1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT - Routines for Spoly creation and reductions |
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6 | */ |
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7 | |
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8 | // #define PDEBUG 2 |
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9 | |
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10 | |
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11 | |
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12 | #include <kernel/mod2.h> |
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13 | #include <misc/options.h> |
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14 | #include <kernel/GBEngine/kutil.h> |
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15 | #include <coeffs/numbers.h> |
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16 | #include <polys/monomials/p_polys.h> |
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17 | #include <polys/templates/p_Procs.h> |
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18 | #include <polys/nc/nc.h> |
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19 | #ifdef KDEBUG |
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20 | #endif |
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21 | #ifdef HAVE_RINGS |
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22 | #include <kernel/polys.h> |
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23 | #endif |
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24 | |
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25 | #ifdef KDEBUG |
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26 | int red_count = 0; |
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27 | int create_count = 0; |
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28 | // define this if reductions are reported on TEST_OPT_DEBUG |
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29 | #define TEST_OPT_DEBUG_RED |
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30 | #endif |
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31 | |
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32 | /*************************************************************** |
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33 | * |
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34 | * Reduces PR with PW |
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35 | * Assumes PR != NULL, PW != NULL, Lm(PW) divides Lm(PR) |
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36 | * |
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37 | ***************************************************************/ |
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38 | int ksReducePoly(LObject* PR, |
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39 | TObject* PW, |
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40 | poly spNoether, |
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41 | number *coef, |
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42 | kStrategy strat) |
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43 | { |
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44 | #ifdef KDEBUG |
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45 | red_count++; |
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46 | #ifdef TEST_OPT_DEBUG_RED |
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47 | if (TEST_OPT_DEBUG) |
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48 | { |
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49 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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50 | PW->wrp(); |
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51 | //printf("\necart(PR)-ecart(PW): %i\n",PR->ecart-PW->ecart); |
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52 | //pWrite(PR->p); |
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53 | } |
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54 | #endif |
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55 | #endif |
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56 | int ret = 0; |
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57 | ring tailRing = PR->tailRing; |
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58 | kTest_L(PR); |
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59 | kTest_T(PW); |
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60 | |
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61 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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62 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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63 | poly t2 = pNext(p2), lm = p1; // t2 = p2 - LT(p2); really compute P = LC(p2)*p1 - LT(p1)/LM(p2)*p2 |
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64 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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65 | p_CheckPolyRing(p1, tailRing); |
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66 | p_CheckPolyRing(p2, tailRing); |
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67 | |
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68 | pAssume1(p2 != NULL && p1 != NULL && |
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69 | p_DivisibleBy(p2, p1, tailRing)); |
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70 | |
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71 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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72 | (p_GetComp(p2, tailRing) == 0 && |
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73 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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74 | |
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75 | #ifdef HAVE_PLURAL |
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76 | if (rIsPluralRing(currRing)) |
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77 | { |
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78 | // for the time being: we know currRing==strat->tailRing |
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79 | // no exp-bound checking needed |
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80 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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81 | if (PR->bucket!=NULL) nc_kBucketPolyRed(PR->bucket, p2,coef); |
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82 | else |
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83 | { |
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84 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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85 | assume(_p != NULL); |
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86 | nc_PolyPolyRed(_p, p2,coef, currRing); |
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87 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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88 | PR->pLength=0; // usually not used, GetpLength re-computes it if needed |
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89 | } |
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90 | return 0; |
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91 | } |
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92 | #endif |
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93 | |
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94 | if (t2==NULL) // Divisor is just one term, therefore it will |
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95 | { // just cancel the leading term |
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96 | PR->LmDeleteAndIter(); |
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97 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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98 | return 0; |
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99 | } |
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100 | |
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101 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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102 | |
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103 | if (tailRing != currRing) |
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104 | { |
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105 | // check that reduction does not violate exp bound |
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106 | while (PW->max != NULL && !p_LmExpVectorAddIsOk(lm, PW->max, tailRing)) |
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107 | { |
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108 | // undo changes of lm |
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109 | p_ExpVectorAdd(lm, p2, tailRing); |
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110 | if (strat == NULL) return 2; |
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111 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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112 | tailRing = strat->tailRing; |
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113 | p1 = PR->GetLmTailRing(); |
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114 | p2 = PW->GetLmTailRing(); |
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115 | t2 = pNext(p2); |
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116 | lm = p1; |
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117 | p_ExpVectorSub(lm, p2, tailRing); |
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118 | ret = 1; |
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119 | } |
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120 | } |
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121 | |
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122 | // take care of coef buisness |
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123 | if (! n_IsOne(pGetCoeff(p2), tailRing)) |
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124 | { |
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125 | number bn = pGetCoeff(lm); |
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126 | number an = pGetCoeff(p2); |
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127 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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128 | p_SetCoeff(lm, bn, tailRing); |
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129 | if ((ct == 0) || (ct == 2)) |
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130 | PR->Tail_Mult_nn(an); |
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131 | if (coef != NULL) *coef = an; |
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132 | else n_Delete(&an, tailRing); |
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133 | } |
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134 | else |
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135 | { |
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136 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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137 | } |
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138 | |
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139 | |
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140 | // and finally, |
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141 | PR->Tail_Minus_mm_Mult_qq(lm, t2, PW->GetpLength() - 1, spNoether); |
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142 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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143 | PR->LmDeleteAndIter(); |
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144 | |
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145 | // the following is commented out: shrinking |
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146 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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147 | if ( (currRing->isLPring) && (!strat->homog) ) |
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148 | { |
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149 | // assume? h->p in currRing |
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150 | PR->GetP(); |
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151 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
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152 | PR->Clear(); // does the right things |
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153 | PR->p = qq; |
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154 | PR->t_p = NULL; |
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155 | PR->SetShortExpVector(); |
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156 | } |
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157 | #endif |
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158 | |
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159 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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160 | if (TEST_OPT_DEBUG) |
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161 | { |
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162 | Print(" to: "); PR->wrp(); Print("\n"); |
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163 | //printf("\nt^%i ", PR->ecart);pWrite(pHead(PR->p)); |
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164 | } |
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165 | #endif |
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166 | return ret; |
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167 | } |
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168 | |
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169 | /*************************************************************** |
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170 | * |
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171 | * Reduces PR with PW |
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172 | * Assumes PR != NULL, PW != NULL, Lm(PW) divides Lm(PR) |
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173 | * |
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174 | ***************************************************************/ |
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175 | int ksReducePolySig(LObject* PR, |
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176 | TObject* PW, |
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177 | long /*idx*/, |
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178 | poly spNoether, |
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179 | number *coef, |
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180 | kStrategy strat) |
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181 | { |
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182 | #ifdef KDEBUG |
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183 | red_count++; |
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184 | #ifdef TEST_OPT_DEBUG_RED |
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185 | if (TEST_OPT_DEBUG) |
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186 | { |
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187 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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188 | PW->wrp(); |
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189 | } |
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190 | #endif |
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191 | #endif |
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192 | int ret = 0; |
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193 | ring tailRing = PR->tailRing; |
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194 | kTest_L(PR); |
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195 | kTest_T(PW); |
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196 | |
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197 | // signature-based stuff: |
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198 | // checking for sig-safeness first |
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199 | // NOTE: This has to be done in the current ring |
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200 | // |
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201 | /********************************************** |
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202 | * |
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203 | * TODO: |
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204 | * -------------------------------------------- |
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205 | * if strat->sbaOrder == 1 |
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206 | * Since we are subdividing lower index and |
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207 | * current index reductions it is enough to |
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208 | * look at the polynomial part of the signature |
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209 | * for a check. This should speed-up checking |
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210 | * a lot! |
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211 | * if !strat->sbaOrder == 0 |
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212 | * We are not subdividing lower and current index |
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213 | * due to the fact that we are using the induced |
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214 | * Schreyer order |
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215 | * |
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216 | * nevertheless, this different behaviour is |
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217 | * taken care of by is_sigsafe |
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218 | * => one reduction procedure can be used for |
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219 | * both, the incremental and the non-incremental |
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220 | * attempt! |
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221 | * -------------------------------------------- |
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222 | * |
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223 | *********************************************/ |
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224 | //printf("COMPARE IDX: %ld -- %ld\n",idx,strat->currIdx); |
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225 | if (!PW->is_sigsafe) |
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226 | { |
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227 | poly sigMult = pCopy(PW->sig); // copy signature of reducer |
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228 | //#if 1 |
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229 | #ifdef DEBUGF5 |
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230 | printf("IN KSREDUCEPOLYSIG: \n"); |
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231 | pWrite(pHead(f1)); |
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232 | pWrite(pHead(f2)); |
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233 | pWrite(sigMult); |
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234 | printf("--------------\n"); |
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235 | #endif |
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236 | p_ExpVectorAddSub(sigMult,PR->GetLmCurrRing(),PW->GetLmCurrRing(),currRing); |
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237 | //#if 1 |
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238 | #ifdef DEBUGF5 |
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239 | printf("------------------- IN KSREDUCEPOLYSIG: --------------------\n"); |
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240 | pWrite(pHead(f1)); |
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241 | pWrite(pHead(f2)); |
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242 | pWrite(sigMult); |
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243 | pWrite(PR->sig); |
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244 | printf("--------------\n"); |
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245 | #endif |
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246 | int sigSafe = p_LmCmp(PR->sig,sigMult,currRing); |
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247 | // now we can delete the copied polynomial data used for checking for |
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248 | // sig-safeness of the reduction step |
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249 | //#if 1 |
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250 | #ifdef DEBUGF5 |
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251 | printf("%d -- %d sig\n",sigSafe,PW->is_sigsafe); |
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252 | |
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253 | #endif |
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254 | //pDelete(&f1); |
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255 | pDelete(&sigMult); |
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256 | // go on with the computations only if the signature of p2 is greater than the |
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257 | // signature of fm*p1 |
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258 | if(sigSafe != 1) |
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259 | { |
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260 | PR->is_redundant = TRUE; |
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261 | return 3; |
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262 | } |
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263 | //PW->is_sigsafe = TRUE; |
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264 | } |
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265 | PR->is_redundant = FALSE; |
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266 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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267 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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268 | poly t2 = pNext(p2), lm = p1; // t2 = p2 - LT(p2); really compute P = LC(p2)*p1 - LT(p1)/LM(p2)*p2 |
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269 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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270 | p_CheckPolyRing(p1, tailRing); |
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271 | p_CheckPolyRing(p2, tailRing); |
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272 | |
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273 | pAssume1(p2 != NULL && p1 != NULL && |
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274 | p_DivisibleBy(p2, p1, tailRing)); |
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275 | |
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276 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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277 | (p_GetComp(p2, tailRing) == 0 && |
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278 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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279 | |
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280 | #ifdef HAVE_PLURAL |
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281 | if (rIsPluralRing(currRing)) |
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282 | { |
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283 | // for the time being: we know currRing==strat->tailRing |
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284 | // no exp-bound checking needed |
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285 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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286 | if (PR->bucket!=NULL) nc_kBucketPolyRed(PR->bucket, p2,coef); |
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287 | else |
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288 | { |
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289 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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290 | assume(_p != NULL); |
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291 | nc_PolyPolyRed(_p, p2, coef, currRing); |
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292 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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293 | PR->pLength=0; // usaully not used, GetpLength re-comoutes it if needed |
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294 | } |
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295 | return 0; |
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296 | } |
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297 | #endif |
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298 | |
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299 | if (t2==NULL) // Divisor is just one term, therefore it will |
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300 | { // just cancel the leading term |
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301 | PR->LmDeleteAndIter(); |
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302 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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303 | return 0; |
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304 | } |
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305 | |
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306 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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307 | |
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308 | if (tailRing != currRing) |
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309 | { |
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310 | // check that reduction does not violate exp bound |
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311 | while (PW->max != NULL && !p_LmExpVectorAddIsOk(lm, PW->max, tailRing)) |
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312 | { |
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313 | // undo changes of lm |
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314 | p_ExpVectorAdd(lm, p2, tailRing); |
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315 | if (strat == NULL) return 2; |
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316 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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317 | tailRing = strat->tailRing; |
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318 | p1 = PR->GetLmTailRing(); |
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319 | p2 = PW->GetLmTailRing(); |
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320 | t2 = pNext(p2); |
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321 | lm = p1; |
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322 | p_ExpVectorSub(lm, p2, tailRing); |
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323 | ret = 1; |
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324 | } |
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325 | } |
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326 | |
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327 | // take care of coef buisness |
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328 | if (! n_IsOne(pGetCoeff(p2), tailRing)) |
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329 | { |
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330 | number bn = pGetCoeff(lm); |
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331 | number an = pGetCoeff(p2); |
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332 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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333 | p_SetCoeff(lm, bn, tailRing); |
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334 | if ((ct == 0) || (ct == 2)) |
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335 | PR->Tail_Mult_nn(an); |
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336 | if (coef != NULL) *coef = an; |
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337 | else n_Delete(&an, tailRing); |
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338 | } |
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339 | else |
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340 | { |
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341 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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342 | } |
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343 | |
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344 | |
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345 | // and finally, |
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346 | PR->Tail_Minus_mm_Mult_qq(lm, t2, PW->GetpLength() - 1, spNoether); |
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347 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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348 | PR->LmDeleteAndIter(); |
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349 | |
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350 | // the following is commented out: shrinking |
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351 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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352 | if ( (currRing->isLPring) && (!strat->homog) ) |
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353 | { |
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354 | // assume? h->p in currRing |
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355 | PR->GetP(); |
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356 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
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357 | PR->Clear(); // does the right things |
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358 | PR->p = qq; |
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359 | PR->t_p = NULL; |
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360 | PR->SetShortExpVector(); |
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361 | } |
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362 | #endif |
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363 | |
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364 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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365 | if (TEST_OPT_DEBUG) |
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366 | { |
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367 | Print(" to: "); PR->wrp(); Print("\n"); |
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368 | } |
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369 | #endif |
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370 | return ret; |
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371 | } |
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372 | |
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373 | /*************************************************************** |
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374 | * |
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375 | * Creates S-Poly of p1 and p2 |
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376 | * |
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377 | * |
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378 | ***************************************************************/ |
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379 | void ksCreateSpoly(LObject* Pair, poly spNoether, |
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380 | int use_buckets, ring tailRing, |
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381 | poly m1, poly m2, TObject** R) |
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382 | { |
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383 | #ifdef KDEBUG |
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384 | create_count++; |
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385 | #endif |
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386 | kTest_L(Pair); |
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387 | poly p1 = Pair->p1; |
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388 | poly p2 = Pair->p2; |
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389 | Pair->tailRing = tailRing; |
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390 | |
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391 | assume(p1 != NULL); |
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392 | assume(p2 != NULL); |
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393 | assume(tailRing != NULL); |
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394 | |
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395 | poly a1 = pNext(p1), a2 = pNext(p2); |
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396 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
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397 | int co=0/*, ct = ksCheckCoeff(&lc1, &lc2, currRing->cf)*/; // gcd and zero divisors |
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398 | (void) ksCheckCoeff(&lc1, &lc2, currRing->cf); |
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399 | |
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400 | int l1=0, l2=0; |
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401 | |
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402 | if (p_GetComp(p1, currRing)!=p_GetComp(p2, currRing)) |
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403 | { |
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404 | if (p_GetComp(p1, currRing)==0) |
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405 | { |
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406 | co=1; |
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407 | p_SetCompP(p1,p_GetComp(p2, currRing), currRing, tailRing); |
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408 | } |
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409 | else |
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410 | { |
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411 | co=2; |
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412 | p_SetCompP(p2, p_GetComp(p1, currRing), currRing, tailRing); |
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413 | } |
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414 | } |
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415 | |
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416 | // get m1 = LCM(LM(p1), LM(p2))/LM(p1) |
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417 | // m2 = LCM(LM(p1), LM(p2))/LM(p2) |
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418 | if (m1 == NULL) |
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419 | k_GetLeadTerms(p1, p2, currRing, m1, m2, tailRing); |
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420 | |
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421 | pSetCoeff0(m1, lc2); |
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422 | pSetCoeff0(m2, lc1); // and now, m1 * LT(p1) == m2 * LT(p2) |
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423 | |
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424 | if (R != NULL) |
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425 | { |
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426 | if (Pair->i_r1 == -1) |
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427 | { |
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428 | l1 = pLength(p1) - 1; |
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429 | } |
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430 | else |
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431 | { |
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432 | l1 = (R[Pair->i_r1])->GetpLength() - 1; |
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433 | } |
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434 | if ((Pair->i_r2 == -1)||(R[Pair->i_r2]==NULL)) |
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435 | { |
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436 | l2 = pLength(p2) - 1; |
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437 | } |
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438 | else |
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439 | { |
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440 | l2 = (R[Pair->i_r2])->GetpLength() - 1; |
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441 | } |
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442 | } |
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443 | |
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444 | // get m2 * a2 |
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445 | if (spNoether != NULL) |
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446 | { |
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447 | l2 = -1; |
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448 | a2 = tailRing->p_Procs->pp_Mult_mm_Noether(a2, m2, spNoether, l2, tailRing); |
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449 | assume(l2 == pLength(a2)); |
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450 | } |
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451 | else |
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452 | a2 = tailRing->p_Procs->pp_Mult_mm(a2, m2, tailRing); |
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453 | #ifdef HAVE_RINGS |
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454 | if (!(rField_is_Domain(currRing))) l2 = pLength(a2); |
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455 | #endif |
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456 | |
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457 | Pair->SetLmTail(m2, a2, l2, use_buckets, tailRing); |
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458 | |
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459 | // get m2*a2 - m1*a1 |
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460 | Pair->Tail_Minus_mm_Mult_qq(m1, a1, l1, spNoether); |
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461 | |
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462 | // Clean-up time |
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463 | Pair->LmDeleteAndIter(); |
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464 | p_LmDelete(m1, tailRing); |
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465 | |
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466 | if (co != 0) |
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467 | { |
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468 | if (co==1) |
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469 | { |
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470 | p_SetCompP(p1,0, currRing, tailRing); |
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471 | } |
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472 | else |
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473 | { |
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474 | p_SetCompP(p2,0, currRing, tailRing); |
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475 | } |
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476 | } |
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477 | |
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478 | // the following is commented out: shrinking |
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479 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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480 | if (currRing->isLPring) |
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481 | { |
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482 | // assume? h->p in currRing |
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483 | Pair->GetP(); |
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484 | poly qq = p_Shrink(Pair->p, currRing->isLPring, currRing); |
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485 | Pair->Clear(); // does the right things |
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486 | Pair->p = qq; |
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487 | Pair->t_p = NULL; |
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488 | Pair->SetShortExpVector(); |
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489 | } |
---|
490 | #endif |
---|
491 | |
---|
492 | } |
---|
493 | |
---|
494 | int ksReducePolyTail(LObject* PR, TObject* PW, poly Current, poly spNoether) |
---|
495 | { |
---|
496 | BOOLEAN ret; |
---|
497 | number coef; |
---|
498 | poly Lp = PR->GetLmCurrRing(); |
---|
499 | poly Save = PW->GetLmCurrRing(); |
---|
500 | |
---|
501 | kTest_L(PR); |
---|
502 | kTest_T(PW); |
---|
503 | pAssume(pIsMonomOf(Lp, Current)); |
---|
504 | |
---|
505 | assume(Lp != NULL && Current != NULL && pNext(Current) != NULL); |
---|
506 | assume(PR->bucket == NULL); |
---|
507 | |
---|
508 | LObject Red(pNext(Current), PR->tailRing); |
---|
509 | TObject With(PW, Lp == Save); |
---|
510 | |
---|
511 | pAssume(!pHaveCommonMonoms(Red.p, With.p)); |
---|
512 | ret = ksReducePoly(&Red, &With, spNoether, &coef); |
---|
513 | |
---|
514 | if (!ret) |
---|
515 | { |
---|
516 | if (! n_IsOne(coef, currRing)) |
---|
517 | { |
---|
518 | pNext(Current) = NULL; |
---|
519 | if (Current == PR->p && PR->t_p != NULL) |
---|
520 | pNext(PR->t_p) = NULL; |
---|
521 | PR->Mult_nn(coef); |
---|
522 | } |
---|
523 | |
---|
524 | n_Delete(&coef, currRing); |
---|
525 | pNext(Current) = Red.GetLmTailRing(); |
---|
526 | if (Current == PR->p && PR->t_p != NULL) |
---|
527 | pNext(PR->t_p) = pNext(Current); |
---|
528 | } |
---|
529 | |
---|
530 | if (Lp == Save) |
---|
531 | With.Delete(); |
---|
532 | |
---|
533 | // the following is commented out: shrinking |
---|
534 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
---|
535 | if (currRing->isLPring) |
---|
536 | { |
---|
537 | // assume? h->p in currRing |
---|
538 | PR->GetP(); |
---|
539 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
---|
540 | PR->Clear(); // does the right things |
---|
541 | PR->p = qq; |
---|
542 | PR->t_p = NULL; |
---|
543 | PR->SetShortExpVector(); |
---|
544 | } |
---|
545 | #endif |
---|
546 | |
---|
547 | return ret; |
---|
548 | } |
---|
549 | |
---|
550 | /*************************************************************** |
---|
551 | * |
---|
552 | * Auxillary Routines |
---|
553 | * |
---|
554 | * |
---|
555 | ***************************************************************/ |
---|
556 | |
---|
557 | /*2 |
---|
558 | * creates the leading term of the S-polynomial of p1 and p2 |
---|
559 | * do not destroy p1 and p2 |
---|
560 | * remarks: |
---|
561 | * 1. the coefficient is 0 (nNew) |
---|
562 | * 1. a) in the case of coefficient ring, the coefficient is calculated |
---|
563 | * 2. pNext is undefined |
---|
564 | */ |
---|
565 | //static void bbb() { int i=0; } |
---|
566 | poly ksCreateShortSpoly(poly p1, poly p2, ring tailRing) |
---|
567 | { |
---|
568 | poly a1 = pNext(p1), a2 = pNext(p2); |
---|
569 | long c1=p_GetComp(p1, currRing),c2=p_GetComp(p2, currRing); |
---|
570 | long c; |
---|
571 | poly m1,m2; |
---|
572 | number t1 = NULL,t2 = NULL; |
---|
573 | int cm,i; |
---|
574 | BOOLEAN equal; |
---|
575 | |
---|
576 | #ifdef HAVE_RINGS |
---|
577 | BOOLEAN is_Ring=rField_is_Ring(currRing); |
---|
578 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
---|
579 | if (is_Ring) |
---|
580 | { |
---|
581 | ksCheckCoeff(&lc1, &lc2, currRing->cf); // gcd and zero divisors |
---|
582 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
---|
583 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
---|
584 | while (a1 != NULL && nIsZero(t2)) |
---|
585 | { |
---|
586 | pIter(a1); |
---|
587 | nDelete(&t2); |
---|
588 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
---|
589 | } |
---|
590 | while (a2 != NULL && nIsZero(t1)) |
---|
591 | { |
---|
592 | pIter(a2); |
---|
593 | nDelete(&t1); |
---|
594 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
---|
595 | } |
---|
596 | } |
---|
597 | #endif |
---|
598 | |
---|
599 | if (a1==NULL) |
---|
600 | { |
---|
601 | if(a2!=NULL) |
---|
602 | { |
---|
603 | m2=p_Init(currRing); |
---|
604 | x2: |
---|
605 | for (i = (currRing->N); i; i--) |
---|
606 | { |
---|
607 | c = p_GetExpDiff(p1, p2,i, currRing); |
---|
608 | if (c>0) |
---|
609 | { |
---|
610 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)),currRing); |
---|
611 | } |
---|
612 | else |
---|
613 | { |
---|
614 | p_SetExp(m2,i,p_GetExp(a2,i,tailRing),currRing); |
---|
615 | } |
---|
616 | } |
---|
617 | if ((c1==c2)||(c2!=0)) |
---|
618 | { |
---|
619 | p_SetComp(m2,p_GetComp(a2,tailRing), currRing); |
---|
620 | } |
---|
621 | else |
---|
622 | { |
---|
623 | p_SetComp(m2,c1,currRing); |
---|
624 | } |
---|
625 | p_Setm(m2, currRing); |
---|
626 | #ifdef HAVE_RINGS |
---|
627 | if (is_Ring) |
---|
628 | { |
---|
629 | nDelete(&lc1); |
---|
630 | nDelete(&lc2); |
---|
631 | nDelete(&t2); |
---|
632 | pSetCoeff0(m2, t1); |
---|
633 | } |
---|
634 | else |
---|
635 | #endif |
---|
636 | nNew(&(pGetCoeff(m2))); |
---|
637 | return m2; |
---|
638 | } |
---|
639 | else |
---|
640 | { |
---|
641 | #ifdef HAVE_RINGS |
---|
642 | if (is_Ring) |
---|
643 | { |
---|
644 | nDelete(&lc1); |
---|
645 | nDelete(&lc2); |
---|
646 | nDelete(&t1); |
---|
647 | nDelete(&t2); |
---|
648 | } |
---|
649 | #endif |
---|
650 | return NULL; |
---|
651 | } |
---|
652 | } |
---|
653 | if (a2==NULL) |
---|
654 | { |
---|
655 | m1=p_Init(currRing); |
---|
656 | x1: |
---|
657 | for (i = (currRing->N); i; i--) |
---|
658 | { |
---|
659 | c = p_GetExpDiff(p2, p1,i,currRing); |
---|
660 | if (c>0) |
---|
661 | { |
---|
662 | p_SetExp(m1,i,(c+p_GetExp(a1,i, tailRing)),currRing); |
---|
663 | } |
---|
664 | else |
---|
665 | { |
---|
666 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
---|
667 | } |
---|
668 | } |
---|
669 | if ((c1==c2)||(c1!=0)) |
---|
670 | { |
---|
671 | p_SetComp(m1,p_GetComp(a1,tailRing),currRing); |
---|
672 | } |
---|
673 | else |
---|
674 | { |
---|
675 | p_SetComp(m1,c2,currRing); |
---|
676 | } |
---|
677 | p_Setm(m1, currRing); |
---|
678 | #ifdef HAVE_RINGS |
---|
679 | if (is_Ring) |
---|
680 | { |
---|
681 | pSetCoeff0(m1, t2); |
---|
682 | nDelete(&lc1); |
---|
683 | nDelete(&lc2); |
---|
684 | nDelete(&t1); |
---|
685 | } |
---|
686 | else |
---|
687 | #endif |
---|
688 | nNew(&(pGetCoeff(m1))); |
---|
689 | return m1; |
---|
690 | } |
---|
691 | m1 = p_Init(currRing); |
---|
692 | m2 = p_Init(currRing); |
---|
693 | loop |
---|
694 | { |
---|
695 | for (i = (currRing->N); i; i--) |
---|
696 | { |
---|
697 | c = p_GetExpDiff(p1, p2,i,currRing); |
---|
698 | if (c > 0) |
---|
699 | { |
---|
700 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)), currRing); |
---|
701 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
---|
702 | } |
---|
703 | else |
---|
704 | { |
---|
705 | p_SetExp(m1,i,(p_GetExp(a1,i,tailRing)-c), currRing); |
---|
706 | p_SetExp(m2,i,p_GetExp(a2,i, tailRing), currRing); |
---|
707 | } |
---|
708 | } |
---|
709 | if(c1==c2) |
---|
710 | { |
---|
711 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
712 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
713 | } |
---|
714 | else |
---|
715 | { |
---|
716 | if(c1!=0) |
---|
717 | { |
---|
718 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
719 | p_SetComp(m2,c1, currRing); |
---|
720 | } |
---|
721 | else |
---|
722 | { |
---|
723 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
724 | p_SetComp(m1,c2, currRing); |
---|
725 | } |
---|
726 | } |
---|
727 | p_Setm(m1,currRing); |
---|
728 | p_Setm(m2,currRing); |
---|
729 | cm = p_LmCmp(m1, m2,currRing); |
---|
730 | if (cm!=0) |
---|
731 | { |
---|
732 | if(cm==1) |
---|
733 | { |
---|
734 | p_LmFree(m2,currRing); |
---|
735 | #ifdef HAVE_RINGS |
---|
736 | if (is_Ring) |
---|
737 | { |
---|
738 | pSetCoeff0(m1, t2); |
---|
739 | nDelete(&lc1); |
---|
740 | nDelete(&lc2); |
---|
741 | nDelete(&t1); |
---|
742 | } |
---|
743 | else |
---|
744 | #endif |
---|
745 | nNew(&(pGetCoeff(m1))); |
---|
746 | return m1; |
---|
747 | } |
---|
748 | else |
---|
749 | { |
---|
750 | p_LmFree(m1,currRing); |
---|
751 | #ifdef HAVE_RINGS |
---|
752 | if (is_Ring) |
---|
753 | { |
---|
754 | pSetCoeff0(m2, t1); |
---|
755 | nDelete(&lc1); |
---|
756 | nDelete(&lc2); |
---|
757 | nDelete(&t2); |
---|
758 | } |
---|
759 | else |
---|
760 | #endif |
---|
761 | nNew(&(pGetCoeff(m2))); |
---|
762 | return m2; |
---|
763 | } |
---|
764 | } |
---|
765 | #ifdef HAVE_RINGS |
---|
766 | if (is_Ring) |
---|
767 | { |
---|
768 | equal = nEqual(t1,t2); |
---|
769 | } |
---|
770 | else |
---|
771 | #endif |
---|
772 | { |
---|
773 | t1 = nMult(pGetCoeff(a2),pGetCoeff(p1)); |
---|
774 | t2 = nMult(pGetCoeff(a1),pGetCoeff(p2)); |
---|
775 | equal = nEqual(t1,t2); |
---|
776 | nDelete(&t2); |
---|
777 | nDelete(&t1); |
---|
778 | } |
---|
779 | if (!equal) |
---|
780 | { |
---|
781 | p_LmFree(m2,currRing); |
---|
782 | #ifdef HAVE_RINGS |
---|
783 | if (is_Ring) |
---|
784 | { |
---|
785 | pSetCoeff0(m1, nSub(t1, t2)); |
---|
786 | nDelete(&lc1); |
---|
787 | nDelete(&lc2); |
---|
788 | nDelete(&t1); |
---|
789 | nDelete(&t2); |
---|
790 | } |
---|
791 | else |
---|
792 | #endif |
---|
793 | nNew(&(pGetCoeff(m1))); |
---|
794 | return m1; |
---|
795 | } |
---|
796 | pIter(a1); |
---|
797 | pIter(a2); |
---|
798 | #ifdef HAVE_RINGS |
---|
799 | if (is_Ring) |
---|
800 | { |
---|
801 | if (a2 != NULL) |
---|
802 | { |
---|
803 | nDelete(&t1); |
---|
804 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
805 | } |
---|
806 | if (a1 != NULL) |
---|
807 | { |
---|
808 | nDelete(&t2); |
---|
809 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
810 | } |
---|
811 | while ((a1 != NULL) && nIsZero(t2)) |
---|
812 | { |
---|
813 | pIter(a1); |
---|
814 | if (a1 != NULL) |
---|
815 | { |
---|
816 | nDelete(&t2); |
---|
817 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
818 | } |
---|
819 | } |
---|
820 | while ((a2 != NULL) && nIsZero(t1)) |
---|
821 | { |
---|
822 | pIter(a2); |
---|
823 | if (a2 != NULL) |
---|
824 | { |
---|
825 | nDelete(&t1); |
---|
826 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
827 | } |
---|
828 | } |
---|
829 | } |
---|
830 | #endif |
---|
831 | if (a2==NULL) |
---|
832 | { |
---|
833 | p_LmFree(m2,currRing); |
---|
834 | if (a1==NULL) |
---|
835 | { |
---|
836 | #ifdef HAVE_RINGS |
---|
837 | if (is_Ring) |
---|
838 | { |
---|
839 | nDelete(&lc1); |
---|
840 | nDelete(&lc2); |
---|
841 | nDelete(&t1); |
---|
842 | nDelete(&t2); |
---|
843 | } |
---|
844 | #endif |
---|
845 | p_LmFree(m1,currRing); |
---|
846 | return NULL; |
---|
847 | } |
---|
848 | goto x1; |
---|
849 | } |
---|
850 | if (a1==NULL) |
---|
851 | { |
---|
852 | p_LmFree(m1,currRing); |
---|
853 | goto x2; |
---|
854 | } |
---|
855 | } |
---|
856 | } |
---|