1 | #include <kernel/polys.h> |
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2 | #include <libpolys/polys/monomials/p_polys.h> |
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3 | #include <singularWishlist.h> |
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4 | |
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5 | #include <Singular/ipid.h> |
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6 | |
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7 | /*** |
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8 | * changes a polynomial g with the help p-t such that |
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9 | * 1) each term of g has a distinct monomial in x |
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10 | * 2) no term of g has a coefficient divisible by p |
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11 | * in particular, this means that all g_\alpha can be obtained |
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12 | * by reading the coefficients and that g is initially reduced |
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13 | * with respect to p-t |
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14 | **/ |
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15 | static bool pReduce(poly g, const number p) |
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16 | { |
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17 | poly toBeChecked = pNext(g); |
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18 | pNext(g) = NULL; poly gEnd = g; |
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19 | poly gCache; |
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20 | |
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21 | number coeff, pPower; int power; poly subst; |
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22 | while(toBeChecked) |
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23 | { |
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24 | for (gCache = g; gCache; pIter(gCache)) |
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25 | if (p_LeadmonomDivisibleBy(gCache,toBeChecked,currRing)) break; |
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26 | if (gCache) |
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27 | { |
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28 | n_Power(p,p_GetExp(toBeChecked,1,currRing)-p_GetExp(gCache,1,currRing),&pPower,currRing->cf); |
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29 | coeff = n_Mult(p_GetCoeff(toBeChecked,currRing),pPower,currRing->cf); |
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30 | p_SetCoeff(gCache,n_Add(p_GetCoeff(gCache,currRing),coeff,currRing->cf),currRing); |
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31 | n_Delete(&pPower,currRing->cf); n_Delete(&coeff,currRing->cf); |
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32 | toBeChecked=p_LmDeleteAndNext(toBeChecked,currRing); |
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33 | } |
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34 | else |
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35 | { |
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36 | if (n_DivBy(p_GetCoeff(toBeChecked,currRing),p,currRing->cf)) |
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37 | { |
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38 | coeff=n_Div(p_GetCoeff(toBeChecked,currRing),p,currRing->cf); |
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39 | power=1; |
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40 | while (n_DivBy(coeff,p,currRing->cf)) |
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41 | { |
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42 | coeff=n_Div(p_GetCoeff(pNext(g),currRing),p,currRing->cf); |
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43 | power++; |
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44 | if (power<1) |
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45 | { |
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46 | WerrorS("pReduce: overflow in exponent"); |
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47 | return true; |
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48 | } |
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49 | } |
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50 | subst=p_LmInit(toBeChecked,currRing); |
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51 | p_AddExp(subst,1,power,currRing); |
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52 | p_SetCoeff(subst,coeff,currRing); |
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53 | p_Setm(subst,currRing); pTest(subst); |
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54 | toBeChecked=p_LmDeleteAndNext(toBeChecked,currRing); |
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55 | toBeChecked=p_Add_q(toBeChecked,subst,currRing); |
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56 | pTest(toBeChecked); |
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57 | } |
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58 | else |
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59 | { |
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60 | pNext(gEnd)=toBeChecked; |
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61 | pIter(gEnd); pIter(toBeChecked); |
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62 | pNext(gEnd)=NULL; |
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63 | } |
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64 | } |
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65 | } |
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66 | return false; |
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67 | } |
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68 | |
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69 | |
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70 | #ifndef NDEBUG |
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71 | BOOLEAN pReduce(leftv res, leftv args) |
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72 | { |
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73 | leftv u = args; |
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74 | if ((u != NULL) && (u->Typ() == POLY_CMD)) |
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75 | { |
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76 | poly g; number p = n_Init(3,currRing->cf); |
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77 | omUpdateInfo(); |
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78 | Print("usedBytesBefore=%ld\n",om_Info.UsedBytes); |
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79 | g = (poly) u->CopyD(); |
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80 | (void) pReduce(g,p); |
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81 | p_Delete(&g,currRing); |
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82 | omUpdateInfo(); |
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83 | Print("usedBytesAfter=%ld\n",om_Info.UsedBytes); |
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84 | g = (poly) u->CopyD(); |
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85 | (void) pReduce(g,p); |
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86 | n_Delete(&p,currRing->cf); |
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87 | res->rtyp = POLY_CMD; |
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88 | res->data = (char*) g; |
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89 | return FALSE; |
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90 | } |
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91 | return TRUE; |
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92 | } |
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93 | #endif //NDEBUG |
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94 | |
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95 | |
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96 | /*** |
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97 | * Returns, if it exists, a pointer to the first term in g |
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98 | * that is divisible by (the leading monomial of) m or, if it does not exist, the NULL pointer |
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99 | * If g is homogeneous in x with the same degree as m, |
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100 | * then it returns the first term with the same monomial in x as m, |
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101 | * if the t-degree of the term is higher than the t-degree of m, or NULL otherwise. |
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102 | **/ |
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103 | static inline poly firstTermDivisibleBy(const poly g, const poly m) |
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104 | { |
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105 | poly gCache = NULL; |
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106 | for (gCache=g; gCache; pIter(gCache)) |
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107 | if (p_LeadmonomDivisibleBy(m,gCache,currRing)) break; |
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108 | return gCache; |
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109 | } |
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110 | |
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111 | |
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112 | /*** |
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113 | * reduces h initially with respect to g, |
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114 | * returns NULL if h was initially reduced in the first place. if reductions have taken place, |
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115 | * returns a pointer to a term from which onwards changes have taken place. |
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116 | * assumes that h and g are in pReduced form and homogeneous in x of the same degree |
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117 | **/ |
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118 | poly reduceInitially(poly &h, const poly g) |
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119 | { |
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120 | poly hCache=h; |
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121 | if (p_LeadmonomDivisibleBy(g,hCache,currRing)) |
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122 | { |
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123 | number gAlpha = p_GetCoeff(g,currRing); |
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124 | poly hAlphaT = p_Init(currRing); |
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125 | p_SetCoeff(hAlphaT,n_Copy(p_GetCoeff(hCache,currRing),currRing->cf),currRing); |
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126 | p_SetExp(hAlphaT,1,p_GetExp(hCache,1,currRing)-p_GetExp(g,1,currRing),currRing); |
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127 | for (int i=2; i<=currRing->N; i++) |
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128 | p_SetExp(hAlphaT,i,0,currRing); |
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129 | p_Setm(hAlphaT,currRing); pTest(hAlphaT); |
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130 | h = p_Add_q(p_Mult_nn(h,gAlpha,currRing), |
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131 | p_Neg(p_Mult_q(p_Copy(g,currRing),hAlphaT,currRing),currRing), |
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132 | currRing); |
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133 | pTest(h); |
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134 | return(h); |
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135 | } |
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136 | for (; pNext(hCache); pIter(hCache)) |
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137 | if (p_LeadmonomDivisibleBy(g,pNext(hCache),currRing)) break; |
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138 | if (pNext(hCache)) |
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139 | { |
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140 | number gAlpha = p_GetCoeff(g,currRing); |
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141 | poly hAlphaT = p_Init(currRing); |
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142 | p_SetCoeff(hAlphaT,n_Copy(p_GetCoeff(pNext(hCache),currRing),currRing->cf),currRing); |
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143 | p_SetExp(hAlphaT,1,p_GetExp(pNext(hCache),1,currRing)-p_GetExp(g,1,currRing),currRing); |
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144 | for (int i=2; i<=currRing->N; i++) |
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145 | p_SetExp(hAlphaT,i,0,currRing); |
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146 | p_Setm(hAlphaT,currRing); pTest(hAlphaT); |
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147 | h = p_Add_q(p_Mult_nn(h,gAlpha,currRing), |
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148 | p_Neg(p_Mult_q(p_Copy(g,currRing),hAlphaT,currRing),currRing), |
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149 | currRing); |
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150 | pTest(h); |
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151 | } |
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152 | return pNext(hCache); |
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153 | } |
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154 | |
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155 | |
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156 | #ifndef NDEBUG |
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157 | BOOLEAN reduceInitially0(leftv res, leftv args) |
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158 | { |
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159 | leftv u = args; |
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160 | if ((u != NULL) && (u->Typ() == POLY_CMD)) |
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161 | { |
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162 | leftv v = u->next; |
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163 | if ((v != NULL) && (v->Typ() == POLY_CMD)) |
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164 | { |
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165 | poly g,h; |
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166 | omUpdateInfo(); |
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167 | Print("usedBytesBefore=%ld\n",om_Info.UsedBytes); |
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168 | h = (poly) u->CopyD(); |
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169 | g = (poly) v->CopyD(); |
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170 | (void)reduceInitially(h,g); |
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171 | p_Delete(&h,currRing); |
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172 | p_Delete(&g,currRing); |
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173 | omUpdateInfo(); |
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174 | Print("usedBytesAfter=%ld\n",om_Info.UsedBytes); |
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175 | h = (poly) u->CopyD(); |
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176 | g = (poly) v->CopyD(); |
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177 | (void)reduceInitially(h,g); |
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178 | p_Delete(&g,currRing); |
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179 | res->rtyp = POLY_CMD; |
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180 | res->data = (char*) h; |
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181 | return FALSE; |
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182 | } |
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183 | } |
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184 | return TRUE; |
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185 | } |
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186 | #endif //NDEBUG |
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187 | |
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188 | |
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189 | static inline void sortByLeadmonom(ideal I) |
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190 | { |
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191 | poly cache; int i, n=IDELEMS(I), newn; |
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192 | do |
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193 | { |
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194 | newn=0; |
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195 | for (i=1; i<n; i++) |
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196 | { |
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197 | if (pLmCmp(I->m[i-1],I->m[i])<0) |
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198 | { |
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199 | cache=I->m[i-1]; |
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200 | I->m[i-1]=I->m[i]; |
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201 | I->m[i]=cache; |
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202 | newn = i; |
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203 | } |
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204 | } |
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205 | n=newn; |
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206 | } while(n); |
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207 | } |
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208 | |
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209 | |
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210 | /*** |
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211 | * reduces I initially with respect to itself and with respect to p-t. |
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212 | * assumes that I is generated by elements which are homogeneous in x of the same degree. |
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213 | **/ |
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214 | bool reduceInitially(ideal I, const number p) |
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215 | { |
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216 | sortByLeadmonom(I); int i,j; |
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217 | for (i=1; i<IDELEMS(I); i++) |
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218 | if (pReduce(I->m[i],p)) return true; |
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219 | |
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220 | /*** |
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221 | * the first pass. removing terms with the same monomials in x as lt(g_i) out of g_j for i<j |
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222 | **/ |
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223 | poly cache = NULL; |
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224 | for (i=0; i<IDELEMS(I)-1; i++) |
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225 | { |
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226 | for (j=i+1; j<IDELEMS(I); j++) |
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227 | { |
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228 | cache = reduceInitially(I->m[j], I->m[i]); |
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229 | if (cache) |
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230 | { |
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231 | if(pReduce(cache,p)) return true; |
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232 | cache = NULL; |
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233 | } |
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234 | } |
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235 | } |
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236 | |
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237 | /*** |
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238 | * the second pass. removing terms divisible by lt(g_j) out of g_i for i<j |
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239 | **/ |
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240 | for (i=0; i<IDELEMS(I)-1; i++) |
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241 | { |
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242 | for (j=i+1; j<IDELEMS(I); j++) |
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243 | { |
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244 | cache = reduceInitially(I->m[i], I->m[j]); |
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245 | if (cache) |
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246 | { |
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247 | if (pReduce(cache,p)) return true; |
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248 | cache = NULL; |
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249 | } |
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250 | } |
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251 | } |
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252 | return false; |
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253 | } |
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254 | |
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255 | |
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256 | #ifndef NDEBUG |
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257 | BOOLEAN reduceInitially1(leftv res, leftv args) |
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258 | { |
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259 | leftv u = args; |
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260 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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261 | { |
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262 | leftv v = u->next; |
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263 | if ((v != NULL) && (v->Typ() == NUMBER_CMD)) |
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264 | { |
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265 | ideal I = (ideal) u->CopyD(); |
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266 | number p = (number) v->CopyD(); |
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267 | omUpdateInfo(); |
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268 | Print("usedBytesBefore=%ld\n",om_Info.UsedBytes); |
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269 | (void) reduceInitially(I,p); |
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270 | omUpdateInfo(); |
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271 | Print("usedBytesAfter=%ld\n",om_Info.UsedBytes); |
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272 | n_Delete(&p,currRing->cf); |
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273 | res->rtyp = IDEAL_CMD; |
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274 | res->data = (char*) I; |
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275 | return FALSE; |
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276 | } |
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277 | } |
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278 | return TRUE; |
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279 | } |
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280 | #endif //NDEBUG |
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