1 | // -*- c++ -*- |
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2 | //***************************************************************************** |
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3 | /** @file facNTLzzpEXGCD.cc |
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4 | * |
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5 | * @author Martin Lee |
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6 | * |
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7 | * @note the following code is slightly modified code out of |
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8 | * lzz_pEX.c from Victor Shoup's NTL. Below is NTL's copyright notice. |
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9 | * |
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10 | * Univariate GCD and extended GCD over Z/p[t]/(f)[x] for reducible f |
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11 | * |
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12 | * @par Copyright: |
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13 | * (c) by The SINGULAR Team, see LICENSE file |
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14 | * |
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15 | |
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16 | COPYRIGHT NOTICE |
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17 | for NTL 5.5 |
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18 | (modified for Singular 2-0-6 - 3-1) |
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19 | |
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20 | NTL -- A Library for Doing Number Theory |
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21 | Copyright (C) 1996-2009 Victor Shoup |
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22 | |
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23 | The most recent version of NTL is available at http://www.shoup.net |
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24 | |
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25 | This program is free software; you can redistribute it and/or |
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26 | modify it under the terms of the GNU General Public License |
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27 | as published by the Free Software Foundation; either version 2 |
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28 | of the License, or (at your option) any later version. |
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29 | |
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30 | This program is distributed in the hope that it will be useful, |
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31 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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32 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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33 | GNU General Public License for more details. |
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34 | |
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35 | You should have received a copy of the GNU General Public License |
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36 | along with this program; if not, write to the Free Software |
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37 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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38 | |
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39 | This entire copyright notice should be placed in an appropriately |
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40 | conspicuous place accompanying all distributions of software that |
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41 | make use of NTL. |
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42 | |
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43 | The above terms apply to all of the software modules distributed with NTL, |
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44 | i.e., all source files in either the ntl-xxx.tar.gz or WinNTL-xxx.zip |
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45 | distributions. In general, the individual files do not contain |
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46 | copyright notices. |
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47 | |
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48 | Note that the quad_float package is derived from the doubledouble package, |
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49 | originally developed by Keith Briggs, and also licensed unger the GNU GPL. |
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50 | The files quad_float.c and quad_float.h contain more detailed copyright |
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51 | notices. |
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52 | |
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53 | Note that the traditional long integer package used by NTL, lip.c, is derived |
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54 | from---and represents an extensive modification of--- |
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55 | a package originally developed and copyrighted by Arjen Lenstra, |
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56 | who has agreed to renounce any copyright claims on the particular |
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57 | version of the long integer package appearing in NTL, so that the |
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58 | this package now is covered by the GNU GPL as well. |
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59 | |
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60 | Note that the alternative long integer package used by NTL is GMP, |
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61 | which is written by Torbjorn Granlund <tege@swox.com>. |
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62 | GMP is licensed under the terms of the GNU Lesser General Public License. |
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63 | |
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64 | Note that NTL makes use of the RSA Data Security, Inc. MD5 Message |
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65 | Digest Algorithm. |
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66 | |
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67 | Note that prior to version 4.0, NTL was distributed under the following terms: |
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68 | NTL is freely available for research and educational purposes. |
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69 | I don't want to attach any legalistic licensing restrictions on |
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70 | users of NTL. |
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71 | However, NTL should not be linked in a commercial program |
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72 | (although using data in a commercial |
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73 | product produced by a program that used NTL is fine). |
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74 | |
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75 | The hope is that the GNU GPL is actually less restrictive than these |
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76 | older terms; however, in any circumstances such that GNU GPL is more |
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77 | restrictive, then the following rule is in force: |
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78 | versions prior to 4.0 may continue to be used under the old terms, |
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79 | but users of versions 4.0 or later should adhere to the terms of the GNU GPL. |
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80 | **/ |
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81 | |
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82 | |
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83 | #ifdef HAVE_CONFIG_H |
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84 | #include "config.h" |
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85 | #endif /* HAVE_CONFIG_H */ |
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86 | |
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87 | #include "facNTLzzpEXGCD.h" |
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88 | |
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89 | #ifdef HAVE_NTL |
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90 | #include "NTLconvert.h" |
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91 | #endif |
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92 | |
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93 | #ifdef HAVE_NTL |
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94 | |
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95 | long InvModStatus (zz_pE& x, const zz_pE& a) |
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96 | { |
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97 | return InvModStatus(x._zz_pE__rep, a._zz_pE__rep, zz_pE::modulus()); |
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98 | } |
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99 | |
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100 | static |
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101 | void SetSize(vec_zz_pX& x, long n, long m) |
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102 | { |
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103 | x.SetLength(n); |
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104 | long i; |
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105 | for (i = 0; i < n; i++) |
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106 | x[i].rep.SetMaxLength(m); |
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107 | } |
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108 | |
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109 | void tryPlainRem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b, vec_zz_pX& x, |
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110 | bool& fail) |
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111 | { |
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112 | long da, db, dq, i, j, LCIsOne; |
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113 | const zz_pE *bp; |
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114 | zz_pX *xp; |
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115 | |
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116 | |
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117 | zz_pE LCInv, t; |
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118 | zz_pX s; |
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119 | |
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120 | da = deg(a); |
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121 | db = deg(b); |
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122 | |
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123 | if (db < 0) Error("zz_pEX: division by zero"); |
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124 | |
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125 | if (da < db) { |
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126 | r = a; |
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127 | return; |
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128 | } |
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129 | |
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130 | bp = b.rep.elts(); |
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131 | |
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132 | if (IsOne(bp[db])) |
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133 | LCIsOne = 1; |
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134 | else { |
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135 | LCIsOne = 0; |
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136 | fail= InvModStatus (LCInv, bp[db]); |
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137 | //inv(LCInv, bp[db]); |
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138 | if (fail) |
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139 | return; |
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140 | } |
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141 | |
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142 | for (i = 0; i <= da; i++) |
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143 | x[i] = rep(a.rep[i]); |
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144 | |
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145 | xp = x.elts(); |
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146 | |
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147 | dq = da - db; |
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148 | |
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149 | for (i = dq; i >= 0; i--) { |
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150 | conv(t, xp[i+db]); |
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151 | if (!LCIsOne) |
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152 | mul(t, t, LCInv); |
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153 | NTL::negate(t, t); |
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154 | |
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155 | for (j = db-1; j >= 0; j--) { |
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156 | mul(s, rep(t), rep(bp[j])); |
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157 | add(xp[i+j], xp[i+j], s); |
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158 | } |
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159 | } |
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160 | |
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161 | r.rep.SetLength(db); |
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162 | for (i = 0; i < db; i++) |
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163 | conv(r.rep[i], xp[i]); |
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164 | r.normalize(); |
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165 | } |
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166 | |
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167 | void tryPlainDivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b, |
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168 | bool& fail) |
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169 | { |
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170 | long da, db, dq, i, j, LCIsOne; |
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171 | const zz_pE *bp; |
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172 | zz_pE *qp; |
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173 | zz_pX *xp; |
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174 | |
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175 | |
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176 | zz_pE LCInv, t; |
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177 | zz_pX s; |
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178 | |
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179 | da = deg(a); |
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180 | db = deg(b); |
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181 | |
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182 | if (db < 0) Error("zz_pEX: division by zero"); |
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183 | |
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184 | if (da < db) { |
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185 | r = a; |
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186 | clear(q); |
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187 | return; |
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188 | } |
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189 | |
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190 | zz_pEX lb; |
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191 | |
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192 | if (&q == &b) { |
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193 | lb = b; |
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194 | bp = lb.rep.elts(); |
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195 | } |
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196 | else |
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197 | bp = b.rep.elts(); |
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198 | |
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199 | if (IsOne(bp[db])) |
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200 | LCIsOne = 1; |
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201 | else { |
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202 | LCIsOne = 0; |
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203 | fail= InvModStatus (LCInv, bp[db]); |
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204 | //inv(LCInv, bp[db]); |
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205 | if (fail) |
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206 | return; |
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207 | } |
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208 | |
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209 | vec_zz_pX x; |
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210 | |
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211 | SetSize(x, da+1, 2*zz_pE::degree()); |
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212 | |
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213 | for (i = 0; i <= da; i++) |
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214 | x[i] = rep(a.rep[i]); |
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215 | |
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216 | xp = x.elts(); |
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217 | |
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218 | dq = da - db; |
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219 | q.rep.SetLength(dq+1); |
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220 | qp = q.rep.elts(); |
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221 | |
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222 | for (i = dq; i >= 0; i--) { |
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223 | conv(t, xp[i+db]); |
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224 | if (!LCIsOne) |
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225 | mul(t, t, LCInv); |
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226 | qp[i] = t; |
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227 | NTL::negate(t, t); |
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228 | |
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229 | for (j = db-1; j >= 0; j--) { |
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230 | mul(s, rep(t), rep(bp[j])); |
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231 | add(xp[i+j], xp[i+j], s); |
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232 | } |
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233 | } |
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234 | |
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235 | r.rep.SetLength(db); |
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236 | for (i = 0; i < db; i++) |
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237 | conv(r.rep[i], xp[i]); |
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238 | r.normalize(); |
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239 | } |
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240 | |
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241 | |
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242 | void tryNTLGCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, bool& fail) |
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243 | { |
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244 | zz_pE t; |
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245 | |
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246 | if (IsZero(b)) |
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247 | x = a; |
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248 | else if (IsZero(a)) |
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249 | x = b; |
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250 | else { |
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251 | long n = max(deg(a),deg(b)) + 1; |
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252 | zz_pEX u(INIT_SIZE, n), v(INIT_SIZE, n); |
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253 | |
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254 | vec_zz_pX tmp; |
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255 | SetSize(tmp, n, 2*zz_pE::degree()); |
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256 | |
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257 | u = a; |
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258 | v = b; |
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259 | do { |
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260 | tryPlainRem(u, u, v, tmp, fail); |
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261 | if (fail) |
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262 | return; |
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263 | swap(u, v); |
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264 | } while (!IsZero(v)); |
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265 | |
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266 | x = u; |
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267 | } |
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268 | |
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269 | if (IsZero(x)) return; |
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270 | if (IsOne(LeadCoeff(x))) return; |
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271 | |
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272 | /* make gcd monic */ |
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273 | |
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274 | |
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275 | fail= InvModStatus (t, LeadCoeff(x)); |
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276 | if (fail) |
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277 | return; |
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278 | mul(x, x, t); |
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279 | } |
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280 | |
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281 | void tryNTLXGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, |
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282 | const zz_pEX& b, bool& fail) |
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283 | { |
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284 | zz_pE z; |
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285 | |
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286 | |
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287 | if (IsZero(b)) { |
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288 | set(s); |
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289 | clear(t); |
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290 | d = a; |
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291 | } |
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292 | else if (IsZero(a)) { |
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293 | clear(s); |
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294 | set(t); |
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295 | d = b; |
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296 | } |
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297 | else { |
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298 | long e = max(deg(a), deg(b)) + 1; |
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299 | |
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300 | zz_pEX temp(INIT_SIZE, e), u(INIT_SIZE, e), v(INIT_SIZE, e), |
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301 | u0(INIT_SIZE, e), v0(INIT_SIZE, e), |
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302 | u1(INIT_SIZE, e), v1(INIT_SIZE, e), |
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303 | u2(INIT_SIZE, e), v2(INIT_SIZE, e), q(INIT_SIZE, e); |
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304 | |
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305 | |
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306 | set(u1); clear(v1); |
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307 | clear(u2); set(v2); |
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308 | u = a; v = b; |
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309 | |
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310 | do { |
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311 | fail= InvModStatus (z, LeadCoeff(v)); |
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312 | if (fail) |
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313 | return; |
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314 | DivRem(q, u, u, v); |
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315 | swap(u, v); |
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316 | u0 = u2; |
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317 | v0 = v2; |
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318 | mul(temp, q, u2); |
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319 | sub(u2, u1, temp); |
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320 | mul(temp, q, v2); |
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321 | sub(v2, v1, temp); |
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322 | u1 = u0; |
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323 | v1 = v0; |
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324 | } while (!IsZero(v)); |
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325 | |
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326 | d = u; |
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327 | s = u1; |
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328 | t = v1; |
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329 | } |
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330 | |
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331 | if (IsZero(d)) return; |
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332 | if (IsOne(LeadCoeff(d))) return; |
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333 | |
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334 | /* make gcd monic */ |
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335 | |
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336 | fail= InvModStatus (z, LeadCoeff(d)); |
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337 | if (fail) |
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338 | return; |
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339 | mul(d, d, z); |
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340 | mul(s, s, z); |
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341 | mul(t, t, z); |
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342 | } |
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343 | #endif |
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344 | |
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