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