1 | #include "kernel/mod2.h" |
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2 | |
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3 | #include "misc/options.h" |
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4 | |
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5 | #include "polys.h" |
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6 | #include "kernel/ideals.h" |
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7 | #include "kernel/ideals.h" |
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8 | #include "polys/clapsing.h" |
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9 | #include "polys/clapconv.h" |
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10 | |
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11 | /// Widely used global variable which specifies the current polynomial ring for Singular interpreter and legacy implementatins. |
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12 | /// @Note: one should avoid using it in newer designs, for example due to possible problems in parallelization with threads. |
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13 | VAR ring currRing = NULL; |
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14 | |
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15 | void rChangeCurrRing(ring r) |
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16 | { |
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17 | //------------ set global ring vars -------------------------------- |
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18 | currRing = r; |
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19 | if( r != NULL ) |
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20 | { |
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21 | rTest(r); |
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22 | //------------ global variables related to coefficients ------------ |
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23 | assume( r->cf!= NULL ); |
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24 | nSetChar(r->cf); |
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25 | //------------ global variables related to polys |
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26 | p_SetGlobals(r); // also setting TEST_RINGDEP_OPTS |
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27 | //------------ global variables related to factory ----------------- |
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28 | } |
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29 | } |
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30 | |
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31 | poly p_Divide(poly p, poly q, const ring r) |
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32 | { |
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33 | assume(q!=NULL); |
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34 | if (q==NULL) |
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35 | { |
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36 | WerrorS("div. by 0"); |
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37 | return NULL; |
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38 | } |
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39 | if (p==NULL) |
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40 | { |
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41 | p_Delete(&q,r); |
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42 | return NULL; |
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43 | } |
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44 | if ((pNext(q)!=NULL)||rIsPluralRing(r)) |
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45 | { /* This means that q != 0 consists of at least two terms*/ |
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46 | if(p_GetComp(p,r)==0) |
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47 | { |
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48 | if((rFieldType(r)==n_transExt) |
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49 | &&(convSingTrP(p,r)) |
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50 | &&(convSingTrP(q,r)) |
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51 | &&(!rIsNCRing(r))) |
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52 | { |
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53 | poly res=singclap_pdivide(p, q, r); |
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54 | p_Delete(&p,r); |
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55 | p_Delete(&q,r); |
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56 | return res; |
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57 | } |
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58 | else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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59 | &&(!rField_is_Ring(r)) |
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60 | &&(!rIsNCRing(r))) |
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61 | { |
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62 | poly res=singclap_pdivide(p, q, r); |
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63 | p_Delete(&p,r); |
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64 | p_Delete(&q,r); |
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65 | return res; |
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66 | } |
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67 | else |
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68 | { |
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69 | ideal vi=idInit(1,1); vi->m[0]=q; |
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70 | ideal ui=idInit(1,1); ui->m[0]=p; |
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71 | ideal R; matrix U; |
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72 | ring save_ring=currRing; |
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73 | if (r!=currRing) rChangeCurrRing(r); |
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74 | int save_opt; |
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75 | SI_SAVE_OPT1(save_opt); |
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76 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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77 | ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U); |
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78 | SI_RESTORE_OPT1(save_opt); |
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79 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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80 | matrix T = id_Module2formatedMatrix(m,1,1,r); |
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81 | p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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82 | id_Delete((ideal *)&T,r); |
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83 | id_Delete((ideal *)&U,r); |
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84 | id_Delete(&R,r); |
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85 | //vi->m[0]=NULL; ui->m[0]=NULL; |
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86 | id_Delete(&vi,r); |
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87 | id_Delete(&ui,r); |
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88 | return p; |
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89 | } |
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90 | } |
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91 | else |
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92 | { |
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93 | int comps=p_MaxComp(p,r); |
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94 | ideal I=idInit(comps,1); |
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95 | poly h; |
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96 | int i; |
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97 | // conversion to a list of polys: |
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98 | while (p!=NULL) |
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99 | { |
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100 | i=p_GetComp(p,r)-1; |
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101 | h=pNext(p); |
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102 | pNext(p)=NULL; |
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103 | p_SetComp(p,0,r); |
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104 | I->m[i]=p_Add_q(I->m[i],p,r); |
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105 | p=h; |
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106 | } |
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107 | // division and conversion to vector: |
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108 | h=NULL; |
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109 | p=NULL; |
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110 | for(i=comps-1;i>=0;i--) |
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111 | { |
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112 | if (I->m[i]!=NULL) |
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113 | { |
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114 | if((rFieldType(r)==n_transExt) |
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115 | &&(convSingTrP(I->m[i],r)) |
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116 | &&(convSingTrP(q,r)) |
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117 | &&(!rIsNCRing(r))) |
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118 | { |
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119 | h=singclap_pdivide(I->m[i],q,r); |
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120 | } |
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121 | else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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122 | &&(!rField_is_Ring(r)) |
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123 | &&(!rIsNCRing(r))) |
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124 | h=singclap_pdivide(I->m[i],q,r); |
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125 | else |
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126 | { |
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127 | ideal vi=idInit(1,1); vi->m[0]=q; |
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128 | ideal ui=idInit(1,1); ui->m[0]=I->m[i]; |
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129 | ideal R; matrix U; |
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130 | ring save_ring=currRing; |
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131 | if (r!=currRing) rChangeCurrRing(r); |
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132 | int save_opt; |
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133 | SI_SAVE_OPT1(save_opt); |
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134 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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135 | ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U); |
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136 | SI_RESTORE_OPT1(save_opt); |
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137 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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138 | if (idIs0(R)) |
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139 | { |
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140 | matrix T = id_Module2formatedMatrix(m,1,1,r); |
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141 | p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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142 | id_Delete((ideal *)&T,r); |
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143 | } |
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144 | else p=NULL; |
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145 | id_Delete((ideal*)&U,r); |
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146 | id_Delete(&R,r); |
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147 | vi->m[0]=NULL; ui->m[0]=NULL; |
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148 | id_Delete(&vi,r); |
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149 | id_Delete(&ui,r); |
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150 | } |
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151 | p_SetCompP(h,i+1,r); |
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152 | p=p_Add_q(p,h,r); |
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153 | } |
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154 | } |
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155 | id_Delete(&I,r); |
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156 | p_Delete(&q,r); |
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157 | return p; |
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158 | } |
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159 | } |
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160 | else |
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161 | { /* This means that q != 0 consists of just one term, or LetterPlace */ |
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162 | #ifdef HAVE_RINGS |
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163 | if (pNext(q)!=NULL) |
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164 | { |
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165 | WerrorS("division over a coefficient domain only implemented for terms"); |
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166 | return NULL; |
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167 | } |
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168 | #endif |
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169 | return p_DivideM(p,q,r); |
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170 | } |
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171 | return NULL; |
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172 | } |
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173 | |
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174 | poly pp_Divide(poly p, poly q, const ring r) |
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175 | { |
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176 | assume(q!=NULL); |
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177 | if (q==NULL) |
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178 | { |
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179 | WerrorS("div. by 0"); |
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180 | return NULL; |
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181 | } |
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182 | if (p==NULL) |
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183 | { |
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184 | return NULL; |
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185 | } |
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186 | if ((pNext(q)!=NULL)||rIsPluralRing(r)) |
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187 | { /* This means that q != 0 consists of at least two terms*/ |
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188 | if(p_GetComp(p,r)==0) |
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189 | { |
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190 | if((rFieldType(r)==n_transExt) |
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191 | &&(convSingTrP(p,r)) |
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192 | &&(convSingTrP(q,r)) |
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193 | &&(!rIsNCRing(r))) |
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194 | { |
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195 | poly res=singclap_pdivide(p, q, r); |
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196 | return res; |
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197 | } |
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198 | else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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199 | &&(!rField_is_Ring(r)) |
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200 | &&(!rIsNCRing(r))) |
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201 | { |
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202 | poly res=singclap_pdivide(p, q, r); |
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203 | return res; |
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204 | } |
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205 | else |
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206 | { |
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207 | ideal vi=idInit(1,1); vi->m[0]=p_Copy(q,r); |
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208 | ideal ui=idInit(1,1); ui->m[0]=p_Copy(p,r); |
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209 | ideal R; matrix U; |
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210 | ring save_ring=currRing; |
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211 | if (r!=currRing) rChangeCurrRing(r); |
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212 | int save_opt; |
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213 | SI_SAVE_OPT1(save_opt); |
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214 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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215 | ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U); |
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216 | SI_RESTORE_OPT1(save_opt); |
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217 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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218 | matrix T = id_Module2formatedMatrix(m,1,1,r); |
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219 | p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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220 | id_Delete((ideal *)&T,r); |
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221 | id_Delete((ideal *)&U,r); |
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222 | id_Delete(&R,r); |
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223 | //vi->m[0]=NULL; ui->m[0]=NULL; |
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224 | id_Delete(&vi,r); |
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225 | id_Delete(&ui,r); |
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226 | return p; |
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227 | } |
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228 | } |
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229 | else |
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230 | { |
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231 | p=p_Copy(p,r); |
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232 | int comps=p_MaxComp(p,r); |
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233 | ideal I=idInit(comps,1); |
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234 | poly h; |
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235 | int i; |
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236 | // conversion to a list of polys: |
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237 | while (p!=NULL) |
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238 | { |
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239 | i=p_GetComp(p,r)-1; |
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240 | h=pNext(p); |
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241 | pNext(p)=NULL; |
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242 | p_SetComp(p,0,r); |
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243 | I->m[i]=p_Add_q(I->m[i],p,r); |
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244 | p=h; |
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245 | } |
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246 | // division and conversion to vector: |
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247 | h=NULL; |
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248 | p=NULL; |
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249 | q=p_Copy(q,r); |
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250 | for(i=comps-1;i>=0;i--) |
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251 | { |
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252 | if (I->m[i]!=NULL) |
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253 | { |
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254 | if((rFieldType(r)==n_transExt) |
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255 | &&(convSingTrP(I->m[i],r)) |
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256 | &&(convSingTrP(q,r)) |
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257 | &&(!rIsNCRing(r))) |
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258 | { |
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259 | h=singclap_pdivide(I->m[i],q,r); |
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260 | } |
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261 | else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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262 | &&(!rField_is_Ring(r)) |
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263 | &&(!rIsNCRing(r))) |
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264 | h=singclap_pdivide(I->m[i],q,r); |
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265 | else |
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266 | { |
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267 | ideal vi=idInit(1,1); vi->m[0]=q; |
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268 | ideal ui=idInit(1,1); ui->m[0]=I->m[i]; |
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269 | ideal R; matrix U; |
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270 | ring save_ring=currRing; |
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271 | if (r!=currRing) rChangeCurrRing(r); |
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272 | int save_opt; |
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273 | SI_SAVE_OPT1(save_opt); |
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274 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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275 | ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U); |
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276 | SI_RESTORE_OPT1(save_opt); |
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277 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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278 | if (idIs0(R)) |
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279 | { |
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280 | matrix T = id_Module2formatedMatrix(m,1,1,r); |
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281 | p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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282 | id_Delete((ideal *)&T,r); |
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283 | } |
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284 | else p=NULL; |
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285 | id_Delete((ideal*)&U,r); |
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286 | id_Delete(&R,r); |
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287 | vi->m[0]=NULL; ui->m[0]=NULL; |
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288 | id_Delete(&vi,r); |
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289 | id_Delete(&ui,r); |
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290 | } |
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291 | p_SetCompP(h,i+1,r); |
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292 | p=p_Add_q(p,h,r); |
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293 | } |
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294 | } |
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295 | id_Delete(&I,r); |
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296 | p_Delete(&q,r); |
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297 | return p; |
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298 | } |
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299 | } |
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300 | else |
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301 | { /* This means that q != 0 consists of just one term, |
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302 | or that r is over a coefficient ring. */ |
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303 | #ifdef HAVE_RINGS |
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304 | if (pNext(q)!=NULL) |
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305 | { |
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306 | WerrorS("division over a coefficient domain only implemented for terms"); |
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307 | return NULL; |
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308 | } |
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309 | #endif |
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310 | return pp_DivideM(p,q,r); |
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311 | } |
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312 | return NULL; |
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313 | } |
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314 | |
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315 | poly p_DivRem(poly p, poly q, poly &rest, const ring r) |
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316 | { |
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317 | assume(q!=NULL); |
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318 | rest=NULL; |
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319 | if (q==NULL) |
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320 | { |
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321 | WerrorS("div. by 0"); |
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322 | return NULL; |
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323 | } |
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324 | if (p==NULL) |
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325 | { |
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326 | p_Delete(&q,r); |
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327 | return NULL; |
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328 | } |
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329 | if(p_GetComp(p,r)==0) |
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330 | { |
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331 | if((rFieldType(r)==n_transExt) |
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332 | &&(convSingTrP(p,r)) |
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333 | &&(convSingTrP(q,r)) |
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334 | &&(!rIsNCRing(r))) |
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335 | { |
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336 | poly res=singclap_pdivide(p, q, r); |
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337 | rest=singclap_pmod(p,q,r); |
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338 | p_Delete(&p,r); |
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339 | p_Delete(&q,r); |
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340 | return res; |
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341 | } |
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342 | else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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343 | &&(!rField_is_Ring(r)) |
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344 | &&(!rIsNCRing(r))) |
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345 | { |
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346 | poly res=singclap_pdivide(p, q, r); |
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347 | rest=singclap_pmod(p,q,r); |
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348 | p_Delete(&p,r); |
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349 | p_Delete(&q,r); |
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350 | return res; |
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351 | } |
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352 | else |
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353 | { |
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354 | ideal vi=idInit(1,1); vi->m[0]=q; |
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355 | ideal ui=idInit(1,1); ui->m[0]=p; |
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356 | ideal R; matrix U; |
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357 | ring save_ring=currRing; |
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358 | if (r!=currRing) rChangeCurrRing(r); |
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359 | int save_opt; |
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360 | SI_SAVE_OPT1(save_opt); |
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361 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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362 | ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U); |
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363 | SI_RESTORE_OPT1(save_opt); |
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364 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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365 | matrix T = id_Module2formatedMatrix(m,1,1,r); |
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366 | p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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367 | id_Delete((ideal *)&T,r); |
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368 | T = id_Module2formatedMatrix(R,1,1,r); |
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369 | rest=MATELEM(T,1,1); MATELEM(T,1,1)=NULL; |
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370 | id_Delete((ideal *)&T,r); |
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371 | id_Delete((ideal *)&U,r); |
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372 | id_Delete(&R,r); |
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373 | //vi->m[0]=NULL; ui->m[0]=NULL; |
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374 | id_Delete(&vi,r); |
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375 | id_Delete(&ui,r); |
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376 | return p; |
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377 | } |
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378 | } |
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379 | return NULL; |
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380 | } |
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381 | |
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382 | poly singclap_gcd ( poly f, poly g, const ring r ) |
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383 | { |
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384 | poly res=NULL; |
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385 | |
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386 | if (f!=NULL) |
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387 | { |
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388 | //if (r->cf->has_simple_Inverse) p_Norm(f,r); |
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389 | if (rField_is_Zp(r)) p_Norm(f,r); |
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390 | else p_Cleardenom(f, r); |
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391 | } |
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392 | if (g!=NULL) |
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393 | { |
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394 | //if (r->cf->has_simple_Inverse) p_Norm(g,r); |
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395 | if (rField_is_Zp(r)) p_Norm(g,r); |
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396 | else p_Cleardenom(g, r); |
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397 | } |
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398 | else return f; // g==0 => gcd=f (but do a p_Cleardenom/pNorm) |
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399 | if (f==NULL) return g; // f==0 => gcd=g (but do a p_Cleardenom/pNorm) |
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400 | if(!rField_is_Ring(r) |
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401 | && (p_IsConstant(f,r) |
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402 | ||p_IsConstant(g,r))) |
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403 | { |
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404 | res=p_One(r); |
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405 | } |
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406 | else if (r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
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407 | { |
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408 | res=singclap_gcd_r(f,g,r); |
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409 | } |
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410 | else |
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411 | { |
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412 | ideal I=idInit(2,1); |
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413 | I->m[0]=f; |
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414 | I->m[1]=p_Copy(g,r); |
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415 | intvec *w=NULL; |
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416 | ring save_ring=currRing; |
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417 | if (r!=currRing) rChangeCurrRing(r); |
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418 | int save_opt; |
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419 | SI_SAVE_OPT1(save_opt); |
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420 | si_opt_1 &= ~(Sy_bit(OPT_PROT)); |
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421 | ideal S1=idSyzygies(I,testHomog,&w); |
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422 | if (w!=NULL) delete w; |
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423 | // expect S1->m[0]=(-g/gcd,f/gcd) |
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424 | if (IDELEMS(S1)!=1) WarnS("error in syzygy computation for GCD"); |
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425 | int lp; |
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426 | p_TakeOutComp(&S1->m[0],1,&res,&lp,r); |
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427 | p_Delete(&S1->m[0],r); |
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428 | // GCD is g divided iby (-g/gcd): |
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429 | res=p_Divide(g,res,r); |
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430 | // restore, r, opt: |
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431 | SI_RESTORE_OPT1(save_opt); |
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432 | if (r!=save_ring) rChangeCurrRing(save_ring); |
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433 | // clean the result |
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434 | res=p_Cleardenom(res,r); |
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435 | p_Content(res,r); |
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436 | return res; |
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437 | } |
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438 | p_Delete(&f, r); |
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439 | p_Delete(&g, r); |
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440 | return res; |
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441 | } |
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