1 | // ---------------------------------------------------------------------------- |
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2 | // spectrum.cc |
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3 | // begin of file |
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4 | // Stephan Endrass, endrass@mathematik.uni-mainz.de |
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5 | // 23.7.99 |
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6 | // ---------------------------------------------------------------------------- |
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7 | |
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8 | #define SPECTRUM_CC |
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9 | |
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10 | #include "mod2.h" |
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11 | |
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12 | #ifdef HAVE_SPECTRUM |
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13 | |
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14 | #ifdef SPECTRUM_PRINT |
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15 | #include <iostream.h> |
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16 | #ifndef SPECTRUM_IOSTREAM |
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17 | #include <stdio.h> |
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18 | #endif |
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19 | #endif |
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20 | |
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21 | #include <mylimits.h> |
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22 | |
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23 | #include "numbers.h" |
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24 | #include "polys.h" |
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25 | #include "ideals.h" |
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26 | #include "kstd1.h" |
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27 | #include "stairc.h" |
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28 | #include "intvec.h" |
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29 | #include "ring.h" |
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30 | |
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31 | #include "multicnt.h" |
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32 | #include "GMPrat.h" |
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33 | #include "kmatrix.h" |
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34 | #include "npolygon.h" |
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35 | #include "splist.h" |
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36 | #include "semic.h" |
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37 | |
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38 | // ---------------------------------------------------------------------------- |
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39 | // test if the polynomial h has a term of total degree d |
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40 | // ---------------------------------------------------------------------------- |
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41 | |
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42 | BOOLEAN hasTermOfDegree( poly h, int d ) |
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43 | { |
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44 | do |
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45 | { |
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46 | if( pTotaldegree( h )== d ) |
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47 | return TRUE; |
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48 | pIter(h); |
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49 | } |
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50 | while( h!=NULL ); |
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51 | |
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52 | return FALSE; |
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53 | } |
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54 | |
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55 | // ---------------------------------------------------------------------------- |
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56 | // test if the polynomial h has a constant term |
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57 | // ---------------------------------------------------------------------------- |
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58 | |
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59 | static BOOLEAN inline hasConstTerm( poly h ) |
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60 | { |
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61 | return hasTermOfDegree(h,0); |
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62 | } |
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63 | |
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64 | // ---------------------------------------------------------------------------- |
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65 | // test if the polynomial h has a linear term |
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66 | // ---------------------------------------------------------------------------- |
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67 | |
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68 | static BOOLEAN inline hasLinearTerm( poly h ) |
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69 | { |
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70 | return hasTermOfDegree(h,1); |
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71 | } |
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72 | |
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73 | // ---------------------------------------------------------------------------- |
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74 | // test if the ideal J has a lead monomial on the axis number k |
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75 | // ---------------------------------------------------------------------------- |
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76 | |
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77 | BOOLEAN hasAxis( ideal J,int k ) |
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78 | { |
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79 | int i; |
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80 | |
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81 | for( i=0; i<IDELEMS(J); i++ ) |
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82 | { |
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83 | if (pIsPurePower( J->m[i] ) == k) return TRUE; |
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84 | } |
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85 | return FALSE; |
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86 | } |
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87 | |
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88 | // ---------------------------------------------------------------------------- |
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89 | // test if the ideal J has 1 as a lead monomial |
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90 | // ---------------------------------------------------------------------------- |
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91 | |
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92 | int hasOne( ideal J ) |
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93 | { |
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94 | int i; |
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95 | |
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96 | for( i=0; i<IDELEMS(J); i++ ) |
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97 | { |
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98 | if (pIsConstant(J->m[i])) return TRUE; |
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99 | } |
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100 | return FALSE; |
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101 | } |
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102 | // ---------------------------------------------------------------------------- |
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103 | // test if m is a multiple of one of the monomials of f |
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104 | // ---------------------------------------------------------------------------- |
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105 | |
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106 | int isMultiple( poly f,poly m ) |
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107 | { |
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108 | while( f!=NULL ) |
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109 | { |
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110 | // --------------------------------------------------- |
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111 | // for a local order f|m is only possible if f>=m |
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112 | // --------------------------------------------------- |
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113 | |
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114 | if( pLmCmp( f,m )>=0 ) |
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115 | { |
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116 | if( pLmDivisibleByNoComp( f,m ) ) |
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117 | { |
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118 | return TRUE; |
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119 | } |
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120 | else |
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121 | { |
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122 | pIter( f ); |
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123 | } |
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124 | } |
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125 | else |
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126 | { |
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127 | return FALSE; |
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128 | } |
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129 | } |
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130 | |
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131 | return FALSE; |
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132 | } |
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133 | |
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134 | // ---------------------------------------------------------------------------- |
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135 | // compute the minimal monomial of minimmal weight>=max_weight |
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136 | // ---------------------------------------------------------------------------- |
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137 | |
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138 | poly computeWC( const newtonPolygon &np,Rational max_weight ) |
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139 | { |
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140 | poly m = pOne(); |
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141 | poly wc = NULL; |
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142 | int mdegree; |
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143 | |
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144 | for( int i=1; i<=pVariables; i++ ) |
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145 | { |
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146 | mdegree = 1; |
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147 | pSetExp( m,i,mdegree ); |
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148 | // pSetm( m ); |
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149 | // np.weight_shift does not need pSetm( m ), postpone it |
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150 | |
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151 | while( np.weight_shift( m )<max_weight ) |
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152 | { |
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153 | mdegree++; |
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154 | pSetExp( m,i,mdegree ); |
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155 | // pSetm( m ); |
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156 | // np.weight_shift does not need pSetm( m ), postpone it |
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157 | } |
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158 | pSetm( m ); |
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159 | |
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160 | if( i==1 || pCmp( m,wc )<0 ) |
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161 | { |
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162 | pDelete( &wc ); |
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163 | wc = pHead( m ); |
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164 | } |
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165 | |
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166 | pSetExp( m,i,0 ); |
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167 | } |
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168 | |
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169 | pDelete( &m ); |
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170 | |
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171 | return wc; |
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172 | } |
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173 | |
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174 | // ---------------------------------------------------------------------------- |
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175 | // deletes all monomials of f which are less than hc |
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176 | // ---------------------------------------------------------------------------- |
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177 | |
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178 | static inline poly normalFormHC( poly f,poly hc ) |
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179 | { |
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180 | poly *ptr = &f; |
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181 | |
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182 | while( (*ptr)!=NULL ) |
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183 | { |
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184 | if( pLmCmp( *ptr,hc )>=0 ) |
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185 | { |
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186 | ptr = &(pNext( *ptr )); |
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187 | } |
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188 | else |
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189 | { |
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190 | pDelete( ptr ); |
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191 | return f; |
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192 | } |
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193 | } |
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194 | |
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195 | return f; |
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196 | } |
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197 | |
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198 | // ---------------------------------------------------------------------------- |
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199 | // deletes all monomials of f which are multiples of monomials of Z |
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200 | // ---------------------------------------------------------------------------- |
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201 | |
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202 | static inline poly normalFormZ( poly f,poly Z ) |
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203 | { |
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204 | poly *ptr = &f; |
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205 | |
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206 | while( (*ptr)!=NULL ) |
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207 | { |
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208 | if( !isMultiple( Z,*ptr ) ) |
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209 | { |
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210 | ptr = &(pNext( *ptr )); |
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211 | } |
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212 | else |
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213 | { |
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214 | pLmDelete(ptr); |
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215 | } |
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216 | } |
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217 | |
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218 | return f; |
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219 | } |
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220 | |
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221 | // ?? HS: |
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222 | // Looks for the shortest polynomial f in stdJ which is divisible |
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223 | // by the monimial m, return its index in stdJ |
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224 | // ---------------------------------------------------------------------------- |
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225 | // Looks for the first polynomial f in stdJ which satisfies m=LT(f)*eta |
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226 | // for a monomial eta. The return eta*f-m and cancel all monomials |
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227 | // which are smaller than the highest corner hc |
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228 | // ---------------------------------------------------------------------------- |
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229 | |
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230 | static inline int isLeadMonomial( poly m,ideal stdJ ) |
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231 | { |
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232 | int length = INT_MAX; |
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233 | int result = -1; |
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234 | |
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235 | for( int i=0; i<IDELEMS(stdJ); i++ ) |
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236 | { |
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237 | if( pCmp( stdJ->m[i],m )>=0 && pDivisibleBy( stdJ->m[i],m ) ) |
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238 | { |
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239 | int tmp = pLength( stdJ->m[i] ); |
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240 | |
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241 | if( tmp < length ) |
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242 | { |
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243 | length = tmp; |
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244 | result = i; |
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245 | } |
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246 | } |
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247 | } |
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248 | |
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249 | return result; |
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250 | } |
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251 | |
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252 | // ---------------------------------------------------------------------------- |
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253 | // set the exponent of a monomial t an integer array |
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254 | // ---------------------------------------------------------------------------- |
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255 | |
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256 | static void setExp( poly m,int *r ) |
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257 | { |
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258 | for( int i=pVariables; i>0; i-- ) |
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259 | { |
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260 | pSetExp( m,i,r[i-1] ); |
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261 | } |
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262 | pSetm( m ); |
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263 | } |
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264 | |
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265 | // ---------------------------------------------------------------------------- |
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266 | // check if the ordering is a reverse wellordering, i.e. every monomial |
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267 | // is smaller than only finitely monomials |
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268 | // ---------------------------------------------------------------------------- |
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269 | |
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270 | static BOOLEAN isWell( void ) |
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271 | { |
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272 | int b = rBlocks( currRing ); |
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273 | |
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274 | if( b==3 && |
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275 | ( currRing->order[0] == ringorder_ds || |
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276 | currRing->order[0] == ringorder_Ds || |
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277 | currRing->order[0] == ringorder_ws || |
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278 | currRing->order[0] == ringorder_Ws ) ) |
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279 | { |
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280 | return TRUE; |
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281 | } |
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282 | else if( b>=3 |
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283 | && (( currRing->order[0] ==ringorder_a |
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284 | && currRing->block1[0]==pVariables ) |
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285 | || (currRing->order[0]==ringorder_M |
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286 | && currRing->block1[0]==pVariables*pVariables ))) |
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287 | { |
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288 | for( int i=pVariables-1; i>=0; i-- ) |
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289 | { |
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290 | if( currRing->wvhdl[0][i]>=0 ) |
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291 | { |
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292 | return FALSE; |
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293 | } |
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294 | } |
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295 | return TRUE; |
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296 | } |
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297 | |
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298 | return FALSE; |
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299 | } |
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300 | |
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301 | // ---------------------------------------------------------------------------- |
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302 | // compute all monomials not in stdJ and their normal forms |
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303 | // ---------------------------------------------------------------------------- |
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304 | |
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305 | void computeNF( ideal stdJ,poly hc,poly wc,spectrumPolyList *NF ) |
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306 | { |
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307 | int carry,k; |
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308 | multiCnt C( pVariables,0 ); |
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309 | poly Z = NULL; |
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310 | |
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311 | int well = isWell( ); |
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312 | |
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313 | do |
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314 | { |
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315 | poly m = pOne(); |
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316 | setExp( m,C.cnt ); |
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317 | |
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318 | carry = FALSE; |
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319 | |
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320 | k = isLeadMonomial( m,stdJ ); |
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321 | |
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322 | if( k < 0 ) |
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323 | { |
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324 | // --------------------------- |
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325 | // m is not a lead monomial |
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326 | // --------------------------- |
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327 | |
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328 | NF->insert_node( m,NULL ); |
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329 | } |
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330 | else if( isMultiple( Z,m ) ) |
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331 | { |
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332 | // ------------------------------------ |
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333 | // m is trivially in the ideal stdJ |
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334 | // ------------------------------------ |
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335 | |
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336 | pDelete( &m ); |
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337 | carry = TRUE; |
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338 | } |
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339 | else if( pCmp( m,hc ) < 0 || pCmp( m,wc ) < 0 ) |
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340 | { |
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341 | // ------------------- |
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342 | // we do not need m |
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343 | // ------------------- |
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344 | |
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345 | pDelete( &m ); |
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346 | carry = TRUE; |
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347 | } |
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348 | else |
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349 | { |
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350 | // -------------------------- |
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351 | // compute lazy normal form |
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352 | // -------------------------- |
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353 | |
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354 | poly multiplicant = pDivide( m,stdJ->m[k] ); |
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355 | pGetCoeff( multiplicant ) = nInit(1); |
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356 | |
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357 | poly nf = pMult_mm( pCopy( stdJ->m[k] ), multiplicant ); |
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358 | |
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359 | pDelete( &multiplicant ); |
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360 | |
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361 | nf = normalFormHC( nf,hc ); |
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362 | |
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363 | if( pNext( nf )==NULL ) |
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364 | { |
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365 | // ---------------------------------- |
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366 | // normal form of m is m itself |
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367 | // ---------------------------------- |
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368 | |
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369 | pDelete( &nf ); |
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370 | NF->delete_monomial( m ); |
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371 | Z = pAdd( Z,m ); |
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372 | carry = TRUE; |
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373 | } |
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374 | else |
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375 | { |
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376 | nf = normalFormZ( nf,Z ); |
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377 | |
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378 | if( pNext( nf )==NULL ) |
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379 | { |
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380 | // ---------------------------------- |
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381 | // normal form of m is m itself |
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382 | // ---------------------------------- |
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383 | |
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384 | pDelete( &nf ); |
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385 | NF->delete_monomial( m ); |
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386 | Z = pAdd( Z,m ); |
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387 | carry = TRUE; |
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388 | } |
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389 | else |
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390 | { |
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391 | // ------------------------------------ |
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392 | // normal form of m is a polynomial |
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393 | // ------------------------------------ |
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394 | |
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395 | pNorm( nf ); |
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396 | if( well==TRUE ) |
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397 | { |
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398 | NF->insert_node( m,nf ); |
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399 | } |
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400 | else |
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401 | { |
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402 | poly nfhard = kNF( stdJ,(ideal)NULL,pNext( nf ),0,0 ); |
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403 | nfhard = normalFormHC( nfhard,hc ); |
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404 | nfhard = normalFormZ ( nfhard,Z ); |
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405 | |
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406 | if( nfhard==NULL ) |
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407 | { |
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408 | NF->delete_monomial( m ); |
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409 | Z = pAdd( Z,m ); |
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410 | carry = TRUE; |
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411 | } |
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412 | else |
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413 | { |
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414 | pDelete( &pNext( nf ) ); |
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415 | pNext( nf ) = nfhard; |
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416 | NF->insert_node( m,nf ); |
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417 | } |
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418 | } |
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419 | } |
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420 | } |
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421 | } |
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422 | } |
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423 | while( C.inc( carry ) ); |
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424 | |
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425 | // delete single monomials |
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426 | |
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427 | BOOLEAN not_finished; |
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428 | |
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429 | do |
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430 | { |
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431 | not_finished = FALSE; |
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432 | |
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433 | spectrumPolyNode *node = NF->root; |
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434 | |
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435 | while( node!=(spectrumPolyNode*)NULL ) |
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436 | { |
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437 | if( node->nf!=NULL && pNext( node->nf )==NULL ) |
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438 | { |
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439 | NF->delete_monomial( node->nf ); |
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440 | not_finished = TRUE; |
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441 | node = (spectrumPolyNode*)NULL; |
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442 | } |
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443 | else |
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444 | { |
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445 | node = node->next; |
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446 | } |
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447 | } |
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448 | } while( not_finished ); |
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449 | |
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450 | pDelete( &Z ); |
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451 | } |
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452 | |
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453 | // ---------------------------------------------------------------------------- |
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454 | // check if currRing is local |
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455 | // ---------------------------------------------------------------------------- |
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456 | |
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457 | BOOLEAN ringIsLocal( void ) |
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458 | { |
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459 | poly m = pOne(); |
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460 | poly one = pOne(); |
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461 | BOOLEAN res=TRUE; |
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462 | |
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463 | for( int i=pVariables; i>0; i-- ) |
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464 | { |
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465 | pSetExp( m,i,1 ); |
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466 | pSetm( m ); |
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467 | |
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468 | if( pCmp( m,one )>0 ) |
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469 | { |
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470 | res=FALSE; |
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471 | break; |
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472 | } |
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473 | pSetExp( m,i,0 ); |
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474 | } |
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475 | |
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476 | pDelete( &m ); |
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477 | pDelete( &one ); |
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478 | |
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479 | return res; |
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480 | } |
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481 | |
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482 | // ---------------------------------------------------------------------------- |
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483 | // print error message corresponding to spectrumState state: |
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484 | // ---------------------------------------------------------------------------- |
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485 | void spectrumPrintError(spectrumState state) |
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486 | { |
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487 | switch( state ) |
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488 | { |
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489 | case spectrumZero: |
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490 | WerrorS( "polynomial is zero" ); |
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491 | break; |
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492 | case spectrumBadPoly: |
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493 | WerrorS( "polynomial has constant term" ); |
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494 | break; |
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495 | case spectrumNoSingularity: |
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496 | WerrorS( "not a singularity" ); |
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497 | break; |
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498 | case spectrumNotIsolated: |
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499 | WerrorS( "the singularity is not isolated" ); |
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500 | break; |
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501 | case spectrumNoHC: |
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502 | WerrorS( "highest corner cannot be computed" ); |
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503 | break; |
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504 | case spectrumDegenerate: |
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505 | WerrorS( "principal part is degenerate" ); |
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506 | break; |
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507 | case spectrumOK: |
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508 | break; |
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509 | |
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510 | default: |
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511 | WerrorS( "unknown error occurred" ); |
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512 | break; |
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513 | } |
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514 | } |
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515 | #endif /* HAVE_SPECTRUM */ |
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516 | // ---------------------------------------------------------------------------- |
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517 | // spectrum.cc |
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518 | // end of file |
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519 | // ---------------------------------------------------------------------------- |
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