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 <kernel/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 <omalloc/mylimits.h> |
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22 | |
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23 | #include <coeffs/numbers.h> |
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24 | #include <polys/monomials/p_polys.h> |
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25 | #include <polys/simpleideals.h> |
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26 | #include <misc/intvec.h> |
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27 | #include <polys/monomials/ring.h> |
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28 | //extern ring currRing; |
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29 | |
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30 | #include <kernel/kstd1.h> |
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31 | #include <kernel/stairc.h> |
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32 | #include <kernel/multicnt.h> |
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33 | #include <kernel/GMPrat.h> |
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34 | #include <kernel/kmatrix.h> |
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35 | #include <kernel/npolygon.h> |
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36 | #include <kernel/splist.h> |
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37 | #include <kernel/semic.h> |
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38 | |
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39 | // ---------------------------------------------------------------------------- |
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40 | // test if the polynomial h has a term of total degree d |
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41 | // ---------------------------------------------------------------------------- |
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42 | |
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43 | BOOLEAN hasTermOfDegree( poly h, int d, const ring r ) |
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44 | { |
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45 | do |
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46 | { |
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47 | if( p_Totaldegree( h,r )== d ) |
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48 | return TRUE; |
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49 | pIter(h); |
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50 | } |
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51 | while( h!=NULL ); |
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52 | |
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53 | return FALSE; |
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54 | } |
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55 | |
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56 | // ---------------------------------------------------------------------------- |
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57 | // test if the polynomial h has a constant term |
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58 | // ---------------------------------------------------------------------------- |
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59 | |
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60 | static BOOLEAN inline hasConstTerm( poly h, const ring r ) |
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61 | { |
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62 | return hasTermOfDegree(h,0,r); |
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63 | } |
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64 | |
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65 | // ---------------------------------------------------------------------------- |
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66 | // test if the polynomial h has a linear term |
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67 | // ---------------------------------------------------------------------------- |
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68 | |
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69 | static BOOLEAN inline hasLinearTerm( poly h, const ring r ) |
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70 | { |
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71 | return hasTermOfDegree(h,1,r); |
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72 | } |
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73 | |
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74 | // ---------------------------------------------------------------------------- |
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75 | // test if the ideal J has a lead monomial on the axis number k |
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76 | // ---------------------------------------------------------------------------- |
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77 | |
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78 | BOOLEAN hasAxis( ideal J,int k, const ring r ) |
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79 | { |
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80 | int i; |
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81 | |
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82 | for( i=0; i<IDELEMS(J); i++ ) |
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83 | { |
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84 | if (p_IsPurePower( J->m[i],r ) == k) return TRUE; |
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85 | } |
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86 | return FALSE; |
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87 | } |
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88 | |
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89 | // ---------------------------------------------------------------------------- |
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90 | // test if the ideal J has 1 as a lead monomial |
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91 | // ---------------------------------------------------------------------------- |
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92 | |
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93 | int hasOne( ideal J, const ring r ) |
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94 | { |
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95 | int i; |
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96 | |
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97 | for( i=0; i<IDELEMS(J); i++ ) |
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98 | { |
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99 | if (p_IsConstant(J->m[i],r)) return TRUE; |
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100 | } |
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101 | return FALSE; |
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102 | } |
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103 | // ---------------------------------------------------------------------------- |
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104 | // test if m is a multiple of one of the monomials of f |
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105 | // ---------------------------------------------------------------------------- |
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106 | |
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107 | int isMultiple( poly f,poly m, const ring r ) |
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108 | { |
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109 | while( f!=NULL ) |
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110 | { |
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111 | // --------------------------------------------------- |
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112 | // for a local order f|m is only possible if f>=m |
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113 | // --------------------------------------------------- |
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114 | |
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115 | if( p_LmCmp( f,m,r )>=0 ) |
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116 | { |
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117 | if( p_LmDivisibleByNoComp( f,m,r ) ) |
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118 | { |
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119 | return TRUE; |
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120 | } |
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121 | else |
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122 | { |
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123 | pIter( f ); |
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124 | } |
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125 | } |
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126 | else |
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127 | { |
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128 | return FALSE; |
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129 | } |
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130 | } |
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131 | |
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132 | return FALSE; |
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133 | } |
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134 | |
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135 | // ---------------------------------------------------------------------------- |
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136 | // compute the minimal monomial of minimmal weight>=max_weight |
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137 | // ---------------------------------------------------------------------------- |
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138 | |
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139 | poly computeWC( const newtonPolygon &np,Rational max_weight, const ring r ) |
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140 | { |
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141 | poly m = p_One(r); |
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142 | poly wc = NULL; |
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143 | int mdegree; |
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144 | |
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145 | for( int i=1; i<=r->N; i++ ) |
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146 | { |
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147 | mdegree = 1; |
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148 | p_SetExp( m,i,mdegree,r ); |
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149 | // pSetm( m ); |
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150 | // np.weight_shift does not need pSetm( m ), postpone it |
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151 | |
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152 | while( np.weight_shift( m,r )<max_weight ) |
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153 | { |
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154 | mdegree++; |
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155 | p_SetExp( m,i,mdegree,r ); |
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156 | // pSetm( m ); |
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157 | // np.weight_shift does not need pSetm( m ), postpone it |
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158 | } |
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159 | p_Setm( m,r ); |
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160 | |
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161 | if( i==1 || p_Cmp( m,wc,r )<0 ) |
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162 | { |
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163 | p_Delete( &wc,r ); |
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164 | wc = p_Head( m,r ); |
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165 | } |
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166 | |
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167 | p_SetExp( m,i,0,r ); |
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168 | } |
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169 | |
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170 | p_Delete( &m,r ); |
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171 | |
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172 | return wc; |
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173 | } |
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174 | |
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175 | // ---------------------------------------------------------------------------- |
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176 | // deletes all monomials of f which are less than hc |
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177 | // ---------------------------------------------------------------------------- |
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178 | |
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179 | static inline poly normalFormHC( poly f,poly hc, const ring r ) |
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180 | { |
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181 | poly *ptr = &f; |
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182 | |
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183 | while( (*ptr)!=NULL ) |
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184 | { |
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185 | if( p_LmCmp( *ptr,hc,r )>=0 ) |
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186 | { |
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187 | ptr = &(pNext( *ptr )); |
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188 | } |
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189 | else |
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190 | { |
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191 | p_Delete( ptr,r ); |
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192 | return f; |
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193 | } |
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194 | } |
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195 | |
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196 | return f; |
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197 | } |
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198 | |
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199 | // ---------------------------------------------------------------------------- |
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200 | // deletes all monomials of f which are multiples of monomials of Z |
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201 | // ---------------------------------------------------------------------------- |
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202 | |
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203 | static inline poly normalFormZ( poly f,poly Z, const ring r ) |
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204 | { |
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205 | poly *ptr = &f; |
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206 | |
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207 | while( (*ptr)!=NULL ) |
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208 | { |
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209 | if( !isMultiple( Z,*ptr,r ) ) |
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210 | { |
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211 | ptr = &(pNext( *ptr )); |
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212 | } |
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213 | else |
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214 | { |
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215 | p_LmDelete(ptr,r); |
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216 | } |
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217 | } |
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218 | |
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219 | return f; |
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220 | } |
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221 | |
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222 | // ?? HS: |
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223 | // Looks for the shortest polynomial f in stdJ which is divisible |
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224 | // by the monimial m, return its index in stdJ |
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225 | // ---------------------------------------------------------------------------- |
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226 | // Looks for the first polynomial f in stdJ which satisfies m=LT(f)*eta |
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227 | // for a monomial eta. The return eta*f-m and cancel all monomials |
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228 | // which are smaller than the highest corner hc |
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229 | // ---------------------------------------------------------------------------- |
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230 | |
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231 | static inline int isLeadMonomial( poly m,ideal stdJ, const ring r ) |
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232 | { |
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233 | int length = INT_MAX; |
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234 | int result = -1; |
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235 | |
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236 | for( int i=0; i<IDELEMS(stdJ); i++ ) |
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237 | { |
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238 | if( p_Cmp( stdJ->m[i],m,r )>=0 && p_DivisibleBy( stdJ->m[i],m,r ) ) |
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239 | { |
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240 | int tmp = pLength( stdJ->m[i] ); |
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241 | |
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242 | if( tmp < length ) |
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243 | { |
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244 | length = tmp; |
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245 | result = i; |
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246 | } |
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247 | } |
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248 | } |
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249 | |
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250 | return result; |
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251 | } |
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252 | |
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253 | // ---------------------------------------------------------------------------- |
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254 | // set the exponent of a monomial t an integer array |
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255 | // ---------------------------------------------------------------------------- |
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256 | |
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257 | static void setExp( poly m,int *r, const ring s ) |
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258 | { |
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259 | for( int i=s->N; i>0; i-- ) |
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260 | { |
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261 | p_SetExp( m,i,r[i-1],s ); |
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262 | } |
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263 | p_Setm( m,s ); |
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264 | } |
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265 | |
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266 | // ---------------------------------------------------------------------------- |
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267 | // check if the ordering is a reverse wellordering, i.e. every monomial |
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268 | // is smaller than only finitely monomials |
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269 | // ---------------------------------------------------------------------------- |
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270 | |
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271 | static BOOLEAN isWell( const ring r ) |
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272 | { |
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273 | int b = rBlocks( r ); |
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274 | |
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275 | if( b==3 && |
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276 | ( r->order[0] == ringorder_ds || |
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277 | r->order[0] == ringorder_Ds || |
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278 | r->order[0] == ringorder_ws || |
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279 | r->order[0] == ringorder_Ws ) ) |
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280 | { |
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281 | return TRUE; |
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282 | } |
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283 | else if( b>=3 |
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284 | && (( r->order[0] ==ringorder_a |
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285 | && r->block1[0]==r->N ) |
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286 | || (r->order[0]==ringorder_M |
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287 | && r->block1[0]==r->N*r->N ))) |
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288 | { |
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289 | for( int i=r->N-1; i>=0; i-- ) |
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290 | { |
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291 | if( r->wvhdl[0][i]>=0 ) |
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292 | { |
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293 | return FALSE; |
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294 | } |
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295 | } |
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296 | return TRUE; |
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297 | } |
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298 | |
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299 | return FALSE; |
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300 | } |
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301 | |
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302 | // ---------------------------------------------------------------------------- |
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303 | // compute all monomials not in stdJ and their normal forms |
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304 | // ---------------------------------------------------------------------------- |
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305 | |
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306 | void computeNF( ideal stdJ,poly hc,poly wc,spectrumPolyList *NF, const ring r ) |
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307 | { |
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308 | int carry,k; |
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309 | multiCnt C( r->N,0 ); |
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310 | poly Z = NULL; |
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311 | |
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312 | int well = isWell(r); |
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313 | |
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314 | do |
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315 | { |
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316 | poly m = p_One(r); |
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317 | setExp( m,C.cnt,r ); |
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318 | |
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319 | carry = FALSE; |
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320 | |
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321 | k = isLeadMonomial( m,stdJ,r ); |
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322 | |
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323 | if( k < 0 ) |
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324 | { |
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325 | // --------------------------- |
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326 | // m is not a lead monomial |
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327 | // --------------------------- |
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328 | |
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329 | NF->insert_node( m,NULL ); |
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330 | } |
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331 | else if( isMultiple( Z,m,r ) ) |
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332 | { |
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333 | // ------------------------------------ |
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334 | // m is trivially in the ideal stdJ |
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335 | // ------------------------------------ |
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336 | |
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337 | p_Delete( &m,r ); |
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338 | carry = TRUE; |
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339 | } |
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340 | else if( p_Cmp( m,hc,r ) < 0 || p_Cmp( m,wc,r ) < 0 ) |
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341 | { |
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342 | // ------------------- |
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343 | // we do not need m |
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344 | // ------------------- |
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345 | |
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346 | p_Delete( &m,r ); |
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347 | carry = TRUE; |
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348 | } |
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349 | else |
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350 | { |
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351 | // -------------------------- |
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352 | // compute lazy normal form |
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353 | // -------------------------- |
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354 | |
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355 | poly multiplicant = p_Divide( m,stdJ->m[k],r ); |
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356 | pGetCoeff( multiplicant ) = n_Init(1,r->cf); |
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357 | |
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358 | poly nf = p_Mult_mm( p_Copy( stdJ->m[k],r ), multiplicant,r ); |
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359 | |
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360 | p_Delete( &multiplicant,r ); |
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361 | |
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362 | nf = normalFormHC( nf,hc,r ); |
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363 | |
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364 | if( pNext( nf )==NULL ) |
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365 | { |
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366 | // ---------------------------------- |
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367 | // normal form of m is m itself |
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368 | // ---------------------------------- |
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369 | |
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370 | p_Delete( &nf,r ); |
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371 | NF->delete_monomial( m ); |
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372 | Z = p_Add_q( Z,m,r ); |
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373 | carry = TRUE; |
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374 | } |
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375 | else |
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376 | { |
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377 | nf = normalFormZ( nf,Z,r ); |
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378 | |
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379 | if( pNext( nf )==NULL ) |
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380 | { |
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381 | // ---------------------------------- |
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382 | // normal form of m is m itself |
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383 | // ---------------------------------- |
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384 | |
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385 | p_Delete( &nf,r ); |
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386 | NF->delete_monomial( m ); |
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387 | Z = p_Add_q( Z,m,r ); |
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388 | carry = TRUE; |
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389 | } |
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390 | else |
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391 | { |
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392 | // ------------------------------------ |
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393 | // normal form of m is a polynomial |
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394 | // ------------------------------------ |
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395 | |
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396 | p_Norm( nf,r ); |
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397 | if( well==TRUE ) |
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398 | { |
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399 | NF->insert_node( m,nf ); |
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400 | } |
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401 | else |
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402 | { |
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403 | poly nfhard = kNF( stdJ,(ideal)NULL,pNext( nf ),0,0 ); |
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404 | nfhard = normalFormHC( nfhard,hc,r ); |
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405 | nfhard = normalFormZ ( nfhard,Z,r ); |
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406 | |
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407 | if( nfhard==NULL ) |
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408 | { |
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409 | NF->delete_monomial( m ); |
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410 | Z = p_Add_q( Z,m,r ); |
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411 | carry = TRUE; |
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412 | } |
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413 | else |
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414 | { |
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415 | p_Delete( &pNext( nf ),r ); |
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416 | pNext( nf ) = nfhard; |
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417 | NF->insert_node( m,nf ); |
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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 | } |
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424 | while( C.inc( carry ) ); |
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425 | |
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426 | // delete single monomials |
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427 | |
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428 | BOOLEAN not_finished; |
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429 | |
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430 | do |
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431 | { |
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432 | not_finished = FALSE; |
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433 | |
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434 | spectrumPolyNode *node = NF->root; |
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435 | |
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436 | while( node!=(spectrumPolyNode*)NULL ) |
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437 | { |
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438 | if( node->nf!=NULL && pNext( node->nf )==NULL ) |
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439 | { |
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440 | NF->delete_monomial( node->nf ); |
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441 | not_finished = TRUE; |
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442 | node = (spectrumPolyNode*)NULL; |
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443 | } |
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444 | else |
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445 | { |
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446 | node = node->next; |
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447 | } |
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448 | } |
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449 | } while( not_finished ); |
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450 | |
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451 | p_Delete( &Z,r ); |
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452 | } |
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453 | |
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454 | // ---------------------------------------------------------------------------- |
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455 | // check if currRing is local |
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456 | // ---------------------------------------------------------------------------- |
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457 | |
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458 | BOOLEAN ringIsLocal( const ring r ) |
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459 | { |
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460 | poly m = p_One(r); |
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461 | poly one = p_One(r); |
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462 | BOOLEAN res=TRUE; |
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463 | |
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464 | for( int i=r->N; i>0; i-- ) |
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465 | { |
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466 | p_SetExp( m,i,1,r ); |
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467 | p_Setm( m,r ); |
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468 | |
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469 | if( p_Cmp( m,one,r )>0 ) |
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470 | { |
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471 | res=FALSE; |
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472 | break; |
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473 | } |
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474 | p_SetExp( m,i,0,r ); |
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475 | } |
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476 | |
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477 | p_Delete( &m,r ); |
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478 | p_Delete( &one,r ); |
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479 | |
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480 | return res; |
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481 | } |
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482 | |
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483 | // ---------------------------------------------------------------------------- |
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484 | // print error message corresponding to spectrumState state: |
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485 | // ---------------------------------------------------------------------------- |
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486 | void spectrumPrintError(spectrumState state) |
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487 | { |
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488 | switch( state ) |
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489 | { |
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490 | case spectrumZero: |
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491 | WerrorS( "polynomial is zero" ); |
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492 | break; |
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493 | case spectrumBadPoly: |
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494 | WerrorS( "polynomial has constant term" ); |
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495 | break; |
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496 | case spectrumNoSingularity: |
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497 | WerrorS( "not a singularity" ); |
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498 | break; |
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499 | case spectrumNotIsolated: |
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500 | WerrorS( "the singularity is not isolated" ); |
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501 | break; |
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502 | case spectrumNoHC: |
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503 | WerrorS( "highest corner cannot be computed" ); |
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504 | break; |
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505 | case spectrumDegenerate: |
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506 | WerrorS( "principal part is degenerate" ); |
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507 | break; |
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508 | case spectrumOK: |
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509 | break; |
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510 | |
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511 | default: |
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512 | WerrorS( "unknown error occurred" ); |
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513 | break; |
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514 | } |
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515 | } |
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516 | #endif /* HAVE_SPECTRUM */ |
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517 | // ---------------------------------------------------------------------------- |
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518 | // spectrum.cc |
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519 | // end of file |
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520 | // ---------------------------------------------------------------------------- |
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