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 to lift factors via Hensel lifting and |
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7 | * functions for modular multiplication and division with remainder. |
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8 | * |
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9 | * ABSTRACT: Hensel lifting is described in "Efficient Multivariate |
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10 | * Factorization over Finite Fields" by L. Bernardin & M. Monagon. Division with |
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11 | * remainder is described in "Fast Recursive Division" by C. Burnikel and |
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12 | * J. Ziegler. Karatsuba multiplication is described in "Modern Computer |
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13 | * Algebra" by J. von zur Gathen and J. Gerhard. |
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14 | * |
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15 | * @author Martin Lee |
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16 | * |
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17 | * @internal @version \$Id$ |
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18 | * |
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19 | **/ |
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20 | /*****************************************************************************/ |
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21 | |
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22 | #include "config.h" |
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23 | |
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24 | #include "cf_assert.h" |
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25 | #include "debug.h" |
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26 | #include "timing.h" |
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27 | |
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28 | #include "facHensel.h" |
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29 | #include "cf_util.h" |
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30 | #include "fac_util.h" |
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31 | #include "cf_algorithm.h" |
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32 | #include "cf_primes.h" |
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33 | |
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34 | #ifdef HAVE_NTL |
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35 | #include <NTL/lzz_pEX.h> |
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36 | #include "NTLconvert.h" |
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37 | |
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38 | #ifdef HAVE_FLINT |
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39 | #include "FLINTconvert.h" |
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40 | #endif |
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41 | |
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42 | #ifdef HAVE_FLINT |
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43 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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44 | { |
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45 | int degAy= degree (A); |
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46 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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47 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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48 | CFIterator j; |
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49 | for (CFIterator i= A; i.hasTerms(); i++) |
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50 | { |
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51 | if (i.coeff().inBaseDomain()) |
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52 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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53 | else |
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54 | for (j= i.coeff(); j.hasTerms(); j++) |
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55 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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56 | j.coeff()); |
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57 | } |
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58 | _fmpz_poly_normalise(result); |
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59 | } |
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60 | |
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61 | |
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62 | CanonicalForm |
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63 | reverseSubst (const fmpz_poly_t F, int d, const Variable& alpha, |
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64 | const CanonicalForm& den) |
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65 | { |
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66 | Variable x= Variable (1); |
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67 | |
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68 | CanonicalForm result= 0; |
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69 | int i= 0; |
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70 | int degf= fmpz_poly_degree (F); |
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71 | int k= 0; |
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72 | int degfSubK; |
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73 | int repLength, j; |
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74 | CanonicalForm coeff; |
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75 | fmpz* tmp; |
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76 | while (degf >= k) |
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77 | { |
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78 | coeff= 0; |
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79 | degfSubK= degf - k; |
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80 | if (degfSubK >= d) |
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81 | repLength= d; |
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82 | else |
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83 | repLength= degfSubK + 1; |
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84 | |
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85 | for (j= 0; j < repLength; j++) |
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86 | { |
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87 | tmp= fmpz_poly_get_coeff_ptr (F, j+k); |
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88 | if (!fmpz_is_zero (tmp)) |
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89 | { |
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90 | CanonicalForm ff= convertFmpz2CF (tmp)/den; |
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91 | coeff += ff*power (alpha, j); |
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92 | } |
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93 | } |
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94 | result += coeff*power (x, i); |
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95 | i++; |
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96 | k= d*i; |
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97 | } |
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98 | return result; |
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99 | } |
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100 | |
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101 | CanonicalForm |
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102 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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103 | const Variable& alpha) |
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104 | { |
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105 | CanonicalForm A= F; |
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106 | CanonicalForm B= G; |
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107 | |
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108 | CanonicalForm denA= bCommonDen (A); |
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109 | CanonicalForm denB= bCommonDen (B); |
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110 | |
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111 | A *= denA; |
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112 | B *= denB; |
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113 | int degAa= degree (A, alpha); |
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114 | int degBa= degree (B, alpha); |
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115 | int d= degAa + 1 + degBa; |
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116 | |
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117 | fmpz_poly_t FLINTA,FLINTB; |
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118 | fmpz_poly_init (FLINTA); |
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119 | fmpz_poly_init (FLINTB); |
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120 | kronSub (FLINTA, A, d); |
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121 | kronSub (FLINTB, B, d); |
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122 | |
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123 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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124 | |
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125 | denA *= denB; |
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126 | A= reverseSubst (FLINTA, d, alpha, denA); |
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127 | |
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128 | fmpz_poly_clear (FLINTA); |
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129 | fmpz_poly_clear (FLINTB); |
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130 | return A; |
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131 | } |
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132 | |
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133 | CanonicalForm |
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134 | mulFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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135 | { |
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136 | CanonicalForm A= F; |
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137 | CanonicalForm B= G; |
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138 | |
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139 | CanonicalForm denA= bCommonDen (A); |
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140 | CanonicalForm denB= bCommonDen (B); |
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141 | |
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142 | A *= denA; |
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143 | B *= denB; |
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144 | fmpz_poly_t FLINTA,FLINTB; |
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145 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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146 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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147 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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148 | denA *= denB; |
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149 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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150 | A /= denA; |
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151 | fmpz_poly_clear (FLINTA); |
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152 | fmpz_poly_clear (FLINTB); |
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153 | |
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154 | return A; |
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155 | } |
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156 | |
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157 | /*CanonicalForm |
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158 | mulFLINTQ2 (const CanonicalForm& F, const CanonicalForm& G) |
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159 | { |
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160 | CanonicalForm A= F; |
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161 | CanonicalForm B= G; |
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162 | |
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163 | fmpq_poly_t FLINTA,FLINTB; |
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164 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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165 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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166 | |
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167 | fmpq_poly_mul (FLINTA, FLINTA, FLINTB); |
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168 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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169 | fmpq_poly_clear (FLINTA); |
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170 | fmpq_poly_clear (FLINTB); |
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171 | return A; |
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172 | }*/ |
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173 | |
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174 | CanonicalForm |
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175 | divFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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176 | { |
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177 | CanonicalForm A= F; |
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178 | CanonicalForm B= G; |
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179 | |
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180 | fmpq_poly_t FLINTA,FLINTB; |
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181 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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182 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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183 | |
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184 | fmpq_poly_div (FLINTA, FLINTA, FLINTB); |
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185 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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186 | |
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187 | fmpq_poly_clear (FLINTA); |
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188 | fmpq_poly_clear (FLINTB); |
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189 | return A; |
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190 | } |
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191 | |
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192 | CanonicalForm |
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193 | modFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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194 | { |
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195 | CanonicalForm A= F; |
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196 | CanonicalForm B= G; |
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197 | |
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198 | fmpq_poly_t FLINTA,FLINTB; |
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199 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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200 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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201 | |
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202 | fmpq_poly_rem (FLINTA, FLINTA, FLINTB); |
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203 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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204 | |
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205 | fmpq_poly_clear (FLINTA); |
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206 | fmpq_poly_clear (FLINTB); |
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207 | return A; |
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208 | } |
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209 | |
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210 | CanonicalForm |
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211 | mulFLINTQaTrunc (const CanonicalForm& F, const CanonicalForm& G, |
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212 | const Variable& alpha, int m) |
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213 | { |
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214 | CanonicalForm A= F; |
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215 | CanonicalForm B= G; |
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216 | |
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217 | CanonicalForm denA= bCommonDen (A); |
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218 | CanonicalForm denB= bCommonDen (B); |
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219 | |
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220 | A *= denA; |
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221 | B *= denB; |
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222 | |
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223 | int degAa= degree (A, alpha); |
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224 | int degBa= degree (B, alpha); |
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225 | int d= degAa + 1 + degBa; |
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226 | |
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227 | fmpz_poly_t FLINTA,FLINTB; |
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228 | fmpz_poly_init (FLINTA); |
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229 | fmpz_poly_init (FLINTB); |
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230 | kronSub (FLINTA, A, d); |
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231 | kronSub (FLINTB, B, d); |
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232 | |
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233 | int k= d*m; |
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234 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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235 | |
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236 | denA *= denB; |
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237 | A= reverseSubst (FLINTA, d, alpha, denA); |
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238 | fmpz_poly_clear (FLINTA); |
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239 | fmpz_poly_clear (FLINTB); |
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240 | return A; |
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241 | } |
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242 | |
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243 | CanonicalForm |
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244 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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245 | { |
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246 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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247 | return mod (F*G, power (Variable (1), m)); |
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248 | Variable alpha; |
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249 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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250 | return mulFLINTQaTrunc (F, G, alpha, m); |
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251 | |
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252 | CanonicalForm A= F; |
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253 | CanonicalForm B= G; |
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254 | |
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255 | CanonicalForm denA= bCommonDen (A); |
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256 | CanonicalForm denB= bCommonDen (B); |
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257 | |
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258 | A *= denA; |
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259 | B *= denB; |
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260 | fmpz_poly_t FLINTA,FLINTB; |
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261 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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262 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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263 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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264 | denA *= denB; |
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265 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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266 | A /= denA; |
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267 | fmpz_poly_clear (FLINTA); |
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268 | fmpz_poly_clear (FLINTB); |
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269 | |
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270 | return A; |
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271 | } |
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272 | |
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273 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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274 | { |
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275 | if (d == 0) |
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276 | return F; |
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277 | if (F.inCoeffDomain()) |
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278 | return F*power (Variable (1),d); |
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279 | Variable x= Variable (1); |
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280 | CanonicalForm result= 0; |
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281 | CFIterator i= F; |
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282 | while (d - i.exp() < 0) |
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283 | i++; |
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284 | |
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285 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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286 | result += i.coeff()*power (x, d - i.exp()); |
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287 | return result; |
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288 | } |
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289 | |
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290 | CanonicalForm |
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291 | newtonInverse (const CanonicalForm& F, const int n) |
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292 | { |
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293 | int l= ilog2(n); |
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294 | |
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295 | CanonicalForm g= F [0]; |
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296 | |
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297 | ASSERT (!g.isZero(), "expected a unit"); |
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298 | |
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299 | if (!g.isOne()) |
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300 | g = 1/g; |
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301 | Variable x= Variable (1); |
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302 | CanonicalForm result; |
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303 | int exp= 0; |
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304 | if (n & 1) |
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305 | { |
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306 | result= g; |
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307 | exp= 1; |
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308 | } |
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309 | CanonicalForm h; |
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310 | |
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311 | for (int i= 1; i <= l; i++) |
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312 | { |
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313 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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314 | h= mod (h, power (x, (1 << i)) - 1); |
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315 | h= div (h, power (x, (1 << (i - 1)))); |
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316 | g -= power (x, (1 << (i - 1)))* |
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317 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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318 | |
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319 | if (n & (1 << i)) |
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320 | { |
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321 | if (exp) |
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322 | { |
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323 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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324 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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325 | h= div (h, power (x, exp)); |
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326 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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327 | exp += (1 << i); |
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328 | } |
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329 | else |
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330 | { |
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331 | exp= (1 << i); |
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332 | result= g; |
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333 | } |
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334 | } |
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335 | } |
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336 | |
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337 | return result; |
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338 | } |
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339 | |
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340 | void |
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341 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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342 | CanonicalForm& R) |
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343 | { |
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344 | CanonicalForm A= F; |
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345 | CanonicalForm B= G; |
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346 | Variable x= Variable (1); |
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347 | int degA= degree (A, x); |
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348 | int degB= degree (B, x); |
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349 | int m= degA - degB; |
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350 | |
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351 | if (m < 0) |
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352 | { |
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353 | R= A; |
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354 | Q= 0; |
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355 | return; |
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356 | } |
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357 | |
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358 | if (degB <= 1) |
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359 | divrem (A, B, Q, R); |
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360 | else |
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361 | { |
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362 | R= uniReverse (A, degA); |
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363 | |
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364 | CanonicalForm revB= uniReverse (B, degB); |
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365 | CanonicalForm buf= revB; |
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366 | revB= newtonInverse (revB, m + 1); |
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367 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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368 | Q= uniReverse (Q, m); |
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369 | |
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370 | R= A - mulNTL (Q, B); |
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371 | } |
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372 | } |
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373 | |
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374 | void |
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375 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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376 | { |
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377 | CanonicalForm A= F; |
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378 | CanonicalForm B= G; |
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379 | Variable x= Variable (1); |
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380 | int degA= degree (A, x); |
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381 | int degB= degree (B, x); |
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382 | int m= degA - degB; |
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383 | |
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384 | if (m < 0) |
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385 | { |
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386 | Q= 0; |
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387 | return; |
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388 | } |
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389 | |
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390 | if (degB <= 1) |
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391 | Q= div (A, B); |
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392 | else |
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393 | { |
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394 | CanonicalForm R= uniReverse (A, degA); |
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395 | |
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396 | CanonicalForm revB= uniReverse (B, degB); |
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397 | revB= newtonInverse (revB, m + 1); |
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398 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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399 | Q= uniReverse (Q, m); |
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400 | } |
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401 | } |
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402 | |
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403 | #endif |
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404 | |
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405 | static |
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406 | CFList productsNTL (const CFList& factors, const CanonicalForm& M) |
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407 | { |
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408 | zz_p::init (getCharacteristic()); |
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409 | zz_pX NTLMipo= convertFacCF2NTLzzpX (M); |
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410 | zz_pE::init (NTLMipo); |
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411 | zz_pEX prod; |
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412 | vec_zz_pEX v; |
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413 | v.SetLength (factors.length()); |
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414 | int j= 0; |
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415 | for (CFListIterator i= factors; i.hasItem(); i++, j++) |
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416 | { |
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417 | if (i.getItem().inCoeffDomain()) |
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418 | v[j]= to_zz_pEX (to_zz_pE (convertFacCF2NTLzzpX (i.getItem()))); |
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419 | else |
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420 | v[j]= convertFacCF2NTLzz_pEX (i.getItem(), NTLMipo); |
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421 | } |
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422 | CFList result; |
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423 | Variable x= Variable (1); |
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424 | for (int j= 0; j < factors.length(); j++) |
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425 | { |
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426 | int k= 0; |
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427 | set(prod); |
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428 | for (int i= 0; i < factors.length(); i++, k++) |
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429 | { |
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430 | if (k == j) |
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431 | continue; |
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432 | prod *= v[i]; |
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433 | } |
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434 | result.append (convertNTLzz_pEX2CF (prod, x, M.mvar())); |
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435 | } |
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436 | return result; |
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437 | } |
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438 | |
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439 | static |
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440 | void tryDiophantine (CFList& result, const CanonicalForm& F, |
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441 | const CFList& factors, const CanonicalForm& M, bool& fail) |
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442 | { |
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443 | ASSERT (M.isUnivariate(), "expected univariate poly"); |
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444 | |
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445 | CFList bufFactors= factors; |
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446 | bufFactors.removeFirst(); |
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447 | bufFactors.insert (factors.getFirst () (0,2)); |
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448 | CanonicalForm inv, leadingCoeff= Lc (F); |
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449 | CFListIterator i= bufFactors; |
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450 | if (bufFactors.getFirst().inCoeffDomain()) |
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451 | { |
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452 | if (i.hasItem()) |
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453 | i++; |
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454 | } |
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455 | for (; i.hasItem(); i++) |
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456 | { |
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457 | tryInvert (Lc (i.getItem()), M, inv ,fail); |
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458 | if (fail) |
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459 | return; |
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460 | i.getItem()= reduce (i.getItem()*inv, M); |
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461 | } |
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462 | bufFactors= productsNTL (bufFactors, M); |
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463 | |
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464 | CanonicalForm buf1, buf2, buf3, S, T; |
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465 | i= bufFactors; |
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466 | if (i.hasItem()) |
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467 | i++; |
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468 | buf1= bufFactors.getFirst(); |
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469 | buf2= i.getItem(); |
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470 | tryExtgcd (buf1, buf2, M, buf3, S, T, fail); |
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471 | if (fail) |
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472 | return; |
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473 | result.append (S); |
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474 | result.append (T); |
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475 | if (i.hasItem()) |
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476 | i++; |
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477 | for (; i.hasItem(); i++) |
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478 | { |
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479 | buf1= i.getItem(); |
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480 | tryExtgcd (buf3, buf1, M, buf3, S, T, fail); |
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481 | if (fail) |
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482 | return; |
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483 | CFListIterator k= factors; |
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484 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
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485 | { |
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486 | j.getItem() *= S; |
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487 | j.getItem()= mod (j.getItem(), k.getItem()); |
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488 | j.getItem()= reduce (j.getItem(), M); |
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489 | } |
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490 | result.append (T); |
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491 | } |
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492 | } |
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493 | |
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494 | static inline |
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495 | CFList mapinto (const CFList& L) |
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496 | { |
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497 | CFList result; |
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498 | for (CFListIterator i= L; i.hasItem(); i++) |
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499 | result.append (mapinto (i.getItem())); |
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500 | return result; |
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501 | } |
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502 | |
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503 | static inline |
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504 | int mod (const CFList& L, const CanonicalForm& p) |
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505 | { |
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506 | for (CFListIterator i= L; i.hasItem(); i++) |
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507 | { |
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508 | if (mod (i.getItem(), p) == 0) |
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509 | return 0; |
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510 | } |
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511 | return 1; |
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512 | } |
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513 | |
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514 | |
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515 | static inline void |
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516 | chineseRemainder (const CFList & x1, const CanonicalForm & q1, |
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517 | const CFList & x2, const CanonicalForm & q2, |
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518 | CFList & xnew, CanonicalForm & qnew) |
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519 | { |
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520 | ASSERT (x1.length() == x2.length(), "expected lists of equal length"); |
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521 | CanonicalForm tmp1, tmp2; |
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522 | CFListIterator j= x2; |
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523 | for (CFListIterator i= x1; i.hasItem() && j.hasItem(); i++, j++) |
---|
524 | { |
---|
525 | chineseRemainder (i.getItem(), q1, j.getItem(), q2, tmp1, tmp2); |
---|
526 | xnew.append (tmp1); |
---|
527 | } |
---|
528 | qnew= tmp2; |
---|
529 | } |
---|
530 | |
---|
531 | static inline |
---|
532 | CFList Farey (const CFList& L, const CanonicalForm& q) |
---|
533 | { |
---|
534 | CFList result; |
---|
535 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
536 | result.append (Farey (i.getItem(), q)); |
---|
537 | return result; |
---|
538 | } |
---|
539 | |
---|
540 | static inline |
---|
541 | CFList replacevar (const CFList& L, const Variable& a, const Variable& b) |
---|
542 | { |
---|
543 | CFList result; |
---|
544 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
545 | result.append (replacevar (i.getItem(), a, b)); |
---|
546 | return result; |
---|
547 | } |
---|
548 | |
---|
549 | CFList |
---|
550 | modularDiophant (const CanonicalForm& f, const CFList& factors, |
---|
551 | const CanonicalForm& M) |
---|
552 | { |
---|
553 | bool save_rat=!isOn (SW_RATIONAL); |
---|
554 | On (SW_RATIONAL); |
---|
555 | CanonicalForm F= f*bCommonDen (f); |
---|
556 | CFList products= factors; |
---|
557 | for (CFListIterator i= products; i.hasItem(); i++) |
---|
558 | { |
---|
559 | if (products.getFirst().level() == 1) |
---|
560 | i.getItem() /= Lc (i.getItem()); |
---|
561 | i.getItem() *= bCommonDen (i.getItem()); |
---|
562 | } |
---|
563 | if (products.getFirst().level() == 1) |
---|
564 | products.insert (Lc (F)); |
---|
565 | CanonicalForm bound= maxNorm (F); |
---|
566 | CFList leadingCoeffs; |
---|
567 | leadingCoeffs.append (lc (F)); |
---|
568 | CanonicalForm dummy; |
---|
569 | for (CFListIterator i= products; i.hasItem(); i++) |
---|
570 | { |
---|
571 | leadingCoeffs.append (lc (i.getItem())); |
---|
572 | dummy= maxNorm (i.getItem()); |
---|
573 | bound= (dummy > bound) ? dummy : bound; |
---|
574 | } |
---|
575 | bound *= maxNorm (Lc (F))*maxNorm (Lc(F))*bound; |
---|
576 | bound *= bound*bound; |
---|
577 | bound= power (bound, degree (M)); |
---|
578 | bound *= power (CanonicalForm (2),degree (f)); |
---|
579 | CanonicalForm bufBound= bound; |
---|
580 | int i = cf_getNumBigPrimes() - 1; |
---|
581 | int p; |
---|
582 | CFList resultModP, result, newResult; |
---|
583 | CanonicalForm q (0), newQ; |
---|
584 | bool fail= false; |
---|
585 | Variable a= M.mvar(); |
---|
586 | Variable b= Variable (2); |
---|
587 | setReduce (M.mvar(), false); |
---|
588 | CanonicalForm mipo= bCommonDen (M)*M; |
---|
589 | Off (SW_RATIONAL); |
---|
590 | CanonicalForm modMipo; |
---|
591 | leadingCoeffs.append (lc (mipo)); |
---|
592 | CFList tmp1, tmp2; |
---|
593 | bool equal= false; |
---|
594 | int count= 0; |
---|
595 | do |
---|
596 | { |
---|
597 | p = cf_getBigPrime( i ); |
---|
598 | i--; |
---|
599 | while ( i >= 0 && mod( leadingCoeffs, p ) == 0) |
---|
600 | { |
---|
601 | p = cf_getBigPrime( i ); |
---|
602 | i--; |
---|
603 | } |
---|
604 | |
---|
605 | ASSERT (i >= 0, "ran out of primes"); //sic |
---|
606 | |
---|
607 | setCharacteristic (p); |
---|
608 | modMipo= mapinto (mipo); |
---|
609 | modMipo /= lc (modMipo); |
---|
610 | resultModP= CFList(); |
---|
611 | tryDiophantine (resultModP, mapinto (F), mapinto (products), modMipo, fail); |
---|
612 | setCharacteristic (0); |
---|
613 | if (fail) |
---|
614 | { |
---|
615 | fail= false; |
---|
616 | continue; |
---|
617 | } |
---|
618 | |
---|
619 | if ( q.isZero() ) |
---|
620 | { |
---|
621 | result= replacevar (mapinto(resultModP), a, b); |
---|
622 | q= p; |
---|
623 | } |
---|
624 | else |
---|
625 | { |
---|
626 | result= replacevar (result, a, b); |
---|
627 | newResult= CFList(); |
---|
628 | chineseRemainder( result, q, replacevar (mapinto (resultModP), a, b), |
---|
629 | p, newResult, newQ ); |
---|
630 | q= newQ; |
---|
631 | result= newResult; |
---|
632 | if (newQ > bound) |
---|
633 | { |
---|
634 | count++; |
---|
635 | tmp1= replacevar (Farey (result, q), b, a); |
---|
636 | if (tmp2.isEmpty()) |
---|
637 | tmp2= tmp1; |
---|
638 | else |
---|
639 | { |
---|
640 | equal= true; |
---|
641 | CFListIterator k= tmp1; |
---|
642 | for (CFListIterator j= tmp2; j.hasItem(); j++, k++) |
---|
643 | { |
---|
644 | if (j.getItem() != k.getItem()) |
---|
645 | equal= false; |
---|
646 | } |
---|
647 | if (!equal) |
---|
648 | tmp2= tmp1; |
---|
649 | } |
---|
650 | if (count > 2) |
---|
651 | { |
---|
652 | bound *= bufBound; |
---|
653 | equal= false; |
---|
654 | count= 0; |
---|
655 | } |
---|
656 | } |
---|
657 | if (newQ > bound && equal) |
---|
658 | { |
---|
659 | On( SW_RATIONAL ); |
---|
660 | CFList bufResult= result; |
---|
661 | result= tmp2; |
---|
662 | setReduce (M.mvar(), true); |
---|
663 | if (factors.getFirst().level() == 1) |
---|
664 | { |
---|
665 | result.removeFirst(); |
---|
666 | CFListIterator j= factors; |
---|
667 | CanonicalForm denf= bCommonDen (f); |
---|
668 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
669 | i.getItem() *= Lc (j.getItem())*denf; |
---|
670 | } |
---|
671 | if (factors.getFirst().level() != 1 && |
---|
672 | !bCommonDen (factors.getFirst()).isOne()) |
---|
673 | { |
---|
674 | CanonicalForm denFirst= bCommonDen (factors.getFirst()); |
---|
675 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
676 | i.getItem() *= denFirst; |
---|
677 | } |
---|
678 | |
---|
679 | CanonicalForm test= 0; |
---|
680 | CFListIterator jj= factors; |
---|
681 | for (CFListIterator ii= result; ii.hasItem(); ii++, jj++) |
---|
682 | test += ii.getItem()*(f/jj.getItem()); |
---|
683 | if (!test.isOne()) |
---|
684 | { |
---|
685 | bound *= bufBound; |
---|
686 | equal= false; |
---|
687 | count= 0; |
---|
688 | setReduce (M.mvar(), false); |
---|
689 | result= bufResult; |
---|
690 | Off (SW_RATIONAL); |
---|
691 | } |
---|
692 | else |
---|
693 | break; |
---|
694 | } |
---|
695 | } |
---|
696 | } while (1); |
---|
697 | if (save_rat) Off(SW_RATIONAL); |
---|
698 | return result; |
---|
699 | } |
---|
700 | |
---|
701 | CanonicalForm |
---|
702 | mulNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
703 | { |
---|
704 | if (F.inCoeffDomain() || G.inCoeffDomain() || getCharacteristic() == 0) |
---|
705 | { |
---|
706 | Variable alpha; |
---|
707 | #ifdef HAVE_FLINT |
---|
708 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
---|
709 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
---|
710 | { |
---|
711 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
---|
712 | return result; |
---|
713 | } |
---|
714 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
---|
715 | return mulFLINTQ (F, G); |
---|
716 | #endif |
---|
717 | return F*G; |
---|
718 | } |
---|
719 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
720 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
721 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
722 | return F*G; |
---|
723 | zz_p::init (getCharacteristic()); |
---|
724 | Variable alpha; |
---|
725 | CanonicalForm result; |
---|
726 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
727 | { |
---|
728 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
729 | zz_pE::init (NTLMipo); |
---|
730 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
731 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
732 | mul (NTLF, NTLF, NTLG); |
---|
733 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
734 | } |
---|
735 | else |
---|
736 | { |
---|
737 | #ifdef HAVE_FLINT |
---|
738 | nmod_poly_t FLINTF, FLINTG; |
---|
739 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
740 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
741 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
---|
742 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
743 | nmod_poly_clear (FLINTF); |
---|
744 | nmod_poly_clear (FLINTG); |
---|
745 | #else |
---|
746 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
747 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
748 | mul (NTLF, NTLF, NTLG); |
---|
749 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
750 | #endif |
---|
751 | } |
---|
752 | return result; |
---|
753 | } |
---|
754 | |
---|
755 | CanonicalForm |
---|
756 | modNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
757 | { |
---|
758 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
759 | return F; |
---|
760 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
761 | return mod (F, G); |
---|
762 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
763 | return mod (F,G); |
---|
764 | |
---|
765 | if (getCharacteristic() == 0) |
---|
766 | { |
---|
767 | #ifdef HAVE_FLINT |
---|
768 | Variable alpha; |
---|
769 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
770 | return modFLINTQ (F, G); |
---|
771 | else |
---|
772 | { |
---|
773 | CanonicalForm Q, R; |
---|
774 | newtonDivrem (F, G, Q, R); |
---|
775 | return R; |
---|
776 | } |
---|
777 | #else |
---|
778 | return mod (F, G); |
---|
779 | #endif |
---|
780 | } |
---|
781 | |
---|
782 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
783 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
784 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
785 | return mod (F, G); |
---|
786 | zz_p::init (getCharacteristic()); |
---|
787 | Variable alpha; |
---|
788 | CanonicalForm result; |
---|
789 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
790 | { |
---|
791 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
792 | zz_pE::init (NTLMipo); |
---|
793 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
794 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
795 | rem (NTLF, NTLF, NTLG); |
---|
796 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
797 | } |
---|
798 | else |
---|
799 | { |
---|
800 | #ifdef HAVE_FLINT |
---|
801 | nmod_poly_t FLINTF, FLINTG; |
---|
802 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
803 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
804 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
805 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
806 | nmod_poly_clear (FLINTF); |
---|
807 | nmod_poly_clear (FLINTG); |
---|
808 | #else |
---|
809 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
810 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
811 | rem (NTLF, NTLF, NTLG); |
---|
812 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
813 | #endif |
---|
814 | } |
---|
815 | return result; |
---|
816 | } |
---|
817 | |
---|
818 | CanonicalForm |
---|
819 | divNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
820 | { |
---|
821 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
822 | return F; |
---|
823 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
824 | return div (F, G); |
---|
825 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
826 | return div (F,G); |
---|
827 | |
---|
828 | if (getCharacteristic() == 0) |
---|
829 | { |
---|
830 | #ifdef HAVE_FLINT |
---|
831 | Variable alpha; |
---|
832 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
833 | return divFLINTQ (F,G); |
---|
834 | else |
---|
835 | { |
---|
836 | CanonicalForm Q; |
---|
837 | newtonDiv (F, G, Q); |
---|
838 | return Q; |
---|
839 | } |
---|
840 | #else |
---|
841 | return div (F, G); |
---|
842 | #endif |
---|
843 | } |
---|
844 | |
---|
845 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
846 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
847 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
848 | return div (F, G); |
---|
849 | zz_p::init (getCharacteristic()); |
---|
850 | Variable alpha; |
---|
851 | CanonicalForm result; |
---|
852 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
853 | { |
---|
854 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
855 | zz_pE::init (NTLMipo); |
---|
856 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
857 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
858 | div (NTLF, NTLF, NTLG); |
---|
859 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
860 | } |
---|
861 | else |
---|
862 | { |
---|
863 | #ifdef HAVE_FLINT |
---|
864 | nmod_poly_t FLINTF, FLINTG; |
---|
865 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
866 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
867 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
868 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
869 | nmod_poly_clear (FLINTF); |
---|
870 | nmod_poly_clear (FLINTG); |
---|
871 | #else |
---|
872 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
873 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
874 | div (NTLF, NTLF, NTLG); |
---|
875 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
876 | #endif |
---|
877 | } |
---|
878 | return result; |
---|
879 | } |
---|
880 | |
---|
881 | /* |
---|
882 | void |
---|
883 | divremNTL (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
884 | CanonicalForm& R) |
---|
885 | { |
---|
886 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
887 | { |
---|
888 | R= F; |
---|
889 | Q= 0; |
---|
890 | } |
---|
891 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
892 | { |
---|
893 | divrem (F, G, Q, R); |
---|
894 | return; |
---|
895 | } |
---|
896 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
897 | { |
---|
898 | divrem (F, G, Q, R); |
---|
899 | return; |
---|
900 | } |
---|
901 | |
---|
902 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
903 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
904 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
905 | { |
---|
906 | divrem (F, G, Q, R); |
---|
907 | return; |
---|
908 | } |
---|
909 | zz_p::init (getCharacteristic()); |
---|
910 | Variable alpha; |
---|
911 | CanonicalForm result; |
---|
912 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
913 | { |
---|
914 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
915 | zz_pE::init (NTLMipo); |
---|
916 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
917 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
918 | zz_pEX NTLQ; |
---|
919 | zz_pEX NTLR; |
---|
920 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
921 | Q= convertNTLzz_pEX2CF(NTLQ, F.mvar(), alpha); |
---|
922 | R= convertNTLzz_pEX2CF(NTLR, F.mvar(), alpha); |
---|
923 | return; |
---|
924 | } |
---|
925 | else |
---|
926 | { |
---|
927 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
928 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
929 | zz_pX NTLQ; |
---|
930 | zz_pX NTLR; |
---|
931 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
932 | Q= convertNTLzzpX2CF(NTLQ, F.mvar()); |
---|
933 | R= convertNTLzzpX2CF(NTLR, F.mvar()); |
---|
934 | return; |
---|
935 | } |
---|
936 | }*/ |
---|
937 | |
---|
938 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
939 | { |
---|
940 | CanonicalForm A= F; |
---|
941 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
942 | A= mod (A, i.getItem()); |
---|
943 | return A; |
---|
944 | } |
---|
945 | |
---|
946 | #ifdef HAVE_FLINT |
---|
947 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
948 | { |
---|
949 | int degAy= degree (A); |
---|
950 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
951 | |
---|
952 | nmod_poly_t buf; |
---|
953 | |
---|
954 | int j, k, bufRepLength; |
---|
955 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
956 | { |
---|
957 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
958 | |
---|
959 | k= i.exp()*d; |
---|
960 | bufRepLength= (int) nmod_poly_length (buf); |
---|
961 | for (j= 0; j < bufRepLength; j++) |
---|
962 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
963 | nmod_poly_clear (buf); |
---|
964 | } |
---|
965 | _nmod_poly_normalise (result); |
---|
966 | } |
---|
967 | |
---|
968 | /*void kronSubQ (fmpz_poly_t result, const CanonicalForm& A, int d) |
---|
969 | { |
---|
970 | int degAy= degree (A); |
---|
971 | fmpz_poly_init2 (result, d*(degAy + 1)); |
---|
972 | _fmpz_poly_set_length (result, d*(degAy+1)); |
---|
973 | |
---|
974 | CFIterator j; |
---|
975 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
976 | { |
---|
977 | if (i.coeff().inBas |
---|
978 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
979 | |
---|
980 | int k= i.exp()*d; |
---|
981 | int bufRepLength= (int) fmpz_poly_length (buf); |
---|
982 | for (int j= 0; j < bufRepLength; j++) |
---|
983 | { |
---|
984 | fmpz_poly_get_coeff_fmpz (coeff, buf, j); |
---|
985 | fmpz_poly_set_coeff_fmpz (result, j + k, coeff); |
---|
986 | } |
---|
987 | fmpz_poly_clear (buf); |
---|
988 | } |
---|
989 | fmpz_clear (coeff); |
---|
990 | _fmpz_poly_normalise (result); |
---|
991 | }*/ |
---|
992 | |
---|
993 | // A is a bivariate poly over Qa!!!! |
---|
994 | // d2= 2*deg_alpha + 1 |
---|
995 | // d1= 2*deg_x*d2+1 |
---|
996 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
997 | { |
---|
998 | int degAy= degree (A); |
---|
999 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
1000 | |
---|
1001 | fmpq_poly_t buf; |
---|
1002 | fmpq_t coeff; |
---|
1003 | |
---|
1004 | int k, l, bufRepLength; |
---|
1005 | CFIterator j; |
---|
1006 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1007 | { |
---|
1008 | if (i.coeff().inCoeffDomain()) |
---|
1009 | { |
---|
1010 | k= d1*i.exp(); |
---|
1011 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
1012 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
1013 | for (l= 0; l < bufRepLength; l++) |
---|
1014 | { |
---|
1015 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
1016 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
1017 | } |
---|
1018 | fmpq_poly_clear (buf); |
---|
1019 | } |
---|
1020 | else |
---|
1021 | { |
---|
1022 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
1023 | { |
---|
1024 | k= d1*i.exp(); |
---|
1025 | k += d2*j.exp(); |
---|
1026 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
1027 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
1028 | for (l= 0; l < bufRepLength; l++) |
---|
1029 | { |
---|
1030 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
1031 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
1032 | } |
---|
1033 | fmpq_poly_clear (buf); |
---|
1034 | } |
---|
1035 | } |
---|
1036 | } |
---|
1037 | fmpq_clear (coeff); |
---|
1038 | _fmpq_poly_normalise (result); |
---|
1039 | } |
---|
1040 | #endif |
---|
1041 | |
---|
1042 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
1043 | { |
---|
1044 | int degAy= degree (A); |
---|
1045 | zz_pX result; |
---|
1046 | result.rep.SetLength (d*(degAy + 1)); |
---|
1047 | |
---|
1048 | zz_p *resultp; |
---|
1049 | resultp= result.rep.elts(); |
---|
1050 | zz_pX buf; |
---|
1051 | zz_p *bufp; |
---|
1052 | int j, k, bufRepLength; |
---|
1053 | |
---|
1054 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1055 | { |
---|
1056 | if (i.coeff().inCoeffDomain()) |
---|
1057 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1058 | else |
---|
1059 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1060 | |
---|
1061 | k= i.exp()*d; |
---|
1062 | bufp= buf.rep.elts(); |
---|
1063 | bufRepLength= (int) buf.rep.length(); |
---|
1064 | for (j= 0; j < bufRepLength; j++) |
---|
1065 | resultp [j + k]= bufp [j]; |
---|
1066 | } |
---|
1067 | result.normalize(); |
---|
1068 | |
---|
1069 | return result; |
---|
1070 | } |
---|
1071 | |
---|
1072 | zz_pEX kronSub (const CanonicalForm& A, int d, const Variable& alpha) |
---|
1073 | { |
---|
1074 | int degAy= degree (A); |
---|
1075 | zz_pEX result; |
---|
1076 | result.rep.SetLength (d*(degAy + 1)); |
---|
1077 | |
---|
1078 | Variable v; |
---|
1079 | zz_pE *resultp; |
---|
1080 | resultp= result.rep.elts(); |
---|
1081 | zz_pEX buf1; |
---|
1082 | zz_pE *buf1p; |
---|
1083 | zz_pX buf2; |
---|
1084 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1085 | int j, k, buf1RepLength; |
---|
1086 | |
---|
1087 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1088 | { |
---|
1089 | if (i.coeff().inCoeffDomain()) |
---|
1090 | { |
---|
1091 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1092 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
1093 | } |
---|
1094 | else |
---|
1095 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1096 | |
---|
1097 | k= i.exp()*d; |
---|
1098 | buf1p= buf1.rep.elts(); |
---|
1099 | buf1RepLength= (int) buf1.rep.length(); |
---|
1100 | for (j= 0; j < buf1RepLength; j++) |
---|
1101 | resultp [j + k]= buf1p [j]; |
---|
1102 | } |
---|
1103 | result.normalize(); |
---|
1104 | |
---|
1105 | return result; |
---|
1106 | } |
---|
1107 | |
---|
1108 | void |
---|
1109 | kronSubRecipro (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
1110 | const Variable& alpha) |
---|
1111 | { |
---|
1112 | int degAy= degree (A); |
---|
1113 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1114 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1115 | |
---|
1116 | Variable v; |
---|
1117 | zz_pE *subA1p; |
---|
1118 | zz_pE *subA2p; |
---|
1119 | subA1p= subA1.rep.elts(); |
---|
1120 | subA2p= subA2.rep.elts(); |
---|
1121 | zz_pEX buf; |
---|
1122 | zz_pE *bufp; |
---|
1123 | zz_pX buf2; |
---|
1124 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1125 | int j, k, kk, bufRepLength; |
---|
1126 | |
---|
1127 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1128 | { |
---|
1129 | if (i.coeff().inCoeffDomain()) |
---|
1130 | { |
---|
1131 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
1132 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
1133 | } |
---|
1134 | else |
---|
1135 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
1136 | |
---|
1137 | k= i.exp()*d; |
---|
1138 | kk= (degAy - i.exp())*d; |
---|
1139 | bufp= buf.rep.elts(); |
---|
1140 | bufRepLength= (int) buf.rep.length(); |
---|
1141 | for (j= 0; j < bufRepLength; j++) |
---|
1142 | { |
---|
1143 | subA1p [j + k] += bufp [j]; |
---|
1144 | subA2p [j + kk] += bufp [j]; |
---|
1145 | } |
---|
1146 | } |
---|
1147 | subA1.normalize(); |
---|
1148 | subA2.normalize(); |
---|
1149 | } |
---|
1150 | |
---|
1151 | void |
---|
1152 | kronSubRecipro (zz_pX& subA1, zz_pX& subA2,const CanonicalForm& A, int d) |
---|
1153 | { |
---|
1154 | int degAy= degree (A); |
---|
1155 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
1156 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
1157 | |
---|
1158 | zz_p *subA1p; |
---|
1159 | zz_p *subA2p; |
---|
1160 | subA1p= subA1.rep.elts(); |
---|
1161 | subA2p= subA2.rep.elts(); |
---|
1162 | zz_pX buf; |
---|
1163 | zz_p *bufp; |
---|
1164 | int j, k, kk, bufRepLength; |
---|
1165 | |
---|
1166 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1167 | { |
---|
1168 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
1169 | |
---|
1170 | k= i.exp()*d; |
---|
1171 | kk= (degAy - i.exp())*d; |
---|
1172 | bufp= buf.rep.elts(); |
---|
1173 | bufRepLength= (int) buf.rep.length(); |
---|
1174 | for (j= 0; j < bufRepLength; j++) |
---|
1175 | { |
---|
1176 | subA1p [j + k] += bufp [j]; |
---|
1177 | subA2p [j + kk] += bufp [j]; |
---|
1178 | } |
---|
1179 | } |
---|
1180 | subA1.normalize(); |
---|
1181 | subA2.normalize(); |
---|
1182 | } |
---|
1183 | |
---|
1184 | CanonicalForm |
---|
1185 | reverseSubst (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
1186 | const Variable& alpha) |
---|
1187 | { |
---|
1188 | Variable y= Variable (2); |
---|
1189 | Variable x= Variable (1); |
---|
1190 | |
---|
1191 | zz_pEX f= F; |
---|
1192 | zz_pEX g= G; |
---|
1193 | int degf= deg(f); |
---|
1194 | int degg= deg(g); |
---|
1195 | |
---|
1196 | zz_pEX buf1; |
---|
1197 | zz_pEX buf2; |
---|
1198 | zz_pEX buf3; |
---|
1199 | |
---|
1200 | zz_pE *buf1p; |
---|
1201 | zz_pE *buf2p; |
---|
1202 | zz_pE *buf3p; |
---|
1203 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1204 | f.rep.SetLength ((long)d*(k+1)); |
---|
1205 | |
---|
1206 | zz_pE *gp= g.rep.elts(); |
---|
1207 | zz_pE *fp= f.rep.elts(); |
---|
1208 | CanonicalForm result= 0; |
---|
1209 | int i= 0; |
---|
1210 | int lf= 0; |
---|
1211 | int lg= d*k; |
---|
1212 | int degfSubLf= degf; |
---|
1213 | int deggSubLg= degg-lg; |
---|
1214 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1215 | zz_pE zzpEZero= zz_pE(); |
---|
1216 | |
---|
1217 | while (degf >= lf || lg >= 0) |
---|
1218 | { |
---|
1219 | if (degfSubLf >= d) |
---|
1220 | repLengthBuf1= d; |
---|
1221 | else if (degfSubLf < 0) |
---|
1222 | repLengthBuf1= 0; |
---|
1223 | else |
---|
1224 | repLengthBuf1= degfSubLf + 1; |
---|
1225 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1226 | |
---|
1227 | buf1p= buf1.rep.elts(); |
---|
1228 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1229 | buf1p [ind]= fp [ind + lf]; |
---|
1230 | buf1.normalize(); |
---|
1231 | |
---|
1232 | repLengthBuf1= buf1.rep.length(); |
---|
1233 | |
---|
1234 | if (deggSubLg >= d - 1) |
---|
1235 | repLengthBuf2= d - 1; |
---|
1236 | else if (deggSubLg < 0) |
---|
1237 | repLengthBuf2= 0; |
---|
1238 | else |
---|
1239 | repLengthBuf2= deggSubLg + 1; |
---|
1240 | |
---|
1241 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1242 | buf2p= buf2.rep.elts(); |
---|
1243 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1244 | buf2p [ind]= gp [ind + lg]; |
---|
1245 | buf2.normalize(); |
---|
1246 | |
---|
1247 | repLengthBuf2= buf2.rep.length(); |
---|
1248 | |
---|
1249 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1250 | buf3p= buf3.rep.elts(); |
---|
1251 | buf2p= buf2.rep.elts(); |
---|
1252 | buf1p= buf1.rep.elts(); |
---|
1253 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1254 | buf3p [ind]= buf1p [ind]; |
---|
1255 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1256 | buf3p [ind]= zzpEZero; |
---|
1257 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1258 | buf3p [ind + d]= buf2p [ind]; |
---|
1259 | buf3.normalize(); |
---|
1260 | |
---|
1261 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
1262 | i++; |
---|
1263 | |
---|
1264 | |
---|
1265 | lf= i*d; |
---|
1266 | degfSubLf= degf - lf; |
---|
1267 | |
---|
1268 | lg= d*(k-i); |
---|
1269 | deggSubLg= degg - lg; |
---|
1270 | |
---|
1271 | buf1p= buf1.rep.elts(); |
---|
1272 | |
---|
1273 | if (lg >= 0 && deggSubLg > 0) |
---|
1274 | { |
---|
1275 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1276 | degfSubLf= repLengthBuf2 - 1; |
---|
1277 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1278 | for (ind= 0; ind < tmp; ind++) |
---|
1279 | gp [ind + lg] -= buf1p [ind]; |
---|
1280 | } |
---|
1281 | |
---|
1282 | if (lg < 0) |
---|
1283 | break; |
---|
1284 | |
---|
1285 | buf2p= buf2.rep.elts(); |
---|
1286 | if (degfSubLf >= 0) |
---|
1287 | { |
---|
1288 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1289 | fp [ind + lf] -= buf2p [ind]; |
---|
1290 | } |
---|
1291 | } |
---|
1292 | |
---|
1293 | return result; |
---|
1294 | } |
---|
1295 | |
---|
1296 | CanonicalForm |
---|
1297 | reverseSubst (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
1298 | { |
---|
1299 | Variable y= Variable (2); |
---|
1300 | Variable x= Variable (1); |
---|
1301 | |
---|
1302 | zz_pX f= F; |
---|
1303 | zz_pX g= G; |
---|
1304 | int degf= deg(f); |
---|
1305 | int degg= deg(g); |
---|
1306 | |
---|
1307 | zz_pX buf1; |
---|
1308 | zz_pX buf2; |
---|
1309 | zz_pX buf3; |
---|
1310 | |
---|
1311 | zz_p *buf1p; |
---|
1312 | zz_p *buf2p; |
---|
1313 | zz_p *buf3p; |
---|
1314 | |
---|
1315 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
1316 | f.rep.SetLength ((long)d*(k+1)); |
---|
1317 | |
---|
1318 | zz_p *gp= g.rep.elts(); |
---|
1319 | zz_p *fp= f.rep.elts(); |
---|
1320 | CanonicalForm result= 0; |
---|
1321 | int i= 0; |
---|
1322 | int lf= 0; |
---|
1323 | int lg= d*k; |
---|
1324 | int degfSubLf= degf; |
---|
1325 | int deggSubLg= degg-lg; |
---|
1326 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1327 | zz_p zzpZero= zz_p(); |
---|
1328 | while (degf >= lf || lg >= 0) |
---|
1329 | { |
---|
1330 | if (degfSubLf >= d) |
---|
1331 | repLengthBuf1= d; |
---|
1332 | else if (degfSubLf < 0) |
---|
1333 | repLengthBuf1= 0; |
---|
1334 | else |
---|
1335 | repLengthBuf1= degfSubLf + 1; |
---|
1336 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
1337 | |
---|
1338 | buf1p= buf1.rep.elts(); |
---|
1339 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1340 | buf1p [ind]= fp [ind + lf]; |
---|
1341 | buf1.normalize(); |
---|
1342 | |
---|
1343 | repLengthBuf1= buf1.rep.length(); |
---|
1344 | |
---|
1345 | if (deggSubLg >= d - 1) |
---|
1346 | repLengthBuf2= d - 1; |
---|
1347 | else if (deggSubLg < 0) |
---|
1348 | repLengthBuf2= 0; |
---|
1349 | else |
---|
1350 | repLengthBuf2= deggSubLg + 1; |
---|
1351 | |
---|
1352 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
1353 | buf2p= buf2.rep.elts(); |
---|
1354 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1355 | buf2p [ind]= gp [ind + lg]; |
---|
1356 | |
---|
1357 | buf2.normalize(); |
---|
1358 | |
---|
1359 | repLengthBuf2= buf2.rep.length(); |
---|
1360 | |
---|
1361 | |
---|
1362 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
1363 | buf3p= buf3.rep.elts(); |
---|
1364 | buf2p= buf2.rep.elts(); |
---|
1365 | buf1p= buf1.rep.elts(); |
---|
1366 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1367 | buf3p [ind]= buf1p [ind]; |
---|
1368 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1369 | buf3p [ind]= zzpZero; |
---|
1370 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1371 | buf3p [ind + d]= buf2p [ind]; |
---|
1372 | buf3.normalize(); |
---|
1373 | |
---|
1374 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
1375 | i++; |
---|
1376 | |
---|
1377 | |
---|
1378 | lf= i*d; |
---|
1379 | degfSubLf= degf - lf; |
---|
1380 | |
---|
1381 | lg= d*(k-i); |
---|
1382 | deggSubLg= degg - lg; |
---|
1383 | |
---|
1384 | buf1p= buf1.rep.elts(); |
---|
1385 | |
---|
1386 | if (lg >= 0 && deggSubLg > 0) |
---|
1387 | { |
---|
1388 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1389 | degfSubLf= repLengthBuf2 - 1; |
---|
1390 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1391 | for (ind= 0; ind < tmp; ind++) |
---|
1392 | gp [ind + lg] -= buf1p [ind]; |
---|
1393 | } |
---|
1394 | if (lg < 0) |
---|
1395 | break; |
---|
1396 | |
---|
1397 | buf2p= buf2.rep.elts(); |
---|
1398 | if (degfSubLf >= 0) |
---|
1399 | { |
---|
1400 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1401 | fp [ind + lf] -= buf2p [ind]; |
---|
1402 | } |
---|
1403 | } |
---|
1404 | |
---|
1405 | return result; |
---|
1406 | } |
---|
1407 | |
---|
1408 | CanonicalForm reverseSubst (const zz_pEX& F, int d, const Variable& alpha) |
---|
1409 | { |
---|
1410 | Variable y= Variable (2); |
---|
1411 | Variable x= Variable (1); |
---|
1412 | |
---|
1413 | zz_pEX f= F; |
---|
1414 | zz_pE *fp= f.rep.elts(); |
---|
1415 | |
---|
1416 | zz_pEX buf; |
---|
1417 | zz_pE *bufp; |
---|
1418 | CanonicalForm result= 0; |
---|
1419 | int i= 0; |
---|
1420 | int degf= deg(f); |
---|
1421 | int k= 0; |
---|
1422 | int degfSubK, repLength, j; |
---|
1423 | while (degf >= k) |
---|
1424 | { |
---|
1425 | degfSubK= degf - k; |
---|
1426 | if (degfSubK >= d) |
---|
1427 | repLength= d; |
---|
1428 | else |
---|
1429 | repLength= degfSubK + 1; |
---|
1430 | |
---|
1431 | buf.rep.SetLength ((long) repLength); |
---|
1432 | bufp= buf.rep.elts(); |
---|
1433 | for (j= 0; j < repLength; j++) |
---|
1434 | bufp [j]= fp [j + k]; |
---|
1435 | buf.normalize(); |
---|
1436 | |
---|
1437 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
1438 | i++; |
---|
1439 | k= d*i; |
---|
1440 | } |
---|
1441 | |
---|
1442 | return result; |
---|
1443 | } |
---|
1444 | |
---|
1445 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
1446 | { |
---|
1447 | Variable y= Variable (2); |
---|
1448 | Variable x= Variable (1); |
---|
1449 | |
---|
1450 | zz_pX f= F; |
---|
1451 | zz_p *fp= f.rep.elts(); |
---|
1452 | |
---|
1453 | zz_pX buf; |
---|
1454 | zz_p *bufp; |
---|
1455 | CanonicalForm result= 0; |
---|
1456 | int i= 0; |
---|
1457 | int degf= deg(f); |
---|
1458 | int k= 0; |
---|
1459 | int degfSubK, repLength, j; |
---|
1460 | while (degf >= k) |
---|
1461 | { |
---|
1462 | degfSubK= degf - k; |
---|
1463 | if (degfSubK >= d) |
---|
1464 | repLength= d; |
---|
1465 | else |
---|
1466 | repLength= degfSubK + 1; |
---|
1467 | |
---|
1468 | buf.rep.SetLength ((long) repLength); |
---|
1469 | bufp= buf.rep.elts(); |
---|
1470 | for (j= 0; j < repLength; j++) |
---|
1471 | bufp [j]= fp [j + k]; |
---|
1472 | buf.normalize(); |
---|
1473 | |
---|
1474 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
1475 | i++; |
---|
1476 | k= d*i; |
---|
1477 | } |
---|
1478 | |
---|
1479 | return result; |
---|
1480 | } |
---|
1481 | |
---|
1482 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
1483 | CanonicalForm |
---|
1484 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1485 | CanonicalForm& M) |
---|
1486 | { |
---|
1487 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1488 | d1 /= 2; |
---|
1489 | d1 += 1; |
---|
1490 | |
---|
1491 | zz_pX F1, F2; |
---|
1492 | kronSubRecipro (F1, F2, F, d1); |
---|
1493 | zz_pX G1, G2; |
---|
1494 | kronSubRecipro (G1, G2, G, d1); |
---|
1495 | |
---|
1496 | int k= d1*degree (M); |
---|
1497 | MulTrunc (F1, F1, G1, (long) k); |
---|
1498 | |
---|
1499 | int degtailF= degree (tailcoeff (F), 1); |
---|
1500 | int degtailG= degree (tailcoeff (G), 1); |
---|
1501 | int taildegF= taildegree (F); |
---|
1502 | int taildegG= taildegree (G); |
---|
1503 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
1504 | |
---|
1505 | reverse (F2, F2); |
---|
1506 | reverse (G2, G2); |
---|
1507 | MulTrunc (F2, F2, G2, b + 1); |
---|
1508 | reverse (F2, F2, b); |
---|
1509 | |
---|
1510 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
1511 | return reverseSubst (F1, F2, d1, d2); |
---|
1512 | } |
---|
1513 | |
---|
1514 | //Kronecker substitution |
---|
1515 | CanonicalForm |
---|
1516 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1517 | CanonicalForm& M) |
---|
1518 | { |
---|
1519 | CanonicalForm A= F; |
---|
1520 | CanonicalForm B= G; |
---|
1521 | |
---|
1522 | int degAx= degree (A, 1); |
---|
1523 | int degAy= degree (A, 2); |
---|
1524 | int degBx= degree (B, 1); |
---|
1525 | int degBy= degree (B, 2); |
---|
1526 | int d1= degAx + 1 + degBx; |
---|
1527 | int d2= tmax (degAy, degBy); |
---|
1528 | |
---|
1529 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
1530 | return mulMod2NTLFpReci (A, B, M); |
---|
1531 | |
---|
1532 | zz_pX NTLA= kronSubFp (A, d1); |
---|
1533 | zz_pX NTLB= kronSubFp (B, d1); |
---|
1534 | |
---|
1535 | int k= d1*degree (M); |
---|
1536 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
1537 | |
---|
1538 | A= reverseSubstFp (NTLA, d1); |
---|
1539 | |
---|
1540 | return A; |
---|
1541 | } |
---|
1542 | |
---|
1543 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
1544 | CanonicalForm |
---|
1545 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1546 | CanonicalForm& M, const Variable& alpha) |
---|
1547 | { |
---|
1548 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
1549 | d1 /= 2; |
---|
1550 | d1 += 1; |
---|
1551 | |
---|
1552 | zz_pEX F1, F2; |
---|
1553 | kronSubRecipro (F1, F2, F, d1, alpha); |
---|
1554 | zz_pEX G1, G2; |
---|
1555 | kronSubRecipro (G1, G2, G, d1, alpha); |
---|
1556 | |
---|
1557 | int k= d1*degree (M); |
---|
1558 | MulTrunc (F1, F1, G1, (long) k); |
---|
1559 | |
---|
1560 | int degtailF= degree (tailcoeff (F), 1); |
---|
1561 | int degtailG= degree (tailcoeff (G), 1); |
---|
1562 | int taildegF= taildegree (F); |
---|
1563 | int taildegG= taildegree (G); |
---|
1564 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
1565 | |
---|
1566 | reverse (F2, F2); |
---|
1567 | reverse (G2, G2); |
---|
1568 | MulTrunc (F2, F2, G2, b + 1); |
---|
1569 | reverse (F2, F2, b); |
---|
1570 | |
---|
1571 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
1572 | return reverseSubst (F1, F2, d1, d2, alpha); |
---|
1573 | } |
---|
1574 | |
---|
1575 | #ifdef HAVE_FLINT |
---|
1576 | CanonicalForm |
---|
1577 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1578 | CanonicalForm& M); |
---|
1579 | #endif |
---|
1580 | |
---|
1581 | CanonicalForm |
---|
1582 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
1583 | CanonicalForm& M) |
---|
1584 | { |
---|
1585 | Variable alpha; |
---|
1586 | CanonicalForm A= F; |
---|
1587 | CanonicalForm B= G; |
---|
1588 | |
---|
1589 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
1590 | { |
---|
1591 | int degAx= degree (A, 1); |
---|
1592 | int degAy= degree (A, 2); |
---|
1593 | int degBx= degree (B, 1); |
---|
1594 | int degBy= degree (B, 2); |
---|
1595 | int d1= degAx + degBx + 1; |
---|
1596 | int d2= tmax (degAy, degBy); |
---|
1597 | zz_p::init (getCharacteristic()); |
---|
1598 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1599 | zz_pE::init (NTLMipo); |
---|
1600 | |
---|
1601 | int degMipo= degree (getMipo (alpha)); |
---|
1602 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
1603 | (2*degAy > degree (M))) |
---|
1604 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
1605 | |
---|
1606 | zz_pEX NTLA= kronSub (A, d1, alpha); |
---|
1607 | zz_pEX NTLB= kronSub (B, d1, alpha); |
---|
1608 | |
---|
1609 | int k= d1*degree (M); |
---|
1610 | |
---|
1611 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
1612 | |
---|
1613 | A= reverseSubst (NTLA, d1, alpha); |
---|
1614 | |
---|
1615 | return A; |
---|
1616 | } |
---|
1617 | else |
---|
1618 | #ifdef HAVE_FLINT |
---|
1619 | return mulMod2FLINTFp (A, B, M); |
---|
1620 | #else |
---|
1621 | return mulMod2NTLFp (A, B, M); |
---|
1622 | #endif |
---|
1623 | } |
---|
1624 | |
---|
1625 | #ifdef HAVE_FLINT |
---|
1626 | void |
---|
1627 | kronSubRecipro (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
1628 | int d) |
---|
1629 | { |
---|
1630 | int degAy= degree (A); |
---|
1631 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1632 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
1633 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
1634 | |
---|
1635 | nmod_poly_t buf; |
---|
1636 | |
---|
1637 | int k, kk, j, bufRepLength; |
---|
1638 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1639 | { |
---|
1640 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
1641 | |
---|
1642 | k= i.exp()*d; |
---|
1643 | kk= (degAy - i.exp())*d; |
---|
1644 | bufRepLength= (int) nmod_poly_length (buf); |
---|
1645 | for (j= 0; j < bufRepLength; j++) |
---|
1646 | { |
---|
1647 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
1648 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
1649 | nmod_poly_get_coeff_ui (buf, j), |
---|
1650 | getCharacteristic() |
---|
1651 | ) |
---|
1652 | ); |
---|
1653 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
1654 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
1655 | nmod_poly_get_coeff_ui (buf, j), |
---|
1656 | getCharacteristic() |
---|
1657 | ) |
---|
1658 | ); |
---|
1659 | } |
---|
1660 | nmod_poly_clear (buf); |
---|
1661 | } |
---|
1662 | _nmod_poly_normalise (subA1); |
---|
1663 | _nmod_poly_normalise (subA2); |
---|
1664 | } |
---|
1665 | |
---|
1666 | void |
---|
1667 | kronSubRecipro (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
1668 | int d) |
---|
1669 | { |
---|
1670 | int degAy= degree (A); |
---|
1671 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
1672 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
1673 | |
---|
1674 | fmpz_poly_t buf; |
---|
1675 | fmpz_t coeff1, coeff2; |
---|
1676 | |
---|
1677 | int k, kk, j, bufRepLength; |
---|
1678 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
1679 | { |
---|
1680 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
1681 | |
---|
1682 | k= i.exp()*d; |
---|
1683 | kk= (degAy - i.exp())*d; |
---|
1684 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
1685 | for (j= 0; j < bufRepLength; j++) |
---|
1686 | { |
---|
1687 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
1688 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
1689 | fmpz_add (coeff1, coeff1, coeff2); |
---|
1690 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
1691 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
1692 | fmpz_add (coeff1, coeff1, coeff2); |
---|
1693 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
1694 | } |
---|
1695 | fmpz_poly_clear (buf); |
---|
1696 | } |
---|
1697 | fmpz_clear (coeff1); |
---|
1698 | fmpz_clear (coeff2); |
---|
1699 | _fmpz_poly_normalise (subA1); |
---|
1700 | _fmpz_poly_normalise (subA2); |
---|
1701 | } |
---|
1702 | |
---|
1703 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
1704 | { |
---|
1705 | Variable y= Variable (2); |
---|
1706 | Variable x= Variable (1); |
---|
1707 | |
---|
1708 | fmpz_poly_t f; |
---|
1709 | fmpz_poly_init (f); |
---|
1710 | fmpz_poly_set (f, F); |
---|
1711 | |
---|
1712 | fmpz_poly_t buf; |
---|
1713 | CanonicalForm result= 0; |
---|
1714 | int i= 0; |
---|
1715 | int degf= fmpz_poly_degree(f); |
---|
1716 | int k= 0; |
---|
1717 | int degfSubK, repLength, j; |
---|
1718 | fmpz_t coeff; |
---|
1719 | while (degf >= k) |
---|
1720 | { |
---|
1721 | degfSubK= degf - k; |
---|
1722 | if (degfSubK >= d) |
---|
1723 | repLength= d; |
---|
1724 | else |
---|
1725 | repLength= degfSubK + 1; |
---|
1726 | |
---|
1727 | fmpz_poly_init2 (buf, repLength); |
---|
1728 | fmpz_init (coeff); |
---|
1729 | for (j= 0; j < repLength; j++) |
---|
1730 | { |
---|
1731 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
1732 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
1733 | } |
---|
1734 | _fmpz_poly_normalise (buf); |
---|
1735 | |
---|
1736 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
1737 | i++; |
---|
1738 | k= d*i; |
---|
1739 | fmpz_poly_clear (buf); |
---|
1740 | fmpz_clear (coeff); |
---|
1741 | } |
---|
1742 | fmpz_poly_clear (f); |
---|
1743 | |
---|
1744 | return result; |
---|
1745 | } |
---|
1746 | |
---|
1747 | CanonicalForm |
---|
1748 | reverseSubst (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
1749 | { |
---|
1750 | Variable y= Variable (2); |
---|
1751 | Variable x= Variable (1); |
---|
1752 | |
---|
1753 | nmod_poly_t f, g; |
---|
1754 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
1755 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
1756 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
1757 | nmod_poly_set (f, F); |
---|
1758 | nmod_poly_set (g, G); |
---|
1759 | int degf= nmod_poly_degree(f); |
---|
1760 | int degg= nmod_poly_degree(g); |
---|
1761 | |
---|
1762 | |
---|
1763 | nmod_poly_t buf1,buf2, buf3; |
---|
1764 | |
---|
1765 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1766 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
1767 | |
---|
1768 | CanonicalForm result= 0; |
---|
1769 | int i= 0; |
---|
1770 | int lf= 0; |
---|
1771 | int lg= d*k; |
---|
1772 | int degfSubLf= degf; |
---|
1773 | int deggSubLg= degg-lg; |
---|
1774 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1775 | while (degf >= lf || lg >= 0) |
---|
1776 | { |
---|
1777 | if (degfSubLf >= d) |
---|
1778 | repLengthBuf1= d; |
---|
1779 | else if (degfSubLf < 0) |
---|
1780 | repLengthBuf1= 0; |
---|
1781 | else |
---|
1782 | repLengthBuf1= degfSubLf + 1; |
---|
1783 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
1784 | |
---|
1785 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1786 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
1787 | _nmod_poly_normalise (buf1); |
---|
1788 | |
---|
1789 | repLengthBuf1= nmod_poly_length (buf1); |
---|
1790 | |
---|
1791 | if (deggSubLg >= d - 1) |
---|
1792 | repLengthBuf2= d - 1; |
---|
1793 | else if (deggSubLg < 0) |
---|
1794 | repLengthBuf2= 0; |
---|
1795 | else |
---|
1796 | repLengthBuf2= deggSubLg + 1; |
---|
1797 | |
---|
1798 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
1799 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1800 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
1801 | |
---|
1802 | _nmod_poly_normalise (buf2); |
---|
1803 | repLengthBuf2= nmod_poly_length (buf2); |
---|
1804 | |
---|
1805 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
1806 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1807 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
1808 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1809 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
1810 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1811 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
1812 | _nmod_poly_normalise (buf3); |
---|
1813 | |
---|
1814 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1815 | i++; |
---|
1816 | |
---|
1817 | |
---|
1818 | lf= i*d; |
---|
1819 | degfSubLf= degf - lf; |
---|
1820 | |
---|
1821 | lg= d*(k-i); |
---|
1822 | deggSubLg= degg - lg; |
---|
1823 | |
---|
1824 | if (lg >= 0 && deggSubLg > 0) |
---|
1825 | { |
---|
1826 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1827 | degfSubLf= repLengthBuf2 - 1; |
---|
1828 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1829 | for (ind= 0; ind < tmp; ind++) |
---|
1830 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
1831 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
1832 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
1833 | getCharacteristic() |
---|
1834 | ) |
---|
1835 | ); |
---|
1836 | } |
---|
1837 | if (lg < 0) |
---|
1838 | { |
---|
1839 | nmod_poly_clear (buf1); |
---|
1840 | nmod_poly_clear (buf2); |
---|
1841 | nmod_poly_clear (buf3); |
---|
1842 | break; |
---|
1843 | } |
---|
1844 | if (degfSubLf >= 0) |
---|
1845 | { |
---|
1846 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1847 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
1848 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
1849 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
1850 | getCharacteristic() |
---|
1851 | ) |
---|
1852 | ); |
---|
1853 | } |
---|
1854 | nmod_poly_clear (buf1); |
---|
1855 | nmod_poly_clear (buf2); |
---|
1856 | nmod_poly_clear (buf3); |
---|
1857 | } |
---|
1858 | |
---|
1859 | nmod_poly_clear (f); |
---|
1860 | nmod_poly_clear (g); |
---|
1861 | |
---|
1862 | return result; |
---|
1863 | } |
---|
1864 | |
---|
1865 | CanonicalForm |
---|
1866 | reverseSubst (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
1867 | { |
---|
1868 | Variable y= Variable (2); |
---|
1869 | Variable x= Variable (1); |
---|
1870 | |
---|
1871 | fmpz_poly_t f, g; |
---|
1872 | fmpz_poly_init (f); |
---|
1873 | fmpz_poly_init (g); |
---|
1874 | fmpz_poly_set (f, F); |
---|
1875 | fmpz_poly_set (g, G); |
---|
1876 | int degf= fmpz_poly_degree(f); |
---|
1877 | int degg= fmpz_poly_degree(g); |
---|
1878 | |
---|
1879 | |
---|
1880 | fmpz_poly_t buf1,buf2, buf3; |
---|
1881 | |
---|
1882 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
1883 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
1884 | |
---|
1885 | CanonicalForm result= 0; |
---|
1886 | int i= 0; |
---|
1887 | int lf= 0; |
---|
1888 | int lg= d*k; |
---|
1889 | int degfSubLf= degf; |
---|
1890 | int deggSubLg= degg-lg; |
---|
1891 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
1892 | fmpz_t tmp1, tmp2; |
---|
1893 | while (degf >= lf || lg >= 0) |
---|
1894 | { |
---|
1895 | if (degfSubLf >= d) |
---|
1896 | repLengthBuf1= d; |
---|
1897 | else if (degfSubLf < 0) |
---|
1898 | repLengthBuf1= 0; |
---|
1899 | else |
---|
1900 | repLengthBuf1= degfSubLf + 1; |
---|
1901 | |
---|
1902 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
1903 | |
---|
1904 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1905 | { |
---|
1906 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1907 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
1908 | } |
---|
1909 | _fmpz_poly_normalise (buf1); |
---|
1910 | |
---|
1911 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
1912 | |
---|
1913 | if (deggSubLg >= d - 1) |
---|
1914 | repLengthBuf2= d - 1; |
---|
1915 | else if (deggSubLg < 0) |
---|
1916 | repLengthBuf2= 0; |
---|
1917 | else |
---|
1918 | repLengthBuf2= deggSubLg + 1; |
---|
1919 | |
---|
1920 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
1921 | |
---|
1922 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1923 | { |
---|
1924 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1925 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
1926 | } |
---|
1927 | |
---|
1928 | _fmpz_poly_normalise (buf2); |
---|
1929 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
1930 | |
---|
1931 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
1932 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
1933 | { |
---|
1934 | 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)) |
---|
1935 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
1936 | } |
---|
1937 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
1938 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
1939 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1940 | { |
---|
1941 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
1942 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
1943 | } |
---|
1944 | _fmpz_poly_normalise (buf3); |
---|
1945 | |
---|
1946 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
1947 | i++; |
---|
1948 | |
---|
1949 | |
---|
1950 | lf= i*d; |
---|
1951 | degfSubLf= degf - lf; |
---|
1952 | |
---|
1953 | lg= d*(k-i); |
---|
1954 | deggSubLg= degg - lg; |
---|
1955 | |
---|
1956 | if (lg >= 0 && deggSubLg > 0) |
---|
1957 | { |
---|
1958 | if (repLengthBuf2 > degfSubLf + 1) |
---|
1959 | degfSubLf= repLengthBuf2 - 1; |
---|
1960 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
1961 | for (ind= 0; ind < tmp; ind++) |
---|
1962 | { |
---|
1963 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
1964 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
1965 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1966 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
1967 | } |
---|
1968 | } |
---|
1969 | if (lg < 0) |
---|
1970 | { |
---|
1971 | fmpz_poly_clear (buf1); |
---|
1972 | fmpz_poly_clear (buf2); |
---|
1973 | fmpz_poly_clear (buf3); |
---|
1974 | break; |
---|
1975 | } |
---|
1976 | if (degfSubLf >= 0) |
---|
1977 | { |
---|
1978 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
1979 | { |
---|
1980 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
1981 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
1982 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
1983 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
1984 | } |
---|
1985 | } |
---|
1986 | fmpz_poly_clear (buf1); |
---|
1987 | fmpz_poly_clear (buf2); |
---|
1988 | fmpz_poly_clear (buf3); |
---|
1989 | } |
---|
1990 | |
---|
1991 | fmpz_poly_clear (f); |
---|
1992 | fmpz_poly_clear (g); |
---|
1993 | fmpz_clear (tmp1); |
---|
1994 | fmpz_clear (tmp2); |
---|
1995 | |
---|
1996 | return result; |
---|
1997 | } |
---|
1998 | |
---|
1999 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
2000 | { |
---|
2001 | Variable y= Variable (2); |
---|
2002 | Variable x= Variable (1); |
---|
2003 | |
---|
2004 | nmod_poly_t f; |
---|
2005 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
2006 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
2007 | nmod_poly_set (f, F); |
---|
2008 | |
---|
2009 | nmod_poly_t buf; |
---|
2010 | CanonicalForm result= 0; |
---|
2011 | int i= 0; |
---|
2012 | int degf= nmod_poly_degree(f); |
---|
2013 | int k= 0; |
---|
2014 | int degfSubK, repLength, j; |
---|
2015 | while (degf >= k) |
---|
2016 | { |
---|
2017 | degfSubK= degf - k; |
---|
2018 | if (degfSubK >= d) |
---|
2019 | repLength= d; |
---|
2020 | else |
---|
2021 | repLength= degfSubK + 1; |
---|
2022 | |
---|
2023 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
2024 | for (j= 0; j < repLength; j++) |
---|
2025 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
2026 | _nmod_poly_normalise (buf); |
---|
2027 | |
---|
2028 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
2029 | i++; |
---|
2030 | k= d*i; |
---|
2031 | nmod_poly_clear (buf); |
---|
2032 | } |
---|
2033 | nmod_poly_clear (f); |
---|
2034 | |
---|
2035 | return result; |
---|
2036 | } |
---|
2037 | |
---|
2038 | CanonicalForm |
---|
2039 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2040 | CanonicalForm& M) |
---|
2041 | { |
---|
2042 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
2043 | d1 /= 2; |
---|
2044 | d1 += 1; |
---|
2045 | |
---|
2046 | nmod_poly_t F1, F2; |
---|
2047 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
2048 | nmod_poly_init_preinv (F1, getCharacteristic(), ninv); |
---|
2049 | nmod_poly_init_preinv (F2, getCharacteristic(), ninv); |
---|
2050 | kronSubRecipro (F1, F2, F, d1); |
---|
2051 | |
---|
2052 | nmod_poly_t G1, G2; |
---|
2053 | nmod_poly_init_preinv (G1, getCharacteristic(), ninv); |
---|
2054 | nmod_poly_init_preinv (G2, getCharacteristic(), ninv); |
---|
2055 | kronSubRecipro (G1, G2, G, d1); |
---|
2056 | |
---|
2057 | int k= d1*degree (M); |
---|
2058 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
2059 | |
---|
2060 | int degtailF= degree (tailcoeff (F), 1);; |
---|
2061 | int degtailG= degree (tailcoeff (G), 1); |
---|
2062 | int taildegF= taildegree (F); |
---|
2063 | int taildegG= taildegree (G); |
---|
2064 | |
---|
2065 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
2066 | + d1*(2+taildegF + taildegG); |
---|
2067 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
2068 | nmod_poly_shift_right (F2, F2, b); |
---|
2069 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
2070 | |
---|
2071 | |
---|
2072 | CanonicalForm result= reverseSubst (F1, F2, d1, d2); |
---|
2073 | |
---|
2074 | nmod_poly_clear (F1); |
---|
2075 | nmod_poly_clear (F2); |
---|
2076 | nmod_poly_clear (G1); |
---|
2077 | nmod_poly_clear (G2); |
---|
2078 | return result; |
---|
2079 | } |
---|
2080 | |
---|
2081 | CanonicalForm |
---|
2082 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2083 | CanonicalForm& M) |
---|
2084 | { |
---|
2085 | CanonicalForm A= F; |
---|
2086 | CanonicalForm B= G; |
---|
2087 | |
---|
2088 | int degAx= degree (A, 1); |
---|
2089 | int degAy= degree (A, 2); |
---|
2090 | int degBx= degree (B, 1); |
---|
2091 | int degBy= degree (B, 2); |
---|
2092 | int d1= degAx + 1 + degBx; |
---|
2093 | int d2= tmax (degAy, degBy); |
---|
2094 | |
---|
2095 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
2096 | return mulMod2FLINTFpReci (A, B, M); |
---|
2097 | |
---|
2098 | nmod_poly_t FLINTA, FLINTB; |
---|
2099 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
2100 | nmod_poly_init_preinv (FLINTA, getCharacteristic(), ninv); |
---|
2101 | nmod_poly_init_preinv (FLINTB, getCharacteristic(), ninv); |
---|
2102 | kronSubFp (FLINTA, A, d1); |
---|
2103 | kronSubFp (FLINTB, B, d1); |
---|
2104 | |
---|
2105 | int k= d1*degree (M); |
---|
2106 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
2107 | |
---|
2108 | A= reverseSubstFp (FLINTA, d1); |
---|
2109 | |
---|
2110 | nmod_poly_clear (FLINTA); |
---|
2111 | nmod_poly_clear (FLINTB); |
---|
2112 | return A; |
---|
2113 | } |
---|
2114 | |
---|
2115 | CanonicalForm |
---|
2116 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2117 | CanonicalForm& M) |
---|
2118 | { |
---|
2119 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
2120 | d1 /= 2; |
---|
2121 | d1 += 1; |
---|
2122 | |
---|
2123 | fmpz_poly_t F1, F2; |
---|
2124 | fmpz_poly_init (F1); |
---|
2125 | fmpz_poly_init (F2); |
---|
2126 | kronSubRecipro (F1, F2, F, d1); |
---|
2127 | |
---|
2128 | fmpz_poly_t G1, G2; |
---|
2129 | fmpz_poly_init (G1); |
---|
2130 | fmpz_poly_init (G2); |
---|
2131 | kronSubRecipro (G1, G2, G, d1); |
---|
2132 | |
---|
2133 | int k= d1*degree (M); |
---|
2134 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
2135 | |
---|
2136 | int degtailF= degree (tailcoeff (F), 1);; |
---|
2137 | int degtailG= degree (tailcoeff (G), 1); |
---|
2138 | int taildegF= taildegree (F); |
---|
2139 | int taildegG= taildegree (G); |
---|
2140 | |
---|
2141 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
2142 | + d1*(2+taildegF + taildegG); |
---|
2143 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
2144 | fmpz_poly_shift_right (F2, F2, b); |
---|
2145 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
2146 | |
---|
2147 | CanonicalForm result= reverseSubst (F1, F2, d1, d2); |
---|
2148 | |
---|
2149 | fmpz_poly_clear (F1); |
---|
2150 | fmpz_poly_clear (F2); |
---|
2151 | fmpz_poly_clear (G1); |
---|
2152 | fmpz_poly_clear (G2); |
---|
2153 | return result; |
---|
2154 | } |
---|
2155 | |
---|
2156 | CanonicalForm |
---|
2157 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
2158 | CanonicalForm& M) |
---|
2159 | { |
---|
2160 | CanonicalForm A= F; |
---|
2161 | CanonicalForm B= G; |
---|
2162 | |
---|
2163 | int degAx= degree (A, 1); |
---|
2164 | int degBx= degree (B, 1); |
---|
2165 | int d1= degAx + 1 + degBx; |
---|
2166 | |
---|
2167 | CanonicalForm f= bCommonDen (F); |
---|
2168 | CanonicalForm g= bCommonDen (G); |
---|
2169 | A *= f; |
---|
2170 | B *= g; |
---|
2171 | |
---|
2172 | fmpz_poly_t FLINTA, FLINTB; |
---|
2173 | fmpz_poly_init (FLINTA); |
---|
2174 | fmpz_poly_init (FLINTB); |
---|
2175 | kronSub (FLINTA, A, d1); |
---|
2176 | kronSub (FLINTB, B, d1); |
---|
2177 | int k= d1*degree (M); |
---|
2178 | |
---|
2179 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
2180 | A= reverseSubstQ (FLINTA, d1); |
---|
2181 | fmpz_poly_clear (FLINTA); |
---|
2182 | fmpz_poly_clear (FLINTB); |
---|
2183 | return A/(f*g); |
---|
2184 | } |
---|
2185 | |
---|
2186 | #endif |
---|
2187 | |
---|
2188 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
2189 | const CanonicalForm& M) |
---|
2190 | { |
---|
2191 | if (A.isZero() || B.isZero()) |
---|
2192 | return 0; |
---|
2193 | |
---|
2194 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
2195 | |
---|
2196 | CanonicalForm F= mod (A, M); |
---|
2197 | CanonicalForm G= mod (B, M); |
---|
2198 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
2199 | return F*G; |
---|
2200 | Variable y= M.mvar(); |
---|
2201 | int degF= degree (F, y); |
---|
2202 | int degG= degree (G, y); |
---|
2203 | |
---|
2204 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
2205 | (F.level() == G.level())) |
---|
2206 | { |
---|
2207 | CanonicalForm result= mulNTL (F, G); |
---|
2208 | return mod (result, M); |
---|
2209 | } |
---|
2210 | else if (degF <= 1 && degG <= 1) |
---|
2211 | { |
---|
2212 | CanonicalForm result= F*G; |
---|
2213 | return mod (result, M); |
---|
2214 | } |
---|
2215 | |
---|
2216 | int sizeF= size (F); |
---|
2217 | int sizeG= size (G); |
---|
2218 | |
---|
2219 | int fallBackToNaive= 50; |
---|
2220 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
2221 | return mod (F*G, M); |
---|
2222 | |
---|
2223 | #ifdef HAVE_FLINT |
---|
2224 | Variable alpha; |
---|
2225 | if (getCharacteristic() == 0 && !hasFirstAlgVar (F, alpha) && ! hasFirstAlgVar (G, alpha)) |
---|
2226 | return mulMod2FLINTQ (F, G, M); |
---|
2227 | #endif |
---|
2228 | |
---|
2229 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
2230 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
2231 | return mulMod2NTLFq (F, G, M); |
---|
2232 | |
---|
2233 | int m= (int) ceil (degree (M)/2.0); |
---|
2234 | if (degF >= m || degG >= m) |
---|
2235 | { |
---|
2236 | CanonicalForm MLo= power (y, m); |
---|
2237 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2238 | CanonicalForm F0= mod (F, MLo); |
---|
2239 | CanonicalForm F1= div (F, MLo); |
---|
2240 | CanonicalForm G0= mod (G, MLo); |
---|
2241 | CanonicalForm G1= div (G, MLo); |
---|
2242 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
2243 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
2244 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
2245 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2246 | } |
---|
2247 | else |
---|
2248 | { |
---|
2249 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2250 | CanonicalForm yToM= power (y, m); |
---|
2251 | CanonicalForm F0= mod (F, yToM); |
---|
2252 | CanonicalForm F1= div (F, yToM); |
---|
2253 | CanonicalForm G0= mod (G, yToM); |
---|
2254 | CanonicalForm G1= div (G, yToM); |
---|
2255 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
2256 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
2257 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
2258 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2259 | } |
---|
2260 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
2261 | } |
---|
2262 | |
---|
2263 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
2264 | const CFList& MOD) |
---|
2265 | { |
---|
2266 | if (A.isZero() || B.isZero()) |
---|
2267 | return 0; |
---|
2268 | |
---|
2269 | if (MOD.length() == 1) |
---|
2270 | return mulMod2 (A, B, MOD.getLast()); |
---|
2271 | |
---|
2272 | CanonicalForm M= MOD.getLast(); |
---|
2273 | CanonicalForm F= mod (A, M); |
---|
2274 | CanonicalForm G= mod (B, M); |
---|
2275 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
2276 | return F*G; |
---|
2277 | Variable y= M.mvar(); |
---|
2278 | int degF= degree (F, y); |
---|
2279 | int degG= degree (G, y); |
---|
2280 | |
---|
2281 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
2282 | (degG <= 1 && G.level() <= M.level())) |
---|
2283 | { |
---|
2284 | CFList buf= MOD; |
---|
2285 | buf.removeLast(); |
---|
2286 | if (degF == 1 && degG == 1) |
---|
2287 | { |
---|
2288 | CanonicalForm F0= mod (F, y); |
---|
2289 | CanonicalForm F1= div (F, y); |
---|
2290 | CanonicalForm G0= mod (G, y); |
---|
2291 | CanonicalForm G1= div (G, y); |
---|
2292 | if (degree (M) > 2) |
---|
2293 | { |
---|
2294 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
2295 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
2296 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
2297 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
2298 | } |
---|
2299 | else //here degree (M) == 2 |
---|
2300 | { |
---|
2301 | buf.append (y); |
---|
2302 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2303 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2304 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2305 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
2306 | return result; |
---|
2307 | } |
---|
2308 | } |
---|
2309 | else if (degF == 1 && degG == 0) |
---|
2310 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
2311 | else if (degF == 0 && degG == 1) |
---|
2312 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
2313 | else |
---|
2314 | return mulMod (F, G, buf); |
---|
2315 | } |
---|
2316 | int m= (int) ceil (degree (M)/2.0); |
---|
2317 | if (degF >= m || degG >= m) |
---|
2318 | { |
---|
2319 | CanonicalForm MLo= power (y, m); |
---|
2320 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
2321 | CanonicalForm F0= mod (F, MLo); |
---|
2322 | CanonicalForm F1= div (F, MLo); |
---|
2323 | CanonicalForm G0= mod (G, MLo); |
---|
2324 | CanonicalForm G1= div (G, MLo); |
---|
2325 | CFList buf= MOD; |
---|
2326 | buf.removeLast(); |
---|
2327 | buf.append (MHi); |
---|
2328 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
2329 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
2330 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
2331 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
2332 | } |
---|
2333 | else |
---|
2334 | { |
---|
2335 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
2336 | CanonicalForm yToM= power (y, m); |
---|
2337 | CanonicalForm F0= mod (F, yToM); |
---|
2338 | CanonicalForm F1= div (F, yToM); |
---|
2339 | CanonicalForm G0= mod (G, yToM); |
---|
2340 | CanonicalForm G1= div (G, yToM); |
---|
2341 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
2342 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
2343 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
2344 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
2345 | } |
---|
2346 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
2347 | } |
---|
2348 | |
---|
2349 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
2350 | { |
---|
2351 | if (L.isEmpty()) |
---|
2352 | return 1; |
---|
2353 | int l= L.length(); |
---|
2354 | if (l == 1) |
---|
2355 | return mod (L.getFirst(), M); |
---|
2356 | else if (l == 2) { |
---|
2357 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
2358 | return result; |
---|
2359 | } |
---|
2360 | else |
---|
2361 | { |
---|
2362 | l /= 2; |
---|
2363 | CFList tmp1, tmp2; |
---|
2364 | CFListIterator i= L; |
---|
2365 | CanonicalForm buf1, buf2; |
---|
2366 | for (int j= 1; j <= l; j++, i++) |
---|
2367 | tmp1.append (i.getItem()); |
---|
2368 | tmp2= Difference (L, tmp1); |
---|
2369 | buf1= prodMod (tmp1, M); |
---|
2370 | buf2= prodMod (tmp2, M); |
---|
2371 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
2372 | return result; |
---|
2373 | } |
---|
2374 | } |
---|
2375 | |
---|
2376 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
2377 | { |
---|
2378 | if (L.isEmpty()) |
---|
2379 | return 1; |
---|
2380 | else if (L.length() == 1) |
---|
2381 | return L.getFirst(); |
---|
2382 | else if (L.length() == 2) |
---|
2383 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
2384 | else |
---|
2385 | { |
---|
2386 | int l= L.length()/2; |
---|
2387 | CFListIterator i= L; |
---|
2388 | CFList tmp1, tmp2; |
---|
2389 | CanonicalForm buf1, buf2; |
---|
2390 | for (int j= 1; j <= l; j++, i++) |
---|
2391 | tmp1.append (i.getItem()); |
---|
2392 | tmp2= Difference (L, tmp1); |
---|
2393 | buf1= prodMod (tmp1, M); |
---|
2394 | buf2= prodMod (tmp2, M); |
---|
2395 | return mulMod (buf1, buf2, M); |
---|
2396 | } |
---|
2397 | } |
---|
2398 | |
---|
2399 | |
---|
2400 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
2401 | { |
---|
2402 | if (d == 0) |
---|
2403 | return F; |
---|
2404 | CanonicalForm A= F; |
---|
2405 | Variable y= Variable (2); |
---|
2406 | Variable x= Variable (1); |
---|
2407 | if (degree (A, x) > 0) |
---|
2408 | { |
---|
2409 | A= swapvar (A, x, y); |
---|
2410 | CanonicalForm result= 0; |
---|
2411 | CFIterator i= A; |
---|
2412 | while (d - i.exp() < 0) |
---|
2413 | i++; |
---|
2414 | |
---|
2415 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
2416 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
2417 | return result; |
---|
2418 | } |
---|
2419 | else |
---|
2420 | return A*power (x, d); |
---|
2421 | } |
---|
2422 | |
---|
2423 | CanonicalForm |
---|
2424 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
2425 | { |
---|
2426 | int l= ilog2(n); |
---|
2427 | |
---|
2428 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
2429 | |
---|
2430 | ASSERT (!g.isZero(), "expected a unit"); |
---|
2431 | |
---|
2432 | Variable alpha; |
---|
2433 | |
---|
2434 | if (!g.isOne()) |
---|
2435 | g = 1/g; |
---|
2436 | Variable x= Variable (1); |
---|
2437 | CanonicalForm result; |
---|
2438 | int exp= 0; |
---|
2439 | if (n & 1) |
---|
2440 | { |
---|
2441 | result= g; |
---|
2442 | exp= 1; |
---|
2443 | } |
---|
2444 | CanonicalForm h; |
---|
2445 | |
---|
2446 | for (int i= 1; i <= l; i++) |
---|
2447 | { |
---|
2448 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
2449 | h= mod (h, power (x, (1 << i)) - 1); |
---|
2450 | h= div (h, power (x, (1 << (i - 1)))); |
---|
2451 | h= mod (h, M); |
---|
2452 | g -= power (x, (1 << (i - 1)))* |
---|
2453 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
2454 | |
---|
2455 | if (n & (1 << i)) |
---|
2456 | { |
---|
2457 | if (exp) |
---|
2458 | { |
---|
2459 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
2460 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
2461 | h= div (h, power (x, exp)); |
---|
2462 | h= mod (h, M); |
---|
2463 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
2464 | power (x, (1 << i))); |
---|
2465 | exp += (1 << i); |
---|
2466 | } |
---|
2467 | else |
---|
2468 | { |
---|
2469 | exp= (1 << i); |
---|
2470 | result= g; |
---|
2471 | } |
---|
2472 | } |
---|
2473 | } |
---|
2474 | |
---|
2475 | return result; |
---|
2476 | } |
---|
2477 | |
---|
2478 | CanonicalForm |
---|
2479 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
2480 | M) |
---|
2481 | { |
---|
2482 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
2483 | ASSERT (CFFactory::gettype() != GaloisFieldDomain, "no GF expected"); |
---|
2484 | |
---|
2485 | CanonicalForm A= mod (F, M); |
---|
2486 | CanonicalForm B= mod (G, M); |
---|
2487 | |
---|
2488 | Variable x= Variable (1); |
---|
2489 | int degA= degree (A, x); |
---|
2490 | int degB= degree (B, x); |
---|
2491 | int m= degA - degB; |
---|
2492 | if (m < 0) |
---|
2493 | return 0; |
---|
2494 | |
---|
2495 | Variable v; |
---|
2496 | CanonicalForm Q; |
---|
2497 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2498 | { |
---|
2499 | CanonicalForm R; |
---|
2500 | divrem2 (A, B, Q, R, M); |
---|
2501 | } |
---|
2502 | else |
---|
2503 | { |
---|
2504 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2505 | { |
---|
2506 | CanonicalForm R= reverse (A, degA); |
---|
2507 | CanonicalForm revB= reverse (B, degB); |
---|
2508 | revB= newtonInverse (revB, m + 1, M); |
---|
2509 | Q= mulMod2 (R, revB, M); |
---|
2510 | Q= mod (Q, power (x, m + 1)); |
---|
2511 | Q= reverse (Q, m); |
---|
2512 | } |
---|
2513 | else |
---|
2514 | { |
---|
2515 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2516 | Variable y= Variable (2); |
---|
2517 | zz_pEX NTLA, NTLB; |
---|
2518 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2519 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2520 | div (NTLA, NTLA, NTLB); |
---|
2521 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
2522 | } |
---|
2523 | } |
---|
2524 | |
---|
2525 | return Q; |
---|
2526 | } |
---|
2527 | |
---|
2528 | void |
---|
2529 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2530 | CanonicalForm& R, const CanonicalForm& M) |
---|
2531 | { |
---|
2532 | CanonicalForm A= mod (F, M); |
---|
2533 | CanonicalForm B= mod (G, M); |
---|
2534 | Variable x= Variable (1); |
---|
2535 | int degA= degree (A, x); |
---|
2536 | int degB= degree (B, x); |
---|
2537 | int m= degA - degB; |
---|
2538 | |
---|
2539 | if (m < 0) |
---|
2540 | { |
---|
2541 | R= A; |
---|
2542 | Q= 0; |
---|
2543 | return; |
---|
2544 | } |
---|
2545 | |
---|
2546 | Variable v; |
---|
2547 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
2548 | { |
---|
2549 | divrem2 (A, B, Q, R, M); |
---|
2550 | } |
---|
2551 | else |
---|
2552 | { |
---|
2553 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
2554 | { |
---|
2555 | R= reverse (A, degA); |
---|
2556 | |
---|
2557 | CanonicalForm revB= reverse (B, degB); |
---|
2558 | revB= newtonInverse (revB, m + 1, M); |
---|
2559 | Q= mulMod2 (R, revB, M); |
---|
2560 | |
---|
2561 | Q= mod (Q, power (x, m + 1)); |
---|
2562 | Q= reverse (Q, m); |
---|
2563 | |
---|
2564 | R= A - mulMod2 (Q, B, M); |
---|
2565 | } |
---|
2566 | else |
---|
2567 | { |
---|
2568 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
2569 | Variable y= Variable (2); |
---|
2570 | zz_pEX NTLA, NTLB; |
---|
2571 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
2572 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
2573 | zz_pEX NTLQ, NTLR; |
---|
2574 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
2575 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
2576 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
2577 | } |
---|
2578 | } |
---|
2579 | } |
---|
2580 | |
---|
2581 | static inline |
---|
2582 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
2583 | { |
---|
2584 | CanonicalForm A= F; |
---|
2585 | CanonicalForm buf= 0; |
---|
2586 | bool swap= false; |
---|
2587 | if (degree (A, x) <= 0) |
---|
2588 | return CFList(A); |
---|
2589 | else if (x.level() != A.level()) |
---|
2590 | { |
---|
2591 | swap= true; |
---|
2592 | A= swapvar (A, x, A.mvar()); |
---|
2593 | } |
---|
2594 | |
---|
2595 | int j= (int) floor ((double) degree (A)/ m); |
---|
2596 | CFList result; |
---|
2597 | CFIterator i= A; |
---|
2598 | for (; j >= 0; j--) |
---|
2599 | { |
---|
2600 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
2601 | { |
---|
2602 | if (swap) |
---|
2603 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
2604 | else |
---|
2605 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
2606 | i++; |
---|
2607 | } |
---|
2608 | if (swap) |
---|
2609 | result.append (swapvar (buf, x, F.mvar())); |
---|
2610 | else |
---|
2611 | result.append (buf); |
---|
2612 | buf= 0; |
---|
2613 | } |
---|
2614 | return result; |
---|
2615 | } |
---|
2616 | |
---|
2617 | static inline |
---|
2618 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2619 | CanonicalForm& R, const CFList& M); |
---|
2620 | |
---|
2621 | static inline |
---|
2622 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2623 | CanonicalForm& R, const CFList& M) |
---|
2624 | { |
---|
2625 | CanonicalForm A= mod (F, M); |
---|
2626 | CanonicalForm B= mod (G, M); |
---|
2627 | Variable x= Variable (1); |
---|
2628 | int degB= degree (B, x); |
---|
2629 | int degA= degree (A, x); |
---|
2630 | if (degA < degB) |
---|
2631 | { |
---|
2632 | Q= 0; |
---|
2633 | R= A; |
---|
2634 | return; |
---|
2635 | } |
---|
2636 | ASSERT (2*degB > degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
2637 | if (degB < 1) |
---|
2638 | { |
---|
2639 | divrem (A, B, Q, R); |
---|
2640 | Q= mod (Q, M); |
---|
2641 | R= mod (R, M); |
---|
2642 | return; |
---|
2643 | } |
---|
2644 | |
---|
2645 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
2646 | CFList splitA= split (A, m, x); |
---|
2647 | if (splitA.length() == 3) |
---|
2648 | splitA.insert (0); |
---|
2649 | if (splitA.length() == 2) |
---|
2650 | { |
---|
2651 | splitA.insert (0); |
---|
2652 | splitA.insert (0); |
---|
2653 | } |
---|
2654 | if (splitA.length() == 1) |
---|
2655 | { |
---|
2656 | splitA.insert (0); |
---|
2657 | splitA.insert (0); |
---|
2658 | splitA.insert (0); |
---|
2659 | } |
---|
2660 | |
---|
2661 | CanonicalForm xToM= power (x, m); |
---|
2662 | |
---|
2663 | CFListIterator i= splitA; |
---|
2664 | CanonicalForm H= i.getItem(); |
---|
2665 | i++; |
---|
2666 | H *= xToM; |
---|
2667 | H += i.getItem(); |
---|
2668 | i++; |
---|
2669 | H *= xToM; |
---|
2670 | H += i.getItem(); |
---|
2671 | i++; |
---|
2672 | |
---|
2673 | divrem32 (H, B, Q, R, M); |
---|
2674 | |
---|
2675 | CFList splitR= split (R, m, x); |
---|
2676 | if (splitR.length() == 1) |
---|
2677 | splitR.insert (0); |
---|
2678 | |
---|
2679 | H= splitR.getFirst(); |
---|
2680 | H *= xToM; |
---|
2681 | H += splitR.getLast(); |
---|
2682 | H *= xToM; |
---|
2683 | H += i.getItem(); |
---|
2684 | |
---|
2685 | CanonicalForm bufQ; |
---|
2686 | divrem32 (H, B, bufQ, R, M); |
---|
2687 | |
---|
2688 | Q *= xToM; |
---|
2689 | Q += bufQ; |
---|
2690 | return; |
---|
2691 | } |
---|
2692 | |
---|
2693 | static inline |
---|
2694 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2695 | CanonicalForm& R, const CFList& M) |
---|
2696 | { |
---|
2697 | CanonicalForm A= mod (F, M); |
---|
2698 | CanonicalForm B= mod (G, M); |
---|
2699 | Variable x= Variable (1); |
---|
2700 | int degB= degree (B, x); |
---|
2701 | int degA= degree (A, x); |
---|
2702 | if (degA < degB) |
---|
2703 | { |
---|
2704 | Q= 0; |
---|
2705 | R= A; |
---|
2706 | return; |
---|
2707 | } |
---|
2708 | ASSERT (3*(degB/2) > degA, "expected degree (F, 1) < 3*(degree (G, 1)/2)"); |
---|
2709 | if (degB < 1) |
---|
2710 | { |
---|
2711 | divrem (A, B, Q, R); |
---|
2712 | Q= mod (Q, M); |
---|
2713 | R= mod (R, M); |
---|
2714 | return; |
---|
2715 | } |
---|
2716 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
2717 | |
---|
2718 | CFList splitA= split (A, m, x); |
---|
2719 | CFList splitB= split (B, m, x); |
---|
2720 | |
---|
2721 | if (splitA.length() == 2) |
---|
2722 | { |
---|
2723 | splitA.insert (0); |
---|
2724 | } |
---|
2725 | if (splitA.length() == 1) |
---|
2726 | { |
---|
2727 | splitA.insert (0); |
---|
2728 | splitA.insert (0); |
---|
2729 | } |
---|
2730 | CanonicalForm xToM= power (x, m); |
---|
2731 | |
---|
2732 | CanonicalForm H; |
---|
2733 | CFListIterator i= splitA; |
---|
2734 | i++; |
---|
2735 | |
---|
2736 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
2737 | { |
---|
2738 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
2739 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
2740 | } |
---|
2741 | else |
---|
2742 | { |
---|
2743 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
2744 | splitB.getFirst()*xToM; |
---|
2745 | Q= xToM - 1; |
---|
2746 | } |
---|
2747 | |
---|
2748 | H= mulMod (Q, splitB.getLast(), M); |
---|
2749 | |
---|
2750 | R= R*xToM + splitA.getLast() - H; |
---|
2751 | |
---|
2752 | while (degree (R, x) >= degB) |
---|
2753 | { |
---|
2754 | xToM= power (x, degree (R, x) - degB); |
---|
2755 | Q += LC (R, x)*xToM; |
---|
2756 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
2757 | Q= mod (Q, M); |
---|
2758 | R= mod (R, M); |
---|
2759 | } |
---|
2760 | |
---|
2761 | return; |
---|
2762 | } |
---|
2763 | |
---|
2764 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2765 | CanonicalForm& R, const CanonicalForm& M) |
---|
2766 | { |
---|
2767 | CanonicalForm A= mod (F, M); |
---|
2768 | CanonicalForm B= mod (G, M); |
---|
2769 | |
---|
2770 | if (B.inCoeffDomain()) |
---|
2771 | { |
---|
2772 | divrem (A, B, Q, R); |
---|
2773 | return; |
---|
2774 | } |
---|
2775 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
2776 | { |
---|
2777 | Q= 0; |
---|
2778 | R= A; |
---|
2779 | return; |
---|
2780 | } |
---|
2781 | |
---|
2782 | if (B.level() < A.level()) |
---|
2783 | { |
---|
2784 | divrem (A, B, Q, R); |
---|
2785 | return; |
---|
2786 | } |
---|
2787 | if (A.level() > B.level()) |
---|
2788 | { |
---|
2789 | R= A; |
---|
2790 | Q= 0; |
---|
2791 | return; |
---|
2792 | } |
---|
2793 | if (B.level() == 1 && B.isUnivariate()) |
---|
2794 | { |
---|
2795 | divrem (A, B, Q, R); |
---|
2796 | return; |
---|
2797 | } |
---|
2798 | if (!(B.level() == 1 && B.isUnivariate()) && (A.level() == 1 && A.isUnivariate())) |
---|
2799 | { |
---|
2800 | Q= 0; |
---|
2801 | R= A; |
---|
2802 | return; |
---|
2803 | } |
---|
2804 | |
---|
2805 | Variable x= Variable (1); |
---|
2806 | int degB= degree (B, x); |
---|
2807 | if (degB > degree (A, x)) |
---|
2808 | { |
---|
2809 | Q= 0; |
---|
2810 | R= A; |
---|
2811 | return; |
---|
2812 | } |
---|
2813 | |
---|
2814 | CFList splitA= split (A, degB, x); |
---|
2815 | |
---|
2816 | CanonicalForm xToDegB= power (x, degB); |
---|
2817 | CanonicalForm H, bufQ; |
---|
2818 | Q= 0; |
---|
2819 | CFListIterator i= splitA; |
---|
2820 | H= i.getItem()*xToDegB; |
---|
2821 | i++; |
---|
2822 | H += i.getItem(); |
---|
2823 | CFList buf; |
---|
2824 | while (i.hasItem()) |
---|
2825 | { |
---|
2826 | buf= CFList (M); |
---|
2827 | divrem21 (H, B, bufQ, R, buf); |
---|
2828 | i++; |
---|
2829 | if (i.hasItem()) |
---|
2830 | H= R*xToDegB + i.getItem(); |
---|
2831 | Q *= xToDegB; |
---|
2832 | Q += bufQ; |
---|
2833 | } |
---|
2834 | return; |
---|
2835 | } |
---|
2836 | |
---|
2837 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
2838 | CanonicalForm& R, const CFList& MOD) |
---|
2839 | { |
---|
2840 | CanonicalForm A= mod (F, MOD); |
---|
2841 | CanonicalForm B= mod (G, MOD); |
---|
2842 | Variable x= Variable (1); |
---|
2843 | int degB= degree (B, x); |
---|
2844 | if (degB > degree (A, x)) |
---|
2845 | { |
---|
2846 | Q= 0; |
---|
2847 | R= A; |
---|
2848 | return; |
---|
2849 | } |
---|
2850 | |
---|
2851 | if (degB <= 0) |
---|
2852 | { |
---|
2853 | divrem (A, B, Q, R); |
---|
2854 | Q= mod (Q, MOD); |
---|
2855 | R= mod (R, MOD); |
---|
2856 | return; |
---|
2857 | } |
---|
2858 | CFList splitA= split (A, degB, x); |
---|
2859 | |
---|
2860 | CanonicalForm xToDegB= power (x, degB); |
---|
2861 | CanonicalForm H, bufQ; |
---|
2862 | Q= 0; |
---|
2863 | CFListIterator i= splitA; |
---|
2864 | H= i.getItem()*xToDegB; |
---|
2865 | i++; |
---|
2866 | H += i.getItem(); |
---|
2867 | while (i.hasItem()) |
---|
2868 | { |
---|
2869 | divrem21 (H, B, bufQ, R, MOD); |
---|
2870 | i++; |
---|
2871 | if (i.hasItem()) |
---|
2872 | H= R*xToDegB + i.getItem(); |
---|
2873 | Q *= xToDegB; |
---|
2874 | Q += bufQ; |
---|
2875 | } |
---|
2876 | return; |
---|
2877 | } |
---|
2878 | |
---|
2879 | void sortList (CFList& list, const Variable& x) |
---|
2880 | { |
---|
2881 | int l= 1; |
---|
2882 | int k= 1; |
---|
2883 | CanonicalForm buf; |
---|
2884 | CFListIterator m; |
---|
2885 | for (CFListIterator i= list; l <= list.length(); i++, l++) |
---|
2886 | { |
---|
2887 | for (CFListIterator j= list; k <= list.length() - l; k++) |
---|
2888 | { |
---|
2889 | m= j; |
---|
2890 | m++; |
---|
2891 | if (degree (j.getItem(), x) > degree (m.getItem(), x)) |
---|
2892 | { |
---|
2893 | buf= m.getItem(); |
---|
2894 | m.getItem()= j.getItem(); |
---|
2895 | j.getItem()= buf; |
---|
2896 | j++; |
---|
2897 | j.getItem()= m.getItem(); |
---|
2898 | } |
---|
2899 | else |
---|
2900 | j++; |
---|
2901 | } |
---|
2902 | k= 1; |
---|
2903 | } |
---|
2904 | } |
---|
2905 | |
---|
2906 | static inline |
---|
2907 | CFList diophantine (const CanonicalForm& F, const CFList& factors) |
---|
2908 | { |
---|
2909 | if (getCharacteristic() == 0) |
---|
2910 | { |
---|
2911 | Variable v; |
---|
2912 | bool hasAlgVar= hasFirstAlgVar (F, v); |
---|
2913 | for (CFListIterator i= factors; i.hasItem() && !hasAlgVar; i++) |
---|
2914 | hasAlgVar= hasFirstAlgVar (i.getItem(), v); |
---|
2915 | if (hasAlgVar) |
---|
2916 | { |
---|
2917 | CFList result= modularDiophant (F, factors, getMipo (v)); |
---|
2918 | return result; |
---|
2919 | } |
---|
2920 | } |
---|
2921 | |
---|
2922 | CanonicalForm buf1, buf2, buf3, S, T; |
---|
2923 | CFListIterator i= factors; |
---|
2924 | CFList result; |
---|
2925 | if (i.hasItem()) |
---|
2926 | i++; |
---|
2927 | buf1= F/factors.getFirst(); |
---|
2928 | buf2= divNTL (F, i.getItem()); |
---|
2929 | buf3= extgcd (buf1, buf2, S, T); |
---|
2930 | result.append (S); |
---|
2931 | result.append (T); |
---|
2932 | if (i.hasItem()) |
---|
2933 | i++; |
---|
2934 | for (; i.hasItem(); i++) |
---|
2935 | { |
---|
2936 | buf1= divNTL (F, i.getItem()); |
---|
2937 | buf3= extgcd (buf3, buf1, S, T); |
---|
2938 | CFListIterator k= factors; |
---|
2939 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
---|
2940 | { |
---|
2941 | j.getItem()= mulNTL (j.getItem(), S); |
---|
2942 | j.getItem()= modNTL (j.getItem(), k.getItem()); |
---|
2943 | } |
---|
2944 | result.append (T); |
---|
2945 | } |
---|
2946 | return result; |
---|
2947 | } |
---|
2948 | |
---|
2949 | void |
---|
2950 | henselStep12 (const CanonicalForm& F, const CFList& factors, |
---|
2951 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
2952 | CFArray& Pi, int j) |
---|
2953 | { |
---|
2954 | CanonicalForm E; |
---|
2955 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
2956 | Variable x= F.mvar(); |
---|
2957 | // compute the error |
---|
2958 | if (j == 1) |
---|
2959 | E= F[j]; |
---|
2960 | else |
---|
2961 | { |
---|
2962 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
2963 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
2964 | else |
---|
2965 | E= F[j]; |
---|
2966 | } |
---|
2967 | |
---|
2968 | CFArray buf= CFArray (diophant.length()); |
---|
2969 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
2970 | int k= 0; |
---|
2971 | CanonicalForm remainder; |
---|
2972 | // actual lifting |
---|
2973 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
2974 | { |
---|
2975 | if (degree (bufFactors[k], x) > 0) |
---|
2976 | { |
---|
2977 | if (k > 0) |
---|
2978 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
2979 | else |
---|
2980 | remainder= E; |
---|
2981 | } |
---|
2982 | else |
---|
2983 | remainder= modNTL (E, bufFactors[k]); |
---|
2984 | |
---|
2985 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
2986 | if (degree (bufFactors[k], x) > 0) |
---|
2987 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
2988 | else |
---|
2989 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
2990 | } |
---|
2991 | for (k= 1; k < factors.length(); k++) |
---|
2992 | bufFactors[k] += xToJ*buf[k]; |
---|
2993 | |
---|
2994 | // update Pi [0] |
---|
2995 | int degBuf0= degree (bufFactors[0], x); |
---|
2996 | int degBuf1= degree (bufFactors[1], x); |
---|
2997 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
2998 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
2999 | CanonicalForm uIZeroJ; |
---|
3000 | if (j == 1) |
---|
3001 | { |
---|
3002 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3003 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
3004 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
3005 | else if (degBuf0 > 0) |
---|
3006 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
3007 | else if (degBuf1 > 0) |
---|
3008 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
3009 | else |
---|
3010 | uIZeroJ= 0; |
---|
3011 | Pi [0] += xToJ*uIZeroJ; |
---|
3012 | } |
---|
3013 | else |
---|
3014 | { |
---|
3015 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3016 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
3017 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
3018 | else if (degBuf0 > 0) |
---|
3019 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
3020 | else if (degBuf1 > 0) |
---|
3021 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
3022 | else |
---|
3023 | uIZeroJ= 0; |
---|
3024 | Pi [0] += xToJ*uIZeroJ; |
---|
3025 | } |
---|
3026 | CFArray tmp= CFArray (factors.length() - 1); |
---|
3027 | for (k= 0; k < factors.length() - 1; k++) |
---|
3028 | tmp[k]= 0; |
---|
3029 | CFIterator one, two; |
---|
3030 | one= bufFactors [0]; |
---|
3031 | two= bufFactors [1]; |
---|
3032 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3033 | { |
---|
3034 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3035 | { |
---|
3036 | if (k != j - k + 1) |
---|
3037 | { |
---|
3038 | if ((one.hasTerms() && one.exp() == j - k + 1) && (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3039 | { |
---|
3040 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), (bufFactors[1] [k] + |
---|
3041 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
3042 | one++; |
---|
3043 | two++; |
---|
3044 | } |
---|
3045 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3046 | { |
---|
3047 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), bufFactors[1] [k]) - |
---|
3048 | M (k + 1, 1); |
---|
3049 | one++; |
---|
3050 | } |
---|
3051 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3052 | { |
---|
3053 | tmp[0] += mulNTL (bufFactors[0] [k], (bufFactors[1] [k] + two.coeff())) - |
---|
3054 | M (k + 1, 1); |
---|
3055 | two++; |
---|
3056 | } |
---|
3057 | } |
---|
3058 | else |
---|
3059 | { |
---|
3060 | tmp[0] += M (k + 1, 1); |
---|
3061 | } |
---|
3062 | } |
---|
3063 | } |
---|
3064 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
3065 | |
---|
3066 | // update Pi [l] |
---|
3067 | int degPi, degBuf; |
---|
3068 | for (int l= 1; l < factors.length() - 1; l++) |
---|
3069 | { |
---|
3070 | degPi= degree (Pi [l - 1], x); |
---|
3071 | degBuf= degree (bufFactors[l + 1], x); |
---|
3072 | if (degPi > 0 && degBuf > 0) |
---|
3073 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
3074 | if (j == 1) |
---|
3075 | { |
---|
3076 | if (degPi > 0 && degBuf > 0) |
---|
3077 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [0] + Pi [l - 1] [j], |
---|
3078 | bufFactors[l + 1] [0] + buf[l + 1]) - M (j + 1, l +1) - |
---|
3079 | M (1, l + 1)); |
---|
3080 | else if (degPi > 0) |
---|
3081 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [j], bufFactors[l + 1])); |
---|
3082 | else if (degBuf > 0) |
---|
3083 | Pi [l] += xToJ*(mulNTL (Pi [l - 1], buf[l + 1])); |
---|
3084 | } |
---|
3085 | else |
---|
3086 | { |
---|
3087 | if (degPi > 0 && degBuf > 0) |
---|
3088 | { |
---|
3089 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
3090 | uIZeroJ += mulNTL (Pi [l - 1] [0], buf [l + 1]); |
---|
3091 | } |
---|
3092 | else if (degPi > 0) |
---|
3093 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1]); |
---|
3094 | else if (degBuf > 0) |
---|
3095 | { |
---|
3096 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
3097 | uIZeroJ += mulNTL (Pi [l - 1], buf[l + 1]); |
---|
3098 | } |
---|
3099 | Pi[l] += xToJ*uIZeroJ; |
---|
3100 | } |
---|
3101 | one= bufFactors [l + 1]; |
---|
3102 | two= Pi [l - 1]; |
---|
3103 | if (two.hasTerms() && two.exp() == j + 1) |
---|
3104 | { |
---|
3105 | if (degBuf > 0 && degPi > 0) |
---|
3106 | { |
---|
3107 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1][0]); |
---|
3108 | two++; |
---|
3109 | } |
---|
3110 | else if (degPi > 0) |
---|
3111 | { |
---|
3112 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1]); |
---|
3113 | two++; |
---|
3114 | } |
---|
3115 | } |
---|
3116 | if (degBuf > 0 && degPi > 0) |
---|
3117 | { |
---|
3118 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3119 | { |
---|
3120 | if (k != j - k + 1) |
---|
3121 | { |
---|
3122 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
3123 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3124 | { |
---|
3125 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), (Pi[l - 1] [k] + |
---|
3126 | two.coeff())) - M (k + 1, l + 1) - M (j - k + 2, l + 1); |
---|
3127 | one++; |
---|
3128 | two++; |
---|
3129 | } |
---|
3130 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3131 | { |
---|
3132 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), Pi[l - 1] [k]) - |
---|
3133 | M (k + 1, l + 1); |
---|
3134 | one++; |
---|
3135 | } |
---|
3136 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3137 | { |
---|
3138 | tmp[l] += mulNTL (bufFactors[l + 1] [k], (Pi[l - 1] [k] + two.coeff())) - |
---|
3139 | M (k + 1, l + 1); |
---|
3140 | two++; |
---|
3141 | } |
---|
3142 | } |
---|
3143 | else |
---|
3144 | tmp[l] += M (k + 1, l + 1); |
---|
3145 | } |
---|
3146 | } |
---|
3147 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
3148 | } |
---|
3149 | return; |
---|
3150 | } |
---|
3151 | |
---|
3152 | void |
---|
3153 | henselLift12 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
3154 | CFList& diophant, CFMatrix& M, bool sort) |
---|
3155 | { |
---|
3156 | if (sort) |
---|
3157 | sortList (factors, Variable (1)); |
---|
3158 | Pi= CFArray (factors.length() - 1); |
---|
3159 | CFListIterator j= factors; |
---|
3160 | diophant= diophantine (F[0], factors); |
---|
3161 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
3162 | j++; |
---|
3163 | Pi [0]= mulNTL (j.getItem(), mod (factors.getFirst(), F.mvar())); |
---|
3164 | M (1, 1)= Pi [0]; |
---|
3165 | int i= 1; |
---|
3166 | if (j.hasItem()) |
---|
3167 | j++; |
---|
3168 | for (; j.hasItem(); j++, i++) |
---|
3169 | { |
---|
3170 | Pi [i]= mulNTL (Pi [i - 1], j.getItem()); |
---|
3171 | M (1, i + 1)= Pi [i]; |
---|
3172 | } |
---|
3173 | CFArray bufFactors= CFArray (factors.length()); |
---|
3174 | i= 0; |
---|
3175 | for (CFListIterator k= factors; k.hasItem(); i++, k++) |
---|
3176 | { |
---|
3177 | if (i == 0) |
---|
3178 | bufFactors[i]= mod (k.getItem(), F.mvar()); |
---|
3179 | else |
---|
3180 | bufFactors[i]= k.getItem(); |
---|
3181 | } |
---|
3182 | for (i= 1; i < l; i++) |
---|
3183 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
3184 | |
---|
3185 | CFListIterator k= factors; |
---|
3186 | for (i= 0; i < factors.length (); i++, k++) |
---|
3187 | k.getItem()= bufFactors[i]; |
---|
3188 | factors.removeFirst(); |
---|
3189 | return; |
---|
3190 | } |
---|
3191 | |
---|
3192 | void |
---|
3193 | henselLiftResume12 (const CanonicalForm& F, CFList& factors, int start, int |
---|
3194 | end, CFArray& Pi, const CFList& diophant, CFMatrix& M) |
---|
3195 | { |
---|
3196 | CFArray bufFactors= CFArray (factors.length()); |
---|
3197 | int i= 0; |
---|
3198 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
3199 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
3200 | { |
---|
3201 | if (i == 0) |
---|
3202 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
3203 | else |
---|
3204 | bufFactors[i]= k.getItem(); |
---|
3205 | } |
---|
3206 | for (i= start; i < end; i++) |
---|
3207 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
3208 | |
---|
3209 | CFListIterator k= factors; |
---|
3210 | for (i= 0; i < factors.length(); k++, i++) |
---|
3211 | k.getItem()= bufFactors [i]; |
---|
3212 | factors.removeFirst(); |
---|
3213 | return; |
---|
3214 | } |
---|
3215 | |
---|
3216 | static inline |
---|
3217 | CFList |
---|
3218 | biDiophantine (const CanonicalForm& F, const CFList& factors, const int d) |
---|
3219 | { |
---|
3220 | Variable y= F.mvar(); |
---|
3221 | CFList result; |
---|
3222 | if (y.level() == 1) |
---|
3223 | { |
---|
3224 | result= diophantine (F, factors); |
---|
3225 | return result; |
---|
3226 | } |
---|
3227 | else |
---|
3228 | { |
---|
3229 | CFList buf= factors; |
---|
3230 | for (CFListIterator i= buf; i.hasItem(); i++) |
---|
3231 | i.getItem()= mod (i.getItem(), y); |
---|
3232 | CanonicalForm A= mod (F, y); |
---|
3233 | int bufD= 1; |
---|
3234 | CFList recResult= biDiophantine (A, buf, bufD); |
---|
3235 | CanonicalForm e= 1; |
---|
3236 | CFList p; |
---|
3237 | CFArray bufFactors= CFArray (factors.length()); |
---|
3238 | CanonicalForm yToD= power (y, d); |
---|
3239 | int k= 0; |
---|
3240 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
3241 | { |
---|
3242 | bufFactors [k]= i.getItem(); |
---|
3243 | } |
---|
3244 | CanonicalForm b, quot; |
---|
3245 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
3246 | { |
---|
3247 | b= 1; |
---|
3248 | if (fdivides (bufFactors[k], F, quot)) |
---|
3249 | b= quot; |
---|
3250 | else |
---|
3251 | { |
---|
3252 | for (int l= 0; l < factors.length(); l++) |
---|
3253 | { |
---|
3254 | if (l == k) |
---|
3255 | continue; |
---|
3256 | else |
---|
3257 | { |
---|
3258 | b= mulMod2 (b, bufFactors[l], yToD); |
---|
3259 | } |
---|
3260 | } |
---|
3261 | } |
---|
3262 | p.append (b); |
---|
3263 | } |
---|
3264 | |
---|
3265 | CFListIterator j= p; |
---|
3266 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
3267 | e -= i.getItem()*j.getItem(); |
---|
3268 | |
---|
3269 | if (e.isZero()) |
---|
3270 | return recResult; |
---|
3271 | CanonicalForm coeffE; |
---|
3272 | CFList s; |
---|
3273 | result= recResult; |
---|
3274 | CanonicalForm g; |
---|
3275 | for (int i= 1; i < d; i++) |
---|
3276 | { |
---|
3277 | if (degree (e, y) > 0) |
---|
3278 | coeffE= e[i]; |
---|
3279 | else |
---|
3280 | coeffE= 0; |
---|
3281 | if (!coeffE.isZero()) |
---|
3282 | { |
---|
3283 | CFListIterator k= result; |
---|
3284 | CFListIterator l= p; |
---|
3285 | int ii= 0; |
---|
3286 | j= recResult; |
---|
3287 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
3288 | { |
---|
3289 | g= coeffE*j.getItem(); |
---|
3290 | if (degree (bufFactors[ii], y) <= 0) |
---|
3291 | g= mod (g, bufFactors[ii]); |
---|
3292 | else |
---|
3293 | g= mod (g, bufFactors[ii][0]); |
---|
3294 | k.getItem() += g*power (y, i); |
---|
3295 | e -= mulMod2 (g*power(y, i), l.getItem(), yToD); |
---|
3296 | DEBOUTLN (cerr, "mod (e, power (y, i + 1))= " << |
---|
3297 | mod (e, power (y, i + 1))); |
---|
3298 | } |
---|
3299 | } |
---|
3300 | if (e.isZero()) |
---|
3301 | break; |
---|
3302 | } |
---|
3303 | |
---|
3304 | DEBOUTLN (cerr, "mod (e, y)= " << mod (e, y)); |
---|
3305 | |
---|
3306 | #ifdef DEBUGOUTPUT |
---|
3307 | CanonicalForm test= 0; |
---|
3308 | j= p; |
---|
3309 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
3310 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
3311 | DEBOUTLN (cerr, "test= " << test); |
---|
3312 | #endif |
---|
3313 | return result; |
---|
3314 | } |
---|
3315 | } |
---|
3316 | |
---|
3317 | static inline |
---|
3318 | CFList |
---|
3319 | multiRecDiophantine (const CanonicalForm& F, const CFList& factors, |
---|
3320 | const CFList& recResult, const CFList& M, const int d) |
---|
3321 | { |
---|
3322 | Variable y= F.mvar(); |
---|
3323 | CFList result; |
---|
3324 | CFListIterator i; |
---|
3325 | CanonicalForm e= 1; |
---|
3326 | CFListIterator j= factors; |
---|
3327 | CFList p; |
---|
3328 | CFArray bufFactors= CFArray (factors.length()); |
---|
3329 | CanonicalForm yToD= power (y, d); |
---|
3330 | int k= 0; |
---|
3331 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
3332 | bufFactors [k]= i.getItem(); |
---|
3333 | CanonicalForm b, quot; |
---|
3334 | CFList buf= M; |
---|
3335 | buf.removeLast(); |
---|
3336 | buf.append (yToD); |
---|
3337 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
3338 | { |
---|
3339 | b= 1; |
---|
3340 | if (fdivides (bufFactors[k], F, quot)) |
---|
3341 | b= quot; |
---|
3342 | else |
---|
3343 | { |
---|
3344 | for (int l= 0; l < factors.length(); l++) |
---|
3345 | { |
---|
3346 | if (l == k) |
---|
3347 | continue; |
---|
3348 | else |
---|
3349 | { |
---|
3350 | b= mulMod (b, bufFactors[l], buf); |
---|
3351 | } |
---|
3352 | } |
---|
3353 | } |
---|
3354 | p.append (b); |
---|
3355 | } |
---|
3356 | j= p; |
---|
3357 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
3358 | e -= mulMod (i.getItem(), j.getItem(), M); |
---|
3359 | |
---|
3360 | if (e.isZero()) |
---|
3361 | return recResult; |
---|
3362 | CanonicalForm coeffE; |
---|
3363 | CFList s; |
---|
3364 | result= recResult; |
---|
3365 | CanonicalForm g; |
---|
3366 | for (int i= 1; i < d; i++) |
---|
3367 | { |
---|
3368 | if (degree (e, y) > 0) |
---|
3369 | coeffE= e[i]; |
---|
3370 | else |
---|
3371 | coeffE= 0; |
---|
3372 | if (!coeffE.isZero()) |
---|
3373 | { |
---|
3374 | CFListIterator k= result; |
---|
3375 | CFListIterator l= p; |
---|
3376 | j= recResult; |
---|
3377 | int ii= 0; |
---|
3378 | CanonicalForm dummy; |
---|
3379 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
3380 | { |
---|
3381 | g= mulMod (coeffE, j.getItem(), M); |
---|
3382 | if (degree (bufFactors[ii], y) <= 0) |
---|
3383 | divrem (g, mod (bufFactors[ii], Variable (y.level() - 1)), dummy, |
---|
3384 | g, M); |
---|
3385 | else |
---|
3386 | divrem (g, bufFactors[ii][0], dummy, g, M); |
---|
3387 | k.getItem() += g*power (y, i); |
---|
3388 | e -= mulMod (g*power (y, i), l.getItem(), M); |
---|
3389 | } |
---|
3390 | } |
---|
3391 | |
---|
3392 | if (e.isZero()) |
---|
3393 | break; |
---|
3394 | } |
---|
3395 | |
---|
3396 | #ifdef DEBUGOUTPUT |
---|
3397 | CanonicalForm test= 0; |
---|
3398 | j= p; |
---|
3399 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
3400 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
3401 | DEBOUTLN (cerr, "test= " << test); |
---|
3402 | #endif |
---|
3403 | return result; |
---|
3404 | } |
---|
3405 | |
---|
3406 | static inline |
---|
3407 | void |
---|
3408 | henselStep (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
3409 | const CFList& diophant, CFMatrix& M, CFArray& Pi, int j, |
---|
3410 | const CFList& MOD) |
---|
3411 | { |
---|
3412 | CanonicalForm E; |
---|
3413 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
3414 | Variable x= F.mvar(); |
---|
3415 | // compute the error |
---|
3416 | if (j == 1) |
---|
3417 | { |
---|
3418 | E= F[j]; |
---|
3419 | #ifdef DEBUGOUTPUT |
---|
3420 | CanonicalForm test= 1; |
---|
3421 | for (int i= 0; i < factors.length(); i++) |
---|
3422 | { |
---|
3423 | if (i == 0) |
---|
3424 | test= mulMod (test, mod (bufFactors [i], xToJ), MOD); |
---|
3425 | else |
---|
3426 | test= mulMod (test, bufFactors[i], MOD); |
---|
3427 | } |
---|
3428 | CanonicalForm test2= mod (F-test, xToJ); |
---|
3429 | |
---|
3430 | test2= mod (test2, MOD); |
---|
3431 | DEBOUTLN (cerr, "test= " << test2); |
---|
3432 | #endif |
---|
3433 | } |
---|
3434 | else |
---|
3435 | { |
---|
3436 | #ifdef DEBUGOUTPUT |
---|
3437 | CanonicalForm test= 1; |
---|
3438 | for (int i= 0; i < factors.length(); i++) |
---|
3439 | { |
---|
3440 | if (i == 0) |
---|
3441 | test *= mod (bufFactors [i], power (x, j)); |
---|
3442 | else |
---|
3443 | test *= bufFactors[i]; |
---|
3444 | } |
---|
3445 | test= mod (test, power (x, j)); |
---|
3446 | test= mod (test, MOD); |
---|
3447 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
3448 | DEBOUTLN (cerr, "test= " << test2); |
---|
3449 | #endif |
---|
3450 | |
---|
3451 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
3452 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
3453 | else |
---|
3454 | E= F[j]; |
---|
3455 | } |
---|
3456 | |
---|
3457 | CFArray buf= CFArray (diophant.length()); |
---|
3458 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
3459 | int k= 0; |
---|
3460 | // actual lifting |
---|
3461 | CanonicalForm dummy, rest1; |
---|
3462 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
3463 | { |
---|
3464 | if (degree (bufFactors[k], x) > 0) |
---|
3465 | { |
---|
3466 | if (k > 0) |
---|
3467 | divrem (E, bufFactors[k] [0], dummy, rest1, MOD); |
---|
3468 | else |
---|
3469 | rest1= E; |
---|
3470 | } |
---|
3471 | else |
---|
3472 | divrem (E, bufFactors[k], dummy, rest1, MOD); |
---|
3473 | |
---|
3474 | buf[k]= mulMod (i.getItem(), rest1, MOD); |
---|
3475 | |
---|
3476 | if (degree (bufFactors[k], x) > 0) |
---|
3477 | divrem (buf[k], bufFactors[k] [0], dummy, buf[k], MOD); |
---|
3478 | else |
---|
3479 | divrem (buf[k], bufFactors[k], dummy, buf[k], MOD); |
---|
3480 | } |
---|
3481 | for (k= 1; k < factors.length(); k++) |
---|
3482 | bufFactors[k] += xToJ*buf[k]; |
---|
3483 | |
---|
3484 | // update Pi [0] |
---|
3485 | int degBuf0= degree (bufFactors[0], x); |
---|
3486 | int degBuf1= degree (bufFactors[1], x); |
---|
3487 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3488 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
3489 | CanonicalForm uIZeroJ; |
---|
3490 | if (j == 1) |
---|
3491 | { |
---|
3492 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3493 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
3494 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
3495 | else if (degBuf0 > 0) |
---|
3496 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
3497 | else if (degBuf1 > 0) |
---|
3498 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
3499 | else |
---|
3500 | uIZeroJ= 0; |
---|
3501 | Pi [0] += xToJ*uIZeroJ; |
---|
3502 | } |
---|
3503 | else |
---|
3504 | { |
---|
3505 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3506 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
3507 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
3508 | else if (degBuf0 > 0) |
---|
3509 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
3510 | else if (degBuf1 > 0) |
---|
3511 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
3512 | else |
---|
3513 | uIZeroJ= 0; |
---|
3514 | Pi [0] += xToJ*uIZeroJ; |
---|
3515 | } |
---|
3516 | |
---|
3517 | CFArray tmp= CFArray (factors.length() - 1); |
---|
3518 | for (k= 0; k < factors.length() - 1; k++) |
---|
3519 | tmp[k]= 0; |
---|
3520 | CFIterator one, two; |
---|
3521 | one= bufFactors [0]; |
---|
3522 | two= bufFactors [1]; |
---|
3523 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3524 | { |
---|
3525 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3526 | { |
---|
3527 | if (k != j - k + 1) |
---|
3528 | { |
---|
3529 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
3530 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3531 | { |
---|
3532 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
3533 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
3534 | M (j - k + 2, 1); |
---|
3535 | one++; |
---|
3536 | two++; |
---|
3537 | } |
---|
3538 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3539 | { |
---|
3540 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
3541 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
3542 | one++; |
---|
3543 | } |
---|
3544 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3545 | { |
---|
3546 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
3547 | two.coeff()), MOD) - M (k + 1, 1); |
---|
3548 | two++; |
---|
3549 | } |
---|
3550 | } |
---|
3551 | else |
---|
3552 | { |
---|
3553 | tmp[0] += M (k + 1, 1); |
---|
3554 | } |
---|
3555 | } |
---|
3556 | } |
---|
3557 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
3558 | |
---|
3559 | // update Pi [l] |
---|
3560 | int degPi, degBuf; |
---|
3561 | for (int l= 1; l < factors.length() - 1; l++) |
---|
3562 | { |
---|
3563 | degPi= degree (Pi [l - 1], x); |
---|
3564 | degBuf= degree (bufFactors[l + 1], x); |
---|
3565 | if (degPi > 0 && degBuf > 0) |
---|
3566 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
3567 | if (j == 1) |
---|
3568 | { |
---|
3569 | if (degPi > 0 && degBuf > 0) |
---|
3570 | Pi [l] += xToJ*(mulMod ((Pi [l - 1] [0] + Pi [l - 1] [j]), |
---|
3571 | (bufFactors[l + 1] [0] + buf[l + 1]), MOD) - M (j + 1, l +1)- |
---|
3572 | M (1, l + 1)); |
---|
3573 | else if (degPi > 0) |
---|
3574 | Pi [l] += xToJ*(mulMod (Pi [l - 1] [j], bufFactors[l + 1], MOD)); |
---|
3575 | else if (degBuf > 0) |
---|
3576 | Pi [l] += xToJ*(mulMod (Pi [l - 1], buf[l + 1], MOD)); |
---|
3577 | } |
---|
3578 | else |
---|
3579 | { |
---|
3580 | if (degPi > 0 && degBuf > 0) |
---|
3581 | { |
---|
3582 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
3583 | uIZeroJ += mulMod (Pi [l - 1] [0], buf [l + 1], MOD); |
---|
3584 | } |
---|
3585 | else if (degPi > 0) |
---|
3586 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1], MOD); |
---|
3587 | else if (degBuf > 0) |
---|
3588 | { |
---|
3589 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
3590 | uIZeroJ += mulMod (Pi [l - 1], buf[l + 1], MOD); |
---|
3591 | } |
---|
3592 | Pi[l] += xToJ*uIZeroJ; |
---|
3593 | } |
---|
3594 | one= bufFactors [l + 1]; |
---|
3595 | two= Pi [l - 1]; |
---|
3596 | if (two.hasTerms() && two.exp() == j + 1) |
---|
3597 | { |
---|
3598 | if (degBuf > 0 && degPi > 0) |
---|
3599 | { |
---|
3600 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1][0], MOD); |
---|
3601 | two++; |
---|
3602 | } |
---|
3603 | else if (degPi > 0) |
---|
3604 | { |
---|
3605 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1], MOD); |
---|
3606 | two++; |
---|
3607 | } |
---|
3608 | } |
---|
3609 | if (degBuf > 0 && degPi > 0) |
---|
3610 | { |
---|
3611 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3612 | { |
---|
3613 | if (k != j - k + 1) |
---|
3614 | { |
---|
3615 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
3616 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3617 | { |
---|
3618 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
3619 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
3620 | M (j - k + 2, l + 1); |
---|
3621 | one++; |
---|
3622 | two++; |
---|
3623 | } |
---|
3624 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3625 | { |
---|
3626 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
3627 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
3628 | one++; |
---|
3629 | } |
---|
3630 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3631 | { |
---|
3632 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
3633 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
3634 | two++; |
---|
3635 | } |
---|
3636 | } |
---|
3637 | else |
---|
3638 | tmp[l] += M (k + 1, l + 1); |
---|
3639 | } |
---|
3640 | } |
---|
3641 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
3642 | } |
---|
3643 | |
---|
3644 | return; |
---|
3645 | } |
---|
3646 | |
---|
3647 | CFList |
---|
3648 | henselLift23 (const CFList& eval, const CFList& factors, const int* l, CFList& |
---|
3649 | diophant, CFArray& Pi, CFMatrix& M) |
---|
3650 | { |
---|
3651 | CFList buf= factors; |
---|
3652 | int k= 0; |
---|
3653 | int liftBoundBivar= l[k]; |
---|
3654 | diophant= biDiophantine (eval.getFirst(), buf, liftBoundBivar); |
---|
3655 | CFList MOD; |
---|
3656 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
3657 | CFArray bufFactors= CFArray (factors.length()); |
---|
3658 | k= 0; |
---|
3659 | CFListIterator j= eval; |
---|
3660 | j++; |
---|
3661 | buf.removeFirst(); |
---|
3662 | buf.insert (LC (j.getItem(), 1)); |
---|
3663 | for (CFListIterator i= buf; i.hasItem(); i++, k++) |
---|
3664 | bufFactors[k]= i.getItem(); |
---|
3665 | Pi= CFArray (factors.length() - 1); |
---|
3666 | CFListIterator i= buf; |
---|
3667 | i++; |
---|
3668 | Variable y= j.getItem().mvar(); |
---|
3669 | Pi [0]= mulMod (i.getItem(), mod (buf.getFirst(), y), MOD); |
---|
3670 | M (1, 1)= Pi [0]; |
---|
3671 | k= 1; |
---|
3672 | if (i.hasItem()) |
---|
3673 | i++; |
---|
3674 | for (; i.hasItem(); i++, k++) |
---|
3675 | { |
---|
3676 | Pi [k]= mulMod (Pi [k - 1], i.getItem(), MOD); |
---|
3677 | M (1, k + 1)= Pi [k]; |
---|
3678 | } |
---|
3679 | |
---|
3680 | for (int d= 1; d < l[1]; d++) |
---|
3681 | henselStep (j.getItem(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
3682 | CFList result; |
---|
3683 | for (k= 1; k < factors.length(); k++) |
---|
3684 | result.append (bufFactors[k]); |
---|
3685 | return result; |
---|
3686 | } |
---|
3687 | |
---|
3688 | void |
---|
3689 | henselLiftResume (const CanonicalForm& F, CFList& factors, int start, int end, |
---|
3690 | CFArray& Pi, const CFList& diophant, CFMatrix& M, |
---|
3691 | const CFList& MOD) |
---|
3692 | { |
---|
3693 | CFArray bufFactors= CFArray (factors.length()); |
---|
3694 | int i= 0; |
---|
3695 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
3696 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
3697 | { |
---|
3698 | if (i == 0) |
---|
3699 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
3700 | else |
---|
3701 | bufFactors[i]= k.getItem(); |
---|
3702 | } |
---|
3703 | for (i= start; i < end; i++) |
---|
3704 | henselStep (F, factors, bufFactors, diophant, M, Pi, i, MOD); |
---|
3705 | |
---|
3706 | CFListIterator k= factors; |
---|
3707 | for (i= 0; i < factors.length(); k++, i++) |
---|
3708 | k.getItem()= bufFactors [i]; |
---|
3709 | factors.removeFirst(); |
---|
3710 | return; |
---|
3711 | } |
---|
3712 | |
---|
3713 | CFList |
---|
3714 | henselLift (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
3715 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, const int |
---|
3716 | lNew) |
---|
3717 | { |
---|
3718 | diophant= multiRecDiophantine (F.getFirst(), factors, diophant, MOD, lOld); |
---|
3719 | int k= 0; |
---|
3720 | CFArray bufFactors= CFArray (factors.length()); |
---|
3721 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
3722 | { |
---|
3723 | if (k == 0) |
---|
3724 | bufFactors[k]= LC (F.getLast(), 1); |
---|
3725 | else |
---|
3726 | bufFactors[k]= i.getItem(); |
---|
3727 | } |
---|
3728 | CFList buf= factors; |
---|
3729 | buf.removeFirst(); |
---|
3730 | buf.insert (LC (F.getLast(), 1)); |
---|
3731 | CFListIterator i= buf; |
---|
3732 | i++; |
---|
3733 | Variable y= F.getLast().mvar(); |
---|
3734 | Variable x= F.getFirst().mvar(); |
---|
3735 | CanonicalForm xToLOld= power (x, lOld); |
---|
3736 | Pi [0]= mod (Pi[0], xToLOld); |
---|
3737 | M (1, 1)= Pi [0]; |
---|
3738 | k= 1; |
---|
3739 | if (i.hasItem()) |
---|
3740 | i++; |
---|
3741 | for (; i.hasItem(); i++, k++) |
---|
3742 | { |
---|
3743 | Pi [k]= mod (Pi [k], xToLOld); |
---|
3744 | M (1, k + 1)= Pi [k]; |
---|
3745 | } |
---|
3746 | |
---|
3747 | for (int d= 1; d < lNew; d++) |
---|
3748 | henselStep (F.getLast(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
3749 | CFList result; |
---|
3750 | for (k= 1; k < factors.length(); k++) |
---|
3751 | result.append (bufFactors[k]); |
---|
3752 | return result; |
---|
3753 | } |
---|
3754 | |
---|
3755 | CFList |
---|
3756 | henselLift (const CFList& eval, const CFList& factors, const int* l, const int |
---|
3757 | lLength, bool sort) |
---|
3758 | { |
---|
3759 | CFList diophant; |
---|
3760 | CFList buf= factors; |
---|
3761 | buf.insert (LC (eval.getFirst(), 1)); |
---|
3762 | if (sort) |
---|
3763 | sortList (buf, Variable (1)); |
---|
3764 | CFArray Pi; |
---|
3765 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
3766 | CFList result= henselLift23 (eval, buf, l, diophant, Pi, M); |
---|
3767 | if (eval.length() == 2) |
---|
3768 | return result; |
---|
3769 | CFList MOD; |
---|
3770 | for (int i= 0; i < 2; i++) |
---|
3771 | MOD.append (power (Variable (i + 2), l[i])); |
---|
3772 | CFListIterator j= eval; |
---|
3773 | j++; |
---|
3774 | CFList bufEval; |
---|
3775 | bufEval.append (j.getItem()); |
---|
3776 | j++; |
---|
3777 | |
---|
3778 | for (int i= 2; i < lLength && j.hasItem(); i++, j++) |
---|
3779 | { |
---|
3780 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
3781 | bufEval.append (j.getItem()); |
---|
3782 | M= CFMatrix (l[i], factors.length()); |
---|
3783 | result= henselLift (bufEval, result, MOD, diophant, Pi, M, l[i - 1], l[i]); |
---|
3784 | MOD.append (power (Variable (i + 2), l[i])); |
---|
3785 | bufEval.removeFirst(); |
---|
3786 | } |
---|
3787 | return result; |
---|
3788 | } |
---|
3789 | |
---|
3790 | void |
---|
3791 | henselStep122 (const CanonicalForm& F, const CFList& factors, |
---|
3792 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
3793 | CFArray& Pi, int j, const CFArray& /*LCs*/) |
---|
3794 | { |
---|
3795 | Variable x= F.mvar(); |
---|
3796 | CanonicalForm xToJ= power (x, j); |
---|
3797 | |
---|
3798 | CanonicalForm E; |
---|
3799 | // compute the error |
---|
3800 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
3801 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
3802 | else |
---|
3803 | E= F[j]; |
---|
3804 | |
---|
3805 | CFArray buf= CFArray (diophant.length()); |
---|
3806 | |
---|
3807 | int k= 0; |
---|
3808 | CanonicalForm remainder; |
---|
3809 | // actual lifting |
---|
3810 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
3811 | { |
---|
3812 | if (degree (bufFactors[k], x) > 0) |
---|
3813 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
3814 | else |
---|
3815 | remainder= modNTL (E, bufFactors[k]); |
---|
3816 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
3817 | if (degree (bufFactors[k], x) > 0) |
---|
3818 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
3819 | else |
---|
3820 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
3821 | } |
---|
3822 | |
---|
3823 | for (k= 0; k < factors.length(); k++) |
---|
3824 | bufFactors[k] += xToJ*buf[k]; |
---|
3825 | |
---|
3826 | // update Pi [0] |
---|
3827 | int degBuf0= degree (bufFactors[0], x); |
---|
3828 | int degBuf1= degree (bufFactors[1], x); |
---|
3829 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3830 | { |
---|
3831 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
3832 | if (j + 2 <= M.rows()) |
---|
3833 | M (j + 2, 1)= mulNTL (bufFactors[0] [j + 1], bufFactors[1] [j + 1]); |
---|
3834 | } |
---|
3835 | CanonicalForm uIZeroJ; |
---|
3836 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3837 | uIZeroJ= mulNTL(bufFactors[0][0],buf[1])+mulNTL (bufFactors[1][0], buf[0]); |
---|
3838 | else if (degBuf0 > 0) |
---|
3839 | uIZeroJ= mulNTL (buf[0], bufFactors[1]); |
---|
3840 | else if (degBuf1 > 0) |
---|
3841 | uIZeroJ= mulNTL (bufFactors[0], buf [1]); |
---|
3842 | else |
---|
3843 | uIZeroJ= 0; |
---|
3844 | Pi [0] += xToJ*uIZeroJ; |
---|
3845 | |
---|
3846 | CFArray tmp= CFArray (factors.length() - 1); |
---|
3847 | for (k= 0; k < factors.length() - 1; k++) |
---|
3848 | tmp[k]= 0; |
---|
3849 | CFIterator one, two; |
---|
3850 | one= bufFactors [0]; |
---|
3851 | two= bufFactors [1]; |
---|
3852 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
3853 | { |
---|
3854 | while (one.hasTerms() && one.exp() > j) one++; |
---|
3855 | while (two.hasTerms() && two.exp() > j) two++; |
---|
3856 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3857 | { |
---|
3858 | if (one.hasTerms() && two.hasTerms()) |
---|
3859 | { |
---|
3860 | if (k != j - k + 1) |
---|
3861 | { |
---|
3862 | if ((one.hasTerms() && one.exp() == j - k + 1) && + |
---|
3863 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3864 | { |
---|
3865 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()),(bufFactors[1][k] + |
---|
3866 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
3867 | one++; |
---|
3868 | two++; |
---|
3869 | } |
---|
3870 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3871 | { |
---|
3872 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()), bufFactors[1] [k]) - |
---|
3873 | M (k + 1, 1); |
---|
3874 | one++; |
---|
3875 | } |
---|
3876 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3877 | { |
---|
3878 | tmp[0] += mulNTL (bufFactors[0][k],(bufFactors[1][k] + two.coeff())) - |
---|
3879 | M (k + 1, 1); |
---|
3880 | two++; |
---|
3881 | } |
---|
3882 | } |
---|
3883 | else |
---|
3884 | tmp[0] += M (k + 1, 1); |
---|
3885 | } |
---|
3886 | } |
---|
3887 | } |
---|
3888 | |
---|
3889 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
3890 | { |
---|
3891 | if (j + 2 <= M.rows()) |
---|
3892 | tmp [0] += mulNTL ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
3893 | (bufFactors [1] [j + 1] + bufFactors [1] [0])) |
---|
3894 | - M(1,1) - M (j + 2,1); |
---|
3895 | } |
---|
3896 | else if (degBuf0 >= j + 1) |
---|
3897 | { |
---|
3898 | if (degBuf1 > 0) |
---|
3899 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1] [0]); |
---|
3900 | else |
---|
3901 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1]); |
---|
3902 | } |
---|
3903 | else if (degBuf1 >= j + 1) |
---|
3904 | { |
---|
3905 | if (degBuf0 > 0) |
---|
3906 | tmp[0] += mulNTL (bufFactors [0] [0], bufFactors [1] [j + 1]); |
---|
3907 | else |
---|
3908 | tmp[0] += mulNTL (bufFactors [0], bufFactors [1] [j + 1]); |
---|
3909 | } |
---|
3910 | |
---|
3911 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
3912 | |
---|
3913 | int degPi, degBuf; |
---|
3914 | for (int l= 1; l < factors.length() - 1; l++) |
---|
3915 | { |
---|
3916 | degPi= degree (Pi [l - 1], x); |
---|
3917 | degBuf= degree (bufFactors[l + 1], x); |
---|
3918 | if (degPi > 0 && degBuf > 0) |
---|
3919 | { |
---|
3920 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
3921 | if (j + 2 <= M.rows()) |
---|
3922 | M (j + 2, l + 1)= mulNTL (Pi [l - 1][j + 1], bufFactors[l + 1] [j + 1]); |
---|
3923 | } |
---|
3924 | |
---|
3925 | if (degPi > 0 && degBuf > 0) |
---|
3926 | uIZeroJ= mulNTL (Pi[l -1] [0], buf[l + 1]) + |
---|
3927 | mulNTL (uIZeroJ, bufFactors[l+1] [0]); |
---|
3928 | else if (degPi > 0) |
---|
3929 | uIZeroJ= mulNTL (uIZeroJ, bufFactors[l + 1]); |
---|
3930 | else if (degBuf > 0) |
---|
3931 | uIZeroJ= mulNTL (Pi[l - 1], buf[1]); |
---|
3932 | else |
---|
3933 | uIZeroJ= 0; |
---|
3934 | |
---|
3935 | Pi [l] += xToJ*uIZeroJ; |
---|
3936 | |
---|
3937 | one= bufFactors [l + 1]; |
---|
3938 | two= Pi [l - 1]; |
---|
3939 | if (degBuf > 0 && degPi > 0) |
---|
3940 | { |
---|
3941 | while (one.hasTerms() && one.exp() > j) one++; |
---|
3942 | while (two.hasTerms() && two.exp() > j) two++; |
---|
3943 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
3944 | { |
---|
3945 | if (k != j - k + 1) |
---|
3946 | { |
---|
3947 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
3948 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
3949 | { |
---|
3950 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
3951 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1) - |
---|
3952 | M (j - k + 2, l + 1); |
---|
3953 | one++; |
---|
3954 | two++; |
---|
3955 | } |
---|
3956 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
3957 | { |
---|
3958 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
3959 | Pi[l - 1] [k]) - M (k + 1, l + 1); |
---|
3960 | one++; |
---|
3961 | } |
---|
3962 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
3963 | { |
---|
3964 | tmp[l] += mulNTL (bufFactors[l + 1] [k], |
---|
3965 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1); |
---|
3966 | two++; |
---|
3967 | } |
---|
3968 | } |
---|
3969 | else |
---|
3970 | tmp[l] += M (k + 1, l + 1); |
---|
3971 | } |
---|
3972 | } |
---|
3973 | |
---|
3974 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
3975 | { |
---|
3976 | if (j + 2 <= M.rows()) |
---|
3977 | tmp [l] += mulNTL ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
3978 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
3979 | ) - M(1,l+1) - M (j + 2,l+1); |
---|
3980 | } |
---|
3981 | else if (degPi >= j + 1) |
---|
3982 | { |
---|
3983 | if (degBuf > 0) |
---|
3984 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1] [0]); |
---|
3985 | else |
---|
3986 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1]); |
---|
3987 | } |
---|
3988 | else if (degBuf >= j + 1) |
---|
3989 | { |
---|
3990 | if (degPi > 0) |
---|
3991 | tmp[l] += mulNTL (Pi [l - 1] [0], bufFactors [l + 1] [j + 1]); |
---|
3992 | else |
---|
3993 | tmp[l] += mulNTL (Pi [l - 1], bufFactors [l + 1] [j + 1]); |
---|
3994 | } |
---|
3995 | |
---|
3996 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
3997 | } |
---|
3998 | return; |
---|
3999 | } |
---|
4000 | |
---|
4001 | void |
---|
4002 | henselLift122 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
4003 | CFList& diophant, CFMatrix& M, const CFArray& LCs, bool sort) |
---|
4004 | { |
---|
4005 | if (sort) |
---|
4006 | sortList (factors, Variable (1)); |
---|
4007 | Pi= CFArray (factors.length() - 2); |
---|
4008 | CFList bufFactors2= factors; |
---|
4009 | bufFactors2.removeFirst(); |
---|
4010 | diophant= diophantine (F[0], bufFactors2); |
---|
4011 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
4012 | |
---|
4013 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
4014 | int i= 0; |
---|
4015 | for (CFListIterator k= bufFactors2; k.hasItem(); i++, k++) |
---|
4016 | bufFactors[i]= replaceLc (k.getItem(), LCs [i]); |
---|
4017 | |
---|
4018 | Variable x= F.mvar(); |
---|
4019 | if (degree (bufFactors[0], x) > 0 && degree (bufFactors [1], x) > 0) |
---|
4020 | { |
---|
4021 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1] [0]); |
---|
4022 | Pi [0]= M (1, 1) + (mulNTL (bufFactors [0] [1], bufFactors[1] [0]) + |
---|
4023 | mulNTL (bufFactors [0] [0], bufFactors [1] [1]))*x; |
---|
4024 | } |
---|
4025 | else if (degree (bufFactors[0], x) > 0) |
---|
4026 | { |
---|
4027 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1]); |
---|
4028 | Pi [0]= M (1, 1) + |
---|
4029 | mulNTL (bufFactors [0] [1], bufFactors[1])*x; |
---|
4030 | } |
---|
4031 | else if (degree (bufFactors[1], x) > 0) |
---|
4032 | { |
---|
4033 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1] [0]); |
---|
4034 | Pi [0]= M (1, 1) + |
---|
4035 | mulNTL (bufFactors [0], bufFactors[1] [1])*x; |
---|
4036 | } |
---|
4037 | else |
---|
4038 | { |
---|
4039 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1]); |
---|
4040 | Pi [0]= M (1, 1); |
---|
4041 | } |
---|
4042 | |
---|
4043 | for (i= 1; i < Pi.size(); i++) |
---|
4044 | { |
---|
4045 | if (degree (Pi[i-1], x) > 0 && degree (bufFactors [i+1], x) > 0) |
---|
4046 | { |
---|
4047 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors[i+1] [0]); |
---|
4048 | Pi [i]= M (1,i+1) + (mulNTL (Pi[i-1] [1], bufFactors[i+1] [0]) + |
---|
4049 | mulNTL (Pi[i-1] [0], bufFactors [i+1] [1]))*x; |
---|
4050 | } |
---|
4051 | else if (degree (Pi[i-1], x) > 0) |
---|
4052 | { |
---|
4053 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors [i+1]); |
---|
4054 | Pi [i]= M(1,i+1) + mulNTL (Pi[i-1] [1], bufFactors[i+1])*x; |
---|
4055 | } |
---|
4056 | else if (degree (bufFactors[i+1], x) > 0) |
---|
4057 | { |
---|
4058 | M (1,i+1)= mulNTL (Pi[i-1], bufFactors [i+1] [0]); |
---|
4059 | Pi [i]= M (1,i+1) + mulNTL (Pi[i-1], bufFactors[i+1] [1])*x; |
---|
4060 | } |
---|
4061 | else |
---|
4062 | { |
---|
4063 | M (1,i+1)= mulNTL (Pi [i-1], bufFactors [i+1]); |
---|
4064 | Pi [i]= M (1,i+1); |
---|
4065 | } |
---|
4066 | } |
---|
4067 | |
---|
4068 | for (i= 1; i < l; i++) |
---|
4069 | henselStep122 (F, bufFactors2, bufFactors, diophant, M, Pi, i, LCs); |
---|
4070 | |
---|
4071 | factors= CFList(); |
---|
4072 | for (i= 0; i < bufFactors.size(); i++) |
---|
4073 | factors.append (bufFactors[i]); |
---|
4074 | return; |
---|
4075 | } |
---|
4076 | |
---|
4077 | |
---|
4078 | /// solve \f$ E=sum_{i= 1}^{r}{\sigma_{i}prod_{j=1, j\neq i}^{r}{f_{i}}}\f$ |
---|
4079 | /// mod M, products contains \f$ prod_{j=1, j\neq i}^{r}{f_{i}}} \f$ |
---|
4080 | static inline |
---|
4081 | CFList |
---|
4082 | diophantine (const CFList& recResult, const CFList& factors, |
---|
4083 | const CFList& products, const CFList& M, const CanonicalForm& E, |
---|
4084 | bool& bad) |
---|
4085 | { |
---|
4086 | if (M.isEmpty()) |
---|
4087 | { |
---|
4088 | CFList result; |
---|
4089 | CFListIterator j= factors; |
---|
4090 | CanonicalForm buf; |
---|
4091 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
4092 | { |
---|
4093 | ASSERT (E.isUnivariate() || E.inCoeffDomain(), |
---|
4094 | "constant or univariate poly expected"); |
---|
4095 | ASSERT (i.getItem().isUnivariate() || i.getItem().inCoeffDomain(), |
---|
4096 | "constant or univariate poly expected"); |
---|
4097 | ASSERT (j.getItem().isUnivariate() || j.getItem().inCoeffDomain(), |
---|
4098 | "constant or univariate poly expected"); |
---|
4099 | buf= mulNTL (E, i.getItem()); |
---|
4100 | result.append (modNTL (buf, j.getItem())); |
---|
4101 | } |
---|
4102 | return result; |
---|
4103 | } |
---|
4104 | Variable y= M.getLast().mvar(); |
---|
4105 | CFList bufFactors= factors; |
---|
4106 | for (CFListIterator i= bufFactors; i.hasItem(); i++) |
---|
4107 | i.getItem()= mod (i.getItem(), y); |
---|
4108 | CFList bufProducts= products; |
---|
4109 | for (CFListIterator i= bufProducts; i.hasItem(); i++) |
---|
4110 | i.getItem()= mod (i.getItem(), y); |
---|
4111 | CFList buf= M; |
---|
4112 | buf.removeLast(); |
---|
4113 | CanonicalForm bufE= mod (E, y); |
---|
4114 | CFList recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
4115 | bufE, bad); |
---|
4116 | |
---|
4117 | if (bad) |
---|
4118 | return CFList(); |
---|
4119 | |
---|
4120 | CanonicalForm e= E; |
---|
4121 | CFListIterator j= products; |
---|
4122 | for (CFListIterator i= recDiophantine; i.hasItem(); i++, j++) |
---|
4123 | e -= i.getItem()*j.getItem(); |
---|
4124 | |
---|
4125 | CFList result= recDiophantine; |
---|
4126 | int d= degree (M.getLast()); |
---|
4127 | CanonicalForm coeffE; |
---|
4128 | for (int i= 1; i < d; i++) |
---|
4129 | { |
---|
4130 | if (degree (e, y) > 0) |
---|
4131 | coeffE= e[i]; |
---|
4132 | else |
---|
4133 | coeffE= 0; |
---|
4134 | if (!coeffE.isZero()) |
---|
4135 | { |
---|
4136 | CFListIterator k= result; |
---|
4137 | recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
4138 | coeffE, bad); |
---|
4139 | if (bad) |
---|
4140 | return CFList(); |
---|
4141 | CFListIterator l= products; |
---|
4142 | for (j= recDiophantine; j.hasItem(); j++, k++, l++) |
---|
4143 | { |
---|
4144 | k.getItem() += j.getItem()*power (y, i); |
---|
4145 | e -= j.getItem()*power (y, i)*l.getItem(); |
---|
4146 | } |
---|
4147 | } |
---|
4148 | if (e.isZero()) |
---|
4149 | break; |
---|
4150 | } |
---|
4151 | if (!e.isZero()) |
---|
4152 | { |
---|
4153 | bad= true; |
---|
4154 | return CFList(); |
---|
4155 | } |
---|
4156 | return result; |
---|
4157 | } |
---|
4158 | |
---|
4159 | static inline |
---|
4160 | void |
---|
4161 | henselStep2 (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
4162 | const CFList& diophant, CFMatrix& M, CFArray& Pi, |
---|
4163 | const CFList& products, int j, const CFList& MOD, bool& noOneToOne) |
---|
4164 | { |
---|
4165 | CanonicalForm E; |
---|
4166 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
4167 | Variable x= F.mvar(); |
---|
4168 | |
---|
4169 | // compute the error |
---|
4170 | #ifdef DEBUGOUTPUT |
---|
4171 | CanonicalForm test= 1; |
---|
4172 | for (int i= 0; i < factors.length(); i++) |
---|
4173 | { |
---|
4174 | if (i == 0) |
---|
4175 | test *= mod (bufFactors [i], power (x, j)); |
---|
4176 | else |
---|
4177 | test *= bufFactors[i]; |
---|
4178 | } |
---|
4179 | test= mod (test, power (x, j)); |
---|
4180 | test= mod (test, MOD); |
---|
4181 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
4182 | DEBOUTLN (cerr, "test= " << test2); |
---|
4183 | #endif |
---|
4184 | |
---|
4185 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
4186 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
4187 | else |
---|
4188 | E= F[j]; |
---|
4189 | |
---|
4190 | CFArray buf= CFArray (diophant.length()); |
---|
4191 | |
---|
4192 | // actual lifting |
---|
4193 | CFList diophantine2= diophantine (diophant, factors, products, MOD, E, |
---|
4194 | noOneToOne); |
---|
4195 | |
---|
4196 | if (noOneToOne) |
---|
4197 | return; |
---|
4198 | |
---|
4199 | int k= 0; |
---|
4200 | for (CFListIterator i= diophantine2; k < factors.length(); k++, i++) |
---|
4201 | { |
---|
4202 | buf[k]= i.getItem(); |
---|
4203 | bufFactors[k] += xToJ*i.getItem(); |
---|
4204 | } |
---|
4205 | |
---|
4206 | // update Pi [0] |
---|
4207 | int degBuf0= degree (bufFactors[0], x); |
---|
4208 | int degBuf1= degree (bufFactors[1], x); |
---|
4209 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
4210 | { |
---|
4211 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
4212 | if (j + 2 <= M.rows()) |
---|
4213 | M (j + 2, 1)= mulMod (bufFactors[0] [j + 1], bufFactors[1] [j + 1], MOD); |
---|
4214 | } |
---|
4215 | CanonicalForm uIZeroJ; |
---|
4216 | |
---|
4217 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
4218 | uIZeroJ= mulMod (bufFactors[0] [0], buf[1], MOD) + |
---|
4219 | mulMod (bufFactors[1] [0], buf[0], MOD); |
---|
4220 | else if (degBuf0 > 0) |
---|
4221 | uIZeroJ= mulMod (buf[0], bufFactors[1], MOD); |
---|
4222 | else if (degBuf1 > 0) |
---|
4223 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
4224 | else |
---|
4225 | uIZeroJ= 0; |
---|
4226 | Pi [0] += xToJ*uIZeroJ; |
---|
4227 | |
---|
4228 | CFArray tmp= CFArray (factors.length() - 1); |
---|
4229 | for (k= 0; k < factors.length() - 1; k++) |
---|
4230 | tmp[k]= 0; |
---|
4231 | CFIterator one, two; |
---|
4232 | one= bufFactors [0]; |
---|
4233 | two= bufFactors [1]; |
---|
4234 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
4235 | { |
---|
4236 | while (one.hasTerms() && one.exp() > j) one++; |
---|
4237 | while (two.hasTerms() && two.exp() > j) two++; |
---|
4238 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
4239 | { |
---|
4240 | if (k != j - k + 1) |
---|
4241 | { |
---|
4242 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
4243 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
4244 | { |
---|
4245 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
4246 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
4247 | M (j - k + 2, 1); |
---|
4248 | one++; |
---|
4249 | two++; |
---|
4250 | } |
---|
4251 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
4252 | { |
---|
4253 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
4254 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
4255 | one++; |
---|
4256 | } |
---|
4257 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
4258 | { |
---|
4259 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
4260 | two.coeff()), MOD) - M (k + 1, 1); |
---|
4261 | two++; |
---|
4262 | } |
---|
4263 | } |
---|
4264 | else |
---|
4265 | { |
---|
4266 | tmp[0] += M (k + 1, 1); |
---|
4267 | } |
---|
4268 | } |
---|
4269 | } |
---|
4270 | |
---|
4271 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
4272 | { |
---|
4273 | if (j + 2 <= M.rows()) |
---|
4274 | tmp [0] += mulMod ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
4275 | (bufFactors [1] [j + 1] + bufFactors [1] [0]), MOD) |
---|
4276 | - M(1,1) - M (j + 2,1); |
---|
4277 | } |
---|
4278 | else if (degBuf0 >= j + 1) |
---|
4279 | { |
---|
4280 | if (degBuf1 > 0) |
---|
4281 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1] [0], MOD); |
---|
4282 | else |
---|
4283 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1], MOD); |
---|
4284 | } |
---|
4285 | else if (degBuf1 >= j + 1) |
---|
4286 | { |
---|
4287 | if (degBuf0 > 0) |
---|
4288 | tmp[0] += mulMod (bufFactors [0] [0], bufFactors [1] [j + 1], MOD); |
---|
4289 | else |
---|
4290 | tmp[0] += mulMod (bufFactors [0], bufFactors [1] [j + 1], MOD); |
---|
4291 | } |
---|
4292 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
4293 | |
---|
4294 | // update Pi [l] |
---|
4295 | int degPi, degBuf; |
---|
4296 | for (int l= 1; l < factors.length() - 1; l++) |
---|
4297 | { |
---|
4298 | degPi= degree (Pi [l - 1], x); |
---|
4299 | degBuf= degree (bufFactors[l + 1], x); |
---|
4300 | if (degPi > 0 && degBuf > 0) |
---|
4301 | { |
---|
4302 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
4303 | if (j + 2 <= M.rows()) |
---|
4304 | M (j + 2, l + 1)= mulMod (Pi [l - 1] [j + 1], bufFactors[l + 1] [j + 1], |
---|
4305 | MOD); |
---|
4306 | } |
---|
4307 | |
---|
4308 | if (degPi > 0 && degBuf > 0) |
---|
4309 | uIZeroJ= mulMod (Pi[l -1] [0], buf[l + 1], MOD) + |
---|
4310 | mulMod (uIZeroJ, bufFactors[l+1] [0], MOD); |
---|
4311 | else if (degPi > 0) |
---|
4312 | uIZeroJ= mulMod (uIZeroJ, bufFactors[l + 1], MOD); |
---|
4313 | else if (degBuf > 0) |
---|
4314 | uIZeroJ= mulMod (Pi[l - 1], buf[1], MOD); |
---|
4315 | else |
---|
4316 | uIZeroJ= 0; |
---|
4317 | |
---|
4318 | Pi [l] += xToJ*uIZeroJ; |
---|
4319 | |
---|
4320 | one= bufFactors [l + 1]; |
---|
4321 | two= Pi [l - 1]; |
---|
4322 | if (degBuf > 0 && degPi > 0) |
---|
4323 | { |
---|
4324 | while (one.hasTerms() && one.exp() > j) one++; |
---|
4325 | while (two.hasTerms() && two.exp() > j) two++; |
---|
4326 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
4327 | { |
---|
4328 | if (k != j - k + 1) |
---|
4329 | { |
---|
4330 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
4331 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
4332 | { |
---|
4333 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
4334 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
4335 | M (j - k + 2, l + 1); |
---|
4336 | one++; |
---|
4337 | two++; |
---|
4338 | } |
---|
4339 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
4340 | { |
---|
4341 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
4342 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
4343 | one++; |
---|
4344 | } |
---|
4345 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
4346 | { |
---|
4347 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
4348 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
4349 | two++; |
---|
4350 | } |
---|
4351 | } |
---|
4352 | else |
---|
4353 | tmp[l] += M (k + 1, l + 1); |
---|
4354 | } |
---|
4355 | } |
---|
4356 | |
---|
4357 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
4358 | { |
---|
4359 | if (j + 2 <= M.rows()) |
---|
4360 | tmp [l] += mulMod ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
4361 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
4362 | , MOD) - M(1,l+1) - M (j + 2,l+1); |
---|
4363 | } |
---|
4364 | else if (degPi >= j + 1) |
---|
4365 | { |
---|
4366 | if (degBuf > 0) |
---|
4367 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1] [0], MOD); |
---|
4368 | else |
---|
4369 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1], MOD); |
---|
4370 | } |
---|
4371 | else if (degBuf >= j + 1) |
---|
4372 | { |
---|
4373 | if (degPi > 0) |
---|
4374 | tmp[l] += mulMod (Pi [l - 1] [0], bufFactors [l + 1] [j + 1], MOD); |
---|
4375 | else |
---|
4376 | tmp[l] += mulMod (Pi [l - 1], bufFactors [l + 1] [j + 1], MOD); |
---|
4377 | } |
---|
4378 | |
---|
4379 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
4380 | } |
---|
4381 | return; |
---|
4382 | } |
---|
4383 | |
---|
4384 | // wrt. Variable (1) |
---|
4385 | CanonicalForm replaceLC (const CanonicalForm& F, const CanonicalForm& c) |
---|
4386 | { |
---|
4387 | if (degree (F, 1) <= 0) |
---|
4388 | return c; |
---|
4389 | else |
---|
4390 | { |
---|
4391 | CanonicalForm result= swapvar (F, Variable (F.level() + 1), Variable (1)); |
---|
4392 | result += (swapvar (c, Variable (F.level() + 1), Variable (1)) |
---|
4393 | - LC (result))*power (result.mvar(), degree (result)); |
---|
4394 | return swapvar (result, Variable (F.level() + 1), Variable (1)); |
---|
4395 | } |
---|
4396 | } |
---|
4397 | |
---|
4398 | CFList |
---|
4399 | henselLift232 (const CFList& eval, const CFList& factors, int* l, CFList& |
---|
4400 | diophant, CFArray& Pi, CFMatrix& M, const CFList& LCs1, |
---|
4401 | const CFList& LCs2, bool& bad) |
---|
4402 | { |
---|
4403 | CFList buf= factors; |
---|
4404 | int k= 0; |
---|
4405 | int liftBoundBivar= l[k]; |
---|
4406 | CFList bufbuf= factors; |
---|
4407 | Variable v= Variable (2); |
---|
4408 | |
---|
4409 | CFList MOD; |
---|
4410 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
4411 | CFArray bufFactors= CFArray (factors.length()); |
---|
4412 | k= 0; |
---|
4413 | CFListIterator j= eval; |
---|
4414 | j++; |
---|
4415 | CFListIterator iter1= LCs1; |
---|
4416 | CFListIterator iter2= LCs2; |
---|
4417 | iter1++; |
---|
4418 | iter2++; |
---|
4419 | bufFactors[0]= replaceLC (buf.getFirst(), iter1.getItem()); |
---|
4420 | bufFactors[1]= replaceLC (buf.getLast(), iter2.getItem()); |
---|
4421 | |
---|
4422 | CFListIterator i= buf; |
---|
4423 | i++; |
---|
4424 | Variable y= j.getItem().mvar(); |
---|
4425 | if (y.level() != 3) |
---|
4426 | y= Variable (3); |
---|
4427 | |
---|
4428 | Pi[0]= mod (Pi[0], power (v, liftBoundBivar)); |
---|
4429 | M (1, 1)= Pi[0]; |
---|
4430 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
4431 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
4432 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
4433 | else if (degree (bufFactors[0], y) > 0) |
---|
4434 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
4435 | else if (degree (bufFactors[1], y) > 0) |
---|
4436 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
4437 | |
---|
4438 | CFList products; |
---|
4439 | for (int i= 0; i < bufFactors.size(); i++) |
---|
4440 | { |
---|
4441 | if (degree (bufFactors[i], y) > 0) |
---|
4442 | products.append (eval.getFirst()/bufFactors[i] [0]); |
---|
4443 | else |
---|
4444 | products.append (eval.getFirst()/bufFactors[i]); |
---|
4445 | } |
---|
4446 | |
---|
4447 | for (int d= 1; d < l[1]; d++) |
---|
4448 | { |
---|
4449 | henselStep2 (j.getItem(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
4450 | if (bad) |
---|
4451 | return CFList(); |
---|
4452 | } |
---|
4453 | CFList result; |
---|
4454 | for (k= 0; k < factors.length(); k++) |
---|
4455 | result.append (bufFactors[k]); |
---|
4456 | return result; |
---|
4457 | } |
---|
4458 | |
---|
4459 | |
---|
4460 | CFList |
---|
4461 | henselLift2 (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
4462 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, int& |
---|
4463 | lNew, const CFList& LCs1, const CFList& LCs2, bool& bad) |
---|
4464 | { |
---|
4465 | int k= 0; |
---|
4466 | CFArray bufFactors= CFArray (factors.length()); |
---|
4467 | bufFactors[0]= replaceLC (factors.getFirst(), LCs1.getLast()); |
---|
4468 | bufFactors[1]= replaceLC (factors.getLast(), LCs2.getLast()); |
---|
4469 | CFList buf= factors; |
---|
4470 | Variable y= F.getLast().mvar(); |
---|
4471 | Variable x= F.getFirst().mvar(); |
---|
4472 | CanonicalForm xToLOld= power (x, lOld); |
---|
4473 | Pi [0]= mod (Pi[0], xToLOld); |
---|
4474 | M (1, 1)= Pi [0]; |
---|
4475 | |
---|
4476 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
4477 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
4478 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
4479 | else if (degree (bufFactors[0], y) > 0) |
---|
4480 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
4481 | else if (degree (bufFactors[1], y) > 0) |
---|
4482 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
4483 | |
---|
4484 | CFList products; |
---|
4485 | CanonicalForm quot; |
---|
4486 | for (int i= 0; i < bufFactors.size(); i++) |
---|
4487 | { |
---|
4488 | if (degree (bufFactors[i], y) > 0) |
---|
4489 | { |
---|
4490 | if (!fdivides (bufFactors[i] [0], F.getFirst(), quot)) |
---|
4491 | { |
---|
4492 | bad= true; |
---|
4493 | return CFList(); |
---|
4494 | } |
---|
4495 | products.append (quot); |
---|
4496 | } |
---|
4497 | else |
---|
4498 | { |
---|
4499 | if (!fdivides (bufFactors[i], F.getFirst(), quot)) |
---|
4500 | { |
---|
4501 | bad= true; |
---|
4502 | return CFList(); |
---|
4503 | } |
---|
4504 | products.append (quot); |
---|
4505 | } |
---|
4506 | } |
---|
4507 | |
---|
4508 | for (int d= 1; d < lNew; d++) |
---|
4509 | { |
---|
4510 | henselStep2 (F.getLast(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
4511 | if (bad) |
---|
4512 | return CFList(); |
---|
4513 | } |
---|
4514 | |
---|
4515 | CFList result; |
---|
4516 | for (k= 0; k < factors.length(); k++) |
---|
4517 | result.append (bufFactors[k]); |
---|
4518 | return result; |
---|
4519 | } |
---|
4520 | |
---|
4521 | CFList |
---|
4522 | henselLift2 (const CFList& eval, const CFList& factors, int* l, const int |
---|
4523 | lLength, bool sort, const CFList& LCs1, const CFList& LCs2, |
---|
4524 | const CFArray& Pi, const CFList& diophant, bool& bad) |
---|
4525 | { |
---|
4526 | CFList bufDiophant= diophant; |
---|
4527 | CFList buf= factors; |
---|
4528 | if (sort) |
---|
4529 | sortList (buf, Variable (1)); |
---|
4530 | CFArray bufPi= Pi; |
---|
4531 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
4532 | CFList result= henselLift232(eval, buf, l, bufDiophant, bufPi, M, LCs1, LCs2, |
---|
4533 | bad); |
---|
4534 | if (bad) |
---|
4535 | return CFList(); |
---|
4536 | |
---|
4537 | if (eval.length() == 2) |
---|
4538 | return result; |
---|
4539 | CFList MOD; |
---|
4540 | for (int i= 0; i < 2; i++) |
---|
4541 | MOD.append (power (Variable (i + 2), l[i])); |
---|
4542 | CFListIterator j= eval; |
---|
4543 | j++; |
---|
4544 | CFList bufEval; |
---|
4545 | bufEval.append (j.getItem()); |
---|
4546 | j++; |
---|
4547 | CFListIterator jj= LCs1; |
---|
4548 | CFListIterator jjj= LCs2; |
---|
4549 | CFList bufLCs1, bufLCs2; |
---|
4550 | jj++, jjj++; |
---|
4551 | bufLCs1.append (jj.getItem()); |
---|
4552 | bufLCs2.append (jjj.getItem()); |
---|
4553 | jj++, jjj++; |
---|
4554 | |
---|
4555 | for (int i= 2; i < lLength && j.hasItem(); i++, j++, jj++, jjj++) |
---|
4556 | { |
---|
4557 | bufEval.append (j.getItem()); |
---|
4558 | bufLCs1.append (jj.getItem()); |
---|
4559 | bufLCs2.append (jjj.getItem()); |
---|
4560 | M= CFMatrix (l[i], factors.length()); |
---|
4561 | result= henselLift2 (bufEval, result, MOD, bufDiophant, bufPi, M, l[i - 1], |
---|
4562 | l[i], bufLCs1, bufLCs2, bad); |
---|
4563 | if (bad) |
---|
4564 | return CFList(); |
---|
4565 | MOD.append (power (Variable (i + 2), l[i])); |
---|
4566 | bufEval.removeFirst(); |
---|
4567 | bufLCs1.removeFirst(); |
---|
4568 | bufLCs2.removeFirst(); |
---|
4569 | } |
---|
4570 | return result; |
---|
4571 | } |
---|
4572 | |
---|
4573 | CFList |
---|
4574 | nonMonicHenselLift23 (const CanonicalForm& F, const CFList& factors, const |
---|
4575 | CFList& LCs, CFList& diophant, CFArray& Pi, int liftBound, |
---|
4576 | int bivarLiftBound, bool& bad) |
---|
4577 | { |
---|
4578 | CFList bufFactors2= factors; |
---|
4579 | |
---|
4580 | Variable y= Variable (2); |
---|
4581 | for (CFListIterator i= bufFactors2; i.hasItem(); i++) |
---|
4582 | i.getItem()= mod (i.getItem(), y); |
---|
4583 | |
---|
4584 | CanonicalForm bufF= F; |
---|
4585 | bufF= mod (bufF, y); |
---|
4586 | bufF= mod (bufF, Variable (3)); |
---|
4587 | |
---|
4588 | diophant= diophantine (bufF, bufFactors2); |
---|
4589 | |
---|
4590 | CFMatrix M= CFMatrix (liftBound, bufFactors2.length() - 1); |
---|
4591 | |
---|
4592 | Pi= CFArray (bufFactors2.length() - 1); |
---|
4593 | |
---|
4594 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
4595 | CFListIterator j= LCs; |
---|
4596 | int i= 0; |
---|
4597 | for (CFListIterator k= factors; k.hasItem(); j++, k++, i++) |
---|
4598 | bufFactors[i]= replaceLC (k.getItem(), j.getItem()); |
---|
4599 | |
---|
4600 | //initialise Pi |
---|
4601 | Variable v= Variable (3); |
---|
4602 | CanonicalForm yToL= power (y, bivarLiftBound); |
---|
4603 | if (degree (bufFactors[0], v) > 0 && degree (bufFactors [1], v) > 0) |
---|
4604 | { |
---|
4605 | M (1, 1)= mulMod2 (bufFactors [0] [0], bufFactors[1] [0], yToL); |
---|
4606 | Pi [0]= M (1,1) + (mulMod2 (bufFactors [0] [1], bufFactors[1] [0], yToL) + |
---|
4607 | mulMod2 (bufFactors [0] [0], bufFactors [1] [1], yToL))*v; |
---|
4608 | } |
---|
4609 | else if (degree (bufFactors[0], v) > 0) |
---|
4610 | { |
---|
4611 | M (1,1)= mulMod2 (bufFactors [0] [0], bufFactors [1], yToL); |
---|
4612 | Pi [0]= M(1,1) + mulMod2 (bufFactors [0] [1], bufFactors[1], yToL)*v; |
---|
4613 | } |
---|
4614 | else if (degree (bufFactors[1], v) > 0) |
---|
4615 | { |
---|
4616 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1] [0], yToL); |
---|
4617 | Pi [0]= M (1,1) + mulMod2 (bufFactors [0], bufFactors[1] [1], yToL)*v; |
---|
4618 | } |
---|
4619 | else |
---|
4620 | { |
---|
4621 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1], yToL); |
---|
4622 | Pi [0]= M (1,1); |
---|
4623 | } |
---|
4624 | |
---|
4625 | for (i= 1; i < Pi.size(); i++) |
---|
4626 | { |
---|
4627 | if (degree (Pi[i-1], v) > 0 && degree (bufFactors [i+1], v) > 0) |
---|
4628 | { |
---|
4629 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors[i+1] [0], yToL); |
---|
4630 | Pi [i]= M (1,i+1) + (mulMod2 (Pi[i-1] [1], bufFactors[i+1] [0], yToL) + |
---|
4631 | mulMod2 (Pi[i-1] [0], bufFactors [i+1] [1], yToL))*v; |
---|
4632 | } |
---|
4633 | else if (degree (Pi[i-1], v) > 0) |
---|
4634 | { |
---|
4635 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors [i+1], yToL); |
---|
4636 | Pi [i]= M(1,i+1) + mulMod2 (Pi[i-1] [1], bufFactors[i+1], yToL)*v; |
---|
4637 | } |
---|
4638 | else if (degree (bufFactors[i+1], v) > 0) |
---|
4639 | { |
---|
4640 | M (1,i+1)= mulMod2 (Pi[i-1], bufFactors [i+1] [0], yToL); |
---|
4641 | Pi [i]= M (1,i+1) + mulMod2 (Pi[i-1], bufFactors[i+1] [1], yToL)*v; |
---|
4642 | } |
---|
4643 | else |
---|
4644 | { |
---|
4645 | M (1,i+1)= mulMod2 (Pi [i-1], bufFactors [i+1], yToL); |
---|
4646 | Pi [i]= M (1,i+1); |
---|
4647 | } |
---|
4648 | } |
---|
4649 | |
---|
4650 | CFList products; |
---|
4651 | bufF= mod (F, Variable (3)); |
---|
4652 | for (CFListIterator k= factors; k.hasItem(); k++) |
---|
4653 | products.append (bufF/k.getItem()); |
---|
4654 | |
---|
4655 | CFList MOD= CFList (power (v, liftBound)); |
---|
4656 | MOD.insert (yToL); |
---|
4657 | for (int d= 1; d < liftBound; d++) |
---|
4658 | { |
---|
4659 | henselStep2 (F, factors, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
4660 | if (bad) |
---|
4661 | return CFList(); |
---|
4662 | } |
---|
4663 | |
---|
4664 | CFList result; |
---|
4665 | for (i= 0; i < factors.length(); i++) |
---|
4666 | result.append (bufFactors[i]); |
---|
4667 | return result; |
---|
4668 | } |
---|
4669 | |
---|
4670 | CFList |
---|
4671 | nonMonicHenselLift (const CFList& F, const CFList& factors, const CFList& LCs, |
---|
4672 | CFList& diophant, CFArray& Pi, CFMatrix& M, const int lOld, |
---|
4673 | int& lNew, const CFList& MOD, bool& noOneToOne |
---|
4674 | ) |
---|
4675 | { |
---|
4676 | |
---|
4677 | int k= 0; |
---|
4678 | CFArray bufFactors= CFArray (factors.length()); |
---|
4679 | CFListIterator j= LCs; |
---|
4680 | for (CFListIterator i= factors; i.hasItem(); i++, j++, k++) |
---|
4681 | bufFactors [k]= replaceLC (i.getItem(), j.getItem()); |
---|
4682 | |
---|
4683 | Variable y= F.getLast().mvar(); |
---|
4684 | Variable x= F.getFirst().mvar(); |
---|
4685 | CanonicalForm xToLOld= power (x, lOld); |
---|
4686 | |
---|
4687 | Pi [0]= mod (Pi[0], xToLOld); |
---|
4688 | M (1, 1)= Pi [0]; |
---|
4689 | |
---|
4690 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
4691 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
4692 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
4693 | else if (degree (bufFactors[0], y) > 0) |
---|
4694 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
4695 | else if (degree (bufFactors[1], y) > 0) |
---|
4696 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
4697 | |
---|
4698 | for (int i= 1; i < Pi.size(); i++) |
---|
4699 | { |
---|
4700 | Pi [i]= mod (Pi [i], xToLOld); |
---|
4701 | M (1, i + 1)= Pi [i]; |
---|
4702 | |
---|
4703 | if (degree (Pi[i-1], y) > 0 && degree (bufFactors [i+1], y) > 0) |
---|
4704 | Pi [i] += (mulMod (Pi[i-1] [1], bufFactors[i+1] [0], MOD) + |
---|
4705 | mulMod (Pi[i-1] [0], bufFactors [i+1] [1], MOD))*y; |
---|
4706 | else if (degree (Pi[i-1], y) > 0) |
---|
4707 | Pi [i] += mulMod (Pi[i-1] [1], bufFactors[i+1], MOD)*y; |
---|
4708 | else if (degree (bufFactors[i+1], y) > 0) |
---|
4709 | Pi [i] += mulMod (Pi[i-1], bufFactors[i+1] [1], MOD)*y; |
---|
4710 | } |
---|
4711 | |
---|
4712 | CFList products; |
---|
4713 | CanonicalForm quot, bufF= F.getFirst(); |
---|
4714 | |
---|
4715 | for (int i= 0; i < bufFactors.size(); i++) |
---|
4716 | { |
---|
4717 | if (degree (bufFactors[i], y) > 0) |
---|
4718 | { |
---|
4719 | if (!fdivides (bufFactors[i] [0], bufF, quot)) |
---|
4720 | { |
---|
4721 | noOneToOne= true; |
---|
4722 | return factors; |
---|
4723 | } |
---|
4724 | products.append (quot); |
---|
4725 | } |
---|
4726 | else |
---|
4727 | { |
---|
4728 | if (!fdivides (bufFactors[i], bufF, quot)) |
---|
4729 | { |
---|
4730 | noOneToOne= true; |
---|
4731 | return factors; |
---|
4732 | } |
---|
4733 | products.append (quot); |
---|
4734 | } |
---|
4735 | } |
---|
4736 | |
---|
4737 | for (int d= 1; d < lNew; d++) |
---|
4738 | { |
---|
4739 | henselStep2 (F.getLast(), factors, bufFactors, diophant, M, Pi, products, d, |
---|
4740 | MOD, noOneToOne); |
---|
4741 | if (noOneToOne) |
---|
4742 | return CFList(); |
---|
4743 | } |
---|
4744 | |
---|
4745 | CFList result; |
---|
4746 | for (k= 0; k < factors.length(); k++) |
---|
4747 | result.append (bufFactors[k]); |
---|
4748 | return result; |
---|
4749 | } |
---|
4750 | |
---|
4751 | CFList |
---|
4752 | nonMonicHenselLift (const CFList& eval, const CFList& factors, |
---|
4753 | CFList* const& LCs, CFList& diophant, CFArray& Pi, |
---|
4754 | int* liftBound, int length, bool& noOneToOne |
---|
4755 | ) |
---|
4756 | { |
---|
4757 | CFList bufDiophant= diophant; |
---|
4758 | CFList buf= factors; |
---|
4759 | CFArray bufPi= Pi; |
---|
4760 | CFMatrix M= CFMatrix (liftBound[1], factors.length() - 1); |
---|
4761 | int k= 0; |
---|
4762 | |
---|
4763 | CFList result= |
---|
4764 | nonMonicHenselLift23 (eval.getFirst(), factors, LCs [0], diophant, bufPi, |
---|
4765 | liftBound[1], liftBound[0], noOneToOne); |
---|
4766 | |
---|
4767 | if (noOneToOne) |
---|
4768 | return CFList(); |
---|
4769 | |
---|
4770 | if (eval.length() == 1) |
---|
4771 | return result; |
---|
4772 | |
---|
4773 | k++; |
---|
4774 | CFList MOD; |
---|
4775 | for (int i= 0; i < 2; i++) |
---|
4776 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
4777 | |
---|
4778 | CFListIterator j= eval; |
---|
4779 | CFList bufEval; |
---|
4780 | bufEval.append (j.getItem()); |
---|
4781 | j++; |
---|
4782 | |
---|
4783 | for (int i= 2; i <= length && j.hasItem(); i++, j++, k++) |
---|
4784 | { |
---|
4785 | bufEval.append (j.getItem()); |
---|
4786 | M= CFMatrix (liftBound[i], factors.length() - 1); |
---|
4787 | result= nonMonicHenselLift (bufEval, result, LCs [i-1], diophant, bufPi, M, |
---|
4788 | liftBound[i-1], liftBound[i], MOD, noOneToOne); |
---|
4789 | if (noOneToOne) |
---|
4790 | return result; |
---|
4791 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
4792 | bufEval.removeFirst(); |
---|
4793 | } |
---|
4794 | |
---|
4795 | return result; |
---|
4796 | } |
---|
4797 | |
---|
4798 | #endif |
---|
4799 | /* HAVE_NTL */ |
---|
4800 | |
---|