.inCoeffDomain()) |
---|
2709 | { |
---|
2710 | divrem (A, B, Q, R); |
---|
2711 | return; |
---|
2712 | } |
---|
2713 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
2714 | { |
---|
2715 | Q= 0; |
---|
2716 | R= A; |
---|
2717 | return; |
---|
2718 | } |
---|
2719 | |
---|
2720 | if (B.level() < A.level()) |
---|
2721 | { |
---|
2722 | divrem (A, B, Q, R); |
---|
2723 | return; |
---|
2724 | } |
---|
2725 | if (A.level() > B.level()) |
---|
2726 | { |
---|
2727 | R= A; |
---|
2728 | Q= 0; |
---|
2729 | return; |
---|
2730 | } |
---|
2731 | if (B.level() == 1 && B.isUnivariate()) |
---|
2732 | { |
---|
2733 | divrem (A, B, Q, R); |
---|
2734 | return; |
---|
2735 | } |
---|
2736 | if (!(B.level() == 1 && B.isUnivariate()) && |
---|
2737 | (A.level() == 1 && A.isUnivariate())) |
---|
2738 | { |
---|
2739 | Q= 0; |
---|
2740 | R= A; |
---|
2741 | return; |
---|
2742 | } |
---|
2743 | |
---|
2744 | Variable x= Variable (1); |
---|
2745 | int degB= degree (B, x); |
---|
2746 | if (degB > degree (A, x)) |
---|
2747 | { |
---|
2748 | Q= 0; |
---|
2749 | R= A; |
---|
2750 | return; |
---|
2751 | } |
---|
2752 | |
---|
2753 | CFList splitA= split (A, degB, x); |
---|
2754 | |
---|
2755 | CanonicalForm xToDegB= power (x, degB); |
---|
2756 | CanonicalForm H, bufQ; |
---|
2757 | Q= 0; |
---|
2758 | CFListIterator i= splitA; |
---|
2759 | H= i.getItem()*xToDegB; |
---|
2760 | i++; |
---|
2761 | H += i.getItem(); |
---|
2762 | CFList buf; |
---|
2763 | while (i.hasItem()) |
---|
2764 | { |
---|
2765 | buf= CFList (M); |
---|
2766 | divrem21 (H, B, bufQ, R, buf); |
---|
2767 | i++; |
---|
2768 | if (i.hasItem()) |
---|
2769 | H= R*xToDegB + i.getItem(); |
---|
2770 | Q *= xToDegB; |
---|
2771 | Q += bufQ; |
---|
2772 | } |
---|
2773 | return; |
---|
2774 | } |
---|
2775 | |
---|
2776 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2777 | CanonicalForm& R, const CFList& MOD) |
---|
2778 | { |
---|
2779 | CanonicalForm A= mod (F, MOD); |
---|
2780 | CanonicalForm B= mod (G, MOD); |
---|
2781 | Variable x= Variable (1); |
---|
2782 | int degB= degree (B, x); |
---|
2783 | if (degB > degree (A, x)) |
---|
2784 | { |
---|
2785 | Q= 0; |
---|
2786 | R= A; |
---|
2787 | return; |
---|
2788 | } |
---|
2789 | |
---|
2790 | if (degB <= 0) |
---|
2791 | { |
---|
2792 | divrem (A, B, Q, R); |
---|
2793 | Q= mod (Q, MOD); |
---|
2794 | R= mod (R, MOD); |
---|
2795 | return; |
---|
2796 | } |
---|
2797 | CFList splitA= split (A, degB, x); |
---|
2798 | |
---|
2799 | CanonicalForm xToDegB= power (x, degB); |
---|
2800 | CanonicalForm H, bufQ; |
---|
2801 | Q= 0; |
---|
2802 | CFListIterator i= splitA; |
---|
2803 | H= i.getItem()*xToDegB; |
---|
2804 | i++; |
---|
2805 | H += i.getItem(); |
---|
2806 | while (i.hasItem()) |
---|
2807 | { |
---|
2808 | divrem21 (H, B, bufQ, R, MOD); |
---|
2809 | i++; |
---|
2810 | if (i.hasItem()) |
---|
2811 | H= R*xToDegB + i.getItem(); |
---|
2812 | Q *= xToDegB; |
---|
2813 | Q += bufQ; |
---|
2814 | } |
---|
2815 | return; |
---|
2816 | } |
---|
2817 | |
---|
2818 | bool |
---|
2819 | uniFdivides (const CanonicalForm& A, const CanonicalForm& B) |
---|
2820 | { |
---|
2821 | if (B.isZero()) |
---|
2822 | return true; |
---|
2823 | if (A.isZero()) |
---|
2824 | return false; |
---|
2825 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
2826 | return fdivides (A, B); |
---|
2827 | int p= getCharacteristic(); |
---|
2828 | if (A.inCoeffDomain() || B.inCoeffDomain()) |
---|
2829 | { |
---|
2830 | if (A.inCoeffDomain()) |
---|
2831 | return true; |
---|
2832 | else |
---|
2833 | return false; |
---|
2834 | } |
---|
2835 | if (p > 0) |
---|
2836 | { |
---|
2837 | zz_p::init (p); |
---|
2838 | Variable alpha; |
---|
2839 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
2840 | { |
---|
2841 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2842 | zz_pE::init (NTLMipo); |
---|
2843 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
---|
2844 | zz_pEX NTLB= convertFacCF2NTLzz_pEX (B, NTLMipo); |
---|
2845 | return divide (NTLB, NTLA); |
---|
2846 | } |
---|
2847 | #ifdef HAVE_FLINT |
---|
2848 | nmod_poly_t FLINTA, FLINTB; |
---|
2849 | convertFacCF2nmod_poly_t (FLINTA, A); |
---|
2850 | convertFacCF2nmod_poly_t (FLINTB, B); |
---|
2851 | nmod_poly_divrem (FLINTB, FLINTA, FLINTB, FLINTA); |
---|
2852 | bool result= nmod_poly_is_zero (FLINTA); |
---|
2853 | nmod_poly_clear (FLINTA); |
---|
2854 | nmod_poly_clear (FLINTB); |
---|
2855 | return result; |
---|
2856 | #else |
---|
2857 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
---|
2858 | zz_pX NTLB= convertFacCF2NTLzzpX (B); |
---|
2859 | return divide (NTLB, NTLA); |
---|
2860 | #endif |
---|
2861 | } |
---|
2862 | #ifdef HAVE_FLINT |
---|
2863 | Variable alpha; |
---|
2864 | bool isRat= isOn (SW_RATIONAL); |
---|
2865 | if (!isRat) |
---|
2866 | On (SW_RATIONAL); |
---|
2867 | if (!hasFirstAlgVar (A, alpha) && !hasFirstAlgVar (B, alpha)) |
---|
2868 | { |
---|
2869 | fmpq_poly_t FLINTA,FLINTB; |
---|
2870 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
---|
2871 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
---|
2872 | fmpq_poly_rem (FLINTA, FLINTB, FLINTA); |
---|
2873 | bool result= fmpq_poly_is_zero (FLINTA); |
---|
2874 | fmpq_poly_clear (FLINTA); |
---|
2875 | fmpq_poly_clear (FLINTB); |
---|
2876 | if (!isRat) |
---|
2877 | Off (SW_RATIONAL); |
---|
2878 | return result; |
---|
2879 | } |
---|
2880 | CanonicalForm Q, R; |
---|
2881 | Variable x= Variable (1); |
---|
2882 | Variable y= Variable (2); |
---|
2883 | newtonDivrem (swapvar (B, y, x), swapvar (A, y, x), Q, R); |
---|
2884 | if (!isRat) |
---|
2885 | Off (SW_RATIONAL); |
---|
2886 | return R.isZero(); |
---|
2887 | #else |
---|
2888 | bool isRat= isOn (SW_RATIONAL); |
---|
2889 | if (!isRat) |
---|
2890 | On (SW_RATIONAL); |
---|
2891 | bool result= fdivides (A, B); |
---|
2892 | if (!isRat) |
---|
2893 | Off (SW_RATIONAL); |
---|
2894 | return result; //maybe NTL? |
---|
2895 | #endif |
---|
2896 | } |
---|
2897 | |
---|
2898 | // end division |
---|
2899 | |
---|
2900 | #endif |
---|