1 | /* Copyright 1996 Michael Messollen. All rights reserved. */ |
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2 | /////////////////////////////////////////////////////////////////////////////// |
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3 | // emacs edit mode for this file is -*- C++ -*- |
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4 | // static char * rcsid = "$Id: MVMultiHensel.cc,v 1.7 2001-08-22 14:21:17 Singular Exp $"; |
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5 | /////////////////////////////////////////////////////////////////////////////// |
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6 | // FACTORY - Includes |
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7 | #include <factory.h> |
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8 | #ifndef NOSTREAMIO |
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9 | #include <iostream.h> |
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10 | #endif |
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11 | // Factor - Includes |
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12 | #include "tmpl_inst.h" |
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13 | #include "helpstuff.h" |
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14 | // some CC's need this: |
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15 | #include "MVMultiHensel.h" |
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16 | |
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17 | #ifdef SINGULAR |
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18 | #define HAVE_SINGULAR_ERROR |
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19 | #endif |
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20 | |
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21 | #ifdef HAVE_SINGULAR_ERROR |
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22 | extern "C" { void WerrorS(char *); } |
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23 | #endif |
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24 | |
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25 | #ifdef HENSELDEBUG |
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26 | # define DEBUGOUTPUT |
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27 | #else |
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28 | # undef DEBUGOUTPUT |
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29 | #endif |
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30 | |
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31 | #include "debug.h" |
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32 | #include "timing.h" |
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33 | |
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34 | /////////////////////////////////////////////////////////////// |
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35 | // some class definition needed in MVMultiHensel |
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36 | /////////////////////////////////////////////////////////////// |
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37 | typedef bool Boolean; |
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38 | |
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39 | class DiophantForm { |
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40 | public: |
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41 | CanonicalForm One; |
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42 | CanonicalForm Two; |
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43 | inline DiophantForm& operator=( const DiophantForm& value ){ |
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44 | if ( this != &value ){ |
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45 | One = value.One; |
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46 | Two = value.Two; |
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47 | } |
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48 | return *this; |
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49 | } |
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50 | }; |
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51 | |
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52 | // We remember an already calculated value; simple class for RememberArray |
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53 | class RememberForm { |
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54 | public: |
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55 | inline RememberForm operator=( CanonicalForm & value ){ |
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56 | this->calculated = true; |
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57 | this->poly = value; |
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58 | return *this; |
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59 | } |
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60 | Boolean calculated; |
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61 | CanonicalForm poly; |
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62 | }; |
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63 | |
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64 | // Array to remember already calculated values; used for the diophantine |
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65 | // equation s*f + t*g = x^i |
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66 | class RememberArray { |
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67 | public: |
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68 | // operations performed on arrays |
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69 | RememberArray( int sz ){ |
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70 | size = sz; |
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71 | ia = new RememberForm[size]; |
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72 | // assert( ia != 0 ); // test if we got the memory |
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73 | init( sz ); |
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74 | } |
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75 | ~RememberArray(){ delete [] ia; } |
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76 | inline RememberForm& operator[]( int index ){ |
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77 | return ia[index]; |
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78 | } |
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79 | protected: |
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80 | void init( int ){ |
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81 | for ( int ix=0; ix < size; ++ix) |
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82 | ia[ix].calculated=false; |
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83 | } |
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84 | // internal data representation |
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85 | int size; |
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86 | RememberForm *ia; |
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87 | }; |
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88 | |
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89 | |
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90 | /////////////////////////////////////////////////////////////// |
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91 | // Solve the Diophantine equation: ( levelU == mainvar ) // |
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92 | // s*F1 + t*F2 = (mainvar)^i // |
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93 | // Returns s and t. // |
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94 | /////////////////////////////////////////////////////////////// |
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95 | static DiophantForm |
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96 | diophant( int levelU , const CanonicalForm & F1 , const CanonicalForm & F2 , int i , RememberArray & A, RememberArray & B ) { |
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97 | DiophantForm Retvalue; |
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98 | CanonicalForm s,t,q,r; |
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99 | Variable x(levelU); |
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100 | |
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101 | DEBOUT(cout, "diophant: called with: ", F1); |
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102 | DEBOUT(cout, " ", F2); DEBOUTLN(cout, " ", i); |
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103 | |
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104 | // Did we solve the diophantine equation yet? |
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105 | // If so, return the calculated values |
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106 | if ( A[i].calculated && B[i].calculated ){ |
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107 | Retvalue.One=A[i].poly; |
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108 | Retvalue.Two=B[i].poly; |
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109 | return Retvalue; |
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110 | } |
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111 | |
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112 | // Degrees ok? degree(F1,mainvar) + degree(F2,mainvar) <= i ? |
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113 | if ( (degree(F1,levelU) + degree(F2,levelU) ) <= i ) { |
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114 | #ifdef HAVE_SINGULAR_ERROR |
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115 | WerrorS("libfac: diophant ERROR: degree too large! "); |
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116 | #else |
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117 | #ifndef NOSTREAMIO |
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118 | cerr << "libfac: diophant ERROR: degree too large! " |
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119 | << (degree(F1,levelU) + degree(F2,levelU) ) <<endl; |
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120 | #else |
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121 | ; |
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122 | #endif |
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123 | #endif |
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124 | Retvalue.One=F1;Retvalue.Two=F2; |
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125 | return Retvalue; |
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126 | } |
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127 | |
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128 | if ( i == 0 ) { // call the extended gcd |
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129 | r=extgcd(F1,F2,s,t); |
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130 | // check if gcd(F1,F2) <> 1 , i.e. F1 and F2 are not relatively prime |
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131 | if ( ! r.isOne() ){ |
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132 | #ifdef HAVE_SINGULAR_ERROR |
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133 | WerrorS("libfac: diophant ERROR: F1 and F2 are not relatively prime! "); |
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134 | #else |
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135 | #ifndef NOSTREAMIO |
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136 | cerr << "libfac: diophant ERROR: " << F1 << " and " << F2 |
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137 | << " are not relatively prime!" << endl; |
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138 | #else |
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139 | ; |
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140 | #endif |
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141 | #endif |
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142 | Retvalue.One=F1;Retvalue.Two=F2; |
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143 | return Retvalue; |
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144 | } |
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145 | Retvalue.One = s; Retvalue.Two = t; |
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146 | } |
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147 | else { // recursively call diophant |
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148 | Retvalue=diophant(levelU,F1,F2,i-1,A,B); |
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149 | Retvalue.One *= x; // createVar(levelU,1); |
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150 | Retvalue.Two *= x; // createVar(levelU,1); |
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151 | // Check degrees. |
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152 | |
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153 | if ( degree(Retvalue.One,levelU) > degree(F2,levelU) ){ |
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154 | // Make degree(Retvalue.one,mainvar) < degree(F2,mainvar) |
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155 | divrem(Retvalue.One,F2,q,r); |
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156 | Retvalue.One = r; Retvalue.Two += F1*q; |
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157 | } |
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158 | else { |
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159 | if ( degree(Retvalue.Two,levelU) >= degree(F1,levelU) ){ |
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160 | // Make degree(Retvalue.Two,mainvar) <= degree(F1,mainvar) |
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161 | divrem(Retvalue.Two,F1,q,r); |
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162 | Retvalue.One += F2*q; Retvalue.Two = r; |
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163 | } |
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164 | } |
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165 | |
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166 | } |
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167 | A[i].poly = Retvalue.One ; |
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168 | B[i].poly = Retvalue.Two ; |
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169 | A[i].calculated = true ; B[i].calculated = true ; |
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170 | |
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171 | DEBOUT(cout, "diophant: Returnvalue is: ", Retvalue.One); |
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172 | DEBOUTLN(cout, " ", Retvalue.Two); |
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173 | |
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174 | return Retvalue; |
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175 | } |
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176 | |
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177 | /////////////////////////////////////////////////////////////// |
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178 | // A more efficient way to solve s*F1 + t*F2 = W // |
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179 | // as in Wang and Rothschild [Wang&Roth75]. // |
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180 | /////////////////////////////////////////////////////////////// |
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181 | static CanonicalForm |
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182 | make_delta( int levelU, const CanonicalForm & W, |
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183 | const CanonicalForm & F1, const CanonicalForm & F2, |
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184 | RememberArray & A, RememberArray & B){ |
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185 | CanonicalForm Retvalue; |
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186 | DiophantForm intermediate; |
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187 | |
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188 | DEBOUT(cout, "make_delta: W= ", W); |
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189 | DEBOUTLN(cout, " degree(W,levelU)= ", degree(W,levelU) ); |
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190 | |
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191 | if ( levelU == level(W) ){ // same level, good |
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192 | for ( CFIterator i=W; i.hasTerms(); i++){ |
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193 | intermediate=diophant(levelU,F1,F2,i.exp(),A,B); |
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194 | Retvalue += i.coeff() * intermediate.One; |
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195 | } |
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196 | } |
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197 | else{ // level(W) < levelU ; i.e. degree(w,levelU) == 0 |
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198 | intermediate=diophant(levelU,F1,F2,0,A,B); |
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199 | Retvalue = W * intermediate.One; |
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200 | } |
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201 | DEBOUTLN(cout, "make_delta: Returnvalue= ", Retvalue); |
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202 | return Retvalue; |
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203 | } |
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204 | |
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205 | static CanonicalForm |
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206 | make_square( int levelU, const CanonicalForm & W, |
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207 | const CanonicalForm & F1, const CanonicalForm & F2, |
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208 | RememberArray & A, RememberArray & B){ |
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209 | CanonicalForm Retvalue; |
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210 | DiophantForm intermediate; |
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211 | |
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212 | DEBOUT(cout, "make_square: W= ", W ); |
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213 | DEBOUTLN(cout, " degree(W,levelU)= ", degree(W,levelU)); |
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214 | |
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215 | if ( levelU == level(W) ){ // same level, good |
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216 | for ( CFIterator i=W; i.hasTerms(); i++){ |
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217 | intermediate=diophant(levelU,F1,F2,i.exp(),A,B); |
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218 | Retvalue += i.coeff() * intermediate.Two; |
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219 | } |
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220 | } |
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221 | else{ // level(W) < levelU ; i.e. degree(w,levelU) == 0 |
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222 | intermediate=diophant(levelU,F1,F2,0,A,B); |
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223 | Retvalue = W * intermediate.Two; |
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224 | } |
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225 | DEBOUTLN(cout, "make_square: Returnvalue= ", Retvalue); |
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226 | |
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227 | return Retvalue; |
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228 | } |
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229 | |
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230 | |
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231 | /////////////////////////////////////////////////////////////// |
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232 | // Multivariat Hensel routine for two factors F and G . // |
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233 | // U is the monic univariat polynomial; we manage two arrays // |
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234 | // to remember already calculated values for the diophantine // |
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235 | // equation. This is suggested by Joel Moses [Moses71] . // |
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236 | // Return the fully lifted factors. // |
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237 | /////////////////////////////////////////////////////////////// |
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238 | static DiophantForm |
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239 | mvhensel( const CanonicalForm & U , const CanonicalForm & F , |
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240 | const CanonicalForm & G , const SFormList & Substitutionlist){ |
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241 | CanonicalForm V,Fk=F,Gk=G,Rk,W,D,S; |
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242 | int levelU=level(U), degU=subvardegree(U,levelU); // degree(U,{x_1,..,x_(level(U)-1)}) |
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243 | DiophantForm Retvalue; |
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244 | RememberArray A(degree(F)+degree(G)+1); |
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245 | RememberArray B(degree(F)+degree(G)+1); |
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246 | |
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247 | DEBOUTLN(cout, "mvhensel called with: U= ", U); |
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248 | DEBOUTLN(cout, " F= ", F); |
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249 | DEBOUTLN(cout, " G= ", G); |
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250 | DEBOUTLN(cout, " degU= ", degU); |
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251 | |
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252 | V=change_poly(U,Substitutionlist,0); // change x_i <- x_i + a_i for all i |
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253 | Rk = F*G-V; |
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254 | #ifdef HENSELDEBUG2 |
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255 | cout << "mvhensel: V = " << V << endl |
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256 | << " Fk= " << F << endl |
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257 | << " Gk= " << G << endl |
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258 | << " Rk= " << Rk << endl; |
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259 | #endif |
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260 | for ( int k=2; k<=degU+1; k++){//2; k++){//degU+1; k++){ |
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261 | W = mod_power(Rk,k,levelU); |
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262 | #ifdef HENSELDEBUG2 |
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263 | cout << "mvhensel: Iteration: " << k << endl; |
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264 | cout << "mvhensel: W= " << W << endl; |
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265 | #endif |
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266 | D = make_delta(levelU,W,F,G,A,B); |
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267 | #ifdef HENSELDEBUG2 |
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268 | cout << "mvhensel: D= " << D << endl; |
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269 | #endif |
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270 | S = make_square(levelU,W,F,G,A,B); |
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271 | #ifdef HENSELDEBUG2 |
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272 | cout << "mvhensel: S= " << S << endl; |
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273 | #endif |
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274 | Rk += S*D - D*Fk - S*Gk; |
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275 | #ifdef HENSELDEBUG2 |
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276 | cout << "mvhensel: Rk= " << Rk << endl; |
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277 | #endif |
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278 | Fk -= S; |
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279 | #ifdef HENSELDEBUG2 |
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280 | cout << "mvhensel: Fk= " << Fk << endl; |
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281 | #endif |
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282 | Gk -= D; |
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283 | #ifdef HENSELDEBUG2 |
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284 | cout << "mvhensel: Gk= " << Gk << endl; |
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285 | #endif |
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286 | if ( Rk.isZero() ) break; |
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287 | } |
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288 | Retvalue.One = change_poly(Fk,Substitutionlist,1); |
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289 | Retvalue.Two = change_poly(Gk,Substitutionlist,1); |
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290 | |
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291 | DEBOUTLN(cout, "mvhensel: Retvalue: ", Retvalue.One); |
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292 | DEBOUTLN(cout, " ", Retvalue.Two); |
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293 | |
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294 | return Retvalue ; |
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295 | } |
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296 | |
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297 | /////////////////////////////////////////////////////////////// |
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298 | // Recursive Version of MultiHensel. // |
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299 | /////////////////////////////////////////////////////////////// |
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300 | CFFList |
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301 | multihensel( const CanonicalForm & mF, const CFFList & Factorlist, |
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302 | const SFormList & Substitutionlist){ |
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303 | CFFList Returnlist,factorlist=Factorlist; |
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304 | DiophantForm intermediat; |
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305 | CanonicalForm Pl,Pr; |
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306 | int n = factorlist.length(); |
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307 | |
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308 | DEBOUT(cout, "multihensel: called with ", mF); |
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309 | DEBOUTLN(cout, " ", factorlist); |
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310 | |
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311 | if ( n == 1 ) { |
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312 | Returnlist.append(CFFactor(mF,1)); |
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313 | } |
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314 | else { |
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315 | if ( n == 2 ){ |
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316 | intermediat= mvhensel(mF, factorlist.getFirst().factor(), |
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317 | Factorlist.getLast().factor(), |
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318 | Substitutionlist); |
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319 | Returnlist.append(CFFactor(intermediat.One,1)); |
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320 | Returnlist.append(CFFactor(intermediat.Two,1)); |
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321 | } |
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322 | else { // more then two factors |
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323 | #ifdef HENSELDEBUG2 |
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324 | cout << "multihensel: more than two factors!" << endl; |
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325 | #endif |
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326 | Pl=factorlist.getFirst().factor(); factorlist.removeFirst(); |
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327 | Pr=Pl.genOne(); |
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328 | for ( ListIterator<CFFactor> i=factorlist; i.hasItem(); i++ ) |
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329 | Pr *= i.getItem().factor() ; |
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330 | #ifdef HENSELDEBUG2 |
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331 | cout << "multihensel: Pl,Pr, factorlist: " << Pl << " " << Pr |
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332 | << " " << factorlist << endl; |
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333 | #endif |
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334 | intermediat= mvhensel(mF,Pl,Pr,Substitutionlist); |
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335 | Returnlist.append(CFFactor(intermediat.One,1)); |
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336 | Returnlist=Union( multihensel(intermediat.Two,factorlist,Substitutionlist), Returnlist); |
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337 | } |
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338 | } |
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339 | |
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340 | return Returnlist; |
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341 | } |
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342 | |
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343 | /////////////////////////////////////////////////////////////// |
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344 | // Generalized Hensel routine. // |
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345 | // mF is the monic multivariat polynomial, Factorlist is the // |
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346 | // list of factors, Substitutionlist represents the ideal // |
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347 | // <x_1+a_1, .. , x_r+a_r>, where r=level(mF)-1 . // |
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348 | // Returns the list of fully lifted factors. // |
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349 | /////////////////////////////////////////////////////////////// |
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350 | CFFList |
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351 | MultiHensel( const CanonicalForm & mF, const CFFList & Factorlist, |
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352 | const SFormList & Substitutionlist){ |
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353 | CFFList Returnlist,Retlistinter,factorlist=Factorlist,Ll; |
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354 | CFFListIterator i; |
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355 | DiophantForm intermediat; |
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356 | CanonicalForm Pl,Pr; |
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357 | int n = factorlist.length(),h=n/2, k; |
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358 | |
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359 | DEBOUT(cout, "MultiHensel: called with ", mF); |
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360 | DEBOUTLN(cout, " ", factorlist); |
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361 | DEBOUT(cout," : n,h = ", n); |
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362 | DEBOUTLN(cout," ", h); |
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363 | |
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364 | if ( n == 1 ) { |
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365 | Returnlist.append(CFFactor(mF,1)); |
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366 | } |
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367 | else { |
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368 | if ( n == 2 ){ |
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369 | intermediat= mvhensel(mF, factorlist.getFirst().factor(), |
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370 | Factorlist.getLast().factor(), |
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371 | Substitutionlist); |
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372 | Returnlist.append(CFFactor(intermediat.One,1)); |
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373 | Returnlist.append(CFFactor(intermediat.Two,1)); |
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374 | } |
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375 | else { // more then two factors |
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376 | for ( k=1 ; k<=h; k++){ |
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377 | Ll.append(factorlist.getFirst()); |
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378 | factorlist.removeFirst(); |
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379 | } |
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380 | |
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381 | DEBOUTLN(cout, "MultiHensel: Ll= ", Ll); |
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382 | DEBOUTLN(cout, " factorlist= ", factorlist); |
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383 | |
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384 | Pl = 1; Pr = 1; |
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385 | for ( i = Ll; i.hasItem(); i++) |
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386 | Pl *= i.getItem().factor(); |
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387 | DEBOUTLN(cout, "MultiHensel: Pl= ", Pl); |
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388 | for ( i = factorlist; i.hasItem(); i++) |
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389 | Pr *= i.getItem().factor(); |
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390 | DEBOUTLN(cout, "MultiHensel: Pr= ", Pr); |
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391 | intermediat = mvhensel(mF,Pl,Pr,Substitutionlist); |
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392 | // divison test for intermediat.One and intermediat.Two ? |
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393 | CanonicalForm a,b; |
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394 | // we add a division test now for intermediat.One and intermediat.Two |
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395 | if ( mydivremt (mF,intermediat.One,a,b) && b == mF.genZero() ) |
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396 | Retlistinter.append(CFFactor(intermediat.One,1) ); |
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397 | if ( mydivremt (mF,intermediat.Two,a,b) && b == mF.genZero() ) |
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398 | Retlistinter.append(CFFactor(intermediat.Two,1) ); |
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399 | |
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400 | Ll = MultiHensel(intermediat.One, Ll, Substitutionlist); |
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401 | Returnlist = MultiHensel(intermediat.Two, factorlist, Substitutionlist); |
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402 | Returnlist = Union(Returnlist,Ll); |
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403 | |
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404 | Returnlist = Union(Retlistinter,Returnlist); |
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405 | |
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406 | } |
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407 | } |
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408 | return Returnlist; |
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409 | } |
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410 | |
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411 | /* |
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412 | $Log: not supported by cvs2svn $ |
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413 | Revision 1.6 2001/08/08 14:26:55 Singular |
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414 | *hannes: Dan's HAVE_SINGULAR_ERROR |
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415 | |
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416 | Revision 1.5 2001/08/08 11:59:12 Singular |
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417 | *hannes: Dan's NOSTREAMIO changes |
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418 | |
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419 | Revision 1.4 1997/11/18 16:39:05 Singular |
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420 | * hannes: moved WerrorS from C++ to C |
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421 | (Factor.cc MVMultiHensel.cc SqrFree.cc Truefactor.cc) |
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422 | |
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423 | Revision 1.3 1997/09/12 07:19:48 Singular |
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424 | * hannes/michael: libfac-0.3.0 |
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425 | |
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426 | Revision 1.4 1997/04/25 22:40:02 michael |
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427 | changed cerr and cout messages for use with Singular |
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428 | Version for libfac-0.2.1 |
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429 | |
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430 | */ |
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