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: SqrFree.cc,v 1.12 2008-01-07 13:34:56 Singular Exp $"; |
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5 | static char * errmsg = "\nYou found a bug!\nPlease inform (Michael Messollen) michael@math.uni-sb.de .\n Please include above information and your input (the ideal/polynomial and characteristic) in your bug-report.\nThank you."; |
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6 | /////////////////////////////////////////////////////////////////////////////// |
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7 | // FACTORY - Includes |
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8 | #include<factory.h> |
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9 | #ifndef NOSTREAMIO |
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10 | #ifdef HAVE_IOSTREAM |
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11 | #include <iostream> |
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12 | #define OSTREAM std::ostream |
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13 | #define ISTREAM std::istream |
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14 | #define CERR std::cerr |
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15 | #define CIN std::cin |
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16 | #elif defined(HAVE_IOSTREAM_H) |
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17 | #include <iostream.h> |
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18 | #define OSTREAM ostream |
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19 | #define ISTREAM istream |
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20 | #define CERR cerr |
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21 | #define CIN cin |
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22 | #endif |
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23 | #endif |
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24 | // Factor - Includes |
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25 | #include "tmpl_inst.h" |
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26 | #include "helpstuff.h" |
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27 | // some CC's need this: |
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28 | #include "SqrFree.h" |
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29 | |
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30 | #ifdef SINGULAR |
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31 | #define HAVE_SINGULAR_ERROR |
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32 | #endif |
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33 | |
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34 | #ifdef HAVE_SINGULAR_ERROR |
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35 | extern "C" { void WerrorS(char *); } |
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36 | #endif |
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37 | |
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38 | #ifdef SQRFREEDEBUG |
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39 | # define DEBUGOUTPUT |
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40 | #else |
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41 | # undef DEBUGOUTPUT |
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42 | #endif |
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43 | |
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44 | #include "debug.h" |
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45 | #include "timing.h" |
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46 | TIMING_DEFINE_PRINT(squarefree_time); |
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47 | TIMING_DEFINE_PRINT(gcd_time); |
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48 | |
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49 | static inline CFFactor |
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50 | Powerup( const CFFactor & F , int exp=1){ |
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51 | return CFFactor(F.factor(), exp*F.exp()) ; |
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52 | } |
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53 | |
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54 | static CFFList |
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55 | Powerup( const CFFList & Inputlist , int exp=1 ){ |
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56 | CFFList Outputlist; |
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57 | |
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58 | for ( CFFListIterator i=Inputlist; i.hasItem(); i++ ) |
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59 | Outputlist.append(Powerup(i.getItem(), exp)); |
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60 | return Outputlist ; |
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61 | } |
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62 | |
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63 | /////////////////////////////////////////////////////////////// |
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64 | // Compute the Pth root of a polynomial in characteristic p // |
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65 | // f must be a polynomial which we can take the Pth root of. // |
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66 | // Domain is q=p^m , f a uni/multivariate polynomial // |
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67 | /////////////////////////////////////////////////////////////// |
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68 | static CanonicalForm |
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69 | PthRoot( const CanonicalForm & f ){ |
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70 | CanonicalForm RES, R = f; |
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71 | int n= max(level(R),getNumVars(R)), p= getCharacteristic(); |
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72 | |
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73 | if (n==0){ // constant |
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74 | if (R.inExtension()) // not in prime field; f over |F(q=p^k) |
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75 | { |
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76 | R = power(R,Powerup(p,getGFDegree() - 1)) ; |
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77 | } |
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78 | // if f in prime field, do nothing |
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79 | return R; |
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80 | } |
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81 | // we assume R is a Pth power here |
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82 | RES = R.genZero(); |
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83 | Variable x(n); |
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84 | for (int i=0; i<= (int) (degree(R,level(R))/p) ; i++) |
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85 | RES += PthRoot( R[i*p] ) * power(x,i); |
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86 | return RES; |
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87 | } |
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88 | |
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89 | /////////////////////////////////////////////////////////////// |
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90 | // Compute the Pth root of a polynomial in characteristic p // |
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91 | // f must be a polynomial which we can take the Pth root of. // |
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92 | // Domain is q=p^m , f a uni/multivariate polynomial // |
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93 | /////////////////////////////////////////////////////////////// |
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94 | static CanonicalForm |
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95 | PthRoot( const CanonicalForm & f ,const CanonicalForm & mipo){ |
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96 | CanonicalForm RES, R = f; |
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97 | int n= max(level(R),getNumVars(R)), p= getCharacteristic(); |
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98 | int mipodeg=-1; |
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99 | if (f.level()==mipo.level()) mipodeg=mipo.degree(); |
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100 | else if ((f.level()==1) &&(mipo.level()!=-1000000)) |
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101 | { |
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102 | Variable t; |
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103 | CanonicalForm tt=getMipo(mipo.mvar(),t); |
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104 | mipodeg=degree(tt,t); |
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105 | } |
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106 | |
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107 | if ((n==0) |
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108 | ||(mipodeg!=-1)) |
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109 | { // constant |
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110 | if (R.inExtension()) // not in prime field; f over |F(q=p^k) |
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111 | { |
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112 | R = power(R,Powerup(p,getGFDegree() - 1)) ; |
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113 | } |
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114 | else if ((f.level()==mipo.level()) |
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115 | ||((f.level()==1) &&(mipo.level()!=-1000000))) |
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116 | { |
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117 | R = power(R,Powerup(p,mipodeg - 1)) ; |
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118 | R=mod(R, mipo); |
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119 | } |
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120 | // if f in prime field, do nothing |
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121 | return R; |
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122 | } |
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123 | // we assume R is a Pth power here |
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124 | RES = R.genZero(); |
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125 | Variable x(n); |
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126 | for (int i=0; i<= (int) (degree(R,level(R))/p) ; i++) |
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127 | RES += PthRoot( R[i*p], mipo ) * power(x,i); |
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128 | return RES; |
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129 | } |
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130 | |
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131 | /////////////////////////////////////////////////////////////// |
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132 | // A uni/multivariate SqrFreeTest routine. // |
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133 | // Cheaper to run if all you want is a test. // |
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134 | // Works for charcteristic 0 and q=p^m // |
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135 | // Returns 1 if poly r is SqrFree, 0 if SqrFree will do some // |
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136 | // kind of factorization. // |
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137 | // Would be much more effcient iff we had *good* // |
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138 | // uni/multivariate gcd's and/or gcdtest's // |
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139 | /////////////////////////////////////////////////////////////// |
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140 | int |
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141 | SqrFreeTest( const CanonicalForm & r, int opt){ |
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142 | CanonicalForm f=r, g; |
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143 | int n=level(f); |
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144 | |
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145 | if (getNumVars(f)==0) return 1 ; // a constant is SqrFree |
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146 | if ( f.isUnivariate() ) { |
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147 | g= f.deriv(); |
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148 | if ( getCharacteristic() > 0 && g.isZero() ) return 0 ; |
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149 | // Next: it would be best to have a *univariate* gcd-test which returns |
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150 | // 0 iff gcdtest(f,g) == 1 or a constant ( for real Polynomials ) |
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151 | g = gcd(f,g); |
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152 | if ( g.isOne() || (-g).isOne() ) return 1; |
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153 | else |
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154 | if ( getNumVars(g) == 0 ) return 1;// <- totaldegree!!! |
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155 | else return 0 ; |
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156 | } |
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157 | else { // multivariate case |
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158 | for ( int k=1; k<=n; k++ ) { |
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159 | g = swapvar(f,k,n); g = content(g); |
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160 | // g = 1 || -1 : sqr-free, g poly : not sqr-free, g number : opt helps |
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161 | if ( ! (g.isOne() || (-g).isOne() || getNumVars(g)==0 ) ) { |
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162 | if ( opt==0 ) return 0; |
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163 | else { |
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164 | if ( SqrFreeTest(g,1) == 0 ) return 0; |
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165 | g = swapvar(g,k,n); |
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166 | f /=g ; |
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167 | } |
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168 | } |
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169 | } |
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170 | // Now f is primitive |
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171 | n = level(f); // maybe less indeterminants |
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172 | // if ( totaldegree(f) <= 1 ) return 1; |
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173 | |
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174 | // Let`s look if it is a Pth root |
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175 | if ( getCharacteristic() > 0 ) |
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176 | for (int k=1; k<=n; k++ ) { |
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177 | g=swapvar(f,k,n); g=g.deriv(); |
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178 | if ( ! g.isZero() ) break ; |
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179 | else if ( k==n) return 0 ; // really is Pth root |
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180 | } |
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181 | g = f.deriv() ; |
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182 | // Next: it would be best to have a *multivariate* gcd-test which returns |
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183 | // 0 iff gcdtest(f,g) == 1 or a constant ( for real Polynomials ) |
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184 | g= gcd(f,g); |
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185 | if ( g.isOne() || (-g).isOne() || (g==f) || (getNumVars(g)==0) ) return 1 ; |
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186 | else return 0 ; |
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187 | } |
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188 | #ifdef HAVE_SINGULAR_ERROR |
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189 | WerrorS("libfac: ERROR: SqrFreeTest: we should never fall trough here!"); |
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190 | #else |
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191 | #ifndef NOSTREAMIO |
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192 | CERR << "\nlibfac: ERROR: SqrFreeTest: we should never fall trough here!\n" |
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193 | << rcsid << errmsg << "\n"; |
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194 | #endif |
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195 | #endif |
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196 | return 0; |
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197 | } |
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198 | |
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199 | /////////////////////////////////////////////////////////////// |
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200 | // A uni/multivariate SqrFree routine.Works for polynomials // |
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201 | // which don\'t have a constant as the content. // |
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202 | // Works for charcteristic 0 and q=p^m // |
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203 | // returns a list of polys each of sqrfree, but gcd(f_i,f_j) // |
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204 | // needs not to be 1 !!!!! // |
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205 | /////////////////////////////////////////////////////////////// |
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206 | static CFFList |
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207 | SqrFreed( const CanonicalForm & r , const CanonicalForm &mipo=0){ |
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208 | CanonicalForm h, g, f = r; |
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209 | CFFList Outputlist; |
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210 | int n = level(f); |
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211 | |
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212 | DEBINCLEVEL(CERR, "SqrFreed"); |
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213 | DEBOUTLN(CERR, "Called with r= ", r); |
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214 | if (getNumVars(f)==0 ) { // just a constant; return it |
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215 | Outputlist= myappend(Outputlist,CFFactor(f,1)); |
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216 | return Outputlist ; |
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217 | } |
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218 | |
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219 | // We look if we do have a content; if so, SqrFreed the content |
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220 | // and continue computations with pp(f) |
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221 | for (int k=1; k<=n; k++) { |
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222 | if ((mipo.level()==-1000000)||(k!=1)) |
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223 | { |
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224 | g = swapvar(f,k,n); g = content(g); |
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225 | if ( ! (g.isOne() || (-g).isOne() || degree(g)==0 )) { |
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226 | g = swapvar(g,k,n); |
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227 | DEBOUTLN(CERR, "We have a content: ", g); |
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228 | Outputlist = myUnion(InternalSqrFree(g,mipo),Outputlist); // should we add a |
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229 | // SqrFreeTest(g) first ? |
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230 | DEBOUTLN(CERR, "Outputlist is now: ", Outputlist); |
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231 | f /=g; |
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232 | DEBOUTLN(CERR, "f is now: ", f); |
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233 | } |
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234 | } |
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235 | } |
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236 | |
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237 | // Now f is primitive; Let`s look if f is univariate |
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238 | if ( f.isUnivariate() ) { |
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239 | DEBOUTLN(CERR, "f is univariate: ", f); |
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240 | g = content(g); |
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241 | if ( ! (g.isOne() || (-g).isOne() ) ){ |
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242 | Outputlist= myappend(Outputlist,CFFactor(g,1)) ; |
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243 | f /= g; |
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244 | } |
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245 | Outputlist = Union(sqrFree(f),Outputlist) ; |
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246 | DEBOUTLN(CERR, "Outputlist after univ. sqrFree(f) = ", Outputlist); |
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247 | DEBDECLEVEL(CERR, "SqrFreed"); |
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248 | return Outputlist ; |
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249 | } |
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250 | |
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251 | // Linear? |
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252 | if ( totaldegree(f) <= 1 ) { |
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253 | Outputlist= myappend(Outputlist,CFFactor(f,1)) ; |
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254 | DEBDECLEVEL(CERR, "SqrFreed"); |
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255 | return Outputlist ; |
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256 | } |
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257 | |
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258 | // is it Pth root? |
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259 | n=level(f); // maybe less indeterminants |
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260 | g= f.deriv(); |
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261 | if ( getCharacteristic() > 0 && g.isZero() ){ // Pth roots only apply to char > 0 |
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262 | for (int k=1; k<=n; k++) |
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263 | { |
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264 | if ((mipo.level()==-1000000)||(k!=1)) |
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265 | { |
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266 | g=swapvar(f,k,n) ; |
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267 | g = g.deriv(); |
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268 | |
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269 | if ( ! g.isZero() ) |
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270 | { // can`t be Pth root |
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271 | CFFList Outputlist2= SqrFreed(swapvar(f,k,n)); |
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272 | for (CFFListIterator inter=Outputlist2; inter.hasItem(); inter++){ |
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273 | Outputlist= myappend(Outputlist, CFFactor(swapvar(inter.getItem().factor(),k,n), inter.getItem().exp())); |
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274 | } |
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275 | return Outputlist; |
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276 | } |
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277 | } |
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278 | if ( k==n ) |
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279 | { // really is Pth power |
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280 | DEBOUTLN(CERR, "f is a p'th root: ", f); |
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281 | CFMap m; |
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282 | g = compress(f,m); |
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283 | if (mipo==0) |
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284 | f = m(PthRoot(g)); |
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285 | else |
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286 | f = m(PthRoot(g,mipo)); |
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287 | DEBOUTLN(CERR, " that is : ", f); |
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288 | // now : Outputlist union ( SqrFreed(f) )^getCharacteristic() |
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289 | Outputlist=myUnion(Powerup(InternalSqrFree(f),getCharacteristic()),Outputlist); |
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290 | DEBDECLEVEL(CERR, "SqrFreed"); |
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291 | return Outputlist ; |
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292 | } |
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293 | } |
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294 | } |
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295 | g = f.deriv(); |
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296 | DEBOUTLN(CERR, "calculating gcd of ", f); |
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297 | DEBOUTLN(CERR, " and ", g); |
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298 | h = gcd(f,pp(g)); h /= lc(h); |
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299 | DEBOUTLN(CERR,"gcd(f,g)= ",h); |
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300 | if ( (h.isOne()) || ( h==f) || ((-h).isOne()) || getNumVars(h)==0 ) { // no common factor |
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301 | Outputlist= myappend(Outputlist,CFFactor(f,1)) ; |
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302 | DEBOUTLN(CERR, "Outputlist= ", Outputlist); |
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303 | DEBDECLEVEL(CERR, "SqrFreed"); |
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304 | return Outputlist ; |
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305 | } |
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306 | else // we can split into two nontrivial pieces |
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307 | { |
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308 | f /= h; // Now we have split the poly into f and h |
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309 | g = lc(f); |
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310 | //if ( g != f.genOne() && getNumVars(g) == 0 ){ |
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311 | if ( (!g.isOne()) && getNumVars(g) == 0 ) |
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312 | { |
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313 | Outputlist= myappend(Outputlist,CFFactor(g,1)) ; |
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314 | f /= g; |
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315 | } |
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316 | DEBOUTLN(CERR, "Split into f= ", f); |
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317 | DEBOUTLN(CERR, " and h= ", h); |
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318 | // For char > 0 the polys f and h can have Pth roots; so we need a test |
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319 | // Test is disabled because timing is the same |
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320 | |
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321 | // if ( SqrFreeTest(f,0) ) |
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322 | // Outputlist= myappend(Outputlist,CFFactor(f,1)) ; |
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323 | // else |
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324 | Outputlist=myUnion(Outputlist, InternalSqrFree(f)); |
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325 | // if ( SqrFreeTest(h,0) ) |
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326 | // Outputlist= myappend(Outputlist,CFFactor(h,1)) ; |
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327 | // else |
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328 | Outputlist=myUnion(Outputlist,InternalSqrFree(h)); |
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329 | DEBOUTLN(CERR, "Returning list ", Outputlist); |
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330 | DEBDECLEVEL(CERR, "SqrFreed"); |
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331 | return Outputlist ; |
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332 | } |
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333 | #ifdef HAVE_SINGULAR_ERROR |
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334 | WerrorS("libfac: ERROR: SqrFreed: we should never fall trough here!"); |
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335 | #else |
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336 | #ifndef NOSTREAMIO |
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337 | CERR << "\nlibfac: ERROR: SqrFreed: we should never fall trough here!\n" |
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338 | << rcsid << errmsg << "\n"; |
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339 | #endif |
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340 | #endif |
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341 | DEBDECLEVEL(CERR, "SqrFreed"); |
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342 | return Outputlist; // for safety purpose |
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343 | } |
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344 | |
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345 | /////////////////////////////////////////////////////////////// |
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346 | // The user front-end for the SqrFreed routine. // |
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347 | // Input can have a constant as content // |
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348 | /////////////////////////////////////////////////////////////// |
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349 | CFFList |
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350 | InternalSqrFree( const CanonicalForm & r , const CanonicalForm & mipo ){ |
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351 | CanonicalForm g=icontent(r), f = r; |
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352 | CFFList Outputlist, Outputlist2; |
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353 | |
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354 | DEBINCLEVEL(CERR, "InternalSqrFree"); |
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355 | DEBOUTMSG(CERR, rcsid); |
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356 | DEBOUTLN(CERR,"Called with f= ", f); |
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357 | |
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358 | // Take care of stupid users giving us constants |
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359 | if ( getNumVars(f) == 0 ) { // a constant ; Exp==1 even if f==0 |
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360 | Outputlist= myappend(Outputlist,CFFactor(f,1)); |
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361 | } |
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362 | else{ |
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363 | // Now we are sure: we have a nonconstant polynomial |
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364 | g = lc(f); |
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365 | while ( getNumVars(g) != 0 ) g=content(g); |
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366 | if ( ! g.isOne() ) Outputlist= myappend(Outputlist,CFFactor(g,1)) ; |
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367 | f /= g; |
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368 | if ( getNumVars(f) != 0 ) // a real polynomial |
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369 | { |
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370 | if (mipo!=0) |
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371 | Outputlist=myUnion(SqrFreed(f,mipo),Outputlist) ; |
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372 | else |
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373 | Outputlist=myUnion(SqrFreed(f),Outputlist) ; |
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374 | } |
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375 | } |
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376 | DEBOUTLN(CERR,"Outputlist = ", Outputlist); |
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377 | for ( CFFListIterator i=Outputlist; i.hasItem(); i++ ) |
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378 | if ( getNumVars(i.getItem().factor()) > 0 ) |
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379 | Outputlist2.append(i.getItem()); |
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380 | |
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381 | DEBOUTLN(CERR,"Outputlist2 = ", Outputlist2); |
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382 | DEBDECLEVEL(CERR, "InternalSqrFree"); |
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383 | return Outputlist2 ; |
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384 | } |
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385 | |
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386 | CFFList |
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387 | SqrFree(const CanonicalForm & r ){ |
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388 | CFFList outputlist, sqrfreelist = InternalSqrFree(r); |
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389 | CFFListIterator i; |
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390 | CanonicalForm elem; |
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391 | int n=totaldegree(r); |
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392 | |
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393 | DEBINCLEVEL(CERR, "SqrFree"); |
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394 | |
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395 | if ( sqrfreelist.length() < 2 ){ |
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396 | DEBDECLEVEL(CERR, "SqrFree"); |
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397 | return sqrfreelist; |
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398 | } |
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399 | for ( int j=1; j<=n; j++ ){ |
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400 | elem =1; |
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401 | for ( i = sqrfreelist; i.hasItem() ; i++ ){ |
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402 | if ( i.getItem().exp() == j ) elem *= i.getItem().factor(); |
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403 | } |
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404 | if ( !(elem.isOne()) ) outputlist.append(CFFactor(elem,j)); |
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405 | } |
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406 | elem=1; |
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407 | for ( i=outputlist; i.hasItem(); i++ ) |
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408 | if ( getNumVars(i.getItem().factor()) > 0 ) |
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409 | elem*= power(i.getItem().factor(),i.getItem().exp()); |
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410 | elem= r/elem; |
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411 | outputlist.insert(CFFactor(elem,1)); |
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412 | |
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413 | DEBOUTLN(CERR, "SqrFree returns list:", outputlist); |
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414 | DEBDECLEVEL(CERR, "SqrFree"); |
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415 | return outputlist; |
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416 | } |
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417 | |
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418 | /* |
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419 | $Log: not supported by cvs2svn $ |
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420 | Revision 1.11 2007/05/15 14:46:49 Singular |
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421 | *hannes: factorize in Zp(a)[x...] |
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422 | |
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423 | Revision 1.10 2006/05/16 14:46:50 Singular |
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424 | *hannes: gcc 4.1 fixes |
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425 | |
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426 | Revision 1.9 2006/04/28 13:46:29 Singular |
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427 | *hannes: better tests for 0, 1 |
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428 | |
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429 | Revision 1.8 2002/08/19 11:11:33 Singular |
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430 | * hannes/pfister: alg_gcd etc. |
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431 | |
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432 | Revision 1.7 2001/08/08 14:27:38 Singular |
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433 | *hannes: Dan's HAVE_SINGULAR_ERROR |
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434 | |
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435 | Revision 1.6 2001/08/08 14:26:56 Singular |
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436 | *hannes: Dan's HAVE_SINGULAR_ERROR |
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437 | |
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438 | Revision 1.5 2001/08/08 11:59:13 Singular |
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439 | *hannes: Dan's NOSTREAMIO changes |
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440 | |
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441 | Revision 1.4 1997/11/18 16:39:06 Singular |
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442 | * hannes: moved WerrorS from C++ to C |
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443 | (Factor.cc MVMultiHensel.cc SqrFree.cc Truefactor.cc) |
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444 | |
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445 | Revision 1.3 1997/09/12 07:19:50 Singular |
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446 | * hannes/michael: libfac-0.3.0 |
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447 | |
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448 | Revision 1.4 1997/04/25 22:19:46 michael |
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449 | changed cerr and cout messages for use with Singular |
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450 | Version for libfac-0.2.1 |
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451 | |
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452 | */ |
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