1 | |
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2 | #ifndef NTL_zz_pEX__H |
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3 | #define NTL_zz_pEX__H |
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4 | |
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5 | #include <NTL/vec_lzz_pE.h> |
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6 | |
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7 | NTL_OPEN_NNS |
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8 | |
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9 | class zz_pEX { |
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10 | |
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11 | public: |
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12 | |
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13 | vec_zz_pE rep; |
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14 | |
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15 | |
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16 | /*************************************************************** |
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17 | |
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18 | Constructors, Destructors, and Assignment |
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19 | |
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20 | ****************************************************************/ |
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21 | |
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22 | |
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23 | zz_pEX() |
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24 | // initial value 0 |
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25 | |
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26 | { } |
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27 | |
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28 | |
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29 | zz_pEX(INIT_SIZE_TYPE, long n) { rep.SetMaxLength(n); } |
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30 | |
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31 | ~zz_pEX() { } |
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32 | |
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33 | void normalize(); |
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34 | // strip leading zeros |
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35 | |
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36 | void SetMaxLength(long n) |
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37 | // pre-allocate space for n coefficients. |
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38 | // Value is unchanged |
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39 | |
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40 | { rep.SetMaxLength(n); } |
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41 | |
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42 | |
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43 | void kill() |
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44 | // free space held by this polynomial. Value becomes 0. |
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45 | |
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46 | { rep.kill(); } |
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47 | |
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48 | static const zz_pEX& zero(); |
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49 | |
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50 | inline zz_pEX(long i, const zz_pE& c); |
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51 | inline zz_pEX(long i, const zz_p& c); |
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52 | inline zz_pEX(long i, long c); |
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53 | |
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54 | |
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55 | inline zz_pEX& operator=(long a); |
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56 | inline zz_pEX& operator=(const zz_p& a); |
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57 | inline zz_pEX& operator=(const zz_pE& a); |
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58 | |
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59 | zz_pEX(zz_pEX& x, INIT_TRANS_TYPE) : rep(x.rep, INIT_TRANS) { } |
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60 | |
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61 | |
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62 | }; |
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63 | |
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64 | |
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65 | |
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66 | /********************************************************** |
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67 | |
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68 | Some utility routines |
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69 | |
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70 | ***********************************************************/ |
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71 | |
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72 | |
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73 | inline long deg(const zz_pEX& a) { return a.rep.length() - 1; } |
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74 | // degree of a polynomial. |
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75 | // note that the zero polynomial has degree -1. |
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76 | |
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77 | const zz_pE& coeff(const zz_pEX& a, long i); |
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78 | // zero if i not in range |
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79 | |
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80 | const zz_pE& LeadCoeff(const zz_pEX& a); |
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81 | // zero if a == 0 |
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82 | |
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83 | const zz_pE& ConstTerm(const zz_pEX& a); |
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84 | // zero if a == 0 |
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85 | |
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86 | void SetCoeff(zz_pEX& x, long i, const zz_pE& a); |
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87 | void SetCoeff(zz_pEX& x, long i, const zz_p& a); |
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88 | void SetCoeff(zz_pEX& x, long i, long a); |
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89 | // x[i] = a, error is raised if i < 0 |
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90 | |
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91 | inline zz_pEX::zz_pEX(long i, const zz_pE& a) |
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92 | { SetCoeff(*this, i, a); } |
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93 | |
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94 | inline zz_pEX::zz_pEX(long i, const zz_p& a) |
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95 | { SetCoeff(*this, i, a); } |
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96 | |
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97 | inline zz_pEX::zz_pEX(long i, long a) |
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98 | { SetCoeff(*this, i, a); } |
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99 | |
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100 | void SetCoeff(zz_pEX& x, long i); |
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101 | // x[i] = 1, error is raised if i < 0 |
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102 | |
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103 | void SetX(zz_pEX& x); |
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104 | // x is set to the monomial X |
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105 | |
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106 | long IsX(const zz_pEX& a); |
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107 | // test if x = X |
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108 | |
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109 | inline void clear(zz_pEX& x) |
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110 | // x = 0 |
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111 | |
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112 | { x.rep.SetLength(0); } |
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113 | |
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114 | inline void set(zz_pEX& x) |
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115 | // x = 1 |
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116 | |
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117 | { x.rep.SetLength(1); set(x.rep[0]); } |
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118 | |
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119 | inline void swap(zz_pEX& x, zz_pEX& y) |
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120 | // swap x & y (only pointers are swapped) |
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121 | |
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122 | { swap(x.rep, y.rep); } |
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123 | |
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124 | void random(zz_pEX& x, long n); |
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125 | inline zz_pEX random_zz_pEX(long n) |
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126 | { zz_pEX x; random(x, n); NTL_OPT_RETURN(zz_pEX, x); } |
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127 | // generate a random polynomial of degree < n |
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128 | |
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129 | void trunc(zz_pEX& x, const zz_pEX& a, long m); |
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130 | inline zz_pEX trunc(const zz_pEX& a, long m) |
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131 | { zz_pEX x; trunc(x, a, m); NTL_OPT_RETURN(zz_pEX, x); } |
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132 | // x = a % X^m |
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133 | |
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134 | void RightShift(zz_pEX& x, const zz_pEX& a, long n); |
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135 | inline zz_pEX RightShift(const zz_pEX& a, long n) |
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136 | { zz_pEX x; RightShift(x, a, n); NTL_OPT_RETURN(zz_pEX, x); } |
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137 | // x = a/X^n |
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138 | |
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139 | void LeftShift(zz_pEX& x, const zz_pEX& a, long n); |
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140 | inline zz_pEX LeftShift(const zz_pEX& a, long n) |
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141 | { zz_pEX x; LeftShift(x, a, n); NTL_OPT_RETURN(zz_pEX, x); } |
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142 | // x = a*X^n |
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143 | |
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144 | #ifndef NTL_TRANSITION |
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145 | |
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146 | inline zz_pEX operator>>(const zz_pEX& a, long n) |
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147 | { zz_pEX x; RightShift(x, a, n); NTL_OPT_RETURN(zz_pEX, x); } |
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148 | |
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149 | inline zz_pEX operator<<(const zz_pEX& a, long n) |
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150 | { zz_pEX x; LeftShift(x, a, n); NTL_OPT_RETURN(zz_pEX, x); } |
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151 | |
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152 | inline zz_pEX& operator<<=(zz_pEX& x, long n) |
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153 | { LeftShift(x, x, n); return x; } |
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154 | |
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155 | inline zz_pEX& operator>>=(zz_pEX& x, long n) |
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156 | { RightShift(x, x, n); return x; } |
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157 | |
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158 | #endif |
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159 | |
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160 | |
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161 | |
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162 | void diff(zz_pEX& x, const zz_pEX& a); |
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163 | inline zz_pEX diff(const zz_pEX& a) |
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164 | { zz_pEX x; diff(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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165 | // x = derivative of a |
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166 | |
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167 | |
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168 | |
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169 | void MakeMonic(zz_pEX& x); |
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170 | |
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171 | void reverse(zz_pEX& c, const zz_pEX& a, long hi); |
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172 | |
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173 | inline zz_pEX reverse(const zz_pEX& a, long hi) |
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174 | { zz_pEX x; reverse(x, a, hi); NTL_OPT_RETURN(zz_pEX, x); } |
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175 | |
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176 | inline void reverse(zz_pEX& c, const zz_pEX& a) |
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177 | { reverse(c, a, deg(a)); } |
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178 | |
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179 | inline zz_pEX reverse(const zz_pEX& a) |
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180 | { zz_pEX x; reverse(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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181 | |
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182 | inline void VectorCopy(vec_zz_pE& x, const zz_pEX& a, long n) |
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183 | { VectorCopy(x, a.rep, n); } |
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184 | |
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185 | inline vec_zz_pE VectorCopy(const zz_pEX& a, long n) |
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186 | { return VectorCopy(a.rep, n); } |
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187 | |
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188 | |
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189 | |
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190 | |
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191 | |
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192 | |
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193 | /******************************************************************* |
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194 | |
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195 | conversion routines |
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196 | |
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197 | ********************************************************************/ |
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198 | |
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199 | |
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200 | |
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201 | void conv(zz_pEX& x, long a); |
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202 | |
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203 | void conv(zz_pEX& x, const ZZ& a); |
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204 | |
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205 | void conv(zz_pEX& x, const zz_p& a); |
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206 | void conv(zz_pEX& x, const zz_pX& a); |
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207 | void conv(zz_pEX& x, const zz_pE& a); |
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208 | |
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209 | |
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210 | void conv(zz_pEX& x, const vec_zz_pE& a); |
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211 | |
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212 | inline zz_pEX to_zz_pEX(long a) |
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213 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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214 | |
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215 | inline zz_pEX to_zz_pEX(const ZZ& a) |
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216 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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217 | |
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218 | inline zz_pEX to_zz_pEX(const zz_p& a) |
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219 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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220 | |
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221 | inline zz_pEX to_zz_pEX(const zz_pX& a) |
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222 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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223 | |
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224 | inline zz_pEX to_zz_pEX(const zz_pE& a) |
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225 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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226 | |
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227 | inline zz_pEX to_zz_pEX(const vec_zz_pE& a) |
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228 | { zz_pEX x; conv(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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229 | |
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230 | inline zz_pEX& zz_pEX::operator=(long a) |
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231 | { conv(*this, a); return *this; } |
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232 | |
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233 | inline zz_pEX& zz_pEX::operator=(const zz_p& a) |
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234 | { conv(*this, a); return *this; } |
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235 | |
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236 | inline zz_pEX& zz_pEX::operator=(const zz_pE& a) |
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237 | { conv(*this, a); return *this; } |
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238 | |
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239 | |
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240 | /************************************************************* |
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241 | |
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242 | Comparison |
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243 | |
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244 | **************************************************************/ |
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245 | |
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246 | long IsZero(const zz_pEX& a); |
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247 | |
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248 | long IsOne(const zz_pEX& a); |
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249 | |
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250 | inline long operator==(const zz_pEX& a, const zz_pEX& b) |
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251 | { return a.rep == b.rep; } |
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252 | |
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253 | long operator==(const zz_pEX& a, long b); |
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254 | long operator==(const zz_pEX& a, const zz_p& b); |
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255 | long operator==(const zz_pEX& a, const zz_pE& b); |
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256 | |
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257 | inline long operator==(long a, const zz_pEX& b) |
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258 | { return (b == a); } |
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259 | inline long operator==(const zz_p& a, const zz_pEX& b) |
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260 | { return (b == a); } |
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261 | inline long operator==(const zz_pE& a, const zz_pEX& b) |
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262 | { return (b == a); } |
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263 | |
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264 | inline long operator!=(const zz_pEX& a, const zz_pEX& b) |
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265 | { return !(a == b); } |
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266 | inline long operator!=(const zz_pEX& a, long b) |
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267 | { return !(a == b); } |
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268 | inline long operator!=(const zz_pEX& a, const zz_p& b) |
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269 | { return !(a == b); } |
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270 | inline long operator!=(const zz_pEX& a, const zz_pE& b) |
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271 | { return !(a == b); } |
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272 | inline long operator!=(const long a, const zz_pEX& b) |
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273 | { return !(a == b); } |
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274 | inline long operator!=(const zz_p& a, const zz_pEX& b) |
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275 | { return !(a == b); } |
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276 | inline long operator!=(const zz_pE& a, const zz_pEX& b) |
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277 | { return !(a == b); } |
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278 | |
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279 | |
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280 | /*************************************************************** |
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281 | |
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282 | Addition |
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283 | |
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284 | ****************************************************************/ |
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285 | |
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286 | void add(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); |
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287 | |
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288 | void sub(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); |
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289 | |
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290 | void negate(zz_pEX& x, const zz_pEX& a); |
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291 | |
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292 | // scalar versions |
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293 | |
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294 | void add(zz_pEX & x, const zz_pEX& a, long b); |
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295 | void add(zz_pEX & x, const zz_pEX& a, const zz_p& b); |
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296 | void add(zz_pEX & x, const zz_pEX& a, const zz_pE& b); |
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297 | |
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298 | inline void add(zz_pEX& x, const zz_pE& a, const zz_pEX& b) |
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299 | { add(x, b, a); } |
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300 | inline void add(zz_pEX& x, const zz_p& a, const zz_pEX& b) |
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301 | { add(x, b, a); } |
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302 | inline void add(zz_pEX& x, long a, const zz_pEX& b) |
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303 | { add(x, b, a); } |
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304 | |
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305 | void sub(zz_pEX & x, const zz_pEX& a, long b); |
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306 | void sub(zz_pEX & x, const zz_pEX& a, const zz_p& b); |
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307 | void sub(zz_pEX & x, const zz_pEX& a, const zz_pE& b); |
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308 | |
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309 | void sub(zz_pEX& x, const zz_pE& a, const zz_pEX& b); |
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310 | void sub(zz_pEX& x, const zz_p& a, const zz_pEX& b); |
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311 | void sub(zz_pEX& x, long a, const zz_pEX& b); |
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312 | |
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313 | |
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314 | |
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315 | inline zz_pEX operator+(const zz_pEX& a, const zz_pEX& b) |
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316 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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317 | |
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318 | inline zz_pEX operator+(const zz_pEX& a, const zz_pE& b) |
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319 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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320 | |
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321 | inline zz_pEX operator+(const zz_pEX& a, const zz_p& b) |
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322 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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323 | |
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324 | inline zz_pEX operator+(const zz_pEX& a, long b) |
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325 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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326 | |
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327 | inline zz_pEX operator+(const zz_pE& a, const zz_pEX& b) |
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328 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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329 | |
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330 | inline zz_pEX operator+(const zz_p& a, const zz_pEX& b) |
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331 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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332 | |
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333 | inline zz_pEX operator+(long a, const zz_pEX& b) |
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334 | { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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335 | |
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336 | |
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337 | inline zz_pEX operator-(const zz_pEX& a, const zz_pEX& b) |
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338 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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339 | |
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340 | inline zz_pEX operator-(const zz_pEX& a, const zz_pE& b) |
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341 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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342 | |
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343 | inline zz_pEX operator-(const zz_pEX& a, const zz_p& b) |
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344 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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345 | |
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346 | inline zz_pEX operator-(const zz_pEX& a, long b) |
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347 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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348 | |
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349 | inline zz_pEX operator-(const zz_pE& a, const zz_pEX& b) |
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350 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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351 | |
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352 | inline zz_pEX operator-(const zz_p& a, const zz_pEX& b) |
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353 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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354 | |
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355 | inline zz_pEX operator-(long a, const zz_pEX& b) |
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356 | { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
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357 | |
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358 | |
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359 | inline zz_pEX& operator+=(zz_pEX& x, const zz_pEX& b) |
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360 | { add(x, x, b); return x; } |
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361 | |
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362 | inline zz_pEX& operator+=(zz_pEX& x, const zz_pE& b) |
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363 | { add(x, x, b); return x; } |
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364 | |
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365 | inline zz_pEX& operator+=(zz_pEX& x, const zz_p& b) |
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366 | { add(x, x, b); return x; } |
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367 | |
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368 | inline zz_pEX& operator+=(zz_pEX& x, long b) |
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369 | { add(x, x, b); return x; } |
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370 | |
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371 | inline zz_pEX& operator-=(zz_pEX& x, const zz_pEX& b) |
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372 | { sub(x, x, b); return x; } |
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373 | |
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374 | inline zz_pEX& operator-=(zz_pEX& x, const zz_pE& b) |
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375 | { sub(x, x, b); return x; } |
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376 | |
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377 | inline zz_pEX& operator-=(zz_pEX& x, const zz_p& b) |
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378 | { sub(x, x, b); return x; } |
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379 | |
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380 | inline zz_pEX& operator-=(zz_pEX& x, long b) |
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381 | { sub(x, x, b); return x; } |
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382 | |
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383 | |
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384 | inline zz_pEX operator-(const zz_pEX& a) |
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385 | { zz_pEX x; negate(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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386 | |
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387 | inline zz_pEX& operator++(zz_pEX& x) { add(x, x, 1); return x; } |
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388 | inline void operator++(zz_pEX& x, int) { add(x, x, 1); } |
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389 | inline zz_pEX& operator--(zz_pEX& x) { sub(x, x, 1); return x; } |
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390 | inline void operator--(zz_pEX& x, int) { sub(x, x, 1); } |
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391 | |
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392 | |
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393 | |
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394 | /***************************************************************** |
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395 | |
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396 | Multiplication |
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397 | |
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398 | ******************************************************************/ |
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399 | |
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400 | |
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401 | void mul(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); |
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402 | // x = a * b |
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403 | |
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404 | void sqr(zz_pEX& x, const zz_pEX& a); |
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405 | inline zz_pEX sqr(const zz_pEX& a) |
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406 | { zz_pEX x; sqr(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
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407 | // x = a^2 |
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408 | |
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409 | |
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410 | void mul(zz_pEX & x, const zz_pEX& a, long b); |
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411 | void mul(zz_pEX & x, const zz_pEX& a, const zz_p& b); |
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412 | void mul(zz_pEX & x, const zz_pEX& a, const zz_pE& b); |
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413 | |
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414 | inline void mul(zz_pEX& x, long a, const zz_pEX& b) |
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415 | { mul(x, b, a); } |
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416 | inline void mul(zz_pEX& x, const zz_p& a, const zz_pEX& b) |
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417 | { mul(x, b, a); } |
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418 | inline void mul(zz_pEX& x, const zz_pE& a, const zz_pEX& b) |
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419 | { mul(x, b, a); } |
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420 | |
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421 | void MulTrunc(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, long n); |
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422 | inline zz_pEX MulTrunc(const zz_pEX& a, const zz_pEX& b, long n) |
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423 | { zz_pEX x; MulTrunc(x, a, b, n); NTL_OPT_RETURN(zz_pEX, x); } |
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424 | // x = a * b % X^n |
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425 | |
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426 | void SqrTrunc(zz_pEX& x, const zz_pEX& a, long n); |
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427 | inline zz_pEX SqrTrunc(const zz_pEX& a, long n) |
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428 | { zz_pEX x; SqrTrunc(x, a, n); NTL_OPT_RETURN(zz_pEX, x); } |
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429 | // x = a*a % X^n |
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430 | |
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431 | |
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432 | inline zz_pEX operator*(const zz_pEX& a, const zz_pEX& b) |
---|
433 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
434 | |
---|
435 | inline zz_pEX operator*(const zz_pEX& a, const zz_pE& b) |
---|
436 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
437 | |
---|
438 | inline zz_pEX operator*(const zz_pEX& a, const zz_p& b) |
---|
439 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
440 | |
---|
441 | inline zz_pEX operator*(const zz_pEX& a, long b) |
---|
442 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
443 | |
---|
444 | inline zz_pEX operator*(const zz_pE& a, const zz_pEX& b) |
---|
445 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
446 | |
---|
447 | inline zz_pEX operator*(const zz_p& a, const zz_pEX& b) |
---|
448 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
449 | |
---|
450 | inline zz_pEX operator*(long a, const zz_pEX& b) |
---|
451 | { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
452 | |
---|
453 | inline zz_pEX& operator*=(zz_pEX& x, const zz_pEX& b) |
---|
454 | { mul(x, x, b); return x; } |
---|
455 | |
---|
456 | inline zz_pEX& operator*=(zz_pEX& x, const zz_pE& b) |
---|
457 | { mul(x, x, b); return x; } |
---|
458 | |
---|
459 | inline zz_pEX& operator*=(zz_pEX& x, const zz_p& b) |
---|
460 | { mul(x, x, b); return x; } |
---|
461 | |
---|
462 | inline zz_pEX& operator*=(zz_pEX& x, long b) |
---|
463 | { mul(x, x, b); return x; } |
---|
464 | |
---|
465 | |
---|
466 | void power(zz_pEX& x, const zz_pEX& a, long e); |
---|
467 | inline zz_pEX power(const zz_pEX& a, long e) |
---|
468 | { zz_pEX x; power(x, a, e); NTL_OPT_RETURN(zz_pEX, x); } |
---|
469 | |
---|
470 | |
---|
471 | |
---|
472 | |
---|
473 | |
---|
474 | /************************************************************* |
---|
475 | |
---|
476 | Division |
---|
477 | |
---|
478 | **************************************************************/ |
---|
479 | |
---|
480 | void DivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b); |
---|
481 | // q = a/b, r = a%b |
---|
482 | |
---|
483 | void div(zz_pEX& q, const zz_pEX& a, const zz_pEX& b); |
---|
484 | void div(zz_pEX& q, const zz_pEX& a, const zz_pE& b); |
---|
485 | void div(zz_pEX& q, const zz_pEX& a, const zz_p& b); |
---|
486 | void div(zz_pEX& q, const zz_pEX& a, long b); |
---|
487 | // q = a/b |
---|
488 | |
---|
489 | void rem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b); |
---|
490 | // r = a%b |
---|
491 | |
---|
492 | long divide(zz_pEX& q, const zz_pEX& a, const zz_pEX& b); |
---|
493 | // if b | a, sets q = a/b and returns 1; otherwise returns 0 |
---|
494 | |
---|
495 | long divide(const zz_pEX& a, const zz_pEX& b); |
---|
496 | // if b | a, sets q = a/b and returns 1; otherwise returns 0 |
---|
497 | |
---|
498 | void InvTrunc(zz_pEX& x, const zz_pEX& a, long m); |
---|
499 | inline zz_pEX InvTrunc(const zz_pEX& a, long m) |
---|
500 | { zz_pEX x; InvTrunc(x, a, m); NTL_OPT_RETURN(zz_pEX, x); } |
---|
501 | // computes x = a^{-1} % X^m |
---|
502 | // constant term must be invertible |
---|
503 | |
---|
504 | |
---|
505 | inline zz_pEX operator/(const zz_pEX& a, const zz_pEX& b) |
---|
506 | { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
507 | |
---|
508 | inline zz_pEX operator/(const zz_pEX& a, const zz_pE& b) |
---|
509 | { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
510 | |
---|
511 | inline zz_pEX operator/(const zz_pEX& a, const zz_p& b) |
---|
512 | { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
513 | |
---|
514 | inline zz_pEX operator/(const zz_pEX& a, long b) |
---|
515 | { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
516 | |
---|
517 | inline zz_pEX& operator/=(zz_pEX& x, const zz_pEX& b) |
---|
518 | { div(x, x, b); return x; } |
---|
519 | |
---|
520 | inline zz_pEX& operator/=(zz_pEX& x, const zz_pE& b) |
---|
521 | { div(x, x, b); return x; } |
---|
522 | |
---|
523 | inline zz_pEX& operator/=(zz_pEX& x, const zz_p& b) |
---|
524 | { div(x, x, b); return x; } |
---|
525 | |
---|
526 | inline zz_pEX& operator/=(zz_pEX& x, long b) |
---|
527 | { div(x, x, b); return x; } |
---|
528 | |
---|
529 | |
---|
530 | inline zz_pEX operator%(const zz_pEX& a, const zz_pEX& b) |
---|
531 | { zz_pEX x; rem(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
532 | |
---|
533 | inline zz_pEX& operator%=(zz_pEX& x, const zz_pEX& b) |
---|
534 | { rem(x, x, b); return x; } |
---|
535 | |
---|
536 | |
---|
537 | |
---|
538 | /*********************************************************** |
---|
539 | |
---|
540 | GCD's |
---|
541 | |
---|
542 | ************************************************************/ |
---|
543 | |
---|
544 | |
---|
545 | void GCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b); |
---|
546 | inline zz_pEX GCD(const zz_pEX& a, const zz_pEX& b) |
---|
547 | { zz_pEX x; GCD(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
548 | // x = GCD(a, b), x is always monic (or zero if a==b==0). |
---|
549 | |
---|
550 | void XGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, const zz_pEX& b); |
---|
551 | // d = gcd(a,b), a s + b t = d |
---|
552 | |
---|
553 | |
---|
554 | /************************************************************* |
---|
555 | |
---|
556 | Modular Arithmetic without pre-conditioning |
---|
557 | |
---|
558 | **************************************************************/ |
---|
559 | |
---|
560 | // arithmetic mod f. |
---|
561 | // all inputs and outputs are polynomials of degree less than deg(f). |
---|
562 | // ASSUMPTION: f is assumed monic, and deg(f) > 0. |
---|
563 | // NOTE: if you want to do many computations with a fixed f, |
---|
564 | // use the zz_pEXModulus data structure and associated routines below. |
---|
565 | |
---|
566 | |
---|
567 | |
---|
568 | void MulMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, const zz_pEX& f); |
---|
569 | inline zz_pEX MulMod(const zz_pEX& a, const zz_pEX& b, const zz_pEX& f) |
---|
570 | { zz_pEX x; MulMod(x, a, b, f); NTL_OPT_RETURN(zz_pEX, x); } |
---|
571 | // x = (a * b) % f |
---|
572 | |
---|
573 | void SqrMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f); |
---|
574 | inline zz_pEX SqrMod(const zz_pEX& a, const zz_pEX& f) |
---|
575 | { zz_pEX x; SqrMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); } |
---|
576 | // x = a^2 % f |
---|
577 | |
---|
578 | void MulByXMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f); |
---|
579 | inline zz_pEX MulByXMod(const zz_pEX& a, const zz_pEX& f) |
---|
580 | { zz_pEX x; MulByXMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); } |
---|
581 | // x = (a * X) mod f |
---|
582 | |
---|
583 | void InvMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f); |
---|
584 | inline zz_pEX InvMod(const zz_pEX& a, const zz_pEX& f) |
---|
585 | { zz_pEX x; InvMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); } |
---|
586 | // x = a^{-1} % f, error is a is not invertible |
---|
587 | |
---|
588 | long InvModStatus(zz_pEX& x, const zz_pEX& a, const zz_pEX& f); |
---|
589 | // if (a, f) = 1, returns 0 and sets x = a^{-1} % f |
---|
590 | // otherwise, returns 1 and sets x = (a, f) |
---|
591 | |
---|
592 | |
---|
593 | |
---|
594 | |
---|
595 | |
---|
596 | /****************************************************************** |
---|
597 | |
---|
598 | Modular Arithmetic with Pre-conditioning |
---|
599 | |
---|
600 | *******************************************************************/ |
---|
601 | |
---|
602 | |
---|
603 | // If you need to do a lot of arithmetic modulo a fixed f, |
---|
604 | // build zz_pEXModulus F for f. This pre-computes information about f |
---|
605 | // that speeds up the computation a great deal. |
---|
606 | |
---|
607 | class zz_pEXModulus { |
---|
608 | public: |
---|
609 | zz_pEXModulus(); |
---|
610 | ~zz_pEXModulus(); |
---|
611 | |
---|
612 | zz_pEXModulus(const zz_pEX& ff); |
---|
613 | |
---|
614 | zz_pEX f; // the modulus |
---|
615 | |
---|
616 | operator const zz_pEX& () const { return f; } |
---|
617 | const zz_pEX& val() const { return f; } |
---|
618 | |
---|
619 | long n; // deg(f) |
---|
620 | |
---|
621 | long method; |
---|
622 | |
---|
623 | zz_pEX h0; |
---|
624 | zz_pE hlc; |
---|
625 | zz_pEX f0; |
---|
626 | |
---|
627 | vec_zz_pE tracevec; // mutable |
---|
628 | |
---|
629 | }; |
---|
630 | |
---|
631 | |
---|
632 | |
---|
633 | inline long deg(const zz_pEXModulus& F) { return F.n; } |
---|
634 | |
---|
635 | |
---|
636 | void build(zz_pEXModulus& F, const zz_pEX& f); |
---|
637 | |
---|
638 | void rem(zz_pEX& r, const zz_pEX& a, const zz_pEXModulus& F); |
---|
639 | |
---|
640 | void DivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEXModulus& F); |
---|
641 | |
---|
642 | void div(zz_pEX& q, const zz_pEX& a, const zz_pEXModulus& F); |
---|
643 | |
---|
644 | void MulMod(zz_pEX& c, const zz_pEX& a, const zz_pEX& b, |
---|
645 | const zz_pEXModulus& F); |
---|
646 | inline zz_pEX MulMod(const zz_pEX& a, const zz_pEX& b, |
---|
647 | const zz_pEXModulus& F) |
---|
648 | { zz_pEX x; MulMod(x, a, b, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
649 | |
---|
650 | void SqrMod(zz_pEX& c, const zz_pEX& a, const zz_pEXModulus& F); |
---|
651 | inline zz_pEX SqrMod(const zz_pEX& a, const zz_pEXModulus& F) |
---|
652 | { zz_pEX x; SqrMod(x, a, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
653 | |
---|
654 | |
---|
655 | void PowerMod(zz_pEX& h, const zz_pEX& g, const ZZ& e, const zz_pEXModulus& F); |
---|
656 | |
---|
657 | inline void PowerMod(zz_pEX& h, const zz_pEX& g, long e, |
---|
658 | const zz_pEXModulus& F) |
---|
659 | { PowerMod(h, g, ZZ_expo(e), F); } |
---|
660 | |
---|
661 | inline zz_pEX PowerMod(const zz_pEX& g, const ZZ& e, |
---|
662 | const zz_pEXModulus& F) |
---|
663 | { zz_pEX x; PowerMod(x, g, e, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
664 | |
---|
665 | inline zz_pEX PowerMod(const zz_pEX& g, long e, const zz_pEXModulus& F) |
---|
666 | { zz_pEX x; PowerMod(x, g, e, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
667 | |
---|
668 | void PowerXMod(zz_pEX& hh, const ZZ& e, const zz_pEXModulus& F); |
---|
669 | |
---|
670 | inline void PowerXMod(zz_pEX& h, long e, const zz_pEXModulus& F) |
---|
671 | { PowerXMod(h, ZZ_expo(e), F); } |
---|
672 | |
---|
673 | |
---|
674 | inline zz_pEX PowerXMod(const ZZ& e, const zz_pEXModulus& F) |
---|
675 | { zz_pEX x; PowerXMod(x, e, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
676 | |
---|
677 | inline zz_pEX PowerXMod(long e, const zz_pEXModulus& F) |
---|
678 | { zz_pEX x; PowerXMod(x, e, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
679 | |
---|
680 | |
---|
681 | inline zz_pEX operator%(const zz_pEX& a, const zz_pEXModulus& F) |
---|
682 | { zz_pEX x; rem(x, a, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
683 | |
---|
684 | inline zz_pEX& operator%=(zz_pEX& x, const zz_pEXModulus& F) |
---|
685 | { rem(x, x, F); return x; } |
---|
686 | |
---|
687 | inline zz_pEX operator/(const zz_pEX& a, const zz_pEXModulus& F) |
---|
688 | { zz_pEX x; div(x, a, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
689 | |
---|
690 | inline zz_pEX& operator/=(zz_pEX& x, const zz_pEXModulus& F) |
---|
691 | { div(x, x, F); return x; } |
---|
692 | |
---|
693 | |
---|
694 | |
---|
695 | /***************************************************************** |
---|
696 | |
---|
697 | vectors of zz_pEX's |
---|
698 | |
---|
699 | *****************************************************************/ |
---|
700 | |
---|
701 | |
---|
702 | |
---|
703 | NTL_vector_decl(zz_pEX,vec_zz_pEX) |
---|
704 | |
---|
705 | NTL_eq_vector_decl(zz_pEX,vec_zz_pEX) |
---|
706 | |
---|
707 | |
---|
708 | |
---|
709 | |
---|
710 | |
---|
711 | /******************************************************* |
---|
712 | |
---|
713 | Evaluation and related problems |
---|
714 | |
---|
715 | ********************************************************/ |
---|
716 | |
---|
717 | |
---|
718 | |
---|
719 | |
---|
720 | void BuildFromRoots(zz_pEX& x, const vec_zz_pE& a); |
---|
721 | inline zz_pEX BuildFromRoots(const vec_zz_pE& a) |
---|
722 | { zz_pEX x; BuildFromRoots(x, a); NTL_OPT_RETURN(zz_pEX, x); } |
---|
723 | // computes the polynomial (X-a[0]) ... (X-a[n-1]), where n = a.length() |
---|
724 | |
---|
725 | |
---|
726 | void eval(zz_pE& b, const zz_pEX& f, const zz_pE& a); |
---|
727 | inline zz_pE eval(const zz_pEX& f, const zz_pE& a) |
---|
728 | { zz_pE x; eval(x, f, a); NTL_OPT_RETURN(zz_pE, x); } |
---|
729 | // b = f(a) |
---|
730 | |
---|
731 | void eval(vec_zz_pE& b, const zz_pEX& f, const vec_zz_pE& a); |
---|
732 | inline vec_zz_pE eval(const zz_pEX& f, const vec_zz_pE& a) |
---|
733 | { vec_zz_pE x; eval(x, f, a); NTL_OPT_RETURN(vec_zz_pE, x); } |
---|
734 | // b[i] = f(a[i]) |
---|
735 | |
---|
736 | inline void eval(zz_pE& b, const zz_pX& f, const zz_pE& a) |
---|
737 | { conv(b, CompMod(f, rep(a), zz_pE::modulus())); } |
---|
738 | |
---|
739 | inline zz_pE eval(const zz_pX& f, const zz_pE& a) |
---|
740 | { zz_pE x; eval(x, f, a); NTL_OPT_RETURN(zz_pE, x); } |
---|
741 | // b = f(a) |
---|
742 | |
---|
743 | |
---|
744 | void interpolate(zz_pEX& f, const vec_zz_pE& a, const vec_zz_pE& b); |
---|
745 | inline zz_pEX interpolate(const vec_zz_pE& a, const vec_zz_pE& b) |
---|
746 | { zz_pEX x; interpolate(x, a, b); NTL_OPT_RETURN(zz_pEX, x); } |
---|
747 | // computes f such that f(a[i]) = b[i] |
---|
748 | |
---|
749 | |
---|
750 | |
---|
751 | |
---|
752 | |
---|
753 | /********************************************************** |
---|
754 | |
---|
755 | Modular Composition and Minimal Polynomials |
---|
756 | |
---|
757 | ***********************************************************/ |
---|
758 | |
---|
759 | |
---|
760 | |
---|
761 | void CompMod(zz_pEX& x, const zz_pEX& g, const zz_pEX& h, const zz_pEXModulus& F); |
---|
762 | inline zz_pEX |
---|
763 | CompMod(const zz_pEX& g, const zz_pEX& h, const zz_pEXModulus& F) |
---|
764 | { zz_pEX x; CompMod(x, g, h, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
765 | // x = g(h) mod f |
---|
766 | |
---|
767 | void Comp2Mod(zz_pEX& x1, zz_pEX& x2, const zz_pEX& g1, const zz_pEX& g2, |
---|
768 | const zz_pEX& h, const zz_pEXModulus& F); |
---|
769 | // xi = gi(h) mod f (i=1,2) |
---|
770 | |
---|
771 | void Comp3Mod(zz_pEX& x1, zz_pEX& x2, zz_pEX& x3, |
---|
772 | const zz_pEX& g1, const zz_pEX& g2, const zz_pEX& g3, |
---|
773 | const zz_pEX& h, const zz_pEXModulus& F); |
---|
774 | // xi = gi(h) mod f (i=1..3) |
---|
775 | |
---|
776 | |
---|
777 | |
---|
778 | // The routine build (see below) which is implicitly called |
---|
779 | // by the various compose and UpdateMap routines builds a table |
---|
780 | // of polynomials. |
---|
781 | // If zz_pEXArgBound > 0, then the table is limited in |
---|
782 | // size to approximamtely that many KB. |
---|
783 | // If zz_pEXArgBound <= 0, then it is ignored, and space is allocated |
---|
784 | // so as to maximize speed. |
---|
785 | // Initially, zz_pEXArgBound = 0. |
---|
786 | |
---|
787 | |
---|
788 | // If a single h is going to be used with many g's |
---|
789 | // then you should build a zz_pEXArgument for h, |
---|
790 | // and then use the compose routine below. |
---|
791 | // build computes and stores h, h^2, ..., h^m mod f. |
---|
792 | // After this pre-computation, composing a polynomial of degree |
---|
793 | // roughly n with h takes n/m multiplies mod f, plus n^2 |
---|
794 | // scalar multiplies. |
---|
795 | // Thus, increasing m increases the space requirement and the pre-computation |
---|
796 | // time, but reduces the composition time. |
---|
797 | // If zz_pEXArgBound > 0, a table of size less than m may be built. |
---|
798 | |
---|
799 | struct zz_pEXArgument { |
---|
800 | vec_zz_pEX H; |
---|
801 | }; |
---|
802 | |
---|
803 | extern long zz_pEXArgBound; |
---|
804 | |
---|
805 | |
---|
806 | void build(zz_pEXArgument& H, const zz_pEX& h, const zz_pEXModulus& F, long m); |
---|
807 | |
---|
808 | // m must be > 0, otherwise an error is raised |
---|
809 | |
---|
810 | void CompMod(zz_pEX& x, const zz_pEX& g, const zz_pEXArgument& H, |
---|
811 | const zz_pEXModulus& F); |
---|
812 | |
---|
813 | inline zz_pEX |
---|
814 | CompMod(const zz_pEX& g, const zz_pEXArgument& H, const zz_pEXModulus& F) |
---|
815 | { zz_pEX x; CompMod(x, g, H, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
816 | |
---|
817 | |
---|
818 | |
---|
819 | |
---|
820 | void MinPolySeq(zz_pEX& h, const vec_zz_pE& a, long m); |
---|
821 | inline zz_pEX MinPolySeq(const vec_zz_pE& a, long m) |
---|
822 | { zz_pEX x; MinPolySeq(x, a, m); NTL_OPT_RETURN(zz_pEX, x); } |
---|
823 | |
---|
824 | |
---|
825 | void MinPolyMod(zz_pEX& hh, const zz_pEX& g, const zz_pEXModulus& F); |
---|
826 | inline zz_pEX MinPolyMod(const zz_pEX& g, const zz_pEXModulus& F) |
---|
827 | { zz_pEX x; MinPolyMod(x, g, F); NTL_OPT_RETURN(zz_pEX, x); } |
---|
828 | |
---|
829 | |
---|
830 | void MinPolyMod(zz_pEX& hh, const zz_pEX& g, const zz_pEXModulus& F, long m); |
---|
831 | inline zz_pEX MinPolyMod(const zz_pEX& g, const zz_pEXModulus& F, long m) |
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832 | { zz_pEX x; MinPolyMod(x, g, F, m); NTL_OPT_RETURN(zz_pEX, x); } |
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833 | |
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834 | void ProbMinPolyMod(zz_pEX& hh, const zz_pEX& g, const zz_pEXModulus& F); |
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835 | inline zz_pEX ProbMinPolyMod(const zz_pEX& g, const zz_pEXModulus& F) |
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836 | { zz_pEX x; ProbMinPolyMod(x, g, F); NTL_OPT_RETURN(zz_pEX, x); } |
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837 | |
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838 | void ProbMinPolyMod(zz_pEX& hh, const zz_pEX& g, const zz_pEXModulus& F, long m); |
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839 | inline zz_pEX ProbMinPolyMod(const zz_pEX& g, const zz_pEXModulus& F, long m) |
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840 | { zz_pEX x; ProbMinPolyMod(x, g, F, m); NTL_OPT_RETURN(zz_pEX, x); } |
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841 | |
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842 | void IrredPolyMod(zz_pEX& h, const zz_pEX& g, const zz_pEXModulus& F); |
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843 | inline zz_pEX IrredPolyMod(const zz_pEX& g, const zz_pEXModulus& F) |
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844 | { zz_pEX x; IrredPolyMod(x, g, F); NTL_OPT_RETURN(zz_pEX, x); } |
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845 | |
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846 | void IrredPolyMod(zz_pEX& h, const zz_pEX& g, const zz_pEXModulus& F, long m); |
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847 | inline zz_pEX IrredPolyMod(const zz_pEX& g, const zz_pEXModulus& F, long m) |
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848 | { zz_pEX x; IrredPolyMod(x, g, F, m); NTL_OPT_RETURN(zz_pEX, x); } |
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849 | |
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850 | |
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851 | struct zz_pEXTransMultiplier { |
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852 | zz_pEX f0, fbi, b; |
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853 | long shamt, shamt_fbi, shamt_b; |
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854 | }; |
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855 | |
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856 | void build(zz_pEXTransMultiplier& B, const zz_pEX& b, const zz_pEXModulus& F); |
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857 | |
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858 | void TransMulMod(zz_pEX& x, const zz_pEX& a, const zz_pEXTransMultiplier& B, |
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859 | const zz_pEXModulus& F); |
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860 | |
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861 | void UpdateMap(vec_zz_pE& x, const vec_zz_pE& a, |
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862 | const zz_pEXTransMultiplier& B, const zz_pEXModulus& F); |
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863 | |
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864 | inline vec_zz_pE UpdateMap(const vec_zz_pE& a, |
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865 | const zz_pEXTransMultiplier& B, const zz_pEXModulus& F) |
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866 | { vec_zz_pE x; UpdateMap(x, a, B, F); NTL_OPT_RETURN(vec_zz_pE, x); } |
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867 | |
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868 | void ProjectPowers(vec_zz_pE& x, const vec_zz_pE& a, long k, |
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869 | const zz_pEXArgument& H, const zz_pEXModulus& F); |
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870 | inline vec_zz_pE ProjectPowers(const vec_zz_pE& a, long k, |
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871 | const zz_pEXArgument& H, const zz_pEXModulus& F) |
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872 | { vec_zz_pE x; ProjectPowers(x, a, k, H, F); NTL_OPT_RETURN(vec_zz_pE, x); } |
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873 | |
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874 | void ProjectPowers(vec_zz_pE& x, const vec_zz_pE& a, long k, const zz_pEX& h, |
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875 | const zz_pEXModulus& F); |
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876 | inline vec_zz_pE ProjectPowers(const vec_zz_pE& a, long k, |
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877 | const zz_pEX& H, const zz_pEXModulus& F) |
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878 | { vec_zz_pE x; ProjectPowers(x, a, k, H, F); NTL_OPT_RETURN(vec_zz_pE, x); } |
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879 | |
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880 | inline void project(zz_pE& x, const vec_zz_pE& a, const zz_pEX& b) |
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881 | { InnerProduct(x, a, b.rep); } |
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882 | |
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883 | inline zz_pE project(const vec_zz_pE& a, const zz_pEX& b) |
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884 | { zz_pE x; InnerProduct(x, a, b.rep); NTL_OPT_RETURN(zz_pE, x); } |
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885 | |
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886 | |
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887 | |
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888 | /***************************************************************** |
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889 | |
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890 | modular composition and minimal polynonomials |
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891 | in towers |
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892 | |
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893 | ******************************************************************/ |
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894 | |
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895 | |
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896 | // composition |
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897 | |
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898 | void CompTower(zz_pEX& x, const zz_pX& g, const zz_pEXArgument& A, |
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899 | const zz_pEXModulus& F); |
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900 | |
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901 | inline zz_pEX CompTower(const zz_pX& g, const zz_pEXArgument& A, |
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902 | const zz_pEXModulus& F) |
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903 | { zz_pEX x; CompTower(x, g, A, F); NTL_OPT_RETURN(zz_pEX, x); } |
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904 | |
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905 | void CompTower(zz_pEX& x, const zz_pX& g, const zz_pEX& h, |
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906 | const zz_pEXModulus& F); |
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907 | |
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908 | inline zz_pEX CompTower(const zz_pX& g, const zz_pEX& h, |
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909 | const zz_pEXModulus& F) |
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910 | { zz_pEX x; CompTower(x, g, h, F); NTL_OPT_RETURN(zz_pEX, x); } |
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911 | |
---|
912 | // prob min poly |
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913 | |
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914 | void ProbMinPolyTower(zz_pX& h, const zz_pEX& g, const zz_pEXModulus& F, |
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915 | long m); |
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916 | |
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917 | inline zz_pX ProbMinPolyTower(const zz_pEX& g, const zz_pEXModulus& F, |
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918 | long m) |
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919 | { zz_pX x; ProbMinPolyTower(x, g, F, m); NTL_OPT_RETURN(zz_pX, x); } |
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920 | |
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921 | inline void ProbMinPolyTower(zz_pX& h, const zz_pEX& g, |
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922 | const zz_pEXModulus& F) |
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923 | { ProbMinPolyTower(h, g, F, deg(F)*zz_pE::degree()); } |
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924 | |
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925 | inline zz_pX ProbMinPolyTower(const zz_pEX& g, const zz_pEXModulus& F) |
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926 | { zz_pX x; ProbMinPolyTower(x, g, F); NTL_OPT_RETURN(zz_pX, x); } |
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927 | |
---|
928 | |
---|
929 | // min poly |
---|
930 | |
---|
931 | |
---|
932 | void MinPolyTower(zz_pX& h, const zz_pEX& g, const zz_pEXModulus& F, |
---|
933 | long m); |
---|
934 | |
---|
935 | inline zz_pX MinPolyTower(const zz_pEX& g, const zz_pEXModulus& F, |
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936 | long m) |
---|
937 | { zz_pX x; MinPolyTower(x, g, F, m); NTL_OPT_RETURN(zz_pX, x); } |
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938 | |
---|
939 | inline void MinPolyTower(zz_pX& h, const zz_pEX& g, |
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940 | const zz_pEXModulus& F) |
---|
941 | { MinPolyTower(h, g, F, deg(F)*zz_pE::degree()); } |
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942 | |
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943 | inline zz_pX MinPolyTower(const zz_pEX& g, const zz_pEXModulus& F) |
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944 | { zz_pX x; MinPolyTower(x, g, F); NTL_OPT_RETURN(zz_pX, x); } |
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945 | |
---|
946 | // irred poly |
---|
947 | |
---|
948 | |
---|
949 | void IrredPolyTower(zz_pX& h, const zz_pEX& g, const zz_pEXModulus& F, |
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950 | long m); |
---|
951 | |
---|
952 | inline zz_pX IrredPolyTower(const zz_pEX& g, const zz_pEXModulus& F, |
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953 | long m) |
---|
954 | { zz_pX x; IrredPolyTower(x, g, F, m); NTL_OPT_RETURN(zz_pX, x); } |
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955 | |
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956 | inline void IrredPolyTower(zz_pX& h, const zz_pEX& g, |
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957 | const zz_pEXModulus& F) |
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958 | { IrredPolyTower(h, g, F, deg(F)*zz_pE::degree()); } |
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959 | |
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960 | inline zz_pX IrredPolyTower(const zz_pEX& g, const zz_pEXModulus& F) |
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961 | { zz_pX x; IrredPolyTower(x, g, F); NTL_OPT_RETURN(zz_pX, x); } |
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962 | |
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963 | /***************************************************************** |
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964 | |
---|
965 | Traces, norms, resultants |
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966 | |
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967 | ******************************************************************/ |
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968 | |
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969 | void TraceVec(vec_zz_pE& S, const zz_pEX& f); |
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970 | |
---|
971 | inline vec_zz_pE TraceVec(const zz_pEX& f) |
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972 | { vec_zz_pE x; TraceVec(x, f); NTL_OPT_RETURN(vec_zz_pE, x); } |
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973 | |
---|
974 | |
---|
975 | void TraceMod(zz_pE& x, const zz_pEX& a, const zz_pEXModulus& F); |
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976 | |
---|
977 | inline zz_pE TraceMod(const zz_pEX& a, const zz_pEXModulus& F) |
---|
978 | { zz_pE x; TraceMod(x, a, F); NTL_OPT_RETURN(zz_pE, x); } |
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979 | |
---|
980 | void TraceMod(zz_pE& x, const zz_pEX& a, const zz_pEX& f); |
---|
981 | |
---|
982 | inline zz_pE TraceMod(const zz_pEX& a, const zz_pEX& f) |
---|
983 | { zz_pE x; TraceMod(x, a, f); NTL_OPT_RETURN(zz_pE, x); } |
---|
984 | |
---|
985 | |
---|
986 | |
---|
987 | |
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988 | |
---|
989 | void NormMod(zz_pE& x, const zz_pEX& a, const zz_pEX& f); |
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990 | |
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991 | inline zz_pE NormMod(const zz_pEX& a, const zz_pEX& f) |
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992 | { zz_pE x; NormMod(x, a, f); NTL_OPT_RETURN(zz_pE, x); } |
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993 | |
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994 | void resultant(zz_pE& rres, const zz_pEX& a, const zz_pEX& b); |
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995 | |
---|
996 | inline zz_pE resultant(const zz_pEX& a, const zz_pEX& b) |
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997 | { zz_pE x; resultant(x, a, b); NTL_OPT_RETURN(zz_pE, x); } |
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998 | |
---|
999 | NTL_CLOSE_NNS |
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1000 | |
---|
1001 | #endif |
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