1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT - Routines for Spoly creation and reductions |
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7 | */ |
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8 | |
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9 | // #define PDEBUG 2 |
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10 | #include "mod2.h" |
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11 | #include "kutil.h" |
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12 | #include "numbers.h" |
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13 | #include "p_polys.h" |
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14 | #include "p_Procs.h" |
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15 | #include "gring.h" |
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16 | #ifdef HAVE_RINGS |
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17 | #include "polys.h" |
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18 | #endif |
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19 | |
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20 | #ifdef KDEBUG |
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21 | int red_count = 0; |
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22 | int create_count = 0; |
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23 | // define this if reductions are reported on TEST_OPT_DEBUG |
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24 | // #define TEST_OPT_DEBUG_RED |
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25 | #endif |
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26 | |
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27 | /*************************************************************** |
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28 | * |
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29 | * Reduces PR with PW |
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30 | * Assumes PR != NULL, PW != NULL, Lm(PW) divides Lm(PR) |
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31 | * |
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32 | ***************************************************************/ |
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33 | int ksReducePoly(LObject* PR, |
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34 | TObject* PW, |
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35 | poly spNoether, |
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36 | number *coef, |
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37 | kStrategy strat) |
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38 | { |
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39 | #ifdef KDEBUG |
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40 | red_count++; |
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41 | #ifdef TEST_OPT_DEBUG_RED |
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42 | if (TEST_OPT_DEBUG) |
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43 | { |
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44 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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45 | PW->wrp(); |
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46 | } |
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47 | #endif |
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48 | #endif |
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49 | int ret = 0; |
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50 | ring tailRing = PR->tailRing; |
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51 | kTest_L(PR); |
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52 | kTest_T(PW); |
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53 | |
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54 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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55 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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56 | 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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57 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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58 | p_CheckPolyRing(p1, tailRing); |
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59 | p_CheckPolyRing(p2, tailRing); |
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60 | |
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61 | pAssume1(p2 != NULL && p1 != NULL && |
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62 | p_DivisibleBy(p2, p1, tailRing)); |
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63 | |
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64 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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65 | (p_GetComp(p2, tailRing) == 0 && |
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66 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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67 | |
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68 | #ifdef HAVE_PLURAL |
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69 | if (rIsPluralRing(currRing)) |
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70 | { |
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71 | // for the time being: we know currRing==strat->tailRing |
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72 | // no exp-bound checking needed |
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73 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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74 | number c; |
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75 | if (PR->bucket!=NULL) nc_kBucketPolyRed(PR->bucket, p2,&c); |
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76 | else |
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77 | { |
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78 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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79 | assume(_p != NULL); |
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80 | nc_PolyPolyRed(_p, p2,&c); |
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81 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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82 | PR->pLength=pLength(_p); |
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83 | } |
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84 | if (coef!=NULL) *coef=c; |
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85 | else nDelete(&c); |
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86 | return 0; |
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87 | } |
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88 | #endif |
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89 | |
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90 | if (t2==NULL) // Divisor is just one term, therefore it will |
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91 | { // just cancel the leading term |
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92 | PR->LmDeleteAndIter(); |
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93 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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94 | return 0; |
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95 | } |
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96 | |
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97 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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98 | |
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99 | if (tailRing != currRing) |
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100 | { |
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101 | // check that reduction does not violate exp bound |
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102 | while (PW->max != NULL && !p_LmExpVectorAddIsOk(lm, PW->max, tailRing)) |
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103 | { |
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104 | // undo changes of lm |
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105 | p_ExpVectorAdd(lm, p2, tailRing); |
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106 | if (strat == NULL) return 2; |
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107 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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108 | tailRing = strat->tailRing; |
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109 | p1 = PR->GetLmTailRing(); |
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110 | p2 = PW->GetLmTailRing(); |
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111 | t2 = pNext(p2); |
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112 | lm = p1; |
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113 | p_ExpVectorSub(lm, p2, tailRing); |
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114 | ret = 1; |
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115 | } |
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116 | } |
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117 | |
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118 | // take care of coef buisness |
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119 | if (! n_IsOne(pGetCoeff(p2), tailRing)) |
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120 | { |
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121 | number bn = pGetCoeff(lm); |
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122 | number an = pGetCoeff(p2); |
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123 | int ct = ksCheckCoeff(&an, &bn); // Calculate special LC |
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124 | p_SetCoeff(lm, bn, tailRing); |
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125 | if ((ct == 0) || (ct == 2)) |
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126 | PR->Tail_Mult_nn(an); |
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127 | if (coef != NULL) *coef = an; |
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128 | else n_Delete(&an, tailRing); |
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129 | } |
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130 | else |
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131 | { |
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132 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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133 | } |
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134 | |
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135 | |
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136 | // and finally, |
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137 | PR->Tail_Minus_mm_Mult_qq(lm, t2, PW->GetpLength() - 1, spNoether); |
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138 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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139 | PR->LmDeleteAndIter(); |
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140 | |
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141 | // the following is commented out: shrinking |
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142 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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143 | if ( (currRing->isLPring) && (!strat->homog) ) |
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144 | { |
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145 | // assume? h->p in currRing |
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146 | PR->GetP(); |
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147 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
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148 | PR->Clear(); // does the right things |
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149 | PR->p = qq; |
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150 | PR->t_p = NULL; |
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151 | PR->SetShortExpVector(); |
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152 | } |
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153 | #endif |
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154 | |
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155 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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156 | if (TEST_OPT_DEBUG) |
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157 | { |
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158 | Print(" to: "); PR->wrp(); Print("\n"); |
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159 | } |
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160 | #endif |
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161 | return ret; |
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162 | } |
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163 | |
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164 | /*************************************************************** |
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165 | * |
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166 | * Creates S-Poly of p1 and p2 |
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167 | * |
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168 | * |
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169 | ***************************************************************/ |
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170 | void ksCreateSpoly(LObject* Pair, poly spNoether, |
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171 | int use_buckets, ring tailRing, |
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172 | poly m1, poly m2, TObject** R) |
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173 | { |
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174 | #ifdef KDEBUG |
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175 | create_count++; |
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176 | #endif |
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177 | kTest_L(Pair); |
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178 | poly p1 = Pair->p1; |
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179 | poly p2 = Pair->p2; |
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180 | poly last; |
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181 | Pair->tailRing = tailRing; |
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182 | |
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183 | assume(p1 != NULL); |
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184 | assume(p2 != NULL); |
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185 | assume(tailRing != NULL); |
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186 | |
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187 | poly a1 = pNext(p1), a2 = pNext(p2); |
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188 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
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189 | int co=0, ct = ksCheckCoeff(&lc1, &lc2); // gcd and zero divisors |
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190 | |
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191 | int l1=0, l2=0; |
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192 | |
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193 | if (p_GetComp(p1, currRing)!=p_GetComp(p2, currRing)) |
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194 | { |
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195 | if (p_GetComp(p1, currRing)==0) |
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196 | { |
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197 | co=1; |
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198 | p_SetCompP(p1,p_GetComp(p2, currRing), currRing, tailRing); |
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199 | } |
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200 | else |
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201 | { |
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202 | co=2; |
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203 | p_SetCompP(p2, p_GetComp(p1, currRing), currRing, tailRing); |
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204 | } |
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205 | } |
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206 | |
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207 | // get m1 = LCM(LM(p1), LM(p2))/LM(p1) |
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208 | // m2 = LCM(LM(p1), LM(p2))/LM(p2) |
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209 | if (m1 == NULL) |
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210 | k_GetLeadTerms(p1, p2, currRing, m1, m2, tailRing); |
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211 | |
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212 | pSetCoeff0(m1, lc2); |
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213 | pSetCoeff0(m2, lc1); // and now, m1 * LT(p1) == m2 * LT(p2) |
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214 | |
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215 | if (R != NULL) |
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216 | { |
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217 | if (Pair->i_r1 == -1) |
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218 | { |
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219 | l1 = pLength(p1) - 1; |
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220 | } |
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221 | else |
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222 | { |
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223 | l1 = (R[Pair->i_r1])->GetpLength() - 1; |
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224 | } |
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225 | if (Pair->i_r2 == -1) |
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226 | { |
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227 | l2 = pLength(p2) - 1; |
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228 | } |
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229 | else |
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230 | { |
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231 | l2 = (R[Pair->i_r2])->GetpLength() - 1; |
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232 | } |
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233 | } |
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234 | |
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235 | // get m2 * a2 |
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236 | if (spNoether != NULL) |
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237 | { |
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238 | l2 = -1; |
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239 | a2 = tailRing->p_Procs->pp_Mult_mm_Noether(a2, m2, spNoether, l2, tailRing,last); |
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240 | assume(l2 == pLength(a2)); |
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241 | } |
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242 | else |
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243 | a2 = tailRing->p_Procs->pp_Mult_mm(a2, m2, tailRing,last); |
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244 | #ifdef HAVE_RINGS |
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245 | if (!(rField_is_Domain(currRing))) l2 = pLength(a2); |
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246 | #endif |
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247 | |
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248 | Pair->SetLmTail(m2, a2, l2, use_buckets, tailRing, last); |
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249 | |
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250 | // get m2*a2 - m1*a1 |
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251 | Pair->Tail_Minus_mm_Mult_qq(m1, a1, l1, spNoether); |
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252 | |
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253 | // Clean-up time |
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254 | Pair->LmDeleteAndIter(); |
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255 | p_LmDelete(m1, tailRing); |
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256 | |
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257 | if (co != 0) |
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258 | { |
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259 | if (co==1) |
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260 | { |
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261 | p_SetCompP(p1,0, currRing, tailRing); |
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262 | } |
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263 | else |
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264 | { |
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265 | p_SetCompP(p2,0, currRing, tailRing); |
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266 | } |
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267 | } |
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268 | |
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269 | // the following is commented out: shrinking |
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270 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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271 | if (currRing->isLPring) |
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272 | { |
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273 | // assume? h->p in currRing |
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274 | Pair->GetP(); |
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275 | poly qq = p_Shrink(Pair->p, currRing->isLPring, currRing); |
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276 | Pair->Clear(); // does the right things |
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277 | Pair->p = qq; |
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278 | Pair->t_p = NULL; |
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279 | Pair->SetShortExpVector(); |
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280 | } |
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281 | #endif |
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282 | |
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283 | } |
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284 | |
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285 | int ksReducePolyTail(LObject* PR, TObject* PW, poly Current, poly spNoether) |
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286 | { |
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287 | BOOLEAN ret; |
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288 | number coef; |
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289 | poly Lp = PR->GetLmCurrRing(); |
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290 | poly Save = PW->GetLmCurrRing(); |
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291 | |
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292 | kTest_L(PR); |
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293 | kTest_T(PW); |
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294 | pAssume(pIsMonomOf(Lp, Current)); |
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295 | |
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296 | assume(Lp != NULL && Current != NULL && pNext(Current) != NULL); |
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297 | assume(PR->bucket == NULL); |
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298 | |
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299 | LObject Red(pNext(Current), PR->tailRing); |
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300 | TObject With(PW, Lp == Save); |
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301 | |
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302 | pAssume(!pHaveCommonMonoms(Red.p, With.p)); |
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303 | ret = ksReducePoly(&Red, &With, spNoether, &coef); |
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304 | |
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305 | if (!ret) |
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306 | { |
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307 | if (! n_IsOne(coef, currRing)) |
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308 | { |
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309 | pNext(Current) = NULL; |
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310 | if (Current == PR->p && PR->t_p != NULL) |
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311 | pNext(PR->t_p) = NULL; |
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312 | PR->Mult_nn(coef); |
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313 | } |
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314 | |
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315 | n_Delete(&coef, currRing); |
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316 | pNext(Current) = Red.GetLmTailRing(); |
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317 | if (Current == PR->p && PR->t_p != NULL) |
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318 | pNext(PR->t_p) = pNext(Current); |
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319 | } |
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320 | |
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321 | if (Lp == Save) |
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322 | With.Delete(); |
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323 | |
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324 | // the following is commented out: shrinking |
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325 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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326 | if (currRing->isLPring) |
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327 | { |
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328 | // assume? h->p in currRing |
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329 | PR->GetP(); |
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330 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
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331 | PR->Clear(); // does the right things |
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332 | PR->p = qq; |
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333 | PR->t_p = NULL; |
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334 | PR->SetShortExpVector(); |
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335 | } |
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336 | #endif |
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337 | |
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338 | return ret; |
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339 | } |
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340 | |
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341 | /*************************************************************** |
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342 | * |
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343 | * Auxillary Routines |
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344 | * |
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345 | * |
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346 | ***************************************************************/ |
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347 | |
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348 | /* |
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349 | * input - output: a, b |
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350 | * returns: |
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351 | * a := a/gcd(a,b), b := b/gcd(a,b) |
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352 | * and return value |
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353 | * 0 -> a != 1, b != 1 |
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354 | * 1 -> a == 1, b != 1 |
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355 | * 2 -> a != 1, b == 1 |
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356 | * 3 -> a == 1, b == 1 |
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357 | * this value is used to control the spolys |
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358 | */ |
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359 | int ksCheckCoeff(number *a, number *b) |
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360 | { |
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361 | int c = 0; |
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362 | number an = *a, bn = *b; |
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363 | nTest(an); |
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364 | nTest(bn); |
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365 | |
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366 | number cn = nGcd(an, bn, currRing); |
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367 | |
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368 | if(nIsOne(cn)) |
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369 | { |
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370 | an = nCopy(an); |
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371 | bn = nCopy(bn); |
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372 | } |
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373 | else |
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374 | { |
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375 | an = nIntDiv(an, cn); |
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376 | bn = nIntDiv(bn, cn); |
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377 | } |
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378 | nDelete(&cn); |
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379 | if (nIsOne(an)) |
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380 | { |
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381 | c = 1; |
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382 | } |
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383 | if (nIsOne(bn)) |
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384 | { |
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385 | c += 2; |
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386 | } |
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387 | *a = an; |
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388 | *b = bn; |
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389 | return c; |
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390 | } |
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391 | |
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392 | /*2 |
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393 | * creates the leading term of the S-polynomial of p1 and p2 |
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394 | * do not destroy p1 and p2 |
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395 | * remarks: |
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396 | * 1. the coefficient is 0 (nNew) |
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397 | * 1. a) in the case of coefficient ring, the coefficient is calculated |
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398 | * 2. pNext is undefined |
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399 | */ |
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400 | //static void bbb() { int i=0; } |
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401 | poly ksCreateShortSpoly(poly p1, poly p2, ring tailRing) |
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402 | { |
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403 | poly a1 = pNext(p1), a2 = pNext(p2); |
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404 | Exponent_t c1=p_GetComp(p1, currRing),c2=p_GetComp(p2, currRing); |
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405 | Exponent_t c; |
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406 | poly m1,m2; |
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407 | number t1 = NULL,t2 = NULL; |
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408 | int cm,i; |
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409 | BOOLEAN equal; |
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410 | |
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411 | #ifdef HAVE_RINGS |
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412 | BOOLEAN is_Ring=rField_is_Ring(currRing); |
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413 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
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414 | if (is_Ring) |
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415 | { |
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416 | ksCheckCoeff(&lc1, &lc2); // gcd and zero divisors |
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417 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
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418 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
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419 | while (a1 != NULL && nIsZero(t2)) |
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420 | { |
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421 | pIter(a1); |
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422 | nDelete(&t2); |
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423 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
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424 | } |
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425 | while (a2 != NULL && nIsZero(t1)) |
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426 | { |
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427 | pIter(a2); |
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428 | nDelete(&t1); |
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429 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
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430 | } |
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431 | } |
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432 | #endif |
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433 | |
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434 | if (a1==NULL) |
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435 | { |
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436 | if(a2!=NULL) |
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437 | { |
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438 | m2=p_Init(currRing); |
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439 | x2: |
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440 | for (i = pVariables; i; i--) |
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441 | { |
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442 | c = p_GetExpDiff(p1, p2,i, currRing); |
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443 | if (c>0) |
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444 | { |
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445 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)),currRing); |
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446 | } |
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447 | else |
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448 | { |
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449 | p_SetExp(m2,i,p_GetExp(a2,i,tailRing),currRing); |
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450 | } |
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451 | } |
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452 | if ((c1==c2)||(c2!=0)) |
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453 | { |
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454 | p_SetComp(m2,p_GetComp(a2,tailRing), currRing); |
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455 | } |
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456 | else |
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457 | { |
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458 | p_SetComp(m2,c1,currRing); |
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459 | } |
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460 | p_Setm(m2, currRing); |
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461 | #ifdef HAVE_RINGS |
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462 | if (is_Ring) |
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463 | { |
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464 | nDelete(&lc1); |
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465 | nDelete(&lc2); |
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466 | nDelete(&t2); |
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467 | pSetCoeff0(m2, t1); |
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468 | } |
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469 | else |
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470 | #endif |
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471 | nNew(&(pGetCoeff(m2))); |
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472 | return m2; |
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473 | } |
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474 | else |
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475 | { |
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476 | #ifdef HAVE_RINGS |
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477 | if (is_Ring) |
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478 | { |
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479 | nDelete(&lc1); |
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480 | nDelete(&lc2); |
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481 | nDelete(&t1); |
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482 | nDelete(&t2); |
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483 | } |
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484 | #endif |
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485 | return NULL; |
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486 | } |
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487 | } |
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488 | if (a2==NULL) |
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489 | { |
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490 | m1=p_Init(currRing); |
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491 | x1: |
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492 | for (i = pVariables; i; i--) |
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493 | { |
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494 | c = p_GetExpDiff(p2, p1,i,currRing); |
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495 | if (c>0) |
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496 | { |
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497 | p_SetExp(m1,i,(c+p_GetExp(a1,i, tailRing)),currRing); |
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498 | } |
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499 | else |
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500 | { |
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501 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
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502 | } |
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503 | } |
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504 | if ((c1==c2)||(c1!=0)) |
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505 | { |
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506 | p_SetComp(m1,p_GetComp(a1,tailRing),currRing); |
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507 | } |
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508 | else |
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509 | { |
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510 | p_SetComp(m1,c2,currRing); |
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511 | } |
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512 | p_Setm(m1, currRing); |
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513 | #ifdef HAVE_RINGS |
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514 | if (is_Ring) |
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515 | { |
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516 | pSetCoeff0(m1, t2); |
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517 | nDelete(&lc1); |
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518 | nDelete(&lc2); |
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519 | nDelete(&t1); |
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520 | } |
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521 | else |
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522 | #endif |
---|
523 | nNew(&(pGetCoeff(m1))); |
---|
524 | return m1; |
---|
525 | } |
---|
526 | m1 = p_Init(currRing); |
---|
527 | m2 = p_Init(currRing); |
---|
528 | for(;;) |
---|
529 | { |
---|
530 | for (i = pVariables; i; i--) |
---|
531 | { |
---|
532 | c = p_GetExpDiff(p1, p2,i,currRing); |
---|
533 | if (c > 0) |
---|
534 | { |
---|
535 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)), currRing); |
---|
536 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
---|
537 | } |
---|
538 | else |
---|
539 | { |
---|
540 | p_SetExp(m1,i,(p_GetExp(a1,i,tailRing)-c), currRing); |
---|
541 | p_SetExp(m2,i,p_GetExp(a2,i, tailRing), currRing); |
---|
542 | } |
---|
543 | } |
---|
544 | if(c1==c2) |
---|
545 | { |
---|
546 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
547 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
548 | } |
---|
549 | else |
---|
550 | { |
---|
551 | if(c1!=0) |
---|
552 | { |
---|
553 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
554 | p_SetComp(m2,c1, currRing); |
---|
555 | } |
---|
556 | else |
---|
557 | { |
---|
558 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
559 | p_SetComp(m1,c2, currRing); |
---|
560 | } |
---|
561 | } |
---|
562 | p_Setm(m1,currRing); |
---|
563 | p_Setm(m2,currRing); |
---|
564 | cm = p_LmCmp(m1, m2,currRing); |
---|
565 | if (cm!=0) |
---|
566 | { |
---|
567 | if(cm==1) |
---|
568 | { |
---|
569 | p_LmFree(m2,currRing); |
---|
570 | #ifdef HAVE_RINGS |
---|
571 | if (is_Ring) |
---|
572 | { |
---|
573 | pSetCoeff0(m1, t2); |
---|
574 | nDelete(&lc1); |
---|
575 | nDelete(&lc2); |
---|
576 | nDelete(&t1); |
---|
577 | } |
---|
578 | else |
---|
579 | #endif |
---|
580 | nNew(&(pGetCoeff(m1))); |
---|
581 | return m1; |
---|
582 | } |
---|
583 | else |
---|
584 | { |
---|
585 | p_LmFree(m1,currRing); |
---|
586 | #ifdef HAVE_RINGS |
---|
587 | if (is_Ring) |
---|
588 | { |
---|
589 | pSetCoeff0(m2, t1); |
---|
590 | nDelete(&lc1); |
---|
591 | nDelete(&lc2); |
---|
592 | nDelete(&t2); |
---|
593 | } |
---|
594 | else |
---|
595 | #endif |
---|
596 | nNew(&(pGetCoeff(m2))); |
---|
597 | return m2; |
---|
598 | } |
---|
599 | } |
---|
600 | #ifdef HAVE_RINGS |
---|
601 | if (is_Ring) |
---|
602 | { |
---|
603 | equal = nEqual(t1,t2); |
---|
604 | } |
---|
605 | else |
---|
606 | #endif |
---|
607 | { |
---|
608 | t1 = nMult(pGetCoeff(a2),pGetCoeff(p1)); |
---|
609 | t2 = nMult(pGetCoeff(a1),pGetCoeff(p2)); |
---|
610 | equal = nEqual(t1,t2); |
---|
611 | nDelete(&t2); |
---|
612 | nDelete(&t1); |
---|
613 | } |
---|
614 | if (!equal) |
---|
615 | { |
---|
616 | p_LmFree(m2,currRing); |
---|
617 | #ifdef HAVE_RINGS |
---|
618 | if (is_Ring) |
---|
619 | { |
---|
620 | pSetCoeff0(m1, nSub(t1, t2)); |
---|
621 | nDelete(&lc1); |
---|
622 | nDelete(&lc2); |
---|
623 | nDelete(&t1); |
---|
624 | nDelete(&t2); |
---|
625 | } |
---|
626 | else |
---|
627 | #endif |
---|
628 | nNew(&(pGetCoeff(m1))); |
---|
629 | return m1; |
---|
630 | } |
---|
631 | pIter(a1); |
---|
632 | pIter(a2); |
---|
633 | #ifdef HAVE_RINGS |
---|
634 | if (is_Ring) |
---|
635 | { |
---|
636 | if (a2 != NULL) |
---|
637 | { |
---|
638 | nDelete(&t1); |
---|
639 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
640 | } |
---|
641 | if (a1 != NULL) |
---|
642 | { |
---|
643 | nDelete(&t2); |
---|
644 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
645 | } |
---|
646 | while ((a1 != NULL) && nIsZero(t2)) |
---|
647 | { |
---|
648 | pIter(a1); |
---|
649 | if (a1 != NULL) |
---|
650 | { |
---|
651 | nDelete(&t2); |
---|
652 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
653 | } |
---|
654 | } |
---|
655 | while ((a2 != NULL) && nIsZero(t1)) |
---|
656 | { |
---|
657 | pIter(a2); |
---|
658 | if (a2 != NULL) |
---|
659 | { |
---|
660 | nDelete(&t1); |
---|
661 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
662 | } |
---|
663 | } |
---|
664 | } |
---|
665 | #endif |
---|
666 | if (a2==NULL) |
---|
667 | { |
---|
668 | p_LmFree(m2,currRing); |
---|
669 | if (a1==NULL) |
---|
670 | { |
---|
671 | #ifdef HAVE_RINGS |
---|
672 | if (is_Ring) |
---|
673 | { |
---|
674 | nDelete(&lc1); |
---|
675 | nDelete(&lc2); |
---|
676 | nDelete(&t1); |
---|
677 | nDelete(&t2); |
---|
678 | } |
---|
679 | #endif |
---|
680 | p_LmFree(m1,currRing); |
---|
681 | return NULL; |
---|
682 | } |
---|
683 | goto x1; |
---|
684 | } |
---|
685 | if (a1==NULL) |
---|
686 | { |
---|
687 | p_LmFree(m1,currRing); |
---|
688 | goto x2; |
---|
689 | } |
---|
690 | } |
---|
691 | } |
---|