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 | #ifdef HAVE_CONFIG_H |
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16 | #include "config.h" |
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17 | #endif /* HAVE_CONFIG_H */ |
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18 | |
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19 | #include "canonicalform.h" |
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20 | #include "facMul.h" |
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21 | #include "algext.h" |
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22 | #include "cf_util.h" |
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23 | #include "templates/ftmpl_functions.h" |
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24 | |
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25 | #ifdef HAVE_NTL |
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26 | #include <NTL/lzz_pEX.h> |
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27 | #include "NTLconvert.h" |
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28 | |
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29 | #ifdef HAVE_FLINT |
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30 | #include "FLINTconvert.h" |
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31 | #endif |
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32 | |
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33 | // univariate polys |
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34 | |
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35 | #ifdef HAVE_FLINT |
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36 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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37 | { |
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38 | int degAy= degree (A); |
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39 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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40 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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41 | CFIterator j; |
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42 | for (CFIterator i= A; i.hasTerms(); i++) |
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43 | { |
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44 | if (i.coeff().inBaseDomain()) |
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45 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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46 | else |
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47 | for (j= i.coeff(); j.hasTerms(); j++) |
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48 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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49 | j.coeff()); |
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50 | } |
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51 | _fmpz_poly_normalise(result); |
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52 | } |
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53 | |
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54 | |
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55 | CanonicalForm |
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56 | reverseSubstQa (const fmpz_poly_t F, int d, const Variable& x, |
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57 | const Variable& alpha, const CanonicalForm& den) |
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58 | { |
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59 | |
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60 | CanonicalForm result= 0; |
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61 | int i= 0; |
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62 | int degf= fmpz_poly_degree (F); |
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63 | int k= 0; |
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64 | int degfSubK; |
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65 | int repLength, j; |
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66 | CanonicalForm coeff, ff; |
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67 | fmpz* tmp; |
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68 | while (degf >= k) |
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69 | { |
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70 | coeff= 0; |
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71 | degfSubK= degf - k; |
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72 | if (degfSubK >= d) |
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73 | repLength= d; |
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74 | else |
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75 | repLength= degfSubK + 1; |
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76 | |
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77 | for (j= 0; j < repLength; j++) |
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78 | { |
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79 | tmp= fmpz_poly_get_coeff_ptr (F, j+k); |
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80 | if (!fmpz_is_zero (tmp)) |
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81 | { |
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82 | ff= convertFmpz2CF (tmp); |
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83 | coeff += ff*power (alpha, j); //TODO faster reduction mod alpha |
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84 | } |
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85 | } |
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86 | result += coeff*power (x, i); |
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87 | i++; |
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88 | k= d*i; |
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89 | } |
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90 | result /= den; |
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91 | return result; |
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92 | } |
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93 | |
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94 | CanonicalForm |
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95 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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96 | const Variable& alpha) |
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97 | { |
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98 | CanonicalForm A= F; |
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99 | CanonicalForm B= G; |
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100 | |
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101 | CanonicalForm denA= bCommonDen (A); |
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102 | CanonicalForm denB= bCommonDen (B); |
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103 | |
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104 | A *= denA; |
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105 | B *= denB; |
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106 | int degAa= degree (A, alpha); |
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107 | int degBa= degree (B, alpha); |
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108 | int d= degAa + 1 + degBa; |
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109 | |
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110 | fmpz_poly_t FLINTA,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 | kronSub (FLINTA, A, d); |
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220 | kronSub (FLINTB, B, d); |
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221 | |
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222 | int k= d*m; |
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223 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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224 | |
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225 | denA *= denB; |
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226 | A= reverseSubstQa (FLINTA, d, F.mvar(), alpha, denA); |
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227 | fmpz_poly_clear (FLINTA); |
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228 | fmpz_poly_clear (FLINTB); |
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229 | return A; |
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230 | } |
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231 | |
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232 | CanonicalForm |
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233 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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234 | { |
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235 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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236 | return mod (F*G, power (Variable (1), m)); |
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237 | Variable alpha; |
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238 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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239 | return mulFLINTQaTrunc (F, G, alpha, m); |
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240 | |
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241 | CanonicalForm A= F; |
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242 | CanonicalForm B= G; |
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243 | |
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244 | CanonicalForm denA= bCommonDen (A); |
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245 | CanonicalForm denB= bCommonDen (B); |
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246 | |
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247 | A *= denA; |
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248 | B *= denB; |
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249 | fmpz_poly_t FLINTA,FLINTB; |
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250 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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251 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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252 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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253 | denA *= denB; |
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254 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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255 | A /= denA; |
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256 | fmpz_poly_clear (FLINTA); |
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257 | fmpz_poly_clear (FLINTB); |
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258 | |
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259 | return A; |
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260 | } |
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261 | |
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262 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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263 | { |
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264 | if (d == 0) |
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265 | return F; |
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266 | if (F.inCoeffDomain()) |
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267 | return F*power (Variable (1),d); |
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268 | Variable x= Variable (1); |
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269 | CanonicalForm result= 0; |
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270 | CFIterator i= F; |
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271 | while (d - i.exp() < 0) |
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272 | i++; |
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273 | |
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274 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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275 | result += i.coeff()*power (x, d - i.exp()); |
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276 | return result; |
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277 | } |
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278 | |
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279 | CanonicalForm |
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280 | newtonInverse (const CanonicalForm& F, const int n) |
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281 | { |
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282 | int l= ilog2(n); |
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283 | |
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284 | CanonicalForm g= F [0]; |
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285 | |
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286 | ASSERT (!g.isZero(), "expected a unit"); |
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287 | |
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288 | if (!g.isOne()) |
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289 | g = 1/g; |
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290 | Variable x= Variable (1); |
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291 | CanonicalForm result; |
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292 | int exp= 0; |
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293 | if (n & 1) |
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294 | { |
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295 | result= g; |
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296 | exp= 1; |
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297 | } |
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298 | CanonicalForm h; |
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299 | |
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300 | for (int i= 1; i <= l; i++) |
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301 | { |
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302 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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303 | h= mod (h, power (x, (1 << i)) - 1); |
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304 | h= div (h, power (x, (1 << (i - 1)))); |
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305 | g -= power (x, (1 << (i - 1)))* |
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306 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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307 | |
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308 | if (n & (1 << i)) |
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309 | { |
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310 | if (exp) |
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311 | { |
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312 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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313 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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314 | h= div (h, power (x, exp)); |
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315 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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316 | exp += (1 << i); |
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317 | } |
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318 | else |
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319 | { |
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320 | exp= (1 << i); |
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321 | result= g; |
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322 | } |
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323 | } |
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324 | } |
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325 | |
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326 | return result; |
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327 | } |
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328 | |
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329 | void |
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330 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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331 | CanonicalForm& R) |
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332 | { |
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333 | CanonicalForm A= F; |
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334 | CanonicalForm B= G; |
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335 | Variable x= Variable (1); |
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336 | int degA= degree (A, x); |
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337 | int degB= degree (B, x); |
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338 | int m= degA - degB; |
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339 | |
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340 | if (m < 0) |
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341 | { |
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342 | R= A; |
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343 | Q= 0; |
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344 | return; |
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345 | } |
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346 | |
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347 | if (degB <= 1) |
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348 | divrem (A, B, Q, R); |
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349 | else |
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350 | { |
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351 | R= uniReverse (A, degA); |
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352 | |
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353 | CanonicalForm revB= uniReverse (B, degB); |
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354 | CanonicalForm buf= revB; |
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355 | revB= newtonInverse (revB, m + 1); |
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356 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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357 | Q= uniReverse (Q, m); |
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358 | |
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359 | R= A - mulNTL (Q, B); |
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360 | } |
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361 | } |
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362 | |
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363 | void |
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364 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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365 | { |
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366 | CanonicalForm A= F; |
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367 | CanonicalForm B= G; |
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368 | Variable x= Variable (1); |
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369 | int degA= degree (A, x); |
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370 | int degB= degree (B, x); |
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371 | int m= degA - degB; |
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372 | |
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373 | if (m < 0) |
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374 | { |
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375 | Q= 0; |
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376 | return; |
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377 | } |
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378 | |
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379 | if (degB <= 1) |
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380 | Q= div (A, B); |
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381 | else |
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382 | { |
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383 | CanonicalForm R= uniReverse (A, degA); |
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384 | |
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385 | CanonicalForm revB= uniReverse (B, degB); |
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386 | revB= newtonInverse (revB, m + 1); |
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387 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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388 | Q= uniReverse (Q, m); |
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389 | } |
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390 | } |
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391 | |
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392 | #endif |
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393 | |
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394 | CanonicalForm |
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395 | mulNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
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396 | { |
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397 | if (CFFactory::gettype() == GaloisFieldDomain) |
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398 | return F*G; |
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399 | if (getCharacteristic() == 0) |
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400 | { |
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401 | Variable alpha; |
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402 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
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403 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
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404 | { |
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405 | if (b.getp() != 0) |
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406 | { |
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407 | CanonicalForm mipo= getMipo (alpha); |
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408 | bool is_rat= isOn (SW_RATIONAL); |
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409 | if (!is_rat) |
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410 | On (SW_RATIONAL); |
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411 | mipo *=bCommonDen (mipo); |
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412 | if (!is_rat) |
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413 | Off (SW_RATIONAL); |
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414 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
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415 | fmpz_t FLINTp; |
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416 | fmpz_mod_poly_t FLINTmipo; |
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417 | fq_ctx_t fq_con; |
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418 | fq_poly_t FLINTF, FLINTG; |
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419 | |
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420 | fmpz_init (FLINTp); |
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421 | |
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422 | convertCF2Fmpz (FLINTp, b.getpk()); |
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423 | |
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424 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, mipo, FLINTp); |
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425 | |
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426 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
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427 | |
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428 | convertFacCF2Fq_poly_t (FLINTF, F, fq_con); |
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429 | convertFacCF2Fq_poly_t (FLINTG, G, fq_con); |
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430 | |
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431 | fq_poly_mul (FLINTF, FLINTF, FLINTG, fq_con); |
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432 | |
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433 | CanonicalForm result= convertFq_poly_t2FacCF (FLINTF, F.mvar(), |
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434 | alpha, fq_con); |
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435 | |
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436 | fmpz_clear (FLINTp); |
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437 | fmpz_mod_poly_clear (FLINTmipo); |
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438 | fq_poly_clear (FLINTF, fq_con); |
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439 | fq_poly_clear (FLINTG, fq_con); |
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440 | fq_ctx_clear (fq_con); |
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441 | return b (result); |
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442 | #else |
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443 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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444 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (mipo)); |
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445 | ZZ_pE::init (NTLmipo); |
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446 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
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447 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
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448 | mul (NTLf, NTLf, NTLg); |
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449 | |
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450 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
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451 | #endif |
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452 | } |
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453 | #ifdef HAVE_FLINT |
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454 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
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455 | return result; |
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456 | #else |
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457 | return F*G; |
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458 | #endif |
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459 | } |
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460 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
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461 | { |
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462 | #ifdef HAVE_FLINT |
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463 | if (b.getp() != 0) |
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464 | { |
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465 | fmpz_t FLINTpk; |
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466 | fmpz_init (FLINTpk); |
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467 | convertCF2Fmpz (FLINTpk, b.getpk()); |
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468 | fmpz_mod_poly_t FLINTF, FLINTG; |
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469 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
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470 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
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471 | fmpz_mod_poly_mul (FLINTF, FLINTF, FLINTG); |
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472 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF, F.mvar(),b); |
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473 | fmpz_mod_poly_clear (FLINTG); |
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474 | fmpz_mod_poly_clear (FLINTF); |
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475 | fmpz_clear (FLINTpk); |
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476 | return result; |
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477 | } |
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478 | return mulFLINTQ (F, G); |
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479 | #else |
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480 | if (b.getp() != 0) |
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481 | { |
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482 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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483 | ZZX ZZf= convertFacCF2NTLZZX (F); |
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484 | ZZX ZZg= convertFacCF2NTLZZX (G); |
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485 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
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486 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
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487 | mul (NTLf, NTLf, NTLg); |
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488 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
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489 | } |
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490 | return F*G; |
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491 | #endif |
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492 | } |
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493 | if (b.getp() != 0) |
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494 | { |
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495 | if (!F.inBaseDomain() && !G.inBaseDomain()) |
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496 | { |
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497 | if (hasFirstAlgVar (G, alpha) || hasFirstAlgVar (F, alpha)) |
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498 | { |
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499 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
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500 | fmpz_t FLINTp; |
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501 | fmpz_mod_poly_t FLINTmipo; |
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502 | fq_ctx_t fq_con; |
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503 | |
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504 | fmpz_init (FLINTp); |
---|
505 | convertCF2Fmpz (FLINTp, b.getpk()); |
---|
506 | |
---|
507 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, getMipo (alpha), FLINTp); |
---|
508 | |
---|
509 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
510 | |
---|
511 | CanonicalForm result; |
---|
512 | |
---|
513 | if (F.inCoeffDomain() && !G.inCoeffDomain()) |
---|
514 | { |
---|
515 | fq_poly_t FLINTG; |
---|
516 | fmpz_poly_t FLINTF; |
---|
517 | convertFacCF2Fmpz_poly_t (FLINTF, F); |
---|
518 | convertFacCF2Fq_poly_t (FLINTG, G, fq_con); |
---|
519 | |
---|
520 | fq_poly_scalar_mul_fq (FLINTG, FLINTG, FLINTF, fq_con); |
---|
521 | |
---|
522 | result= convertFq_poly_t2FacCF (FLINTG, G.mvar(), alpha, fq_con); |
---|
523 | fmpz_poly_clear (FLINTF); |
---|
524 | fq_poly_clear (FLINTG, fq_con); |
---|
525 | } |
---|
526 | else if (!F.inCoeffDomain() && G.inCoeffDomain()) |
---|
527 | { |
---|
528 | fq_poly_t FLINTF; |
---|
529 | fmpz_poly_t FLINTG; |
---|
530 | |
---|
531 | convertFacCF2Fmpz_poly_t (FLINTG, G); |
---|
532 | convertFacCF2Fq_poly_t (FLINTF, F, fq_con); |
---|
533 | |
---|
534 | fq_poly_scalar_mul_fq (FLINTF, FLINTF, FLINTG, fq_con); |
---|
535 | |
---|
536 | result= convertFq_poly_t2FacCF (FLINTF, F.mvar(), alpha, fq_con); |
---|
537 | fmpz_poly_clear (FLINTG); |
---|
538 | fq_poly_clear (FLINTF, fq_con); |
---|
539 | } |
---|
540 | else |
---|
541 | { |
---|
542 | fq_t FLINTF, FLINTG; |
---|
543 | |
---|
544 | convertFacCF2Fq_t (FLINTF, F, fq_con); |
---|
545 | convertFacCF2Fq_t (FLINTG, G, fq_con); |
---|
546 | |
---|
547 | fq_mul (FLINTF, FLINTF, FLINTG, fq_con); |
---|
548 | |
---|
549 | result= convertFq_t2FacCF (FLINTF, alpha); |
---|
550 | fq_clear (FLINTF, fq_con); |
---|
551 | fq_clear (FLINTG, fq_con); |
---|
552 | } |
---|
553 | |
---|
554 | fmpz_clear (FLINTp); |
---|
555 | fmpz_mod_poly_clear (FLINTmipo); |
---|
556 | fq_ctx_clear (fq_con); |
---|
557 | |
---|
558 | return b (result); |
---|
559 | #else |
---|
560 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
561 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
562 | ZZ_pE::init (NTLmipo); |
---|
563 | |
---|
564 | if (F.inCoeffDomain() && !G.inCoeffDomain()) |
---|
565 | { |
---|
566 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
567 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
568 | mul (NTLg, to_ZZ_pE (NTLf), NTLg); |
---|
569 | return b (convertNTLZZ_pEX2CF (NTLg, G.mvar(), alpha)); |
---|
570 | } |
---|
571 | else if (!F.inCoeffDomain() && G.inCoeffDomain()) |
---|
572 | { |
---|
573 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
574 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
575 | mul (NTLf, NTLf, to_ZZ_pE (NTLg)); |
---|
576 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
577 | } |
---|
578 | else |
---|
579 | { |
---|
580 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
581 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
582 | ZZ_pE result; |
---|
583 | mul (result, to_ZZ_pE (NTLg), to_ZZ_pE (NTLf)); |
---|
584 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
---|
585 | } |
---|
586 | #endif |
---|
587 | } |
---|
588 | } |
---|
589 | return b (F*G); |
---|
590 | } |
---|
591 | return F*G; |
---|
592 | } |
---|
593 | else if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
594 | return F*G; |
---|
595 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
596 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
597 | if (fac_NTL_char != getCharacteristic()) |
---|
598 | { |
---|
599 | fac_NTL_char= getCharacteristic(); |
---|
600 | zz_p::init (getCharacteristic()); |
---|
601 | } |
---|
602 | Variable alpha; |
---|
603 | CanonicalForm result; |
---|
604 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
605 | { |
---|
606 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
607 | nmod_poly_t FLINTmipo; |
---|
608 | fq_nmod_ctx_t fq_con; |
---|
609 | |
---|
610 | nmod_poly_init (FLINTmipo, getCharacteristic()); |
---|
611 | convertFacCF2nmod_poly_t (FLINTmipo, getMipo (alpha)); |
---|
612 | |
---|
613 | fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
614 | |
---|
615 | fq_nmod_poly_t FLINTF, FLINTG; |
---|
616 | convertFacCF2Fq_nmod_poly_t (FLINTF, F, fq_con); |
---|
617 | convertFacCF2Fq_nmod_poly_t (FLINTG, G, fq_con); |
---|
618 | |
---|
619 | fq_nmod_poly_mul (FLINTF, FLINTF, FLINTG, fq_con); |
---|
620 | |
---|
621 | result= convertFq_nmod_poly_t2FacCF (FLINTF, F.mvar(), alpha, fq_con); |
---|
622 | |
---|
623 | fq_nmod_poly_clear (FLINTF, fq_con); |
---|
624 | fq_nmod_poly_clear (FLINTG, fq_con); |
---|
625 | nmod_poly_clear (FLINTmipo); |
---|
626 | fq_nmod_ctx_clear (fq_con); |
---|
627 | #else |
---|
628 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
629 | zz_pE::init (NTLMipo); |
---|
630 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
631 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
632 | mul (NTLF, NTLF, NTLG); |
---|
633 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
634 | #endif |
---|
635 | } |
---|
636 | else |
---|
637 | { |
---|
638 | #ifdef HAVE_FLINT |
---|
639 | nmod_poly_t FLINTF, FLINTG; |
---|
640 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
641 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
642 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
---|
643 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
644 | nmod_poly_clear (FLINTF); |
---|
645 | nmod_poly_clear (FLINTG); |
---|
646 | #else |
---|
647 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
648 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
649 | mul (NTLF, NTLF, NTLG); |
---|
650 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
651 | #endif |
---|
652 | } |
---|
653 | return result; |
---|
654 | } |
---|
655 | |
---|
656 | CanonicalForm |
---|
657 | modNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
658 | { |
---|
659 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
660 | return mod (F, G); |
---|
661 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
662 | { |
---|
663 | if (b.getp() != 0) |
---|
664 | return b(F); |
---|
665 | return F; |
---|
666 | } |
---|
667 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
668 | { |
---|
669 | if (b.getp() != 0) |
---|
670 | return b(F%G); |
---|
671 | return mod (F, G); |
---|
672 | } |
---|
673 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
674 | { |
---|
675 | if (b.getp() != 0) |
---|
676 | return b(F%G); |
---|
677 | return mod (F,G); |
---|
678 | } |
---|
679 | |
---|
680 | if (getCharacteristic() == 0) |
---|
681 | { |
---|
682 | Variable alpha; |
---|
683 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
684 | { |
---|
685 | #ifdef HAVE_FLINT |
---|
686 | if (b.getp() != 0) |
---|
687 | { |
---|
688 | fmpz_t FLINTpk; |
---|
689 | fmpz_init (FLINTpk); |
---|
690 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
691 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
692 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
693 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
694 | fmpz_mod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
695 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
696 | fmpz_mod_poly_clear (FLINTG); |
---|
697 | fmpz_mod_poly_clear (FLINTF); |
---|
698 | fmpz_clear (FLINTpk); |
---|
699 | return result; |
---|
700 | } |
---|
701 | return modFLINTQ (F, G); |
---|
702 | #else |
---|
703 | if (b.getp() != 0) |
---|
704 | { |
---|
705 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
706 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
707 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
708 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
709 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
710 | rem (NTLf, NTLf, NTLg); |
---|
711 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
712 | } |
---|
713 | return mod (F, G); |
---|
714 | #endif |
---|
715 | } |
---|
716 | else |
---|
717 | { |
---|
718 | if (b.getp() != 0) |
---|
719 | { |
---|
720 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
721 | fmpz_t FLINTp; |
---|
722 | fmpz_mod_poly_t FLINTmipo; |
---|
723 | fq_ctx_t fq_con; |
---|
724 | fq_poly_t FLINTF, FLINTG; |
---|
725 | |
---|
726 | fmpz_init (FLINTp); |
---|
727 | |
---|
728 | convertCF2Fmpz (FLINTp, b.getpk()); |
---|
729 | |
---|
730 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, getMipo (alpha), FLINTp); |
---|
731 | |
---|
732 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
733 | |
---|
734 | convertFacCF2Fq_poly_t (FLINTF, F, fq_con); |
---|
735 | convertFacCF2Fq_poly_t (FLINTG, G, fq_con); |
---|
736 | |
---|
737 | fq_poly_rem (FLINTF, FLINTF, FLINTG, fq_con); |
---|
738 | |
---|
739 | CanonicalForm result= convertFq_poly_t2FacCF (FLINTF, F.mvar(), |
---|
740 | alpha, fq_con); |
---|
741 | |
---|
742 | fmpz_clear (FLINTp); |
---|
743 | fmpz_mod_poly_clear (FLINTmipo); |
---|
744 | fq_poly_clear (FLINTF, fq_con); |
---|
745 | fq_poly_clear (FLINTG, fq_con); |
---|
746 | fq_ctx_clear (fq_con); |
---|
747 | |
---|
748 | return b(result); |
---|
749 | #else |
---|
750 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
751 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
752 | ZZ_pE::init (NTLmipo); |
---|
753 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
754 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
755 | rem (NTLf, NTLf, NTLg); |
---|
756 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
757 | #endif |
---|
758 | } |
---|
759 | #ifdef HAVE_FLINT |
---|
760 | CanonicalForm Q, R; |
---|
761 | newtonDivrem (F, G, Q, R); |
---|
762 | return R; |
---|
763 | #else |
---|
764 | return mod (F,G); |
---|
765 | #endif |
---|
766 | } |
---|
767 | } |
---|
768 | |
---|
769 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
770 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
771 | if (fac_NTL_char != getCharacteristic()) |
---|
772 | { |
---|
773 | fac_NTL_char= getCharacteristic(); |
---|
774 | zz_p::init (getCharacteristic()); |
---|
775 | } |
---|
776 | Variable alpha; |
---|
777 | CanonicalForm result; |
---|
778 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
779 | { |
---|
780 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
781 | nmod_poly_t FLINTmipo; |
---|
782 | fq_nmod_ctx_t fq_con; |
---|
783 | |
---|
784 | nmod_poly_init (FLINTmipo, getCharacteristic()); |
---|
785 | convertFacCF2nmod_poly_t (FLINTmipo, getMipo (alpha)); |
---|
786 | |
---|
787 | fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
788 | |
---|
789 | fq_nmod_poly_t FLINTF, FLINTG; |
---|
790 | convertFacCF2Fq_nmod_poly_t (FLINTF, F, fq_con); |
---|
791 | convertFacCF2Fq_nmod_poly_t (FLINTG, G, fq_con); |
---|
792 | |
---|
793 | fq_nmod_poly_rem (FLINTF, FLINTF, FLINTG, fq_con); |
---|
794 | |
---|
795 | result= convertFq_nmod_poly_t2FacCF (FLINTF, F.mvar(), alpha, fq_con); |
---|
796 | |
---|
797 | fq_nmod_poly_clear (FLINTF, fq_con); |
---|
798 | fq_nmod_poly_clear (FLINTG, fq_con); |
---|
799 | nmod_poly_clear (FLINTmipo); |
---|
800 | fq_nmod_ctx_clear (fq_con); |
---|
801 | #else |
---|
802 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
803 | zz_pE::init (NTLMipo); |
---|
804 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
805 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
806 | rem (NTLF, NTLF, NTLG); |
---|
807 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
808 | #endif |
---|
809 | } |
---|
810 | else |
---|
811 | { |
---|
812 | #ifdef HAVE_FLINT |
---|
813 | nmod_poly_t FLINTF, FLINTG; |
---|
814 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
815 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
816 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
817 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
818 | nmod_poly_clear (FLINTF); |
---|
819 | nmod_poly_clear (FLINTG); |
---|
820 | #else |
---|
821 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
822 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
823 | rem (NTLF, NTLF, NTLG); |
---|
824 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
825 | #endif |
---|
826 | } |
---|
827 | return result; |
---|
828 | } |
---|
829 | |
---|
830 | CanonicalForm |
---|
831 | divNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
832 | { |
---|
833 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
834 | return div (F, G); |
---|
835 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
836 | { |
---|
837 | return 0; |
---|
838 | } |
---|
839 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
840 | { |
---|
841 | if (b.getp() != 0) |
---|
842 | { |
---|
843 | if (!F.inBaseDomain() || !G.inBaseDomain()) |
---|
844 | { |
---|
845 | Variable alpha; |
---|
846 | hasFirstAlgVar (F, alpha); |
---|
847 | hasFirstAlgVar (G, alpha); |
---|
848 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
849 | fmpz_t FLINTp; |
---|
850 | fmpz_mod_poly_t FLINTmipo; |
---|
851 | fq_ctx_t fq_con; |
---|
852 | fq_t FLINTF, FLINTG; |
---|
853 | |
---|
854 | fmpz_init (FLINTp); |
---|
855 | convertCF2Fmpz (FLINTp, b.getpk()); |
---|
856 | |
---|
857 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, getMipo (alpha), FLINTp); |
---|
858 | |
---|
859 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
860 | |
---|
861 | convertFacCF2Fq_t (FLINTF, F, fq_con); |
---|
862 | convertFacCF2Fq_t (FLINTG, G, fq_con); |
---|
863 | |
---|
864 | fq_inv (FLINTG, FLINTG, fq_con); |
---|
865 | fq_mul (FLINTF, FLINTF, FLINTG, fq_con); |
---|
866 | |
---|
867 | CanonicalForm result= convertFq_t2FacCF (FLINTF, alpha); |
---|
868 | |
---|
869 | fmpz_clear (FLINTp); |
---|
870 | fmpz_mod_poly_clear (FLINTmipo); |
---|
871 | fq_clear (FLINTF, fq_con); |
---|
872 | fq_clear (FLINTG, fq_con); |
---|
873 | fq_ctx_clear (fq_con); |
---|
874 | return b (result); |
---|
875 | #else |
---|
876 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
877 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
878 | ZZ_pE::init (NTLmipo); |
---|
879 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
880 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
881 | ZZ_pE result; |
---|
882 | div (result, to_ZZ_pE (NTLf), to_ZZ_pE (NTLg)); |
---|
883 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
---|
884 | #endif |
---|
885 | } |
---|
886 | return b(div (F,G)); |
---|
887 | } |
---|
888 | return div (F, G); |
---|
889 | } |
---|
890 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
891 | { |
---|
892 | if (b.getp() != 0) |
---|
893 | { |
---|
894 | if (!G.inBaseDomain()) |
---|
895 | { |
---|
896 | Variable alpha; |
---|
897 | hasFirstAlgVar (G, alpha); |
---|
898 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
899 | fmpz_t FLINTp; |
---|
900 | fmpz_mod_poly_t FLINTmipo; |
---|
901 | fq_ctx_t fq_con; |
---|
902 | fq_poly_t FLINTF; |
---|
903 | fq_t FLINTG; |
---|
904 | |
---|
905 | fmpz_init (FLINTp); |
---|
906 | convertCF2Fmpz (FLINTp, b.getpk()); |
---|
907 | |
---|
908 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, getMipo (alpha), FLINTp); |
---|
909 | |
---|
910 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
911 | |
---|
912 | convertFacCF2Fq_poly_t (FLINTF, F, fq_con); |
---|
913 | convertFacCF2Fq_t (FLINTG, G, fq_con); |
---|
914 | |
---|
915 | fq_inv (FLINTG, FLINTG, fq_con); |
---|
916 | fq_poly_scalar_mul_fq (FLINTF, FLINTF, FLINTG, fq_con); |
---|
917 | |
---|
918 | CanonicalForm result= convertFq_poly_t2FacCF (FLINTF, F.mvar(), |
---|
919 | alpha, fq_con); |
---|
920 | |
---|
921 | fmpz_clear (FLINTp); |
---|
922 | fmpz_mod_poly_clear (FLINTmipo); |
---|
923 | fq_poly_clear (FLINTF, fq_con); |
---|
924 | fq_clear (FLINTG, fq_con); |
---|
925 | fq_ctx_clear (fq_con); |
---|
926 | return b (result); |
---|
927 | #else |
---|
928 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
929 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
930 | ZZ_pE::init (NTLmipo); |
---|
931 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
932 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
933 | div (NTLf, NTLf, to_ZZ_pE (NTLg)); |
---|
934 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
935 | #endif |
---|
936 | } |
---|
937 | return b(div (F,G)); |
---|
938 | } |
---|
939 | return div (F, G); |
---|
940 | } |
---|
941 | |
---|
942 | if (getCharacteristic() == 0) |
---|
943 | { |
---|
944 | |
---|
945 | Variable alpha; |
---|
946 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
947 | { |
---|
948 | #ifdef HAVE_FLINT |
---|
949 | if (b.getp() != 0) |
---|
950 | { |
---|
951 | fmpz_t FLINTpk; |
---|
952 | fmpz_init (FLINTpk); |
---|
953 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
954 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
955 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
956 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
957 | fmpz_mod_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG); |
---|
958 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
959 | fmpz_mod_poly_clear (FLINTG); |
---|
960 | fmpz_mod_poly_clear (FLINTF); |
---|
961 | fmpz_clear (FLINTpk); |
---|
962 | return result; |
---|
963 | } |
---|
964 | return divFLINTQ (F,G); |
---|
965 | #else |
---|
966 | if (b.getp() != 0) |
---|
967 | { |
---|
968 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
969 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
970 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
971 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
972 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
973 | div (NTLf, NTLf, NTLg); |
---|
974 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
975 | } |
---|
976 | return div (F, G); |
---|
977 | #endif |
---|
978 | } |
---|
979 | else |
---|
980 | { |
---|
981 | if (b.getp() != 0) |
---|
982 | { |
---|
983 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
984 | fmpz_t FLINTp; |
---|
985 | fmpz_mod_poly_t FLINTmipo; |
---|
986 | fq_ctx_t fq_con; |
---|
987 | fq_poly_t FLINTF, FLINTG; |
---|
988 | |
---|
989 | fmpz_init (FLINTp); |
---|
990 | convertCF2Fmpz (FLINTp, b.getpk()); |
---|
991 | |
---|
992 | convertFacCF2Fmpz_mod_poly_t (FLINTmipo, getMipo (alpha), FLINTp); |
---|
993 | |
---|
994 | fq_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
995 | |
---|
996 | convertFacCF2Fq_poly_t (FLINTF, F, fq_con); |
---|
997 | convertFacCF2Fq_poly_t (FLINTG, G, fq_con); |
---|
998 | |
---|
999 | fq_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG, fq_con); |
---|
1000 | |
---|
1001 | CanonicalForm result= convertFq_poly_t2FacCF (FLINTF, F.mvar(), |
---|
1002 | alpha, fq_con); |
---|
1003 | |
---|
1004 | fmpz_clear (FLINTp); |
---|
1005 | fmpz_mod_poly_clear (FLINTmipo); |
---|
1006 | fq_ctx_clear (fq_con); |
---|
1007 | fq_poly_clear (FLINTF, fq_con); |
---|
1008 | fq_poly_clear (FLINTG, fq_con); |
---|
1009 | return b (result); |
---|
1010 | #else |
---|
1011 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
1012 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
1013 | ZZ_pE::init (NTLmipo); |
---|
1014 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
1015 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
1016 | div (NTLf, NTLf, NTLg); |
---|
1017 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
1018 | #endif |
---|
1019 | } |
---|
1020 | #ifdef HAVE_FLINT |
---|
1021 | CanonicalForm Q; |
---|
1022 | newtonDiv (F, G, Q); |
---|
1023 | return Q; |
---|
1024 | #else |
---|
1025 | return div (F,G); |
---|
1026 | #endif |
---|
1027 | } |
---|
1028 | } |
---|
1029 | |
---|
1030 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
1031 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
1032 | if (fac_NTL_char != getCharacteristic()) |
---|
1033 | { |
---|
1034 | fac_NTL_char= getCharacteristic(); |
---|
1035 | zz_p::init (getCharacteristic()); |
---|
1036 | } |
---|
1037 | Variable alpha; |
---|
1038 | CanonicalForm result; |
---|
1039 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
1040 | { |
---|
1041 | #if (HAVE_FLINT && __FLINT_VERSION_MINOR >= 4) |
---|
1042 | nmod_poly_t FLINTmipo; |
---|
1043 | fq_nmod_ctx_t fq_con; |
---|
1044 | |
---|
1045 | nmod_poly_init (FLINTmipo, getCharacteristic()); |
---|
1046 | convertFacCF2nmod_poly_t (FLINTmipo, getMipo (alpha)); |
---|
1047 | |
---|
1048 | fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
---|
1049 | |
---|
1050 | fq_nmod_poly_t FLINTF, FLINTG; |
---|
1051 | convertFacCF2Fq_nmod_poly_t (FLINTF, F, fq_con); |
---|
1052 | convertFacCF2Fq_nmod_poly_t (FLINTG, G, fq_con); |
---|
1053 | |
---|
1054 | fq_nmod_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG, fq_con); |
---|
1055 | |
---|
1056 | result= convertFq_nmod_poly_t2FacCF (FLINTF, F.mvar(), alpha, fq_con); |
---|
1057 | |
---|
1058 | fq_nmod_poly_clear (FLINTF, fq_con); |
---|
1059 | fq_nmod_poly_clear (FLINTG, fq_con); |
---|
1060 | nmod_poly_clear (FLINTmipo); |
---|
1061 | fq_nmod_ctx_clear (fq_con); |
---|
1062 | #else |
---|
1063 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
1064 | zz_pE::init (NTLMipo); |
---|
1065 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
1066 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
1067 | div (NTLF, NTLF, NTLG); |
---|
1068 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
1069 | #endif |
---|
1070 | } |
---|
1071 | else |
---|
1072 | { |
---|
1073 | #ifdef HAVE_FLINT |
---|
1074 | nmod_poly_t FLINTF, FLINTG; |
---|
1075 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
1076 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
1077 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
1078 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
1079 | nmod_poly_clear (FLINTF); |
---|
1080 | nmod_poly_clear (FLINTG); |
---|
1081 | #else |
---|
1082 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
1083 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
1084 | div (NTLF, NTLF, NTLG); |
---|
1085 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
1086 | #endif |
---|
1087 | } |
---|
1088 | return result; |
---|
1089 | } |
---|
1090 | |
---|
1091 | // end univariate polys |
---|
1092 | //************************* |
---|
1093 | // bivariate polys |
---|
1094 | |
---|
1095 | #ifdef HAVE_FLINT |
---|
1096 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
1097 | { |
---|
1098 | int degAy= degree (A); |
---|
1099 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
1100 | |
---|
1101 | nmod_poly_t buf; |
---|
1102 | |
---|
1103 | int j, k, bufRepLength; |
---|
1104 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1105 | { |
---|
1106 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
1107 | |
---|
1108 | k= i.exp()*d; |
---|
1109 | bufRepLength= (int) nmod_poly_length (buf); |
---|
1110 | for (j= 0; j < bufRepLength; j++) |
---|
1111 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
1112 | nmod_poly_clear (buf); |
---|
1113 | } |
---|
1114 | _nmod_poly_normalise (result); |
---|
1115 | } |
---|
1116 | |
---|
1117 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
1118 | { |
---|
1119 | int degAy= degree (A); |
---|
1120 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
1121 | |
---|
1122 | fmpq_poly_t buf; |
---|
1123 | fmpq_t coeff; |
---|
1124 | |
---|
1125 | int k, l, bufRepLength; |
---|
1126 | CFIterator j; |
---|
1127 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1128 | { |
---|
1129 | if (i.coeff().inCoeffDomain()) |
---|
1130 | { |
---|
1131 | k= d1*i.exp(); |
---|
1132 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
1133 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
1134 | for (l= 0; l < bufRepLength; l++) |
---|
1135 | { |
---|
1136 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
1137 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
1138 | } |
---|
1139 | fmpq_poly_clear (buf); |
---|
1140 | } |
---|
1141 | else |
---|
1142 | { |
---|
1143 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
1144 | { |
---|
1145 | k= d1*i.exp(); |
---|
1146 | k += d2*j.exp(); |
---|
1147 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
1148 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
1149 | for (l= 0; l < bufRepLength; l++) |
---|
1150 | { |
---|
1151 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
1152 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
1153 | } |
---|
1154 | fmpq_poly_clear (buf); |
---|
1155 | } |
---|
1156 | } |
---|
1157 | } |
---|
1158 | fmpq_clear (coeff); |
---|
1159 | _fmpq_poly_normalise (result); |
---|
1160 | } |
---|
1161 | |
---|
1162 | void |
---|
1163 | kronSubReciproFp (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
1164 | int d) |
---|
1165 | { |
---|
1166 | int degAy= degree (A); |
---|
1167 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1168 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
1169 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
1170 | |
---|
1171 | nmod_poly_t buf; |
---|
1172 | |
---|
1173 | int k, kk, j, bufRepLength; |
---|
1174 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1175 | { |
---|
1176 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
1177 | |
---|
1178 | k= i.exp()*d; |
---|
1179 | kk= (degAy - i.exp())*d; |
---|
1180 | bufRepLength= (int) nmod_poly_length (buf); |
---|
1181 | for (j= 0; j < bufRepLength; j++) |
---|
1182 | { |
---|
1183 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
1184 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
1185 | nmod_poly_get_coeff_ui (buf, j), |
---|
1186 | getCharacteristic() |
---|
1187 | ) |
---|
1188 | ); |
---|
1189 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
1190 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
1191 | nmod_poly_get_coeff_ui (buf, j), |
---|
1192 | getCharacteristic() |
---|
1193 | ) |
---|
1194 | ); |
---|
1195 | } |
---|
1196 | nmod_poly_clear (buf); |
---|
1197 | } |
---|
1198 | _nmod_poly_normalise (subA1); |
---|
1199 | _nmod_poly_normalise (subA2); |
---|
1200 | } |
---|
1201 | |
---|
1202 | void |
---|
1203 | kronSubReciproQ (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
1204 | int d) |
---|
1205 | { |
---|
1206 | int degAy= degree (A); |
---|
1207 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
1208 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
1209 | |
---|
1210 | fmpz_poly_t buf; |
---|
1211 | fmpz_t coeff1, coeff2; |
---|
1212 | |
---|
1213 | int k, kk, j, bufRepLength; |
---|
1214 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1215 | { |
---|
1216 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
1217 | |
---|
1218 | k= i.exp()*d; |
---|
1219 | kk= (degAy - i.exp())*d; |
---|
1220 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
1221 | for (j= 0; j < bufRepLength; j++) |
---|
1222 | { |
---|
1223 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
1224 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
1225 | fmpz_add (coeff1, coeff1, coeff2); |
---|
1226 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
1227 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
1228 | fmpz_add (coeff1, coeff1, coeff2); |
---|
1229 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
1230 | } |
---|
1231 | fmpz_poly_clear (buf); |
---|
1232 | } |
---|
1233 | fmpz_clear (coeff1); |
---|
1234 | fmpz_clear (coeff2); |
---|
1235 | _fmpz_poly_normalise (subA1); |
---|
1236 | _fmpz_poly_normalise (subA2); |
---|
1237 | } |
---|
1238 | |
---|
1239 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
1240 | { |
---|
1241 | Variable y= Variable (2); |
---|
1242 | Variable x= Variable (1); |
---|
1243 | |
---|
1244 | fmpz_poly_t f; |
---|
1245 | fmpz_poly_init (f); |
---|
1246 | fmpz_poly_set (f, F); |
---|
1247 | |
---|
1248 | fmpz_poly_t buf; |
---|
1249 | CanonicalForm result= 0; |
---|
1250 | int i= 0; |
---|
1251 | int degf= fmpz_poly_degree(f); |
---|
1252 | int k= 0; |
---|
1253 | int degfSubK, repLength, j; |
---|
1254 | fmpz_t coeff; |
---|
1255 | while (degf >= k) |
---|
1256 | { |
---|
1257 | degfSubK= degf - k; |
---|
1258 | if (degfSubK >= d) |
---|
1259 | repLength= d; |
---|
1260 | else |
---|
1261 | repLength= degfSubK + 1; |
---|
1262 | |
---|
1263 | fmpz_poly_init2 (buf, repLength); |
---|
1264 | fmpz_init (coeff); |
---|
1265 | for (j= 0; j < repLength; j++) |
---|
1266 | { |
---|
1267 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
1268 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
1269 | } |
---|
1270 | _fmpz_poly_normalise (buf); |
---|
1271 | |
---|
1272 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
1273 | i++; |
---|
1274 | k= d*i; |
---|
1275 | fmpz_poly_clear (buf); |
---|
1276 | fmpz_clear (coeff); |
---|
1277 | } |
---|
1278 | fmpz_poly_clear (f); |
---|
1279 | |
---|
1280 | return result; |
---|
1281 | } |
---|
1282 | |
---|
1283 | CanonicalForm |
---|
1284 | reverseSubstQa (const fmpq_poly_t F, int d1, int d2, const Variable& alpha, |
---|
1285 | const fmpq_poly_t mipo) |
---|
1286 | { |
---|
1287 | Variable y= Variable (2); |
---|
1288 | Variable x= Variable (1); |
---|
1289 | |
---|
1290 | fmpq_poly_t f; |
---|
1291 | fmpq_poly_init (f); |
---|
1292 | fmpq_poly_set (f, F); |
---|
1293 | |
---|
1294 | fmpq_poly_t buf; |
---|
1295 | CanonicalForm result= 0, result2; |
---|
1296 | int i= 0; |
---|
1297 | int degf= fmpq_poly_degree(f); |
---|
1298 | int k= 0; |
---|
1299 | int degfSubK; |
---|
1300 | int repLength; |
---|
1301 | fmpq_t coeff; |
---|
1302 | while (degf >= k) |
---|
1303 | { |
---|
1304 | degfSubK= degf - k; |
---|
1305 | if (degfSubK >= d1) |
---|
1306 | repLength= d1; |
---|
1307 | else |
---|
1308 | repLength= degfSubK + 1; |
---|
1309 | |
---|
1310 | fmpq_init (coeff); |
---|
1311 | int j= 0; |
---|
1312 | int l; |
---|
1313 | result2= 0; |
---|
1314 | while (j*d2 < repLength) |
---|
1315 | { |
---|
1316 | fmpq_poly_init2 (buf, d2); |
---|
1317 | for (l= 0; l < d2; l++) |
---|
1318 | { |
---|
1319 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
1320 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
1321 | } |
---|
1322 | _fmpq_poly_normalise (buf); |
---|
1323 | fmpq_poly_rem (buf, buf, mipo); |
---|
1324 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
1325 | j++; |
---|
1326 | fmpq_poly_clear (buf); |
---|
1327 | } |
---|
1328 | if (repLength - j*d2 != 0 && j*d2 - repLength < d2) |
---|
1329 | { |
---|
1330 | j--; |
---|
1331 | repLength -= j*d2; |
---|
1332 | fmpq_poly_init2 (buf, repLength); |
---|
1333 | j++; |
---|
1334 | for (l= 0; l < repLength; l++) |
---|
1335 | { |
---|
1336 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
1337 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
1338 | } |
---|
1339 | _fmpq_poly_normalise (buf); |
---|
1340 | fmpq_poly_rem (buf, buf, mipo); |
---|
1341 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
1342 | fmpq_poly_clear (buf); |
---|
1343 | } |
---|
1344 | fmpq_clear (coeff); |
---|
1345 | |
---|
1346 | result += result2*power (y, i); |
---|
1347 | i++; |
---|
1348 | k= d1*i; |
---|
1349 | } |
---|
1350 | |
---|
1351 | fmpq_poly_clear (f); |
---|
1352 | return result; |
---|
1353 | } |
---|
1354 | |
---|
1355 | CanonicalForm |
---|
1356 | reverseSubstReciproFp (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
1357 | { |
---|
1358 | Variable y= Variable (2); |
---|
1359 | Variable x= Variable (1); |
---|
1360 | |
---|
1361 | nmod_poly_t f, g; |
---|
1362 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1363 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1364 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
1365 | nmod_poly_set (f, F); |
---|
1366 | nmod_poly_set (g, G); |
---|
1367 | int degf= nmod_poly_degree(f); |
---|
1368 | int degg= nmod_poly_degree(g); |
---|
1369 | |
---|
1370 | |
---|
1371 | nmod_poly_t buf1,buf2, buf3; |
---|
1372 | |
---|
1373 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1374 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
1375 | |
---|
1376 | CanonicalForm result= 0; |
---|
1377 | int i= 0; |
---|
1378 | int lf= 0; |
---|
1379 | int lg= d*k; |
---|
1380 | int degfSubLf= degf; |
---|
1381 | int deggSubLg= degg-lg; |
---|
1382 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1383 | while (degf >= lf || lg >= 0) |
---|
1384 | { |
---|
1385 | if (degfSubLf >= d) |
---|
1386 | repLengthBuf1= d; |
---|
1387 | else if (degfSubLf < 0) |
---|
1388 | repLengthBuf1= 0; |
---|
1389 | else |
---|
1390 | repLengthBuf1= degfSubLf + 1; |
---|
1391 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
1392 | |
---|
1393 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1394 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
1395 | _nmod_poly_normalise (buf1); |
---|
1396 | |
---|
1397 | repLengthBuf1= nmod_poly_length (buf1); |
---|
1398 | |
---|
1399 | if (deggSubLg >= d - 1) |
---|
1400 | repLengthBuf2= d - 1; |
---|
1401 | else if (deggSubLg < 0) |
---|
1402 | repLengthBuf2= 0; |
---|
1403 | else |
---|
1404 | repLengthBuf2= deggSubLg + 1; |
---|
1405 | |
---|
1406 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
1407 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1408 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
1409 | |
---|
1410 | _nmod_poly_normalise (buf2); |
---|
1411 | repLengthBuf2= nmod_poly_length (buf2); |
---|
1412 | |
---|
1413 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
1414 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1415 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
1416 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1417 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
1418 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1419 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
1420 | _nmod_poly_normalise (buf3); |
---|
1421 | |
---|
1422 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1423 | i++; |
---|
1424 | |
---|
1425 | |
---|
1426 | lf= i*d; |
---|
1427 | degfSubLf= degf - lf; |
---|
1428 | |
---|
1429 | lg= d*(k-i); |
---|
1430 | deggSubLg= degg - lg; |
---|
1431 | |
---|
1432 | if (lg >= 0 && deggSubLg > 0) |
---|
1433 | { |
---|
1434 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1435 | degfSubLf= repLengthBuf2 - 1; |
---|
1436 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1437 | for (ind= 0; ind < tmp; ind++) |
---|
1438 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
1439 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
1440 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
1441 | getCharacteristic() |
---|
1442 | ) |
---|
1443 | ); |
---|
1444 | } |
---|
1445 | if (lg < 0) |
---|
1446 | { |
---|
1447 | nmod_poly_clear (buf1); |
---|
1448 | nmod_poly_clear (buf2); |
---|
1449 | nmod_poly_clear (buf3); |
---|
1450 | break; |
---|
1451 | } |
---|
1452 | if (degfSubLf >= 0) |
---|
1453 | { |
---|
1454 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1455 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
1456 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
1457 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
1458 | getCharacteristic() |
---|
1459 | ) |
---|
1460 | ); |
---|
1461 | } |
---|
1462 | nmod_poly_clear (buf1); |
---|
1463 | nmod_poly_clear (buf2); |
---|
1464 | nmod_poly_clear (buf3); |
---|
1465 | } |
---|
1466 | |
---|
1467 | nmod_poly_clear (f); |
---|
1468 | nmod_poly_clear (g); |
---|
1469 | |
---|
1470 | return result; |
---|
1471 | } |
---|
1472 | |
---|
1473 | CanonicalForm |
---|
1474 | reverseSubstReciproQ (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
1475 | { |
---|
1476 | Variable y= Variable (2); |
---|
1477 | Variable x= Variable (1); |
---|
1478 | |
---|
1479 | fmpz_poly_t f, g; |
---|
1480 | fmpz_poly_init (f); |
---|
1481 | fmpz_poly_init (g); |
---|
1482 | fmpz_poly_set (f, F); |
---|
1483 | fmpz_poly_set (g, G); |
---|
1484 | int degf= fmpz_poly_degree(f); |
---|
1485 | int degg= fmpz_poly_degree(g); |
---|
1486 | |
---|
1487 | |
---|
1488 | fmpz_poly_t buf1,buf2, buf3; |
---|
1489 | |
---|
1490 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1491 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
1492 | |
---|
1493 | CanonicalForm result= 0; |
---|
1494 | int i= 0; |
---|
1495 | int lf= 0; |
---|
1496 | int lg= d*k; |
---|
1497 | int degfSubLf= degf; |
---|
1498 | int deggSubLg= degg-lg; |
---|
1499 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1500 | fmpz_t tmp1, tmp2; |
---|
1501 | while (degf >= lf || lg >= 0) |
---|
1502 | { |
---|
1503 | if (degfSubLf >= d) |
---|
1504 | repLengthBuf1= d; |
---|
1505 | else if (degfSubLf < 0) |
---|
1506 | repLengthBuf1= 0; |
---|
1507 | else |
---|
1508 | repLengthBuf1= degfSubLf + 1; |
---|
1509 | |
---|
1510 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
1511 | |
---|
1512 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1513 | { |
---|
1514 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1515 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
1516 | } |
---|
1517 | _fmpz_poly_normalise (buf1); |
---|
1518 | |
---|
1519 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
1520 | |
---|
1521 | if (deggSubLg >= d - 1) |
---|
1522 | repLengthBuf2= d - 1; |
---|
1523 | else if (deggSubLg < 0) |
---|
1524 | repLengthBuf2= 0; |
---|
1525 | else |
---|
1526 | repLengthBuf2= deggSubLg + 1; |
---|
1527 | |
---|
1528 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
1529 | |
---|
1530 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1531 | { |
---|
1532 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1533 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
1534 | } |
---|
1535 | |
---|
1536 | _fmpz_poly_normalise (buf2); |
---|
1537 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
1538 | |
---|
1539 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
1540 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1541 | { |
---|
1542 | fmpz_poly_get_coeff_fmpz (tmp1, buf1, ind); |
---|
1543 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
1544 | } |
---|
1545 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1546 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
1547 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1548 | { |
---|
1549 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
1550 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
1551 | } |
---|
1552 | _fmpz_poly_normalise (buf3); |
---|
1553 | |
---|
1554 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1555 | i++; |
---|
1556 | |
---|
1557 | |
---|
1558 | lf= i*d; |
---|
1559 | degfSubLf= degf - lf; |
---|
1560 | |
---|
1561 | lg= d*(k-i); |
---|
1562 | deggSubLg= degg - lg; |
---|
1563 | |
---|
1564 | if (lg >= 0 && deggSubLg > 0) |
---|
1565 | { |
---|
1566 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1567 | degfSubLf= repLengthBuf2 - 1; |
---|
1568 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1569 | for (ind= 0; ind < tmp; ind++) |
---|
1570 | { |
---|
1571 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1572 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
1573 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1574 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
1575 | } |
---|
1576 | } |
---|
1577 | if (lg < 0) |
---|
1578 | { |
---|
1579 | fmpz_poly_clear (buf1); |
---|
1580 | fmpz_poly_clear (buf2); |
---|
1581 | fmpz_poly_clear (buf3); |
---|
1582 | break; |
---|
1583 | } |
---|
1584 | if (degfSubLf >= 0) |
---|
1585 | { |
---|
1586 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1587 | { |
---|
1588 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1589 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
1590 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1591 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
1592 | } |
---|
1593 | } |
---|
1594 | fmpz_poly_clear (buf1); |
---|
1595 | fmpz_poly_clear (buf2); |
---|
1596 | fmpz_poly_clear (buf3); |
---|
1597 | } |
---|
1598 | |
---|
1599 | fmpz_poly_clear (f); |
---|
1600 | fmpz_poly_clear (g); |
---|
1601 | fmpz_clear (tmp1); |
---|
1602 | fmpz_clear (tmp2); |
---|
1603 | |
---|
1604 | return result; |
---|
1605 | } |
---|
1606 | |
---|
1607 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
1608 | { |
---|
1609 | Variable y= Variable (2); |
---|
1610 | Variable x= Variable (1); |
---|
1611 | |
---|
1612 | nmod_poly_t f; |
---|
1613 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1614 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1615 | nmod_poly_set (f, F); |
---|
1616 | |
---|
1617 | nmod_poly_t buf; |
---|
1618 | CanonicalForm result= 0; |
---|
1619 | int i= 0; |
---|
1620 | int degf= nmod_poly_degree(f); |
---|
1621 | int k= 0; |
---|
1622 | int degfSubK, repLength, j; |
---|
1623 | while (degf >= k) |
---|
1624 | { |
---|
1625 | degfSubK= degf - k; |
---|
1626 | if (degfSubK >= d) |
---|
1627 | repLength= d; |
---|
1628 | else |
---|
1629 | repLength= degfSubK + 1; |
---|
1630 | |
---|
1631 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
1632 | for (j= 0; j < repLength; j++) |
---|
1633 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
1634 | _nmod_poly_normalise (buf); |
---|
1635 | |
---|
1636 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
1637 | i++; |
---|
1638 | k= d*i; |
---|
1639 | nmod_poly_clear (buf); |
---|
1640 | } |
---|
1641 | nmod_poly_clear (f); |
---|
1642 | |
---|
1643 | return result; |
---|
1644 | } |
---|
1645 | |
---|
1646 | CanonicalForm |
---|
1647 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1648 | CanonicalForm& M) |
---|
1649 | { |
---|
1650 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1651 | d1 /= 2; |
---|
1652 | d1 += 1; |
---|
1653 | |
---|
1654 | nmod_poly_t F1, F2; |
---|
1655 | kronSubReciproFp (F1, F2, F, d1); |
---|
1656 | |
---|
1657 | nmod_poly_t G1, G2; |
---|
1658 | kronSubReciproFp (G1, G2, G, d1); |
---|
1659 | |
---|
1660 | int k= d1*degree (M); |
---|
1661 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
1662 | |
---|
1663 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1664 | int degtailG= degree (tailcoeff (G), 1); |
---|
1665 | int taildegF= taildegree (F); |
---|
1666 | int taildegG= taildegree (G); |
---|
1667 | |
---|
1668 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
1669 | + d1*(2+taildegF + taildegG); |
---|
1670 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
1671 | nmod_poly_shift_right (F2, F2, b); |
---|
1672 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
1673 | |
---|
1674 | |
---|
1675 | CanonicalForm result= reverseSubstReciproFp (F1, F2, d1, d2); |
---|
1676 | |
---|
1677 | nmod_poly_clear (F1); |
---|
1678 | nmod_poly_clear (F2); |
---|
1679 | nmod_poly_clear (G1); |
---|
1680 | nmod_poly_clear (G2); |
---|
1681 | return result; |
---|
1682 | } |
---|
1683 | |
---|
1684 | CanonicalForm |
---|
1685 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1686 | CanonicalForm& M) |
---|
1687 | { |
---|
1688 | CanonicalForm A= F; |
---|
1689 | CanonicalForm B= G; |
---|
1690 | |
---|
1691 | int degAx= degree (A, 1); |
---|
1692 | int degAy= degree (A, 2); |
---|
1693 | int degBx= degree (B, 1); |
---|
1694 | int degBy= degree (B, 2); |
---|
1695 | int d1= degAx + 1 + degBx; |
---|
1696 | int d2= tmax (degAy, degBy); |
---|
1697 | |
---|
1698 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
1699 | return mulMod2FLINTFpReci (A, B, M); |
---|
1700 | |
---|
1701 | nmod_poly_t FLINTA, FLINTB; |
---|
1702 | kronSubFp (FLINTA, A, d1); |
---|
1703 | kronSubFp (FLINTB, B, d1); |
---|
1704 | |
---|
1705 | int k= d1*degree (M); |
---|
1706 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1707 | |
---|
1708 | A= reverseSubstFp (FLINTA, d1); |
---|
1709 | |
---|
1710 | nmod_poly_clear (FLINTA); |
---|
1711 | nmod_poly_clear (FLINTB); |
---|
1712 | return A; |
---|
1713 | } |
---|
1714 | |
---|
1715 | CanonicalForm |
---|
1716 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1717 | CanonicalForm& M) |
---|
1718 | { |
---|
1719 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1720 | d1 /= 2; |
---|
1721 | d1 += 1; |
---|
1722 | |
---|
1723 | fmpz_poly_t F1, F2; |
---|
1724 | kronSubReciproQ (F1, F2, F, d1); |
---|
1725 | |
---|
1726 | fmpz_poly_t G1, G2; |
---|
1727 | kronSubReciproQ (G1, G2, G, d1); |
---|
1728 | |
---|
1729 | int k= d1*degree (M); |
---|
1730 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
1731 | |
---|
1732 | int degtailF= degree (tailcoeff (F), 1);; |
---|
1733 | int degtailG= degree (tailcoeff (G), 1); |
---|
1734 | int taildegF= taildegree (F); |
---|
1735 | int taildegG= taildegree (G); |
---|
1736 | |
---|
1737 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
1738 | + d1*(2+taildegF + taildegG); |
---|
1739 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
1740 | fmpz_poly_shift_right (F2, F2, b); |
---|
1741 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
1742 | |
---|
1743 | CanonicalForm result= reverseSubstReciproQ (F1, F2, d1, d2); |
---|
1744 | |
---|
1745 | fmpz_poly_clear (F1); |
---|
1746 | fmpz_poly_clear (F2); |
---|
1747 | fmpz_poly_clear (G1); |
---|
1748 | fmpz_poly_clear (G2); |
---|
1749 | return result; |
---|
1750 | } |
---|
1751 | |
---|
1752 | CanonicalForm |
---|
1753 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1754 | CanonicalForm& M) |
---|
1755 | { |
---|
1756 | CanonicalForm A= F; |
---|
1757 | CanonicalForm B= G; |
---|
1758 | |
---|
1759 | int degAx= degree (A, 1); |
---|
1760 | int degBx= degree (B, 1); |
---|
1761 | int d1= degAx + 1 + degBx; |
---|
1762 | |
---|
1763 | CanonicalForm f= bCommonDen (F); |
---|
1764 | CanonicalForm g= bCommonDen (G); |
---|
1765 | A *= f; |
---|
1766 | B *= g; |
---|
1767 | |
---|
1768 | fmpz_poly_t FLINTA, FLINTB; |
---|
1769 | kronSub (FLINTA, A, d1); |
---|
1770 | kronSub (FLINTB, B, d1); |
---|
1771 | int k= d1*degree (M); |
---|
1772 | |
---|
1773 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
1774 | A= reverseSubstQ (FLINTA, d1); |
---|
1775 | fmpz_poly_clear (FLINTA); |
---|
1776 | fmpz_poly_clear (FLINTB); |
---|
1777 | return A/(f*g); |
---|
1778 | } |
---|
1779 | |
---|
1780 | CanonicalForm |
---|
1781 | mulMod2FLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
---|
1782 | const CanonicalForm& M) |
---|
1783 | { |
---|
1784 | Variable a; |
---|
1785 | if (!hasFirstAlgVar (F,a) && !hasFirstAlgVar (G, a)) |
---|
1786 | return mulMod2FLINTQ (F, G, M); |
---|
1787 | CanonicalForm A= F; |
---|
1788 | |
---|
1789 | int degFx= degree (F, 1); |
---|
1790 | int degFa= degree (F, a); |
---|
1791 | int degGx= degree (G, 1); |
---|
1792 | int degGa= degree (G, a); |
---|
1793 | |
---|
1794 | int d2= degFa+degGa+1; |
---|
1795 | int d1= degFx + 1 + degGx; |
---|
1796 | d1 *= d2; |
---|
1797 | |
---|
1798 | fmpq_poly_t FLINTF, FLINTG; |
---|
1799 | kronSubQa (FLINTF, F, d1, d2); |
---|
1800 | kronSubQa (FLINTG, G, d1, d2); |
---|
1801 | |
---|
1802 | fmpq_poly_mullow (FLINTF, FLINTF, FLINTG, d1*degree (M)); |
---|
1803 | |
---|
1804 | fmpq_poly_t mipo; |
---|
1805 | convertFacCF2Fmpq_poly_t (mipo, getMipo (a)); |
---|
1806 | CanonicalForm result= reverseSubstQa (FLINTF, d1, d2, a, mipo); |
---|
1807 | fmpq_poly_clear (FLINTF); |
---|
1808 | fmpq_poly_clear (FLINTG); |
---|
1809 | return result; |
---|
1810 | } |
---|
1811 | |
---|
1812 | #endif |
---|
1813 | |
---|
1814 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
1815 | { |
---|
1816 | int degAy= degree (A); |
---|
1817 | zz_pX result; |
---|
1818 | result.rep.SetLength (d*(degAy + 1)); |
---|
1819 | |
---|
1820 | zz_p *resultp; |
---|
1821 | resultp= result.rep.elts(); |
---|
1822 | zz_pX buf; |
---|
1823 | zz_p *bufp; |
---|
1824 | int j, k, bufRepLength; |
---|
1825 | |
---|
1826 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1827 | { |
---|
1828 | if (i.coeff().inCoeffDomain()) |
---|
1829 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1830 | else |
---|
1831 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1832 | |
---|
1833 | k= i.exp()*d; |
---|
1834 | bufp= buf.rep.elts(); |
---|
1835 | bufRepLength= (int) buf.rep.length(); |
---|
1836 | for (j= 0; j < bufRepLength; j++) |
---|
1837 | resultp [j + k]= bufp [j]; |
---|
1838 | } |
---|
1839 | result.normalize(); |
---|
1840 | |
---|
1841 | return result; |
---|
1842 | } |
---|
1843 | |
---|
1844 | zz_pEX kronSubFq (const CanonicalForm& A, int d, const Variable& alpha) |
---|
1845 | { |
---|
1846 | int degAy= degree (A); |
---|
1847 | zz_pEX result; |
---|
1848 | result.rep.SetLength (d*(degAy + 1)); |
---|
1849 | |
---|
1850 | Variable v; |
---|
1851 | zz_pE *resultp; |
---|
1852 | resultp= result.rep.elts(); |
---|
1853 | zz_pEX buf1; |
---|
1854 | zz_pE *buf1p; |
---|
1855 | zz_pX buf2; |
---|
1856 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1857 | int j, k, buf1RepLength; |
---|
1858 | |
---|
1859 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1860 | { |
---|
1861 | if (i.coeff().inCoeffDomain()) |
---|
1862 | { |
---|
1863 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1864 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
1865 | } |
---|
1866 | else |
---|
1867 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1868 | |
---|
1869 | k= i.exp()*d; |
---|
1870 | buf1p= buf1.rep.elts(); |
---|
1871 | buf1RepLength= (int) buf1.rep.length(); |
---|
1872 | for (j= 0; j < buf1RepLength; j++) |
---|
1873 | resultp [j + k]= buf1p [j]; |
---|
1874 | } |
---|
1875 | result.normalize(); |
---|
1876 | |
---|
1877 | return result; |
---|
1878 | } |
---|
1879 | |
---|
1880 | void |
---|
1881 | kronSubReciproFq (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
1882 | const Variable& alpha) |
---|
1883 | { |
---|
1884 | int degAy= degree (A); |
---|
1885 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1886 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1887 | |
---|
1888 | Variable v; |
---|
1889 | zz_pE *subA1p; |
---|
1890 | zz_pE *subA2p; |
---|
1891 | subA1p= subA1.rep.elts(); |
---|
1892 | subA2p= subA2.rep.elts(); |
---|
1893 | zz_pEX buf; |
---|
1894 | zz_pE *bufp; |
---|
1895 | zz_pX buf2; |
---|
1896 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1897 | int j, k, kk, bufRepLength; |
---|
1898 | |
---|
1899 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1900 | { |
---|
1901 | if (i.coeff().inCoeffDomain()) |
---|
1902 | { |
---|
1903 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1904 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
1905 | } |
---|
1906 | else |
---|
1907 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1908 | |
---|
1909 | k= i.exp()*d; |
---|
1910 | kk= (degAy - i.exp())*d; |
---|
1911 | bufp= buf.rep.elts(); |
---|
1912 | bufRepLength= (int) buf.rep.length(); |
---|
1913 | for (j= 0; j < bufRepLength; j++) |
---|
1914 | { |
---|
1915 | subA1p [j + k] += bufp [j]; |
---|
1916 | subA2p [j + kk] += bufp [j]; |
---|
1917 | } |
---|
1918 | } |
---|
1919 | subA1.normalize(); |
---|
1920 | subA2.normalize(); |
---|
1921 | } |
---|
1922 | |
---|
1923 | void |
---|
1924 | kronSubReciproFp (zz_pX& subA1, zz_pX& subA2, const CanonicalForm& A, int d) |
---|
1925 | { |
---|
1926 | int degAy= degree (A); |
---|
1927 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1928 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1929 | |
---|
1930 | zz_p *subA1p; |
---|
1931 | zz_p *subA2p; |
---|
1932 | subA1p= subA1.rep.elts(); |
---|
1933 | subA2p= subA2.rep.elts(); |
---|
1934 | zz_pX buf; |
---|
1935 | zz_p *bufp; |
---|
1936 | int j, k, kk, bufRepLength; |
---|
1937 | |
---|
1938 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1939 | { |
---|
1940 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1941 | |
---|
1942 | k= i.exp()*d; |
---|
1943 | kk= (degAy - i.exp())*d; |
---|
1944 | bufp= buf.rep.elts(); |
---|
1945 | bufRepLength= (int) buf.rep.length(); |
---|
1946 | for (j= 0; j < bufRepLength; j++) |
---|
1947 | { |
---|
1948 | subA1p [j + k] += bufp [j]; |
---|
1949 | subA2p [j + kk] += bufp [j]; |
---|
1950 | } |
---|
1951 | } |
---|
1952 | subA1.normalize(); |
---|
1953 | subA2.normalize(); |
---|
1954 | } |
---|
1955 | |
---|
1956 | CanonicalForm |
---|
1957 | reverseSubstReciproFq (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
1958 | const Variable& alpha) |
---|
1959 | { |
---|
1960 | Variable y= Variable (2); |
---|
1961 | Variable x= Variable (1); |
---|
1962 | |
---|
1963 | zz_pEX f= F; |
---|
1964 | zz_pEX g= G; |
---|
1965 | int degf= deg(f); |
---|
1966 | int degg= deg(g); |
---|
1967 | |
---|
1968 | zz_pEX buf1; |
---|
1969 | zz_pEX buf2; |
---|
1970 | zz_pEX buf3; |
---|
1971 | |
---|
1972 | zz_pE *buf1p; |
---|
1973 | zz_pE *buf2p; |
---|
1974 | zz_pE *buf3p; |
---|
1975 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1976 | f.rep.SetLength ((long)d*(k+1)); |
---|
1977 | |
---|
1978 | zz_pE *gp= g.rep.elts(); |
---|
1979 | zz_pE *fp= f.rep.elts(); |
---|
1980 | CanonicalForm result= 0; |
---|
1981 | int i= 0; |
---|
1982 | int lf= 0; |
---|
1983 | int lg= d*k; |
---|
1984 | int degfSubLf= degf; |
---|
1985 | int deggSubLg= degg-lg; |
---|
1986 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1987 | zz_pE zzpEZero= zz_pE(); |
---|
1988 | |
---|
1989 | while (degf >= lf || lg >= 0) |
---|
1990 | { |
---|
1991 | if (degfSubLf >= d) |
---|
1992 | repLengthBuf1= d; |
---|
1993 | else if (degfSubLf < 0) |
---|
1994 | repLengthBuf1= 0; |
---|
1995 | else |
---|
1996 | repLengthBuf1= degfSubLf + 1; |
---|
1997 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1998 | |
---|
1999 | buf1p= buf1.rep.elts(); |
---|
2000 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
2001 | buf1p [ind]= fp [ind + lf]; |
---|
2002 | buf1.normalize(); |
---|
2003 | |
---|
2004 | repLengthBuf1= buf1.rep.length(); |
---|
2005 | |
---|
2006 | if (deggSubLg >= d - 1) |
---|
2007 | repLengthBuf2= d - 1; |
---|
2008 | else if (deggSubLg < 0) |
---|
2009 | repLengthBuf2= 0; |
---|
2010 | else |
---|
2011 | repLengthBuf2= deggSubLg + 1; |
---|
2012 | |
---|
2013 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
2014 | buf2p= buf2.rep.elts(); |
---|
2015 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2016 | buf2p [ind]= gp [ind + lg]; |
---|
2017 | buf2.normalize(); |
---|
2018 | |
---|
2019 | repLengthBuf2= buf2.rep.length(); |
---|
2020 | |
---|
2021 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
2022 | buf3p= buf3.rep.elts(); |
---|
2023 | buf2p= buf2.rep.elts(); |
---|
2024 | buf1p= buf1.rep.elts(); |
---|
2025 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
2026 | buf3p [ind]= buf1p [ind]; |
---|
2027 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
2028 | buf3p [ind]= zzpEZero; |
---|
2029 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2030 | buf3p [ind + d]= buf2p [ind]; |
---|
2031 | buf3.normalize(); |
---|
2032 | |
---|
2033 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
2034 | i++; |
---|
2035 | |
---|
2036 | |
---|
2037 | lf= i*d; |
---|
2038 | degfSubLf= degf - lf; |
---|
2039 | |
---|
2040 | lg= d*(k-i); |
---|
2041 | deggSubLg= degg - lg; |
---|
2042 | |
---|
2043 | buf1p= buf1.rep.elts(); |
---|
2044 | |
---|
2045 | if (lg >= 0 && deggSubLg > 0) |
---|
2046 | { |
---|
2047 | if (repLengthBuf2 > degfSubLf + 1) |
---|
2048 | degfSubLf= repLengthBuf2 - 1; |
---|
2049 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
2050 | for (ind= 0; ind < tmp; ind++) |
---|
2051 | gp [ind + lg] -= buf1p [ind]; |
---|
2052 | } |
---|
2053 | |
---|
2054 | if (lg < 0) |
---|
2055 | break; |
---|
2056 | |
---|
2057 | buf2p= buf2.rep.elts(); |
---|
2058 | if (degfSubLf >= 0) |
---|
2059 | { |
---|
2060 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2061 | fp [ind + lf] -= buf2p [ind]; |
---|
2062 | } |
---|
2063 | } |
---|
2064 | |
---|
2065 | return result; |
---|
2066 | } |
---|
2067 | |
---|
2068 | CanonicalForm |
---|
2069 | reverseSubstReciproFp (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
2070 | { |
---|
2071 | Variable y= Variable (2); |
---|
2072 | Variable x= Variable (1); |
---|
2073 | |
---|
2074 | zz_pX f= F; |
---|
2075 | zz_pX g= G; |
---|
2076 | int degf= deg(f); |
---|
2077 | int degg= deg(g); |
---|
2078 | |
---|
2079 | zz_pX buf1; |
---|
2080 | zz_pX buf2; |
---|
2081 | zz_pX buf3; |
---|
2082 | |
---|
2083 | zz_p *buf1p; |
---|
2084 | zz_p *buf2p; |
---|
2085 | zz_p *buf3p; |
---|
2086 | |
---|
2087 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
2088 | f.rep.SetLength ((long)d*(k+1)); |
---|
2089 | |
---|
2090 | zz_p *gp= g.rep.elts(); |
---|
2091 | zz_p *fp= f.rep.elts(); |
---|
2092 | CanonicalForm result= 0; |
---|
2093 | int i= 0; |
---|
2094 | int lf= 0; |
---|
2095 | int lg= d*k; |
---|
2096 | int degfSubLf= degf; |
---|
2097 | int deggSubLg= degg-lg; |
---|
2098 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
2099 | zz_p zzpZero= zz_p(); |
---|
2100 | while (degf >= lf || lg >= 0) |
---|
2101 | { |
---|
2102 | if (degfSubLf >= d) |
---|
2103 | repLengthBuf1= d; |
---|
2104 | else if (degfSubLf < 0) |
---|
2105 | repLengthBuf1= 0; |
---|
2106 | else |
---|
2107 | repLengthBuf1= degfSubLf + 1; |
---|
2108 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
2109 | |
---|
2110 | buf1p= buf1.rep.elts(); |
---|
2111 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
2112 | buf1p [ind]= fp [ind + lf]; |
---|
2113 | buf1.normalize(); |
---|
2114 | |
---|
2115 | repLengthBuf1= buf1.rep.length(); |
---|
2116 | |
---|
2117 | if (deggSubLg >= d - 1) |
---|
2118 | repLengthBuf2= d - 1; |
---|
2119 | else if (deggSubLg < 0) |
---|
2120 | repLengthBuf2= 0; |
---|
2121 | else |
---|
2122 | repLengthBuf2= deggSubLg + 1; |
---|
2123 | |
---|
2124 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
2125 | buf2p= buf2.rep.elts(); |
---|
2126 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2127 | buf2p [ind]= gp [ind + lg]; |
---|
2128 | |
---|
2129 | buf2.normalize(); |
---|
2130 | |
---|
2131 | repLengthBuf2= buf2.rep.length(); |
---|
2132 | |
---|
2133 | |
---|
2134 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
2135 | buf3p= buf3.rep.elts(); |
---|
2136 | buf2p= buf2.rep.elts(); |
---|
2137 | buf1p= buf1.rep.elts(); |
---|
2138 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
2139 | buf3p [ind]= buf1p [ind]; |
---|
2140 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
2141 | buf3p [ind]= zzpZero; |
---|
2142 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2143 | buf3p [ind + d]= buf2p [ind]; |
---|
2144 | buf3.normalize(); |
---|
2145 | |
---|
2146 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
2147 | i++; |
---|
2148 | |
---|
2149 | |
---|
2150 | lf= i*d; |
---|
2151 | degfSubLf= degf - lf; |
---|
2152 | |
---|
2153 | lg= d*(k-i); |
---|
2154 | deggSubLg= degg - lg; |
---|
2155 | |
---|
2156 | buf1p= buf1.rep.elts(); |
---|
2157 | |
---|
2158 | if (lg >= 0 && deggSubLg > 0) |
---|
2159 | { |
---|
2160 | if (repLengthBuf2 > degfSubLf + 1) |
---|
2161 | degfSubLf= repLengthBuf2 - 1; |
---|
2162 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
2163 | for (ind= 0; ind < tmp; ind++) |
---|
2164 | gp [ind + lg] -= buf1p [ind]; |
---|
2165 | } |
---|
2166 | if (lg < 0) |
---|
2167 | break; |
---|
2168 | |
---|
2169 | buf2p= buf2.rep.elts(); |
---|
2170 | if (degfSubLf >= 0) |
---|
2171 | { |
---|
2172 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
2173 | fp [ind + lf] -= buf2p [ind]; |
---|
2174 | } |
---|
2175 | } |
---|
2176 | |
---|
2177 | return result; |
---|
2178 | } |
---|
2179 | |
---|
2180 | CanonicalForm reverseSubstFq (const zz_pEX& F, int d, const Variable& alpha) |
---|
2181 | { |
---|
2182 | Variable y= Variable (2); |
---|
2183 | Variable x= Variable (1); |
---|
2184 | |
---|
2185 | zz_pEX f= F; |
---|
2186 | zz_pE *fp= f.rep.elts(); |
---|
2187 | |
---|
2188 | zz_pEX buf; |
---|
2189 | zz_pE *bufp; |
---|
2190 | CanonicalForm result= 0; |
---|
2191 | int i= 0; |
---|
2192 | int degf= deg(f); |
---|
2193 | int k= 0; |
---|
2194 | int degfSubK, repLength, j; |
---|
2195 | while (degf >= k) |
---|
2196 | { |
---|
2197 | degfSubK= degf - k; |
---|
2198 | if (degfSubK >= d) |
---|
2199 | repLength= d; |
---|
2200 | else |
---|
2201 | repLength= degfSubK + 1; |
---|
2202 | |
---|
2203 | buf.rep.SetLength ((long) repLength); |
---|
2204 | bufp= buf.rep.elts(); |
---|
2205 | for (j= 0; j < repLength; j++) |
---|
2206 | bufp [j]= fp [j + k]; |
---|
2207 | buf.normalize(); |
---|
2208 | |
---|
2209 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
2210 | i++; |
---|
2211 | k= d*i; |
---|
2212 | } |
---|
2213 | |
---|
2214 | return result; |
---|
2215 | } |
---|
2216 | |
---|
2217 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
2218 | { |
---|
2219 | Variable y= Variable (2); |
---|
2220 | Variable x= Variable (1); |
---|
2221 | |
---|
2222 | zz_pX f= F; |
---|
2223 | zz_p *fp= f.rep.elts(); |
---|
2224 | |
---|
2225 | zz_pX buf; |
---|
2226 | zz_p *bufp; |
---|
2227 | CanonicalForm result= 0; |
---|
2228 | int i= 0; |
---|
2229 | int degf= deg(f); |
---|
2230 | int k= 0; |
---|
2231 | int degfSubK, repLength, j; |
---|
2232 | while (degf >= k) |
---|
2233 | { |
---|
2234 | degfSubK= degf - k; |
---|
2235 | if (degfSubK >= d) |
---|
2236 | repLength= d; |
---|
2237 | else |
---|
2238 | repLength= degfSubK + 1; |
---|
2239 | |
---|
2240 | buf.rep.SetLength ((long) repLength); |
---|
2241 | bufp= buf.rep.elts(); |
---|
2242 | for (j= 0; j < repLength; j++) |
---|
2243 | bufp [j]= fp [j + k]; |
---|
2244 | buf.normalize(); |
---|
2245 | |
---|
2246 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
2247 | i++; |
---|
2248 | k= d*i; |
---|
2249 | } |
---|
2250 | |
---|
2251 | return result; |
---|
2252 | } |
---|
2253 | |
---|
2254 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
2255 | CanonicalForm |
---|
2256 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2257 | CanonicalForm& M) |
---|
2258 | { |
---|
2259 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
2260 | d1 /= 2; |
---|
2261 | d1 += 1; |
---|
2262 | |
---|
2263 | zz_pX F1, F2; |
---|
2264 | kronSubReciproFp (F1, F2, F, d1); |
---|
2265 | zz_pX G1, G2; |
---|
2266 | kronSubReciproFp (G1, G2, G, d1); |
---|
2267 | |
---|
2268 | int k= d1*degree (M); |
---|
2269 | MulTrunc (F1, F1, G1, (long) k); |
---|
2270 | |
---|
2271 | int degtailF= degree (tailcoeff (F), 1); |
---|
2272 | int degtailG= degree (tailcoeff (G), 1); |
---|
2273 | int taildegF= taildegree (F); |
---|
2274 | int taildegG= taildegree (G); |
---|
2275 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
2276 | |
---|
2277 | reverse (F2, F2); |
---|
2278 | reverse (G2, G2); |
---|
2279 | MulTrunc (F2, F2, G2, b + 1); |
---|
2280 | reverse (F2, F2, b); |
---|
2281 | |
---|
2282 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
2283 | return reverseSubstReciproFp (F1, F2, d1, d2); |
---|
2284 | } |
---|
2285 | |
---|
2286 | //Kronecker substitution |
---|
2287 | CanonicalForm |
---|
2288 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2289 | CanonicalForm& M) |
---|
2290 | { |
---|
2291 | CanonicalForm A= F; |
---|
2292 | CanonicalForm B= G; |
---|
2293 | |
---|
2294 | int degAx= degree (A, 1); |
---|
2295 | int degAy= degree (A, 2); |
---|
2296 | int degBx= degree (B, 1); |
---|
2297 | int degBy= degree (B, 2); |
---|
2298 | int d1= degAx + 1 + degBx; |
---|
2299 | int d2= tmax (degAy, degBy); |
---|
2300 | |
---|
2301 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
2302 | return mulMod2NTLFpReci (A, B, M); |
---|
2303 | |
---|
2304 | zz_pX NTLA= kronSubFp (A, d1); |
---|
2305 | zz_pX NTLB= kronSubFp (B, d1); |
---|
2306 | |
---|
2307 | int k= d1*degree (M); |
---|
2308 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
2309 | |
---|
2310 | A= reverseSubstFp (NTLA, d1); |
---|
2311 | |
---|
2312 | return A; |
---|
2313 | } |
---|
2314 | |
---|
2315 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
2316 | CanonicalForm |
---|
2317 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2318 | CanonicalForm& M, const Variable& alpha) |
---|
2319 | { |
---|
2320 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
2321 | d1 /= 2; |
---|
2322 | d1 += 1; |
---|
2323 | |
---|
2324 | zz_pEX F1, F2; |
---|
2325 | kronSubReciproFq (F1, F2, F, d1, alpha); |
---|
2326 | zz_pEX G1, G2; |
---|
2327 | kronSubReciproFq (G1, G2, G, d1, alpha); |
---|
2328 | |
---|
2329 | int k= d1*degree (M); |
---|
2330 | MulTrunc (F1, F1, G1, (long) k); |
---|
2331 | |
---|
2332 | int degtailF= degree (tailcoeff (F), 1); |
---|
2333 | int degtailG= degree (tailcoeff (G), 1); |
---|
2334 | int taildegF= taildegree (F); |
---|
2335 | int taildegG= taildegree (G); |
---|
2336 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
2337 | |
---|
2338 | reverse (F2, F2); |
---|
2339 | reverse (G2, G2); |
---|
2340 | MulTrunc (F2, F2, G2, b + 1); |
---|
2341 | reverse (F2, F2, b); |
---|
2342 | |
---|
2343 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
2344 | return reverseSubstReciproFq (F1, F2, d1, d2, alpha); |
---|
2345 | } |
---|
2346 | |
---|
2347 | #ifdef HAVE_FLINT |
---|
2348 | CanonicalForm |
---|
2349 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2350 | CanonicalForm& M); |
---|
2351 | #endif |
---|
2352 | |
---|
2353 | CanonicalForm |
---|
2354 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2355 | CanonicalForm& M) |
---|
2356 | { |
---|
2357 | Variable alpha; |
---|
2358 | CanonicalForm A= F; |
---|
2359 | CanonicalForm B= G; |
---|
2360 | |
---|
2361 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
2362 | { |
---|
2363 | int degAx= degree (A, 1); |
---|
2364 | int degAy= degree (A, 2); |
---|
2365 | int degBx= degree (B, 1); |
---|
2366 | int degBy= degree (B, 2); |
---|
2367 | int d1= degAx + degBx + 1; |
---|
2368 | int d2= tmax (degAy, degBy); |
---|
2369 | if (fac_NTL_char != getCharacteristic()) |
---|
2370 | { |
---|
2371 | fac_NTL_char= getCharacteristic(); |
---|
2372 | zz_p::init (getCharacteristic()); |
---|
2373 | } |
---|
2374 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2375 | zz_pE::init (NTLMipo); |
---|
2376 | |
---|
2377 | int degMipo= degree (getMipo (alpha)); |
---|
2378 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
2379 | (2*degAy > degree (M))) |
---|
2380 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
2381 | |
---|
2382 | zz_pEX NTLA= kronSubFq (A, d1, alpha); |
---|
2383 | zz_pEX NTLB= kronSubFq (B, d1, alpha); |
---|
2384 | |
---|
2385 | int k= d1*degree (M); |
---|
2386 | |
---|
2387 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
2388 | |
---|
2389 | A= reverseSubstFq (NTLA, d1, alpha); |
---|
2390 | |
---|
2391 | return A; |
---|
2392 | } |
---|
2393 | else |
---|
2394 | #ifdef HAVE_FLINT |
---|
2395 | return mulMod2FLINTFp (A, B, M); |
---|
2396 | #else |
---|
2397 | return mulMod2NTLFp (A, B, M); |
---|
2398 | #endif |
---|
2399 | } |
---|
2400 | |
---|
2401 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
2402 | const CanonicalForm& M) |
---|
2403 | { |
---|
2404 | if (A.isZero() || B.isZero()) |
---|
2405 | return 0; |
---|
2406 | |
---|
2407 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
2408 | |
---|
2409 | CanonicalForm F= mod (A, M); |
---|
2410 | CanonicalForm G= mod (B, M); |
---|
2411 | if (F.inCoeffDomain()) |
---|
2412 | return G*F; |
---|
2413 | if (G.inCoeffDomain()) |
---|
2414 | return F*G; |
---|
2415 | |
---|
2416 | Variable y= M.mvar(); |
---|
2417 | int degF= degree (F, y); |
---|
2418 | int degG= degree (G, y); |
---|
2419 | |
---|
2420 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
2421 | (F.level() == G.level())) |
---|
2422 | { |
---|
2423 | CanonicalForm result= mulNTL (F, G); |
---|
2424 | return mod (result, M); |
---|
2425 | } |
---|
2426 | else if (degF <= 1 && degG <= 1) |
---|
2427 | { |
---|
2428 | CanonicalForm result= F*G; |
---|
2429 | return mod (result, M); |
---|
2430 | } |
---|
2431 | |
---|
2432 | int sizeF= size (F); |
---|
2433 | int sizeG= size (G); |
---|
2434 | |
---|
2435 | int fallBackToNaive= 50; |
---|
2436 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
2437 | { |
---|
2438 | if (sizeF < sizeG) |
---|
2439 | return mod (G*F, M); |
---|
2440 | else |
---|
2441 | return mod (F*G, M); |
---|
2442 | } |
---|
2443 | |
---|
2444 | #ifdef HAVE_FLINT |
---|
2445 | if (getCharacteristic() == 0) |
---|
2446 | return mulMod2FLINTQa (F, G, M); |
---|
2447 | #endif |
---|
2448 | |
---|
2449 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
2450 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
2451 | return mulMod2NTLFq (F, G, M); |
---|
2452 | |
---|
2453 | int m= (int) ceil (degree (M)/2.0); |
---|
2454 | if (degF >= m || degG >= m) |
---|
2455 | { |
---|
2456 | CanonicalForm MLo= power (y, m); |
---|
2457 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2458 | CanonicalForm F0= mod (F, MLo); |
---|
2459 | CanonicalForm F1= div (F, MLo); |
---|
2460 | CanonicalForm G0= mod (G, MLo); |
---|
2461 | CanonicalForm G1= div (G, MLo); |
---|
2462 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
2463 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
2464 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
2465 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2466 | } |
---|
2467 | else |
---|
2468 | { |
---|
2469 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2470 | CanonicalForm yToM= power (y, m); |
---|
2471 | CanonicalForm F0= mod (F, yToM); |
---|
2472 | CanonicalForm F1= div (F, yToM); |
---|
2473 | CanonicalForm G0= mod (G, yToM); |
---|
2474 | CanonicalForm G1= div (G, yToM); |
---|
2475 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
2476 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
2477 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
2478 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2479 | } |
---|
2480 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
2481 | } |
---|
2482 | |
---|
2483 | // end bivariate polys |
---|
2484 | //********************** |
---|
2485 | // multivariate polys |
---|
2486 | |
---|
2487 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
2488 | { |
---|
2489 | CanonicalForm A= F; |
---|
2490 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
2491 | A= mod (A, i.getItem()); |
---|
2492 | return A; |
---|
2493 | } |
---|
2494 | |
---|
2495 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
2496 | const CFList& MOD) |
---|
2497 | { |
---|
2498 | if (A.isZero() || B.isZero()) |
---|
2499 | return 0; |
---|
2500 | |
---|
2501 | if (MOD.length() == 1) |
---|
2502 | return mulMod2 (A, B, MOD.getLast()); |
---|
2503 | |
---|
2504 | CanonicalForm M= MOD.getLast(); |
---|
2505 | CanonicalForm F= mod (A, M); |
---|
2506 | CanonicalForm G= mod (B, M); |
---|
2507 | if (F.inCoeffDomain()) |
---|
2508 | return G*F; |
---|
2509 | if (G.inCoeffDomain()) |
---|
2510 | return F*G; |
---|
2511 | |
---|
2512 | int sizeF= size (F); |
---|
2513 | int sizeG= size (G); |
---|
2514 | |
---|
2515 | if (sizeF / MOD.length() < 100 || sizeG / MOD.length() < 100) |
---|
2516 | { |
---|
2517 | if (sizeF < sizeG) |
---|
2518 | return mod (G*F, MOD); |
---|
2519 | else |
---|
2520 | return mod (F*G, MOD); |
---|
2521 | } |
---|
2522 | |
---|
2523 | Variable y= M.mvar(); |
---|
2524 | int degF= degree (F, y); |
---|
2525 | int degG= degree (G, y); |
---|
2526 | |
---|
2527 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
2528 | (degG <= 1 && G.level() <= M.level())) |
---|
2529 | { |
---|
2530 | CFList buf= MOD; |
---|
2531 | buf.removeLast(); |
---|
2532 | if (degF == 1 && degG == 1) |
---|
2533 | { |
---|
2534 | CanonicalForm F0= mod (F, y); |
---|
2535 | CanonicalForm F1= div (F, y); |
---|
2536 | CanonicalForm G0= mod (G, y); |
---|
2537 | CanonicalForm G1= div (G, y); |
---|
2538 | if (degree (M) > 2) |
---|
2539 | { |
---|
2540 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
2541 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
2542 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
2543 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
2544 | } |
---|
2545 | else //here degree (M) == 2 |
---|
2546 | { |
---|
2547 | buf.append (y); |
---|
2548 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2549 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2550 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2551 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
2552 | return result; |
---|
2553 | } |
---|
2554 | } |
---|
2555 | else if (degF == 1 && degG == 0) |
---|
2556 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
2557 | else if (degF == 0 && degG == 1) |
---|
2558 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
2559 | else |
---|
2560 | return mulMod (F, G, buf); |
---|
2561 | } |
---|
2562 | int m= (int) ceil (degree (M)/2.0); |
---|
2563 | if (degF >= m || degG >= m) |
---|
2564 | { |
---|
2565 | CanonicalForm MLo= power (y, m); |
---|
2566 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2567 | CanonicalForm F0= mod (F, MLo); |
---|
2568 | CanonicalForm F1= div (F, MLo); |
---|
2569 | CanonicalForm G0= mod (G, MLo); |
---|
2570 | CanonicalForm G1= div (G, MLo); |
---|
2571 | CFList buf= MOD; |
---|
2572 | buf.removeLast(); |
---|
2573 | buf.append (MHi); |
---|
2574 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2575 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2576 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2577 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2578 | } |
---|
2579 | else |
---|
2580 | { |
---|
2581 | m= (int) ceil (tmin (degF, degG)/2.0); |
---|
2582 | CanonicalForm yToM= power (y, m); |
---|
2583 | CanonicalForm F0= mod (F, yToM); |
---|
2584 | CanonicalForm F1= div (F, yToM); |
---|
2585 | CanonicalForm G0= mod (G, yToM); |
---|
2586 | CanonicalForm G1= div (G, yToM); |
---|
2587 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
2588 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
2589 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
2590 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2591 | } |
---|
2592 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
2593 | } |
---|
2594 | |
---|
2595 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
2596 | { |
---|
2597 | if (L.isEmpty()) |
---|
2598 | return 1; |
---|
2599 | int l= L.length(); |
---|
2600 | if (l == 1) |
---|
2601 | return mod (L.getFirst(), M); |
---|
2602 | else if (l == 2) { |
---|
2603 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
2604 | return result; |
---|
2605 | } |
---|
2606 | else |
---|
2607 | { |
---|
2608 | l /= 2; |
---|
2609 | CFList tmp1, tmp2; |
---|
2610 | CFListIterator i= L; |
---|
2611 | CanonicalForm buf1, buf2; |
---|
2612 | for (int j= 1; j <= l; j++, i++) |
---|
2613 | tmp1.append (i.getItem()); |
---|
2614 | tmp2= Difference (L, tmp1); |
---|
2615 | buf1= prodMod (tmp1, M); |
---|
2616 | buf2= prodMod (tmp2, M); |
---|
2617 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
2618 | return result; |
---|
2619 | } |
---|
2620 | } |
---|
2621 | |
---|
2622 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
2623 | { |
---|
2624 | if (L.isEmpty()) |
---|
2625 | return 1; |
---|
2626 | else if (L.length() == 1) |
---|
2627 | return L.getFirst(); |
---|
2628 | else if (L.length() == 2) |
---|
2629 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
2630 | else |
---|
2631 | { |
---|
2632 | int l= L.length()/2; |
---|
2633 | CFListIterator i= L; |
---|
2634 | CFList tmp1, tmp2; |
---|
2635 | CanonicalForm buf1, buf2; |
---|
2636 | for (int j= 1; j <= l; j++, i++) |
---|
2637 | tmp1.append (i.getItem()); |
---|
2638 | tmp2= Difference (L, tmp1); |
---|
2639 | buf1= prodMod (tmp1, M); |
---|
2640 | buf2= prodMod (tmp2, M); |
---|
2641 | return mulMod (buf1, buf2, M); |
---|
2642 | } |
---|
2643 | } |
---|
2644 | |
---|
2645 | // end multivariate polys |
---|
2646 | //*************************** |
---|
2647 | // division |
---|
2648 | |
---|
2649 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
2650 | { |
---|
2651 | if (d == 0) |
---|
2652 | return F; |
---|
2653 | CanonicalForm A= F; |
---|
2654 | Variable y= Variable (2); |
---|
2655 | Variable x= Variable (1); |
---|
2656 | if (degree (A, x) > 0) |
---|
2657 | { |
---|
2658 | A= swapvar (A, x, y); |
---|
2659 | CanonicalForm result= 0; |
---|
2660 | CFIterator i= A; |
---|
2661 | while (d - i.exp() < 0) |
---|
2662 | i++; |
---|
2663 | |
---|
2664 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
2665 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
2666 | return result; |
---|
2667 | } |
---|
2668 | else |
---|
2669 | return A*power (x, d); |
---|
2670 | } |
---|
2671 | |
---|
2672 | CanonicalForm |
---|
2673 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
2674 | { |
---|
2675 | int l= ilog2(n); |
---|
2676 | |
---|
2677 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
2678 | |
---|
2679 | ASSERT (!g.isZero(), "expected a unit"); |
---|
2680 | |
---|
2681 | Variable alpha; |
---|
2682 | |
---|
2683 | if (!g.isOne()) |
---|
2684 | g = 1/g; |
---|
2685 | Variable x= Variable (1); |
---|
2686 | CanonicalForm result; |
---|
2687 | int exp= 0; |
---|
2688 | if (n & 1) |
---|
2689 | { |
---|
2690 | result= g; |
---|
2691 | exp= 1; |
---|
2692 | } |
---|
2693 | CanonicalForm h; |
---|
2694 | |
---|
2695 | for (int i= 1; i <= l; i++) |
---|
2696 | { |
---|
2697 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
2698 | h= mod (h, power (x, (1 << i)) - 1); |
---|
2699 | h= div (h, power (x, (1 << (i - 1)))); |
---|
2700 | h= mod (h, M); |
---|
2701 | g -= power (x, (1 << (i - 1)))* |
---|
2702 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
2703 | |
---|
2704 | if (n & (1 << i)) |
---|
2705 | { |
---|
2706 | if (exp) |
---|
2707 | { |
---|
2708 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
2709 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
2710 | h= div (h, power (x, exp)); |
---|
2711 | h= mod (h, M); |
---|
2712 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
2713 | power (x, (1 << i))); |
---|
2714 | exp += (1 << i); |
---|
2715 | } |
---|
2716 | else |
---|
2717 | { |
---|
2718 | exp= (1 << i); |
---|
2719 | result= g; |
---|
2720 | } |
---|
2721 | } |
---|
2722 | } |
---|
2723 | |
---|
2724 | return result; |
---|
2725 | } |
---|
2726 | |
---|
2727 | CanonicalForm |
---|
2728 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
2729 | M) |
---|
2730 | { |
---|
2731 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
2732 | |
---|
2733 | CanonicalForm A= mod (F, M); |
---|
2734 | CanonicalForm B= mod (G, M); |
---|
2735 | |
---|
2736 | Variable x= Variable (1); |
---|
2737 | int degA= degree (A, x); |
---|
2738 | int degB= degree (B, x); |
---|
2739 | int m= degA - degB; |
---|
2740 | if (m < 0) |
---|
2741 | return 0; |
---|
2742 | |
---|
2743 | Variable v; |
---|
2744 | CanonicalForm Q; |
---|
2745 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2746 | { |
---|
2747 | CanonicalForm R; |
---|
2748 | divrem2 (A, B, Q, R, M); |
---|
2749 | } |
---|
2750 | else |
---|
2751 | { |
---|
2752 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2753 | { |
---|
2754 | CanonicalForm R= reverse (A, degA); |
---|
2755 | CanonicalForm revB= reverse (B, degB); |
---|
2756 | revB= newtonInverse (revB, m + 1, M); |
---|
2757 | Q= mulMod2 (R, revB, M); |
---|
2758 | Q= mod (Q, power (x, m + 1)); |
---|
2759 | Q= reverse (Q, m); |
---|
2760 | } |
---|
2761 | else |
---|
2762 | { |
---|
2763 | bool zz_pEbak= zz_pE::initialized(); |
---|
2764 | zz_pEBak bak; |
---|
2765 | if (zz_pEbak) |
---|
2766 | bak.save(); |
---|
2767 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2768 | Variable y= Variable (2); |
---|
2769 | zz_pEX NTLA, NTLB; |
---|
2770 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2771 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2772 | div (NTLA, NTLA, NTLB); |
---|
2773 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
2774 | if (zz_pEbak) |
---|
2775 | bak.restore(); |
---|
2776 | } |
---|
2777 | } |
---|
2778 | |
---|
2779 | return Q; |
---|
2780 | } |
---|
2781 | |
---|
2782 | void |
---|
2783 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2784 | CanonicalForm& R, const CanonicalForm& M) |
---|
2785 | { |
---|
2786 | CanonicalForm A= mod (F, M); |
---|
2787 | CanonicalForm B= mod (G, M); |
---|
2788 | Variable x= Variable (1); |
---|
2789 | int degA= degree (A, x); |
---|
2790 | int degB= degree (B, x); |
---|
2791 | int m= degA - degB; |
---|
2792 | |
---|
2793 | if (m < 0) |
---|
2794 | { |
---|
2795 | R= A; |
---|
2796 | Q= 0; |
---|
2797 | return; |
---|
2798 | } |
---|
2799 | |
---|
2800 | Variable v; |
---|
2801 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2802 | { |
---|
2803 | divrem2 (A, B, Q, R, M); |
---|
2804 | } |
---|
2805 | else |
---|
2806 | { |
---|
2807 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2808 | { |
---|
2809 | R= reverse (A, degA); |
---|
2810 | |
---|
2811 | CanonicalForm revB= reverse (B, degB); |
---|
2812 | revB= newtonInverse (revB, m + 1, M); |
---|
2813 | Q= mulMod2 (R, revB, M); |
---|
2814 | |
---|
2815 | Q= mod (Q, power (x, m + 1)); |
---|
2816 | Q= reverse (Q, m); |
---|
2817 | |
---|
2818 | R= A - mulMod2 (Q, B, M); |
---|
2819 | } |
---|
2820 | else |
---|
2821 | { |
---|
2822 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2823 | Variable y= Variable (2); |
---|
2824 | zz_pEX NTLA, NTLB; |
---|
2825 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2826 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2827 | zz_pEX NTLQ, NTLR; |
---|
2828 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
2829 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
2830 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
2831 | } |
---|
2832 | } |
---|
2833 | } |
---|
2834 | |
---|
2835 | static inline |
---|
2836 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
2837 | { |
---|
2838 | CanonicalForm A= F; |
---|
2839 | CanonicalForm buf= 0; |
---|
2840 | bool swap= false; |
---|
2841 | if (degree (A, x) <= 0) |
---|
2842 | return CFList(A); |
---|
2843 | else if (x.level() != A.level()) |
---|
2844 | { |
---|
2845 | swap= true; |
---|
2846 | A= swapvar (A, x, A.mvar()); |
---|
2847 | } |
---|
2848 | |
---|
2849 | int j= (int) floor ((double) degree (A)/ m); |
---|
2850 | CFList result; |
---|
2851 | CFIterator i= A; |
---|
2852 | for (; j >= 0; j--) |
---|
2853 | { |
---|
2854 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
2855 | { |
---|
2856 | if (swap) |
---|
2857 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
2858 | else |
---|
2859 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
2860 | i++; |
---|
2861 | } |
---|
2862 | if (swap) |
---|
2863 | result.append (swapvar (buf, x, F.mvar())); |
---|
2864 | else |
---|
2865 | result.append (buf); |
---|
2866 | buf= 0; |
---|
2867 | } |
---|
2868 | return result; |
---|
2869 | } |
---|
2870 | |
---|
2871 | static inline |
---|
2872 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2873 | CanonicalForm& R, const CFList& M); |
---|
2874 | |
---|
2875 | static inline |
---|
2876 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2877 | CanonicalForm& R, const CFList& M) |
---|
2878 | { |
---|
2879 | CanonicalForm A= mod (F, M); |
---|
2880 | CanonicalForm B= mod (G, M); |
---|
2881 | Variable x= Variable (1); |
---|
2882 | int degB= degree (B, x); |
---|
2883 | int degA= degree (A, x); |
---|
2884 | if (degA < degB) |
---|
2885 | { |
---|
2886 | Q= 0; |
---|
2887 | R= A; |
---|
2888 | return; |
---|
2889 | } |
---|
2890 | if (degB < 1) |
---|
2891 | { |
---|
2892 | divrem (A, B, Q, R); |
---|
2893 | Q= mod (Q, M); |
---|
2894 | R= mod (R, M); |
---|
2895 | return; |
---|
2896 | } |
---|
2897 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
2898 | ASSERT (4*m >= degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
2899 | CFList splitA= split (A, m, x); |
---|
2900 | if (splitA.length() == 3) |
---|
2901 | splitA.insert (0); |
---|
2902 | if (splitA.length() == 2) |
---|
2903 | { |
---|
2904 | splitA.insert (0); |
---|
2905 | splitA.insert (0); |
---|
2906 | } |
---|
2907 | if (splitA.length() == 1) |
---|
2908 | { |
---|
2909 | splitA.insert (0); |
---|
2910 | splitA.insert (0); |
---|
2911 | splitA.insert (0); |
---|
2912 | } |
---|
2913 | |
---|
2914 | CanonicalForm xToM= power (x, m); |
---|
2915 | |
---|
2916 | CFListIterator i= splitA; |
---|
2917 | CanonicalForm H= i.getItem(); |
---|
2918 | i++; |
---|
2919 | H *= xToM; |
---|
2920 | H += i.getItem(); |
---|
2921 | i++; |
---|
2922 | H *= xToM; |
---|
2923 | H += i.getItem(); |
---|
2924 | i++; |
---|
2925 | |
---|
2926 | divrem32 (H, B, Q, R, M); |
---|
2927 | |
---|
2928 | CFList splitR= split (R, m, x); |
---|
2929 | if (splitR.length() == 1) |
---|
2930 | splitR.insert (0); |
---|
2931 | |
---|
2932 | H= splitR.getFirst(); |
---|
2933 | H *= xToM; |
---|
2934 | H += splitR.getLast(); |
---|
2935 | H *= xToM; |
---|
2936 | H += i.getItem(); |
---|
2937 | |
---|
2938 | CanonicalForm bufQ; |
---|
2939 | divrem32 (H, B, bufQ, R, M); |
---|
2940 | |
---|
2941 | Q *= xToM; |
---|
2942 | Q += bufQ; |
---|
2943 | return; |
---|
2944 | } |
---|
2945 | |
---|
2946 | static inline |
---|
2947 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2948 | CanonicalForm& R, const CFList& M) |
---|
2949 | { |
---|
2950 | CanonicalForm A= mod (F, M); |
---|
2951 | CanonicalForm B= mod (G, M); |
---|
2952 | Variable x= Variable (1); |
---|
2953 | int degB= degree (B, x); |
---|
2954 | int degA= degree (A, x); |
---|
2955 | if (degA < degB) |
---|
2956 | { |
---|
2957 | Q= 0; |
---|
2958 | R= A; |
---|
2959 | return; |
---|
2960 | } |
---|
2961 | if (degB < 1) |
---|
2962 | { |
---|
2963 | divrem (A, B, Q, R); |
---|
2964 | Q= mod (Q, M); |
---|
2965 | R= mod (R, M); |
---|
2966 | return; |
---|
2967 | } |
---|
2968 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
2969 | ASSERT (3*m > degA, "expected degree (F, 1) < 3*degree (G, 1)"); |
---|
2970 | CFList splitA= split (A, m, x); |
---|
2971 | CFList splitB= split (B, m, x); |
---|
2972 | |
---|
2973 | if (splitA.length() == 2) |
---|
2974 | { |
---|
2975 | splitA.insert (0); |
---|
2976 | } |
---|
2977 | if (splitA.length() == 1) |
---|
2978 | { |
---|
2979 | splitA.insert (0); |
---|
2980 | splitA.insert (0); |
---|
2981 | } |
---|
2982 | CanonicalForm xToM= power (x, m); |
---|
2983 | |
---|
2984 | CanonicalForm H; |
---|
2985 | CFListIterator i= splitA; |
---|
2986 | i++; |
---|
2987 | |
---|
2988 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
2989 | { |
---|
2990 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
2991 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
2992 | } |
---|
2993 | else |
---|
2994 | { |
---|
2995 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
2996 | splitB.getFirst()*xToM; |
---|
2997 | Q= xToM - 1; |
---|
2998 | } |
---|
2999 | |
---|
3000 | H= mulMod (Q, splitB.getLast(), M); |
---|
3001 | |
---|
3002 | R= R*xToM + splitA.getLast() - H; |
---|
3003 | |
---|
3004 | while (degree (R, x) >= degB) |
---|
3005 | { |
---|
3006 | xToM= power (x, degree (R, x) - degB); |
---|
3007 | Q += LC (R, x)*xToM; |
---|
3008 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
3009 | Q= mod (Q, M); |
---|
3010 | R= mod (R, M); |
---|
3011 | } |
---|
3012 | |
---|
3013 | return; |
---|
3014 | } |
---|
3015 | |
---|
3016 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
3017 | CanonicalForm& R, const CanonicalForm& M) |
---|
3018 | { |
---|
3019 | CanonicalForm A= mod (F, M); |
---|
3020 | CanonicalForm B= mod (G, M); |
---|
3021 | |
---|
3022 | if (B.inCoeffDomain()) |
---|
3023 | { |
---|
3024 | divrem (A, B, Q, R); |
---|
3025 | return; |
---|
3026 | } |
---|
3027 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
3028 | { |
---|
3029 | Q= 0; |
---|
3030 | R= A; |
---|
3031 | return; |
---|
3032 | } |
---|
3033 | |
---|
3034 | if (B.level() < A.level()) |
---|
3035 | { |
---|
3036 | divrem (A, B, Q, R); |
---|
3037 | return; |
---|
3038 | } |
---|
3039 | if (A.level() > B.level()) |
---|
3040 | { |
---|
3041 | R= A; |
---|
3042 | Q= 0; |
---|
3043 | return; |
---|
3044 | } |
---|
3045 | if (B.level() == 1 && B.isUnivariate()) |
---|
3046 | { |
---|
3047 | divrem (A, B, Q, R); |
---|
3048 | return; |
---|
3049 | } |
---|
3050 | |
---|
3051 | Variable x= Variable (1); |
---|
3052 | int degB= degree (B, x); |
---|
3053 | if (degB > degree (A, x)) |
---|
3054 | { |
---|
3055 | Q= 0; |
---|
3056 | R= A; |
---|
3057 | return; |
---|
3058 | } |
---|
3059 | |
---|
3060 | CFList splitA= split (A, degB, x); |
---|
3061 | |
---|
3062 | CanonicalForm xToDegB= power (x, degB); |
---|
3063 | CanonicalForm H, bufQ; |
---|
3064 | Q= 0; |
---|
3065 | CFListIterator i= splitA; |
---|
3066 | H= i.getItem()*xToDegB; |
---|
3067 | i++; |
---|
3068 | H += i.getItem(); |
---|
3069 | CFList buf; |
---|
3070 | while (i.hasItem()) |
---|
3071 | { |
---|
3072 | buf= CFList (M); |
---|
3073 | divrem21 (H, B, bufQ, R, buf); |
---|
3074 | i++; |
---|
3075 | if (i.hasItem()) |
---|
3076 | H= R*xToDegB + i.getItem(); |
---|
3077 | Q *= xToDegB; |
---|
3078 | Q += bufQ; |
---|
3079 | } |
---|
3080 | return; |
---|
3081 | } |
---|
3082 | |
---|
3083 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
3084 | CanonicalForm& R, const CFList& MOD) |
---|
3085 | { |
---|
3086 | CanonicalForm A= mod (F, MOD); |
---|
3087 | CanonicalForm B= mod (G, MOD); |
---|
3088 | Variable x= Variable (1); |
---|
3089 | int degB= degree (B, x); |
---|
3090 | if (degB > degree (A, x)) |
---|
3091 | { |
---|
3092 | Q= 0; |
---|
3093 | R= A; |
---|
3094 | return; |
---|
3095 | } |
---|
3096 | |
---|
3097 | if (degB <= 0) |
---|
3098 | { |
---|
3099 | divrem (A, B, Q, R); |
---|
3100 | Q= mod (Q, MOD); |
---|
3101 | R= mod (R, MOD); |
---|
3102 | return; |
---|
3103 | } |
---|
3104 | CFList splitA= split (A, degB, x); |
---|
3105 | |
---|
3106 | CanonicalForm xToDegB= power (x, degB); |
---|
3107 | CanonicalForm H, bufQ; |
---|
3108 | Q= 0; |
---|
3109 | CFListIterator i= splitA; |
---|
3110 | H= i.getItem()*xToDegB; |
---|
3111 | i++; |
---|
3112 | H += i.getItem(); |
---|
3113 | while (i.hasItem()) |
---|
3114 | { |
---|
3115 | divrem21 (H, B, bufQ, R, MOD); |
---|
3116 | i++; |
---|
3117 | if (i.hasItem()) |
---|
3118 | H= R*xToDegB + i.getItem(); |
---|
3119 | Q *= xToDegB; |
---|
3120 | Q += bufQ; |
---|
3121 | } |
---|
3122 | return; |
---|
3123 | } |
---|
3124 | |
---|
3125 | bool |
---|
3126 | uniFdivides (const CanonicalForm& A, const CanonicalForm& B) |
---|
3127 | { |
---|
3128 | if (B.isZero()) |
---|
3129 | return true; |
---|
3130 | if (A.isZero()) |
---|
3131 | return false; |
---|
3132 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
3133 | return fdivides (A, B); |
---|
3134 | int p= getCharacteristic(); |
---|
3135 | if (A.inCoeffDomain() || B.inCoeffDomain()) |
---|
3136 | { |
---|
3137 | if (A.inCoeffDomain()) |
---|
3138 | return true; |
---|
3139 | else |
---|
3140 | return false; |
---|
3141 | } |
---|
3142 | if (p > 0) |
---|
3143 | { |
---|
3144 | if (fac_NTL_char != p) |
---|
3145 | { |
---|
3146 | fac_NTL_char= p; |
---|
3147 | zz_p::init (p); |
---|
3148 | } |
---|
3149 | Variable alpha; |
---|
3150 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
3151 | { |
---|
3152 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
3153 | zz_pE::init (NTLMipo); |
---|
3154 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
---|
3155 | zz_pEX NTLB= convertFacCF2NTLzz_pEX (B, NTLMipo); |
---|
3156 | return divide (NTLB, NTLA); |
---|
3157 | } |
---|
3158 | #ifdef HAVE_FLINT |
---|
3159 | nmod_poly_t FLINTA, FLINTB; |
---|
3160 | convertFacCF2nmod_poly_t (FLINTA, A); |
---|
3161 | convertFacCF2nmod_poly_t (FLINTB, B); |
---|
3162 | nmod_poly_divrem (FLINTB, FLINTA, FLINTB, FLINTA); |
---|
3163 | bool result= nmod_poly_is_zero (FLINTA); |
---|
3164 | nmod_poly_clear (FLINTA); |
---|
3165 | nmod_poly_clear (FLINTB); |
---|
3166 | return result; |
---|
3167 | #else |
---|
3168 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
---|
3169 | zz_pX NTLB= convertFacCF2NTLzzpX (B); |
---|
3170 | return divide (NTLB, NTLA); |
---|
3171 | #endif |
---|
3172 | } |
---|
3173 | #ifdef HAVE_FLINT |
---|
3174 | Variable alpha; |
---|
3175 | bool isRat= isOn (SW_RATIONAL); |
---|
3176 | if (!isRat) |
---|
3177 | On (SW_RATIONAL); |
---|
3178 | if (!hasFirstAlgVar (A, alpha) && !hasFirstAlgVar (B, alpha)) |
---|
3179 | { |
---|
3180 | fmpq_poly_t FLINTA,FLINTB; |
---|
3181 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
---|
3182 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
---|
3183 | fmpq_poly_rem (FLINTA, FLINTB, FLINTA); |
---|
3184 | bool result= fmpq_poly_is_zero (FLINTA); |
---|
3185 | fmpq_poly_clear (FLINTA); |
---|
3186 | fmpq_poly_clear (FLINTB); |
---|
3187 | if (!isRat) |
---|
3188 | Off (SW_RATIONAL); |
---|
3189 | return result; |
---|
3190 | } |
---|
3191 | CanonicalForm Q, R; |
---|
3192 | Variable x= Variable (1); |
---|
3193 | Variable y= Variable (2); |
---|
3194 | newtonDivrem (swapvar (B, y, x), swapvar (A, y, x), Q, R); |
---|
3195 | if (!isRat) |
---|
3196 | Off (SW_RATIONAL); |
---|
3197 | return R.isZero(); |
---|
3198 | #else |
---|
3199 | bool isRat= isOn (SW_RATIONAL); |
---|
3200 | if (!isRat) |
---|
3201 | On (SW_RATIONAL); |
---|
3202 | bool result= fdivides (A, B); |
---|
3203 | if (!isRat) |
---|
3204 | Off (SW_RATIONAL); |
---|
3205 | return result; //maybe NTL? |
---|
3206 | #endif |
---|
3207 | } |
---|
3208 | |
---|
3209 | // end division |
---|
3210 | |
---|
3211 | #endif |
---|