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 HAVE_RINGS |
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20 | #include "kernel/polys.h" |
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21 | #endif |
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22 | #include "kernel/GBEngine/shiftgb.h" |
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23 | |
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24 | #ifdef KDEBUG |
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25 | int red_count = 0; |
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26 | int create_count = 0; |
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27 | // define this if reductions are reported on TEST_OPT_DEBUG |
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28 | #define TEST_OPT_DEBUG_RED |
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29 | #endif |
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30 | |
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31 | /*************************************************************** |
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32 | * |
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33 | * Reduces PR with PW |
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34 | * Assumes PR != NULL, PW != NULL, Lm(PW) divides Lm(PR) |
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35 | * |
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36 | * returns 0: okay |
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37 | * 1: tailRing changed |
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38 | * -1: cannot change tailRing |
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39 | * 2: cannot change tailRing: strat==NULL |
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40 | * |
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41 | ***************************************************************/ |
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42 | int ksReducePoly(LObject* PR, |
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43 | TObject* PW, |
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44 | poly spNoether, |
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45 | number *coef, |
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46 | kStrategy strat) |
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47 | { |
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48 | #ifdef KDEBUG |
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49 | red_count++; |
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50 | #ifdef TEST_OPT_DEBUG_RED |
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51 | // if (TEST_OPT_DEBUG) |
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52 | // { |
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53 | // Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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54 | // PW->wrp(); |
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55 | // //printf("\necart(PR)-ecart(PW): %i\n",PR->ecart-PW->ecart); |
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56 | // //pWrite(PR->p); |
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57 | // } |
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58 | #endif |
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59 | #endif |
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60 | int ret = 0; |
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61 | ring tailRing = PR->tailRing; |
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62 | kTest_L(PR); |
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63 | kTest_T(PW); |
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64 | |
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65 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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66 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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67 | 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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68 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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69 | p_CheckPolyRing(p1, tailRing); |
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70 | p_CheckPolyRing(p2, tailRing); |
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71 | |
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72 | pAssume1(p2 != NULL && p1 != NULL && |
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73 | p_DivisibleBy(p2, p1, tailRing)); |
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74 | |
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75 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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76 | (p_GetComp(p2, tailRing) == 0 && |
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77 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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78 | |
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79 | #ifdef HAVE_PLURAL |
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80 | if (rIsPluralRing(currRing)) |
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81 | { |
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82 | // for the time being: we know currRing==strat->tailRing |
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83 | // no exp-bound checking needed |
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84 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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85 | if (PR->bucket!=NULL) nc_kBucketPolyRed_Z(PR->bucket, p2,coef); |
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86 | else |
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87 | { |
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88 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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89 | assume(_p != NULL); |
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90 | nc_PolyPolyRed(_p, p2,coef, currRing); |
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91 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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92 | PR->pLength=0; // usually not used, GetpLength re-computes it if needed |
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93 | } |
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94 | return 0; |
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95 | } |
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96 | #endif |
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97 | |
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98 | if (t2==NULL) // Divisor is just one term, therefore it will |
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99 | { // just cancel the leading term |
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100 | PR->LmDeleteAndIter(); |
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101 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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102 | return 0; |
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103 | } |
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104 | |
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105 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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106 | |
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107 | //if (tailRing != currRing) |
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108 | { |
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109 | // check that reduction does not violate exp bound |
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110 | while (PW->max_exp != NULL && !p_LmExpVectorAddIsOk(lm, PW->max_exp, tailRing)) |
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111 | { |
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112 | // undo changes of lm |
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113 | p_ExpVectorAdd(lm, p2, tailRing); |
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114 | if (strat == NULL) return 2; |
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115 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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116 | tailRing = strat->tailRing; |
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117 | p1 = PR->GetLmTailRing(); |
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118 | p2 = PW->GetLmTailRing(); |
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119 | t2 = pNext(p2); |
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120 | lm = p1; |
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121 | p_ExpVectorSub(lm, p2, tailRing); |
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122 | ret = 1; |
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123 | } |
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124 | } |
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125 | |
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126 | poly lmRight; |
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127 | if (tailRing->isLPring) { |
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128 | k_SplitFrame(lm, lmRight, PW->shift + 1, tailRing); |
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129 | } |
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130 | |
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131 | // take care of coef buisness |
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132 | if (! n_IsOne(pGetCoeff(p2), tailRing->cf)) |
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133 | { |
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134 | number bn = pGetCoeff(lm); |
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135 | number an = pGetCoeff(p2); |
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136 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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137 | p_SetCoeff(lm, bn, tailRing); |
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138 | if (tailRing->isLPring) pSetCoeff0(p1, bn); // lm doesn't point to p1 anymore, if the coef was a pointer, it has been deleted |
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139 | if ((ct == 0) || (ct == 2)) |
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140 | PR->Tail_Mult_nn(an); |
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141 | if (coef != NULL) *coef = an; |
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142 | else n_Delete(&an, tailRing->cf); |
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143 | } |
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144 | else |
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145 | { |
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146 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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147 | } |
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148 | |
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149 | |
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150 | // and finally, |
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151 | if (tailRing->isLPring) { |
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152 | PR->Tail_Minus_mm_Mult_qq(lm, tailRing->p_Procs->pp_Mult_mm(t2, lmRight, tailRing), pLength(t2), spNoether); |
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153 | } else { |
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154 | PR->Tail_Minus_mm_Mult_qq(lm, t2, pLength(t2) /*PW->GetpLength() - 1*/, spNoether); |
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155 | } |
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156 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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157 | PR->LmDeleteAndIter(); |
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158 | |
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159 | return ret; |
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160 | } |
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161 | |
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162 | /* Computes a reduction of the lead coefficient only. We have already tested |
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163 | * that lm(PW) divides lm(PR), but lc(PW) does not divide lc(PR). We have |
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164 | * computed division with remainder on the lead coefficients, parameter |
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165 | * coef is the corresponding multiple for PW we need. The new lead |
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166 | * coefficient, i.e. the remainder of lc division has already been |
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167 | * set before calling this function. We do not drop the lead term at |
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168 | * the end, but keep the adjusted, correct lead term. */ |
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169 | int ksReducePolyLC(LObject* PR, |
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170 | TObject* PW, |
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171 | poly spNoether, |
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172 | number *coef, |
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173 | kStrategy strat) |
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174 | { |
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175 | #ifdef KDEBUG |
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176 | red_count++; |
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177 | #ifdef TEST_OPT_DEBUG_RED |
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178 | // if (TEST_OPT_DEBUG) |
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179 | // { |
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180 | // Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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181 | // PW->wrp(); |
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182 | // //printf("\necart(PR)-ecart(PW): %i\n",PR->ecart-PW->ecart); |
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183 | // //pWrite(PR->p); |
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184 | // } |
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185 | #endif |
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186 | #endif |
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187 | /* printf("PR->P: "); |
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188 | * p_Write(PR->p, currRing, PR->tailRing); */ |
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189 | int ret = 0; |
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190 | ring tailRing = PR->tailRing; |
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191 | kTest_L(PR); |
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192 | kTest_T(PW); |
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193 | |
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194 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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195 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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196 | 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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197 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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198 | p_CheckPolyRing(p1, tailRing); |
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199 | p_CheckPolyRing(p2, tailRing); |
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200 | |
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201 | pAssume1(p2 != NULL && p1 != NULL && |
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202 | p_DivisibleBy(p2, p1, tailRing)); |
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203 | |
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204 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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205 | (p_GetComp(p2, tailRing) == 0 && |
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206 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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207 | |
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208 | #ifdef HAVE_PLURAL |
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209 | if (rIsPluralRing(currRing)) |
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210 | { |
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211 | // for the time being: we know currRing==strat->tailRing |
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212 | // no exp-bound checking needed |
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213 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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214 | if (PR->bucket!=NULL) nc_kBucketPolyRed_Z(PR->bucket, p2,coef); |
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215 | else |
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216 | { |
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217 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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218 | assume(_p != NULL); |
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219 | nc_PolyPolyRed(_p, p2,coef, currRing); |
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220 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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221 | PR->pLength=0; // usually not used, GetpLength re-computes it if needed |
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222 | } |
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223 | return 0; |
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224 | } |
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225 | #endif |
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226 | /* printf("PR->P2: "); |
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227 | * pWrite(PR->p); */ |
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228 | |
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229 | /* this part never happens since t2 = p2 and NOT t2 = pNext(p2) */ |
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230 | /* if (t2==NULL) // Divisor is just one term, therefore it will |
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231 | * { // just cancel the leading term |
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232 | * PR->LmDeleteAndIter(); |
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233 | * if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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234 | * return 0; |
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235 | * } */ |
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236 | |
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237 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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238 | p_SetCoeff(lm, n_Init(1, tailRing), tailRing); |
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239 | //if (tailRing != currRing) |
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240 | { |
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241 | // check that reduction does not violate exp bound |
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242 | while (PW->max_exp != NULL && !p_LmExpVectorAddIsOk(lm, PW->max_exp, tailRing)) |
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243 | { |
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244 | // undo changes of lm |
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245 | p_ExpVectorAdd(lm, p2, tailRing); |
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246 | if (strat == NULL) return 2; |
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247 | /* if (! kStratChangeTailRing(strat, PR, PW)) return -1; */ |
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248 | tailRing = strat->tailRing; |
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249 | p1 = PR->GetLmTailRing(); |
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250 | p2 = PW->GetLmTailRing(); |
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251 | t2 = pNext(p2); |
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252 | lm = p1; |
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253 | p_ExpVectorSub(lm, p2, tailRing); |
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254 | ret = 1; |
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255 | } |
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256 | } |
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257 | |
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258 | // take care of coef buisness |
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259 | // we have done this already in redRingNew |
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260 | /* if (! n_IsOne(pGetCoeff(p2), tailRing->cf)) |
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261 | * { |
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262 | * number bn = pGetCoeff(lm); |
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263 | * number an = pGetCoeff(p2); |
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264 | * int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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265 | * p_SetCoeff(lm, bn, tailRing); |
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266 | * if ((ct == 0) || (ct == 2)) |
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267 | * PR->Tail_Mult_nn(an); |
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268 | * if (coef != NULL) *coef = an; |
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269 | * else n_Delete(&an, tailRing->cf); |
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270 | * } |
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271 | * else |
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272 | * { |
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273 | * if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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274 | * } */ |
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275 | |
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276 | // and finally, |
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277 | /* printf("NOW WE REDUCE:\n"); |
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278 | * p_Write(lm, tailRing); |
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279 | * p_Write(p2, tailRing); */ |
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280 | /* we use p2, since then lm(p2) is the gcd lead monomial and we are done! */ |
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281 | PR->Tail_Minus_mm_Mult_qq(lm, p2, pLength(p2) /*PW->GetpLength() - 1*/, spNoether); |
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282 | /* PR->Tail_Minus_mm_Mult_qq(lm, t2, pLength(t2) [>PW->GetpLength() - 1<], spNoether); */ |
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283 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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284 | |
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285 | PR->LmDeleteAndIter(); |
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286 | p_SetCoeff(PR->p, *coef, currRing); |
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287 | /* p_SetCoeff(PR->t_p, *coef, tailRing); */ |
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288 | |
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289 | |
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290 | // the following is commented out: shrinking |
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291 | #ifdef HAVE_SHIFTBBA_NONEXISTENT |
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292 | if ( (currRing->isLPring) && (!strat->homog) ) |
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293 | { |
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294 | // assume? h->p in currRing |
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295 | PR->GetP(); |
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296 | poly qq = p_Shrink(PR->p, currRing->isLPring, currRing); |
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297 | PR->Clear(); // does the right things |
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298 | PR->p = qq; |
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299 | PR->t_p = NULL; |
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300 | PR->SetShortExpVector(); |
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301 | } |
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302 | #endif |
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303 | |
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304 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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305 | if (TEST_OPT_DEBUG) |
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306 | { |
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307 | Print(" to: "); PR->wrp(); Print("\n"); |
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308 | //printf("\nt^%i ", PR->ecart);pWrite(pHead(PR->p)); |
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309 | } |
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310 | #endif |
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311 | return ret; |
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312 | } |
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313 | |
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314 | int ksReducePolyBound(LObject* PR, |
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315 | TObject* PW, |
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316 | int bound, |
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317 | poly spNoether, |
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318 | number *coef, |
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319 | kStrategy strat) |
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320 | { |
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321 | #ifdef KDEBUG |
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322 | red_count++; |
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323 | #ifdef TEST_OPT_DEBUG_RED |
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324 | if (TEST_OPT_DEBUG) |
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325 | { |
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326 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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327 | PW->wrp(); |
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328 | //printf("\necart(PR)-ecart(PW): %i\n",PR->ecart-PW->ecart); |
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329 | //pWrite(PR->p); |
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330 | } |
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331 | #endif |
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332 | #endif |
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333 | int ret = 0; |
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334 | ring tailRing = PR->tailRing; |
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335 | kTest_L(PR); |
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336 | kTest_T(PW); |
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337 | |
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338 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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339 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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340 | 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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341 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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342 | p_CheckPolyRing(p1, tailRing); |
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343 | p_CheckPolyRing(p2, tailRing); |
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344 | |
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345 | pAssume1(p2 != NULL && p1 != NULL && |
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346 | p_DivisibleBy(p2, p1, tailRing)); |
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347 | |
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348 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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349 | (p_GetComp(p2, tailRing) == 0 && |
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350 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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351 | |
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352 | #ifdef HAVE_PLURAL |
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353 | if (rIsPluralRing(currRing)) |
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354 | { |
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355 | // for the time being: we know currRing==strat->tailRing |
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356 | // no exp-bound checking needed |
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357 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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358 | if (PR->bucket!=NULL) nc_kBucketPolyRed_Z(PR->bucket, p2,coef); |
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359 | else |
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360 | { |
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361 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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362 | assume(_p != NULL); |
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363 | nc_PolyPolyRed(_p, p2,coef, currRing); |
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364 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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365 | PR->pLength=0; // usually not used, GetpLength re-computes it if needed |
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366 | } |
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367 | return 0; |
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368 | } |
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369 | #endif |
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370 | |
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371 | if (t2==NULL) // Divisor is just one term, therefore it will |
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372 | { // just cancel the leading term |
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373 | PR->LmDeleteAndIter(); |
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374 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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375 | return 0; |
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376 | } |
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377 | |
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378 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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379 | |
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380 | if (tailRing != currRing) |
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381 | { |
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382 | // check that reduction does not violate exp bound |
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383 | while (PW->max_exp != NULL && !p_LmExpVectorAddIsOk(lm, PW->max_exp, tailRing)) |
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384 | { |
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385 | // undo changes of lm |
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386 | p_ExpVectorAdd(lm, p2, tailRing); |
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387 | if (strat == NULL) return 2; |
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388 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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389 | tailRing = strat->tailRing; |
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390 | p1 = PR->GetLmTailRing(); |
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391 | p2 = PW->GetLmTailRing(); |
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392 | t2 = pNext(p2); |
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393 | lm = p1; |
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394 | p_ExpVectorSub(lm, p2, tailRing); |
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395 | ret = 1; |
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396 | } |
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397 | } |
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398 | |
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399 | poly lmRight; |
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400 | if (tailRing->isLPring) { |
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401 | k_SplitFrame(lm, lmRight, PW->shift + 1, tailRing); |
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402 | } |
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403 | |
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404 | // take care of coef buisness |
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405 | if (! n_IsOne(pGetCoeff(p2), tailRing)) |
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406 | { |
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407 | number bn = pGetCoeff(lm); |
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408 | number an = pGetCoeff(p2); |
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409 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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410 | p_SetCoeff(lm, bn, tailRing); |
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411 | if (tailRing->isLPring) pSetCoeff0(p1, bn); // lm doesn't point to p1 anymore, if the coef was a pointer, it has been deleted |
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412 | if ((ct == 0) || (ct == 2)) |
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413 | PR->Tail_Mult_nn(an); |
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414 | if (coef != NULL) *coef = an; |
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415 | else n_Delete(&an, tailRing); |
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416 | } |
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417 | else |
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418 | { |
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419 | if (coef != NULL) *coef = n_Init(1, tailRing); |
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420 | } |
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421 | |
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422 | |
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423 | // and finally, |
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424 | if (tailRing->isLPring) { |
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425 | PR->Tail_Minus_mm_Mult_qq(lm, tailRing->p_Procs->pp_Mult_mm(t2, lmRight, tailRing), pLength(t2), spNoether); |
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426 | } else { |
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427 | PR->Tail_Minus_mm_Mult_qq(lm, t2, pLength(t2) /*PW->GetpLength() - 1*/, spNoether); |
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428 | } |
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429 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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430 | PR->LmDeleteAndIter(); |
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431 | |
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432 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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433 | if (TEST_OPT_DEBUG) |
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434 | { |
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435 | Print(" to: "); PR->wrp(); Print("\n"); |
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436 | //printf("\nt^%i ", PR->ecart);pWrite(pHead(PR->p)); |
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437 | } |
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438 | #endif |
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439 | return ret; |
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440 | } |
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441 | |
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442 | /*************************************************************** |
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443 | * |
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444 | * Reduces PR with PW |
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445 | * Assumes PR != NULL, PW != NULL, Lm(PW) divides Lm(PR) |
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446 | * |
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447 | ***************************************************************/ |
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448 | |
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449 | int ksReducePolySig(LObject* PR, |
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450 | TObject* PW, |
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451 | long /*idx*/, |
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452 | poly spNoether, |
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453 | number *coef, |
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454 | kStrategy strat) |
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455 | { |
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456 | #ifdef KDEBUG |
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457 | red_count++; |
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458 | #ifdef TEST_OPT_DEBUG_RED |
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459 | if (TEST_OPT_DEBUG) |
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460 | { |
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461 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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462 | PW->wrp(); |
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463 | } |
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464 | #endif |
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465 | #endif |
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466 | int ret = 0; |
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467 | ring tailRing = PR->tailRing; |
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468 | kTest_L(PR); |
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469 | kTest_T(PW); |
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470 | |
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471 | // signature-based stuff: |
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472 | // checking for sig-safeness first |
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473 | // NOTE: This has to be done in the current ring |
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474 | // |
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475 | /********************************************** |
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476 | * |
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477 | * TODO: |
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478 | * -------------------------------------------- |
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479 | * if strat->sbaOrder == 1 |
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480 | * Since we are subdividing lower index and |
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481 | * current index reductions it is enough to |
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482 | * look at the polynomial part of the signature |
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483 | * for a check. This should speed-up checking |
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484 | * a lot! |
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485 | * if !strat->sbaOrder == 0 |
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486 | * We are not subdividing lower and current index |
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487 | * due to the fact that we are using the induced |
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488 | * Schreyer order |
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489 | * |
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490 | * nevertheless, this different behaviour is |
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491 | * taken care of by is_sigsafe |
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492 | * => one reduction procedure can be used for |
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493 | * both, the incremental and the non-incremental |
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494 | * attempt! |
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495 | * -------------------------------------------- |
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496 | * |
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497 | *********************************************/ |
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498 | //printf("COMPARE IDX: %ld -- %ld\n",idx,strat->currIdx); |
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499 | if (!PW->is_sigsafe) |
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500 | { |
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501 | poly sigMult = pCopy(PW->sig); // copy signature of reducer |
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502 | //#if 1 |
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503 | #ifdef DEBUGF5 |
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504 | printf("IN KSREDUCEPOLYSIG: \n"); |
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505 | pWrite(pHead(f1)); |
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506 | pWrite(pHead(f2)); |
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507 | pWrite(sigMult); |
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508 | printf("--------------\n"); |
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509 | #endif |
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510 | p_ExpVectorAddSub(sigMult,PR->GetLmCurrRing(),PW->GetLmCurrRing(),currRing); |
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511 | //#if 1 |
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512 | #ifdef DEBUGF5 |
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513 | printf("------------------- IN KSREDUCEPOLYSIG: --------------------\n"); |
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514 | pWrite(pHead(f1)); |
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515 | pWrite(pHead(f2)); |
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516 | pWrite(sigMult); |
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517 | pWrite(PR->sig); |
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518 | printf("--------------\n"); |
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519 | #endif |
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520 | int sigSafe = p_LmCmp(PR->sig,sigMult,currRing); |
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521 | // now we can delete the copied polynomial data used for checking for |
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522 | // sig-safeness of the reduction step |
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523 | //#if 1 |
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524 | #ifdef DEBUGF5 |
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525 | printf("%d -- %d sig\n",sigSafe,PW->is_sigsafe); |
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526 | |
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527 | #endif |
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528 | //pDelete(&f1); |
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529 | pDelete(&sigMult); |
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530 | // go on with the computations only if the signature of p2 is greater than the |
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531 | // signature of fm*p1 |
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532 | if(sigSafe != 1) |
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533 | { |
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534 | PR->is_redundant = TRUE; |
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535 | return 3; |
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536 | } |
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537 | //PW->is_sigsafe = TRUE; |
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538 | } |
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539 | PR->is_redundant = FALSE; |
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540 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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541 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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542 | 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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543 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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544 | p_CheckPolyRing(p1, tailRing); |
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545 | p_CheckPolyRing(p2, tailRing); |
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546 | |
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547 | pAssume1(p2 != NULL && p1 != NULL && |
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548 | p_DivisibleBy(p2, p1, tailRing)); |
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549 | |
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550 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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551 | (p_GetComp(p2, tailRing) == 0 && |
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552 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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553 | |
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554 | #ifdef HAVE_PLURAL |
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555 | if (rIsPluralRing(currRing)) |
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556 | { |
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557 | // for the time being: we know currRing==strat->tailRing |
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558 | // no exp-bound checking needed |
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559 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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560 | if (PR->bucket!=NULL) nc_kBucketPolyRed_Z(PR->bucket, p2,coef); |
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561 | else |
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562 | { |
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563 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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564 | assume(_p != NULL); |
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565 | nc_PolyPolyRed(_p, p2, coef, currRing); |
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566 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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567 | PR->pLength=0; // usaully not used, GetpLength re-comoutes it if needed |
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568 | } |
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569 | return 0; |
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570 | } |
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571 | #endif |
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572 | |
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573 | if (t2==NULL) // Divisor is just one term, therefore it will |
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574 | { // just cancel the leading term |
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575 | PR->LmDeleteAndIter(); |
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576 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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577 | return 0; |
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578 | } |
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579 | |
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580 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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581 | |
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582 | if (tailRing != currRing) |
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583 | { |
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584 | // check that reduction does not violate exp bound |
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585 | while (PW->max_exp != NULL && !p_LmExpVectorAddIsOk(lm, PW->max_exp, tailRing)) |
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586 | { |
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587 | // undo changes of lm |
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588 | p_ExpVectorAdd(lm, p2, tailRing); |
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589 | if (strat == NULL) return 2; |
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590 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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591 | tailRing = strat->tailRing; |
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592 | p1 = PR->GetLmTailRing(); |
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593 | p2 = PW->GetLmTailRing(); |
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594 | t2 = pNext(p2); |
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595 | lm = p1; |
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596 | p_ExpVectorSub(lm, p2, tailRing); |
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597 | ret = 1; |
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598 | } |
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599 | } |
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600 | |
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601 | poly lmRight; |
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602 | if (tailRing->isLPring) { |
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603 | k_SplitFrame(lm, lmRight, PW->shift + 1, tailRing); |
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604 | } |
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605 | |
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606 | // take care of coef buisness |
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607 | if (! n_IsOne(pGetCoeff(p2), tailRing->cf)) |
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608 | { |
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609 | number bn = pGetCoeff(lm); |
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610 | number an = pGetCoeff(p2); |
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611 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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612 | p_SetCoeff(lm, bn, tailRing); |
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613 | if (tailRing->isLPring) pSetCoeff0(p1, bn); // lm doesn't point to p1 anymore, if the coef was a pointer, it has been deleted |
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614 | if ((ct == 0) || (ct == 2)) |
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615 | PR->Tail_Mult_nn(an); |
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616 | if (coef != NULL) *coef = an; |
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617 | else n_Delete(&an, tailRing->cf); |
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618 | } |
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619 | else |
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620 | { |
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621 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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622 | } |
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623 | |
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624 | |
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625 | // and finally, |
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626 | if (tailRing->isLPring) { |
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627 | PR->Tail_Minus_mm_Mult_qq(lm, tailRing->p_Procs->pp_Mult_mm(t2, lmRight, tailRing), pLength(t2), spNoether); |
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628 | } else { |
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629 | PR->Tail_Minus_mm_Mult_qq(lm, t2, PW->GetpLength() - 1, spNoether); |
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630 | } |
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631 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
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632 | PR->LmDeleteAndIter(); |
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633 | |
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634 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
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635 | if (TEST_OPT_DEBUG) |
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636 | { |
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637 | Print(" to: "); PR->wrp(); Print("\n"); |
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638 | } |
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639 | #endif |
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640 | return ret; |
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641 | } |
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642 | |
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643 | int ksReducePolySigRing(LObject* PR, |
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644 | TObject* PW, |
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645 | long /*idx*/, |
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646 | poly spNoether, |
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647 | number *coef, |
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648 | kStrategy strat) |
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649 | { |
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650 | #ifdef KDEBUG |
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651 | red_count++; |
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652 | #ifdef TEST_OPT_DEBUG_RED |
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653 | if (TEST_OPT_DEBUG) |
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654 | { |
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655 | Print("Red %d:", red_count); PR->wrp(); Print(" with:"); |
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656 | PW->wrp(); |
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657 | } |
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658 | #endif |
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659 | #endif |
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660 | int ret = 0; |
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661 | ring tailRing = PR->tailRing; |
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662 | kTest_L(PR); |
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663 | kTest_T(PW); |
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664 | |
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665 | // signature-based stuff: |
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666 | // checking for sig-safeness first |
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667 | // NOTE: This has to be done in the current ring |
---|
668 | // |
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669 | /********************************************** |
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670 | * |
---|
671 | * TODO: |
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672 | * -------------------------------------------- |
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673 | * if strat->sbaOrder == 1 |
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674 | * Since we are subdividing lower index and |
---|
675 | * current index reductions it is enough to |
---|
676 | * look at the polynomial part of the signature |
---|
677 | * for a check. This should speed-up checking |
---|
678 | * a lot! |
---|
679 | * if !strat->sbaOrder == 0 |
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680 | * We are not subdividing lower and current index |
---|
681 | * due to the fact that we are using the induced |
---|
682 | * Schreyer order |
---|
683 | * |
---|
684 | * nevertheless, this different behaviour is |
---|
685 | * taken care of by is_sigsafe |
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686 | * => one reduction procedure can be used for |
---|
687 | * both, the incremental and the non-incremental |
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688 | * attempt! |
---|
689 | * -------------------------------------------- |
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690 | * |
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691 | *********************************************/ |
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692 | //printf("COMPARE IDX: %ld -- %ld\n",idx,strat->currIdx); |
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693 | if (!PW->is_sigsafe) |
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694 | { |
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695 | poly sigMult = pCopy(PW->sig); // copy signature of reducer |
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696 | //#if 1 |
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697 | #ifdef DEBUGF5 |
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698 | printf("IN KSREDUCEPOLYSIG: \n"); |
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699 | pWrite(pHead(f1)); |
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700 | pWrite(pHead(f2)); |
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701 | pWrite(sigMult); |
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702 | printf("--------------\n"); |
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703 | #endif |
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704 | p_ExpVectorAddSub(sigMult,PR->GetLmCurrRing(),PW->GetLmCurrRing(),currRing); |
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705 | //I have also to set the leading coeficient for sigMult (in the case of rings) |
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706 | if(rField_is_Ring(currRing)) |
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707 | { |
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708 | pSetCoeff(sigMult,nMult(nDiv(pGetCoeff(PR->p),pGetCoeff(PW->p)), pGetCoeff(sigMult))); |
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709 | if(nIsZero(pGetCoeff(sigMult))) |
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710 | { |
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711 | sigMult = NULL; |
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712 | } |
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713 | } |
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714 | //#if 1 |
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715 | #ifdef DEBUGF5 |
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716 | printf("------------------- IN KSREDUCEPOLYSIG: --------------------\n"); |
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717 | pWrite(pHead(f1)); |
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718 | pWrite(pHead(f2)); |
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719 | pWrite(sigMult); |
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720 | pWrite(PR->sig); |
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721 | printf("--------------\n"); |
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722 | #endif |
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723 | int sigSafe; |
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724 | if(!rField_is_Ring(currRing)) |
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725 | sigSafe = p_LmCmp(PR->sig,sigMult,currRing); |
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726 | // now we can delete the copied polynomial data used for checking for |
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727 | // sig-safeness of the reduction step |
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728 | //#if 1 |
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729 | #ifdef DEBUGF5 |
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730 | printf("%d -- %d sig\n",sigSafe,PW->is_sigsafe); |
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731 | |
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732 | #endif |
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733 | if(rField_is_Ring(currRing)) |
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734 | { |
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735 | // Set the sig |
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736 | poly origsig = pCopy(PR->sig); |
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737 | if(sigMult != NULL) |
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738 | PR->sig = pHead(pSub(PR->sig, sigMult)); |
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739 | //The sigs have the same lm, have to substract |
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740 | //It may happen that now the signature is 0 (drop) |
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741 | if(PR->sig == NULL) |
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742 | { |
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743 | strat->sigdrop=TRUE; |
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744 | } |
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745 | else |
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746 | { |
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747 | if(pLtCmp(PR->sig,origsig) == 1) |
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748 | { |
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749 | // do not allow this reduction - it will increase it's signature |
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750 | // and the partially standard basis is just till the old sig, not the new one |
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751 | PR->is_redundant = TRUE; |
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752 | pDelete(&PR->sig); |
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753 | PR->sig = origsig; |
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754 | strat->blockred++; |
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755 | return 3; |
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756 | } |
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757 | if(pLtCmp(PR->sig,origsig) == -1) |
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758 | { |
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759 | strat->sigdrop=TRUE; |
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760 | } |
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761 | } |
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762 | pDelete(&origsig); |
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763 | } |
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764 | //pDelete(&f1); |
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765 | // go on with the computations only if the signature of p2 is greater than the |
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766 | // signature of fm*p1 |
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767 | if(sigSafe != 1 && !rField_is_Ring(currRing)) |
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768 | { |
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769 | PR->is_redundant = TRUE; |
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770 | return 3; |
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771 | } |
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772 | //PW->is_sigsafe = TRUE; |
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773 | } |
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774 | PR->is_redundant = FALSE; |
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775 | poly p1 = PR->GetLmTailRing(); // p2 | p1 |
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776 | poly p2 = PW->GetLmTailRing(); // i.e. will reduce p1 with p2; lm = LT(p1) / LM(p2) |
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777 | 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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778 | assume(p1 != NULL && p2 != NULL);// Attention, we have rings and there LC(p2) and LC(p1) are special |
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779 | p_CheckPolyRing(p1, tailRing); |
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780 | p_CheckPolyRing(p2, tailRing); |
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781 | |
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782 | pAssume1(p2 != NULL && p1 != NULL && |
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783 | p_DivisibleBy(p2, p1, tailRing)); |
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784 | |
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785 | pAssume1(p_GetComp(p1, tailRing) == p_GetComp(p2, tailRing) || |
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786 | (p_GetComp(p2, tailRing) == 0 && |
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787 | p_MaxComp(pNext(p2),tailRing) == 0)); |
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788 | |
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789 | #ifdef HAVE_PLURAL |
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790 | if (rIsPluralRing(currRing)) |
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791 | { |
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792 | // for the time being: we know currRing==strat->tailRing |
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793 | // no exp-bound checking needed |
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794 | // (only needed if exp-bound(tailring)<exp-b(currRing)) |
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795 | if (PR->bucket!=NULL) nc_kBucketPolyRed_Z(PR->bucket, p2,coef); |
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796 | else |
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797 | { |
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798 | poly _p = (PR->t_p != NULL ? PR->t_p : PR->p); |
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799 | assume(_p != NULL); |
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800 | nc_PolyPolyRed(_p, p2, coef, currRing); |
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801 | if (PR->t_p!=NULL) PR->t_p=_p; else PR->p=_p; |
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802 | PR->pLength=0; // usaully not used, GetpLength re-comoutes it if needed |
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803 | } |
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804 | return 0; |
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805 | } |
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806 | #endif |
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807 | |
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808 | if (t2==NULL) // Divisor is just one term, therefore it will |
---|
809 | { // just cancel the leading term |
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810 | PR->LmDeleteAndIter(); |
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811 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
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812 | return 0; |
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813 | } |
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814 | |
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815 | p_ExpVectorSub(lm, p2, tailRing); // Calculate the Monomial we must multiply to p2 |
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816 | |
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817 | if (tailRing != currRing) |
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818 | { |
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819 | // check that reduction does not violate exp bound |
---|
820 | while (PW->max_exp != NULL && !p_LmExpVectorAddIsOk(lm, PW->max_exp, tailRing)) |
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821 | { |
---|
822 | // undo changes of lm |
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823 | p_ExpVectorAdd(lm, p2, tailRing); |
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824 | if (strat == NULL) return 2; |
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825 | if (! kStratChangeTailRing(strat, PR, PW)) return -1; |
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826 | tailRing = strat->tailRing; |
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827 | p1 = PR->GetLmTailRing(); |
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828 | p2 = PW->GetLmTailRing(); |
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829 | t2 = pNext(p2); |
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830 | lm = p1; |
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831 | p_ExpVectorSub(lm, p2, tailRing); |
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832 | ret = 1; |
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833 | } |
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834 | } |
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835 | |
---|
836 | poly lmRight; |
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837 | if (tailRing->isLPring) { |
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838 | k_SplitFrame(lm, lmRight, PW->shift + 1, tailRing); |
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839 | } |
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840 | |
---|
841 | // take care of coef buisness |
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842 | if(rField_is_Ring(currRing)) |
---|
843 | { |
---|
844 | p_SetCoeff(lm, nDiv(pGetCoeff(lm),pGetCoeff(p2)), tailRing); |
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845 | if (tailRing->isLPring) pSetCoeff0(p1, pGetCoeff(lm)); // lm doesn't point to p1 anymore, if the coef was a pointer, it has been deleted |
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846 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
---|
847 | } |
---|
848 | else |
---|
849 | { |
---|
850 | if (! n_IsOne(pGetCoeff(p2), tailRing->cf)) |
---|
851 | { |
---|
852 | number bn = pGetCoeff(lm); |
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853 | number an = pGetCoeff(p2); |
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854 | int ct = ksCheckCoeff(&an, &bn, tailRing->cf); // Calculate special LC |
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855 | p_SetCoeff(lm, bn, tailRing); |
---|
856 | if (tailRing->isLPring) pSetCoeff0(p1, bn); // lm doesn't point to p1 anymore, if the coef was a pointer, it has been deleted |
---|
857 | if (((ct == 0) || (ct == 2))) |
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858 | PR->Tail_Mult_nn(an); |
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859 | if (coef != NULL) *coef = an; |
---|
860 | else n_Delete(&an, tailRing->cf); |
---|
861 | } |
---|
862 | else |
---|
863 | { |
---|
864 | if (coef != NULL) *coef = n_Init(1, tailRing->cf); |
---|
865 | } |
---|
866 | } |
---|
867 | |
---|
868 | // and finally, |
---|
869 | if (tailRing->isLPring) { |
---|
870 | PR->Tail_Minus_mm_Mult_qq(lm, tailRing->p_Procs->pp_Mult_mm(t2, lmRight, tailRing), pLength(t2), spNoether); |
---|
871 | } else { |
---|
872 | PR->Tail_Minus_mm_Mult_qq(lm, t2, PW->GetpLength() - 1, spNoether); |
---|
873 | } |
---|
874 | assume(PW->GetpLength() == pLength(PW->p != NULL ? PW->p : PW->t_p)); |
---|
875 | PR->LmDeleteAndIter(); |
---|
876 | |
---|
877 | #if defined(KDEBUG) && defined(TEST_OPT_DEBUG_RED) |
---|
878 | if (TEST_OPT_DEBUG) |
---|
879 | { |
---|
880 | Print(" to: "); PR->wrp(); Print("\n"); |
---|
881 | } |
---|
882 | #endif |
---|
883 | return ret; |
---|
884 | } |
---|
885 | |
---|
886 | /*************************************************************** |
---|
887 | * |
---|
888 | * Creates S-Poly of p1 and p2 |
---|
889 | * |
---|
890 | * |
---|
891 | ***************************************************************/ |
---|
892 | void ksCreateSpoly(LObject* Pair, poly spNoether, |
---|
893 | int use_buckets, ring tailRing, |
---|
894 | poly m1, poly m2, TObject** R) |
---|
895 | { |
---|
896 | #ifdef KDEBUG |
---|
897 | create_count++; |
---|
898 | #endif |
---|
899 | kTest_L(Pair); |
---|
900 | poly p1 = Pair->p1; |
---|
901 | poly p2 = Pair->p2; |
---|
902 | Pair->tailRing = tailRing; |
---|
903 | |
---|
904 | assume(p1 != NULL); |
---|
905 | assume(p2 != NULL); |
---|
906 | assume(tailRing != NULL); |
---|
907 | |
---|
908 | poly a1 = pNext(p1), a2 = pNext(p2); |
---|
909 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
---|
910 | int co=0/*, ct = ksCheckCoeff(&lc1, &lc2, currRing->cf)*/; // gcd and zero divisors |
---|
911 | (void) ksCheckCoeff(&lc1, &lc2, currRing->cf); |
---|
912 | |
---|
913 | int l1=0, l2=0; |
---|
914 | |
---|
915 | if (currRing->pCompIndex >= 0) |
---|
916 | { |
---|
917 | if (__p_GetComp(p1, currRing)!=__p_GetComp(p2, currRing)) |
---|
918 | { |
---|
919 | if (__p_GetComp(p1, currRing)==0) |
---|
920 | { |
---|
921 | co=1; |
---|
922 | p_SetCompP(p1,__p_GetComp(p2, currRing), currRing, tailRing); |
---|
923 | } |
---|
924 | else |
---|
925 | { |
---|
926 | co=2; |
---|
927 | p_SetCompP(p2, __p_GetComp(p1, currRing), currRing, tailRing); |
---|
928 | } |
---|
929 | } |
---|
930 | } |
---|
931 | |
---|
932 | // get m1 = LCM(LM(p1), LM(p2))/LM(p1) |
---|
933 | // m2 = LCM(LM(p1), LM(p2))/LM(p2) |
---|
934 | if (m1 == NULL) |
---|
935 | k_GetLeadTerms(p1, p2, currRing, m1, m2, tailRing); |
---|
936 | |
---|
937 | poly m12, m22; |
---|
938 | if (tailRing->isLPring) |
---|
939 | { |
---|
940 | // note: because of the crits, p2 is never shifted |
---|
941 | int split = p_mFirstVblock(p1, tailRing); |
---|
942 | // TODO: shouldn't we use p1 AND p2 here?? |
---|
943 | k_SplitFrame(m1, m12, split, tailRing); |
---|
944 | k_SplitFrame(m2, m22, split, tailRing); |
---|
945 | // manually free the coeffs, because pSetCoeff0 is used in the next step |
---|
946 | n_Delete(&(m1->coef), tailRing->cf); |
---|
947 | n_Delete(&(m2->coef), tailRing->cf); |
---|
948 | |
---|
949 | a1 = p_LPshift(p_Copy(a1, tailRing), 1 - split, tailRing); // unshift a1 |
---|
950 | } |
---|
951 | |
---|
952 | pSetCoeff0(m1, lc2); |
---|
953 | pSetCoeff0(m2, lc1); // and now, m1 * LT(p1) == m2 * LT(p2) |
---|
954 | |
---|
955 | if (R != NULL) |
---|
956 | { |
---|
957 | if (Pair->i_r1 == -1) |
---|
958 | { |
---|
959 | l1 = pLength(p1) - 1; |
---|
960 | } |
---|
961 | else |
---|
962 | { |
---|
963 | l1 = (R[Pair->i_r1])->GetpLength() - 1; |
---|
964 | } |
---|
965 | if ((Pair->i_r2 == -1)||(R[Pair->i_r2]==NULL)) |
---|
966 | { |
---|
967 | l2 = pLength(p2) - 1; |
---|
968 | } |
---|
969 | else |
---|
970 | { |
---|
971 | l2 = (R[Pair->i_r2])->GetpLength() - 1; |
---|
972 | } |
---|
973 | } |
---|
974 | |
---|
975 | // get m2 * a2 |
---|
976 | if (spNoether != NULL) |
---|
977 | { |
---|
978 | l2 = -1; |
---|
979 | a2 = tailRing->p_Procs->pp_Mult_mm_Noether(a2, m2, spNoether, l2, tailRing); |
---|
980 | assume(l2 == pLength(a2)); |
---|
981 | } |
---|
982 | else |
---|
983 | if (tailRing->isLPring) { |
---|
984 | // m2*a2*m22 |
---|
985 | a2 = tailRing->p_Procs->pp_Mult_mm(tailRing->p_Procs->pp_mm_Mult(a2, m2, tailRing), m22, tailRing); |
---|
986 | } else { |
---|
987 | a2 = tailRing->p_Procs->pp_Mult_mm(a2, m2, tailRing); |
---|
988 | } |
---|
989 | #ifdef HAVE_RINGS |
---|
990 | if (!(rField_is_Domain(currRing))) l2 = pLength(a2); |
---|
991 | #endif |
---|
992 | |
---|
993 | Pair->SetLmTail(m2, a2, l2, use_buckets, tailRing); |
---|
994 | |
---|
995 | if (tailRing->isLPring) { |
---|
996 | // get m2*a2*m22 - m1*a1*m12 |
---|
997 | Pair->Tail_Minus_mm_Mult_qq(m1, tailRing->p_Procs->pp_Mult_mm(a1, m12, tailRing), l1, spNoether); |
---|
998 | } else { |
---|
999 | // get m2*a2 - m1*a1 |
---|
1000 | Pair->Tail_Minus_mm_Mult_qq(m1, a1, l1, spNoether); |
---|
1001 | } |
---|
1002 | |
---|
1003 | // Clean-up time |
---|
1004 | Pair->LmDeleteAndIter(); |
---|
1005 | p_LmDelete(m1, tailRing); |
---|
1006 | if (tailRing->isLPring) { |
---|
1007 | p_LmDelete(m12, tailRing); |
---|
1008 | p_LmDelete(m22, tailRing); |
---|
1009 | // m2 is already deleted |
---|
1010 | p_Delete(&a1, tailRing); // a1 is a copy: safe to destroy |
---|
1011 | } |
---|
1012 | |
---|
1013 | if (co != 0) |
---|
1014 | { |
---|
1015 | if (co==1) |
---|
1016 | { |
---|
1017 | p_SetCompP(p1,0, currRing, tailRing); |
---|
1018 | } |
---|
1019 | else |
---|
1020 | { |
---|
1021 | p_SetCompP(p2,0, currRing, tailRing); |
---|
1022 | } |
---|
1023 | } |
---|
1024 | } |
---|
1025 | |
---|
1026 | int ksReducePolyTail(LObject* PR, TObject* PW, poly Current, poly spNoether) |
---|
1027 | { |
---|
1028 | BOOLEAN ret; |
---|
1029 | number coef; |
---|
1030 | poly Lp = PR->GetLmCurrRing(); |
---|
1031 | poly Save = PW->GetLmCurrRing(); |
---|
1032 | |
---|
1033 | kTest_L(PR); |
---|
1034 | kTest_T(PW); |
---|
1035 | pAssume(pIsMonomOf(Lp, Current)); |
---|
1036 | |
---|
1037 | assume(Lp != NULL && Current != NULL && pNext(Current) != NULL); |
---|
1038 | assume(PR->bucket == NULL); |
---|
1039 | |
---|
1040 | LObject Red(pNext(Current), PR->tailRing); |
---|
1041 | TObject With(PW, Lp == Save); |
---|
1042 | |
---|
1043 | pAssume(!pHaveCommonMonoms(Red.p, With.p)); |
---|
1044 | ret = ksReducePoly(&Red, &With, spNoether, &coef); |
---|
1045 | |
---|
1046 | if (!ret) |
---|
1047 | { |
---|
1048 | if (! n_IsOne(coef, currRing->cf)) |
---|
1049 | { |
---|
1050 | pNext(Current) = NULL; |
---|
1051 | if (Current == PR->p && PR->t_p != NULL) |
---|
1052 | pNext(PR->t_p) = NULL; |
---|
1053 | PR->Mult_nn(coef); |
---|
1054 | } |
---|
1055 | |
---|
1056 | n_Delete(&coef, currRing->cf); |
---|
1057 | pNext(Current) = Red.GetLmTailRing(); |
---|
1058 | if (Current == PR->p && PR->t_p != NULL) |
---|
1059 | pNext(PR->t_p) = pNext(Current); |
---|
1060 | } |
---|
1061 | |
---|
1062 | if (Lp == Save) |
---|
1063 | With.Delete(); |
---|
1064 | |
---|
1065 | return ret; |
---|
1066 | } |
---|
1067 | |
---|
1068 | int ksReducePolyTailBound(LObject* PR, TObject* PW, int bound, poly Current, poly spNoether) |
---|
1069 | { |
---|
1070 | BOOLEAN ret; |
---|
1071 | number coef; |
---|
1072 | poly Lp = PR->GetLmCurrRing(); |
---|
1073 | poly Save = PW->GetLmCurrRing(); |
---|
1074 | |
---|
1075 | kTest_L(PR); |
---|
1076 | kTest_T(PW); |
---|
1077 | pAssume(pIsMonomOf(Lp, Current)); |
---|
1078 | |
---|
1079 | assume(Lp != NULL && Current != NULL && pNext(Current) != NULL); |
---|
1080 | assume(PR->bucket == NULL); |
---|
1081 | |
---|
1082 | LObject Red(pNext(Current), PR->tailRing); |
---|
1083 | TObject With(PW, Lp == Save); |
---|
1084 | |
---|
1085 | pAssume(!pHaveCommonMonoms(Red.p, With.p)); |
---|
1086 | ret = ksReducePolyBound(&Red, &With,bound, spNoether, &coef); |
---|
1087 | |
---|
1088 | if (!ret) |
---|
1089 | { |
---|
1090 | if (! n_IsOne(coef, currRing)) |
---|
1091 | { |
---|
1092 | pNext(Current) = NULL; |
---|
1093 | if (Current == PR->p && PR->t_p != NULL) |
---|
1094 | pNext(PR->t_p) = NULL; |
---|
1095 | PR->Mult_nn(coef); |
---|
1096 | } |
---|
1097 | |
---|
1098 | n_Delete(&coef, currRing); |
---|
1099 | pNext(Current) = Red.GetLmTailRing(); |
---|
1100 | if (Current == PR->p && PR->t_p != NULL) |
---|
1101 | pNext(PR->t_p) = pNext(Current); |
---|
1102 | } |
---|
1103 | |
---|
1104 | if (Lp == Save) |
---|
1105 | With.Delete(); |
---|
1106 | |
---|
1107 | return ret; |
---|
1108 | } |
---|
1109 | |
---|
1110 | /*************************************************************** |
---|
1111 | * |
---|
1112 | * Auxillary Routines |
---|
1113 | * |
---|
1114 | * |
---|
1115 | ***************************************************************/ |
---|
1116 | |
---|
1117 | /*2 |
---|
1118 | * creates the leading term of the S-polynomial of p1 and p2 |
---|
1119 | * do not destroy p1 and p2 |
---|
1120 | * remarks: |
---|
1121 | * 1. the coefficient is 0 (p_Init) |
---|
1122 | * 1. a) in the case of coefficient ring, the coefficient is calculated |
---|
1123 | * 2. pNext is undefined |
---|
1124 | */ |
---|
1125 | //static void bbb() { int i=0; } |
---|
1126 | poly ksCreateShortSpoly(poly p1, poly p2, ring tailRing) |
---|
1127 | { |
---|
1128 | poly a1 = pNext(p1), a2 = pNext(p2); |
---|
1129 | long c1=p_GetComp(p1, currRing),c2=p_GetComp(p2, currRing); |
---|
1130 | long c; |
---|
1131 | poly m1,m2; |
---|
1132 | number t1 = NULL,t2 = NULL; |
---|
1133 | int cm,i; |
---|
1134 | BOOLEAN equal; |
---|
1135 | |
---|
1136 | #ifdef HAVE_RINGS |
---|
1137 | BOOLEAN is_Ring=rField_is_Ring(currRing); |
---|
1138 | number lc1 = pGetCoeff(p1), lc2 = pGetCoeff(p2); |
---|
1139 | if (is_Ring) |
---|
1140 | { |
---|
1141 | ksCheckCoeff(&lc1, &lc2, currRing->cf); // gcd and zero divisors |
---|
1142 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
---|
1143 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
---|
1144 | while (a1 != NULL && nIsZero(t2)) |
---|
1145 | { |
---|
1146 | pIter(a1); |
---|
1147 | nDelete(&t2); |
---|
1148 | if (a1 != NULL) t2 = nMult(pGetCoeff(a1),lc2); |
---|
1149 | } |
---|
1150 | while (a2 != NULL && nIsZero(t1)) |
---|
1151 | { |
---|
1152 | pIter(a2); |
---|
1153 | nDelete(&t1); |
---|
1154 | if (a2 != NULL) t1 = nMult(pGetCoeff(a2),lc1); |
---|
1155 | } |
---|
1156 | } |
---|
1157 | #endif |
---|
1158 | |
---|
1159 | if (a1==NULL) |
---|
1160 | { |
---|
1161 | if(a2!=NULL) |
---|
1162 | { |
---|
1163 | m2=p_Init(currRing); |
---|
1164 | x2: |
---|
1165 | for (i = (currRing->N); i; i--) |
---|
1166 | { |
---|
1167 | c = p_GetExpDiff(p1, p2,i, currRing); |
---|
1168 | if (c>0) |
---|
1169 | { |
---|
1170 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)),currRing); |
---|
1171 | } |
---|
1172 | else |
---|
1173 | { |
---|
1174 | p_SetExp(m2,i,p_GetExp(a2,i,tailRing),currRing); |
---|
1175 | } |
---|
1176 | } |
---|
1177 | if ((c1==c2)||(c2!=0)) |
---|
1178 | { |
---|
1179 | p_SetComp(m2,p_GetComp(a2,tailRing), currRing); |
---|
1180 | } |
---|
1181 | else |
---|
1182 | { |
---|
1183 | p_SetComp(m2,c1,currRing); |
---|
1184 | } |
---|
1185 | p_Setm(m2, currRing); |
---|
1186 | #ifdef HAVE_RINGS |
---|
1187 | if (is_Ring) |
---|
1188 | { |
---|
1189 | nDelete(&lc1); |
---|
1190 | nDelete(&lc2); |
---|
1191 | nDelete(&t2); |
---|
1192 | pSetCoeff0(m2, t1); |
---|
1193 | } |
---|
1194 | #endif |
---|
1195 | return m2; |
---|
1196 | } |
---|
1197 | else |
---|
1198 | { |
---|
1199 | #ifdef HAVE_RINGS |
---|
1200 | if (is_Ring) |
---|
1201 | { |
---|
1202 | nDelete(&lc1); |
---|
1203 | nDelete(&lc2); |
---|
1204 | nDelete(&t1); |
---|
1205 | nDelete(&t2); |
---|
1206 | } |
---|
1207 | #endif |
---|
1208 | return NULL; |
---|
1209 | } |
---|
1210 | } |
---|
1211 | if (a2==NULL) |
---|
1212 | { |
---|
1213 | m1=p_Init(currRing); |
---|
1214 | x1: |
---|
1215 | for (i = (currRing->N); i; i--) |
---|
1216 | { |
---|
1217 | c = p_GetExpDiff(p2, p1,i,currRing); |
---|
1218 | if (c>0) |
---|
1219 | { |
---|
1220 | p_SetExp(m1,i,(c+p_GetExp(a1,i, tailRing)),currRing); |
---|
1221 | } |
---|
1222 | else |
---|
1223 | { |
---|
1224 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
---|
1225 | } |
---|
1226 | } |
---|
1227 | if ((c1==c2)||(c1!=0)) |
---|
1228 | { |
---|
1229 | p_SetComp(m1,p_GetComp(a1,tailRing),currRing); |
---|
1230 | } |
---|
1231 | else |
---|
1232 | { |
---|
1233 | p_SetComp(m1,c2,currRing); |
---|
1234 | } |
---|
1235 | p_Setm(m1, currRing); |
---|
1236 | #ifdef HAVE_RINGS |
---|
1237 | if (is_Ring) |
---|
1238 | { |
---|
1239 | pSetCoeff0(m1, t2); |
---|
1240 | nDelete(&lc1); |
---|
1241 | nDelete(&lc2); |
---|
1242 | nDelete(&t1); |
---|
1243 | } |
---|
1244 | #endif |
---|
1245 | return m1; |
---|
1246 | } |
---|
1247 | m1 = p_Init(currRing); |
---|
1248 | m2 = p_Init(currRing); |
---|
1249 | loop |
---|
1250 | { |
---|
1251 | for (i = (currRing->N); i; i--) |
---|
1252 | { |
---|
1253 | c = p_GetExpDiff(p1, p2,i,currRing); |
---|
1254 | if (c > 0) |
---|
1255 | { |
---|
1256 | p_SetExp(m2,i,(c+p_GetExp(a2,i,tailRing)), currRing); |
---|
1257 | p_SetExp(m1,i,p_GetExp(a1,i, tailRing), currRing); |
---|
1258 | } |
---|
1259 | else |
---|
1260 | { |
---|
1261 | p_SetExp(m1,i,(p_GetExp(a1,i,tailRing)-c), currRing); |
---|
1262 | p_SetExp(m2,i,p_GetExp(a2,i, tailRing), currRing); |
---|
1263 | } |
---|
1264 | } |
---|
1265 | if(c1==c2) |
---|
1266 | { |
---|
1267 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
1268 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
1269 | } |
---|
1270 | else |
---|
1271 | { |
---|
1272 | if(c1!=0) |
---|
1273 | { |
---|
1274 | p_SetComp(m1,p_GetComp(a1, tailRing), currRing); |
---|
1275 | p_SetComp(m2,c1, currRing); |
---|
1276 | } |
---|
1277 | else |
---|
1278 | { |
---|
1279 | p_SetComp(m2,p_GetComp(a2, tailRing), currRing); |
---|
1280 | p_SetComp(m1,c2, currRing); |
---|
1281 | } |
---|
1282 | } |
---|
1283 | p_Setm(m1,currRing); |
---|
1284 | p_Setm(m2,currRing); |
---|
1285 | cm = p_LmCmp(m1, m2,currRing); |
---|
1286 | if (cm!=0) |
---|
1287 | { |
---|
1288 | if(cm==1) |
---|
1289 | { |
---|
1290 | p_LmFree(m2,currRing); |
---|
1291 | #ifdef HAVE_RINGS |
---|
1292 | if (is_Ring) |
---|
1293 | { |
---|
1294 | pSetCoeff0(m1, t2); |
---|
1295 | nDelete(&lc1); |
---|
1296 | nDelete(&lc2); |
---|
1297 | nDelete(&t1); |
---|
1298 | } |
---|
1299 | #endif |
---|
1300 | return m1; |
---|
1301 | } |
---|
1302 | else |
---|
1303 | { |
---|
1304 | p_LmFree(m1,currRing); |
---|
1305 | #ifdef HAVE_RINGS |
---|
1306 | if (is_Ring) |
---|
1307 | { |
---|
1308 | pSetCoeff0(m2, t1); |
---|
1309 | nDelete(&lc1); |
---|
1310 | nDelete(&lc2); |
---|
1311 | nDelete(&t2); |
---|
1312 | } |
---|
1313 | #endif |
---|
1314 | return m2; |
---|
1315 | } |
---|
1316 | } |
---|
1317 | #ifdef HAVE_RINGS |
---|
1318 | if (is_Ring) |
---|
1319 | { |
---|
1320 | equal = nEqual(t1,t2); |
---|
1321 | } |
---|
1322 | else |
---|
1323 | #endif |
---|
1324 | { |
---|
1325 | t1 = nMult(pGetCoeff(a2),pGetCoeff(p1)); |
---|
1326 | t2 = nMult(pGetCoeff(a1),pGetCoeff(p2)); |
---|
1327 | equal = nEqual(t1,t2); |
---|
1328 | nDelete(&t2); |
---|
1329 | nDelete(&t1); |
---|
1330 | } |
---|
1331 | if (!equal) |
---|
1332 | { |
---|
1333 | p_LmFree(m2,currRing); |
---|
1334 | #ifdef HAVE_RINGS |
---|
1335 | if (is_Ring) |
---|
1336 | { |
---|
1337 | pSetCoeff0(m1, nSub(t1, t2)); |
---|
1338 | nDelete(&lc1); |
---|
1339 | nDelete(&lc2); |
---|
1340 | nDelete(&t1); |
---|
1341 | nDelete(&t2); |
---|
1342 | } |
---|
1343 | #endif |
---|
1344 | return m1; |
---|
1345 | } |
---|
1346 | pIter(a1); |
---|
1347 | pIter(a2); |
---|
1348 | #ifdef HAVE_RINGS |
---|
1349 | if (is_Ring) |
---|
1350 | { |
---|
1351 | if (a2 != NULL) |
---|
1352 | { |
---|
1353 | nDelete(&t1); |
---|
1354 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
1355 | } |
---|
1356 | if (a1 != NULL) |
---|
1357 | { |
---|
1358 | nDelete(&t2); |
---|
1359 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
1360 | } |
---|
1361 | while ((a1 != NULL) && nIsZero(t2)) |
---|
1362 | { |
---|
1363 | pIter(a1); |
---|
1364 | if (a1 != NULL) |
---|
1365 | { |
---|
1366 | nDelete(&t2); |
---|
1367 | t2 = nMult(pGetCoeff(a1),lc2); |
---|
1368 | } |
---|
1369 | } |
---|
1370 | while ((a2 != NULL) && nIsZero(t1)) |
---|
1371 | { |
---|
1372 | pIter(a2); |
---|
1373 | if (a2 != NULL) |
---|
1374 | { |
---|
1375 | nDelete(&t1); |
---|
1376 | t1 = nMult(pGetCoeff(a2),lc1); |
---|
1377 | } |
---|
1378 | } |
---|
1379 | } |
---|
1380 | #endif |
---|
1381 | if (a2==NULL) |
---|
1382 | { |
---|
1383 | p_LmFree(m2,currRing); |
---|
1384 | if (a1==NULL) |
---|
1385 | { |
---|
1386 | #ifdef HAVE_RINGS |
---|
1387 | if (is_Ring) |
---|
1388 | { |
---|
1389 | nDelete(&lc1); |
---|
1390 | nDelete(&lc2); |
---|
1391 | nDelete(&t1); |
---|
1392 | nDelete(&t2); |
---|
1393 | } |
---|
1394 | #endif |
---|
1395 | p_LmFree(m1,currRing); |
---|
1396 | return NULL; |
---|
1397 | } |
---|
1398 | goto x1; |
---|
1399 | } |
---|
1400 | if (a1==NULL) |
---|
1401 | { |
---|
1402 | p_LmFree(m1,currRing); |
---|
1403 | goto x2; |
---|
1404 | } |
---|
1405 | } |
---|
1406 | } |
---|