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 | /* |
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6 | * ABSTRACT: resolutions |
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7 | */ |
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8 | |
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9 | |
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10 | |
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11 | |
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12 | |
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13 | #include <kernel/mod2.h> |
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14 | #include <misc/options.h> |
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15 | #include <omalloc/omalloc.h> |
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16 | #include <kernel/polys.h> |
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17 | #include <kernel/febase.h> |
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18 | #include <kernel/GBEngine/kstd1.h> |
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19 | #include <kernel/GBEngine/kutil.h> |
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20 | #include <kernel/GBEngine/stairc.h> |
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21 | #include <misc/intvec.h> |
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22 | #include <coeffs/numbers.h> |
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23 | #include <kernel/ideals.h> |
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24 | #include <misc/intvec.h> |
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25 | #include <polys/monomials/ring.h> |
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26 | #include <kernel/GBEngine/syz.h> |
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27 | #include <polys/prCopy.h> |
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28 | |
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29 | #include <polys/nc/sca.h> |
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30 | |
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31 | static intvec * syPrepareModComp(ideal arg,intvec ** w) |
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32 | { |
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33 | intvec *w1 = NULL; |
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34 | int i; |
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35 | BOOLEAN isIdeal=FALSE; |
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36 | |
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37 | if ((w==NULL) || (*w==NULL)) return w1; |
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38 | int maxxx = (*w)->length(); |
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39 | if (maxxx==1) |
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40 | { |
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41 | maxxx = 2; |
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42 | isIdeal = TRUE; |
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43 | } |
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44 | w1 = new intvec(maxxx+IDELEMS(arg)); |
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45 | if (!isIdeal) |
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46 | { |
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47 | for (i=0;i<maxxx;i++) |
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48 | { |
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49 | (*w1)[i] = (**w)[i]; |
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50 | } |
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51 | } |
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52 | for (i=maxxx;i<maxxx+IDELEMS(arg);i++) |
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53 | { |
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54 | if (arg->m[i-maxxx]!=NULL) |
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55 | { |
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56 | (*w1)[i] = p_FDeg(arg->m[i-maxxx],currRing); |
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57 | if (pGetComp(arg->m[i-maxxx])!=0) |
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58 | { |
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59 | (*w1)[i]+=(**w)[pGetComp(arg->m[i-maxxx])-1]; |
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60 | } |
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61 | } |
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62 | } |
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63 | delete (*w); |
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64 | *w = new intvec(IDELEMS(arg)+1); |
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65 | for (i=0;i<IDELEMS(arg);i++) |
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66 | { |
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67 | (**w)[i+1] = (*w1)[i+maxxx]; |
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68 | } |
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69 | return w1; |
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70 | } |
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71 | |
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72 | static void syDeleteAbove(ideal up, int k) |
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73 | { |
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74 | if (up!=NULL) |
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75 | { |
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76 | for (int i=0;i<IDELEMS(up);i++) |
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77 | { |
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78 | if (up->m[i]!=NULL) |
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79 | pDeleteComp(&(up->m[i]),k+1); |
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80 | } |
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81 | } |
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82 | } |
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83 | |
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84 | /*2 |
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85 | *minimizes the module mod and cancel superfluous syzygies |
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86 | *from syz |
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87 | */ |
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88 | static void syMinStep(ideal mod,ideal syz,BOOLEAN final=FALSE,ideal up=NULL, |
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89 | tHomog h=isNotHomog) |
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90 | { |
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91 | ideal deg0=NULL; |
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92 | poly Unit1,Unit2,actWith; |
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93 | int len,i,j,ModComp,m,k,l; |
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94 | BOOLEAN searchUnit,existsUnit; |
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95 | |
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96 | if (TEST_OPT_PROT) PrintS("m"); |
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97 | if ((final) && (h==isHomog)) |
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98 | /*minim is TRUE, we are in the module: maxlength, maxlength <>0*/ |
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99 | { |
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100 | deg0=id_Jet(syz,0,currRing); |
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101 | idSkipZeroes(deg0); |
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102 | syz=deg0; |
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103 | } |
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104 | /*--cancels empty entees and their related components above--*/ |
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105 | j = IDELEMS(syz); |
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106 | while ((j>0) && (!syz->m[j-1])) j--; |
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107 | k = 0; |
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108 | while (k<j) |
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109 | { |
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110 | if (syz->m[k]!=NULL) |
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111 | k++; |
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112 | else |
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113 | { |
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114 | if (TEST_OPT_PROT) PrintS("."); |
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115 | for (l=k;l<j-1;l++) syz->m[l] = syz->m[l+1]; |
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116 | syz->m[j-1] = NULL; |
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117 | syDeleteAbove(up,k); |
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118 | j--; |
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119 | } |
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120 | } |
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121 | /*--searches for syzygies coming from superfluous elements |
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122 | * in the module below--*/ |
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123 | searchUnit = TRUE; |
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124 | int curr_syz_limit = rGetCurrSyzLimit(currRing); |
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125 | while (searchUnit) |
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126 | { |
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127 | i=0; |
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128 | j=IDELEMS(syz); |
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129 | while ((j>0) && (syz->m[j-1]==NULL)) j--; |
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130 | existsUnit = FALSE; |
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131 | if (rHasGlobalOrdering_currRing()) |
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132 | { |
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133 | while ((i<j) && (!existsUnit)) |
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134 | { |
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135 | existsUnit = pVectorHasUnitB(syz->m[i],&ModComp); |
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136 | i++; |
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137 | } |
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138 | } |
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139 | else |
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140 | { |
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141 | int I=0; |
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142 | l = 0; |
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143 | len=0; |
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144 | for (i=0;i<IDELEMS(syz);i++) |
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145 | { |
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146 | if (syz->m[i]!=NULL) |
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147 | { |
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148 | pVectorHasUnit(syz->m[i],&m, &l); |
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149 | if ((len==0) ||((l>0) && (l<len))) |
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150 | { |
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151 | len = l; |
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152 | ModComp = m; |
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153 | I = i; |
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154 | } |
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155 | } |
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156 | } |
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157 | //Print("Laenge ist: %d\n",len); |
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158 | if (len>0) existsUnit = TRUE; |
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159 | i = I+1; |
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160 | } |
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161 | if (existsUnit) |
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162 | { |
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163 | i--; |
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164 | //--takes out the founded syzygy-- |
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165 | if (TEST_OPT_PROT) PrintS("f"); |
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166 | actWith = syz->m[i]; |
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167 | if (!rField_has_simple_inverse(currRing)) p_Cleardenom(actWith, currRing); |
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168 | //Print("actWith: ");pWrite(actWith); |
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169 | syz->m[i] = NULL; |
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170 | for (k=i;k<j-1;k++) syz->m[k] = syz->m[k+1]; |
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171 | syz->m[j-1] = NULL; |
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172 | syDeleteAbove(up,i); |
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173 | j--; |
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174 | //--makes Gauss alg. for the column ModComp-- |
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175 | Unit1 = pTakeOutComp(&(actWith), ModComp); |
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176 | //PrintS("actWith now: ");pWrite(actWith); |
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177 | //Print("Unit1: ");pWrite(Unit1); |
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178 | k=0; |
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179 | //Print("j= %d",j); |
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180 | while (k<j) |
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181 | { |
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182 | if (syz->m[k]!=NULL) |
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183 | { |
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184 | Unit2 = pTakeOutComp(&(syz->m[k]), ModComp); |
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185 | //Print("element %d: ",k);pWrite(syz->m[k]); |
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186 | //PrintS("Unit2: ");pWrite(Unit2); |
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187 | syz->m[k] = pMult(pCopy(Unit1),syz->m[k]); |
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188 | syz->m[k] = pSub(syz->m[k], |
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189 | pMult(Unit2,pCopy(actWith))); |
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190 | if (syz->m[k]==NULL) |
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191 | { |
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192 | for (l=k;l<j-1;l++) |
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193 | syz->m[l] = syz->m[l+1]; |
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194 | syz->m[j-1] = NULL; |
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195 | j--; |
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196 | syDeleteAbove(up,k); |
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197 | k--; |
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198 | } |
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199 | } |
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200 | k++; |
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201 | } |
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202 | pDelete(&actWith); |
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203 | pDelete(&Unit1); |
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204 | //--deletes superfluous elements from the module below--- |
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205 | pDelete(&(mod->m[ModComp-1 - curr_syz_limit])); |
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206 | for (k=ModComp-1 - curr_syz_limit;k<IDELEMS(mod)-1;k++) |
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207 | mod->m[k] = mod->m[k+1]; |
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208 | mod->m[IDELEMS(mod)-1] = NULL; |
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209 | } |
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210 | else |
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211 | searchUnit = FALSE; |
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212 | } |
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213 | if (TEST_OPT_PROT) PrintLn(); |
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214 | idSkipZeroes(mod); |
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215 | idSkipZeroes(syz); |
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216 | if (deg0!=NULL) |
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217 | idDelete(°0); |
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218 | } |
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219 | |
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220 | /*2 |
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221 | * make Gauss with the element elnum in the module component ModComp |
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222 | * for the generators from - till |
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223 | */ |
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224 | void syGaussForOne(ideal syz, int elnum, int ModComp,int from,int till) |
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225 | { |
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226 | int /*k,j,i,*/lu; |
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227 | poly unit1,unit2; |
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228 | poly actWith=syz->m[elnum]; |
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229 | |
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230 | if (from<0) from = 0; |
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231 | if ((till<=0) || (till>IDELEMS(syz))) till = IDELEMS(syz); |
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232 | syz->m[elnum] = NULL; |
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233 | if (!rField_has_simple_inverse(currRing)) p_Cleardenom(actWith, currRing); |
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234 | /*--makes Gauss alg. for the column ModComp--*/ |
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235 | pTakeOutComp(&(actWith), ModComp, &unit1, &lu); |
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236 | while (from<till) |
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237 | { |
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238 | poly tmp=syz->m[from]; |
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239 | if (/*syz->m[from]*/ tmp!=NULL) |
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240 | { |
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241 | pTakeOutComp(&(tmp), ModComp, &unit2, &lu); |
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242 | tmp = pMult(pCopy(unit1),tmp); |
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243 | syz->m[from] = pSub(tmp, |
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244 | pMult(unit2,pCopy(actWith))); |
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245 | } |
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246 | from++; |
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247 | } |
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248 | pDelete(&actWith); |
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249 | pDelete(&unit1); |
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250 | } |
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251 | static void syDeleteAbove1(ideal up, int k) |
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252 | { |
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253 | poly p/*,pp*/; |
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254 | if (up!=NULL) |
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255 | { |
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256 | for (int i=0;i<IDELEMS(up);i++) |
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257 | { |
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258 | p = up->m[i]; |
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259 | while ((p!=NULL) && (pGetComp(p)==k)) |
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260 | { |
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261 | /* |
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262 | pp = pNext(p); |
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263 | pNext(p) = NULL; |
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264 | pDelete(&p); |
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265 | p = pp; |
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266 | */ |
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267 | pLmDelete(&p); |
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268 | } |
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269 | up->m[i] = p; |
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270 | if (p!=NULL) |
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271 | { |
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272 | while (pNext(p)!=NULL) |
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273 | { |
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274 | if (pGetComp(pNext(p))==k) |
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275 | { |
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276 | /* |
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277 | pp = pNext(pNext(p)); |
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278 | pNext(pNext(p)) = NULL; |
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279 | pDelete(&pNext(p)); |
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280 | pNext(p) = pp; |
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281 | */ |
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282 | pLmDelete(&pNext(p)); |
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283 | } |
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284 | else |
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285 | pIter(p); |
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286 | } |
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287 | } |
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288 | } |
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289 | } |
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290 | } |
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291 | /*2 |
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292 | *minimizes the resolution res |
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293 | *assumes homogeneous or local case |
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294 | */ |
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295 | static void syMinStep1(resolvente res, int length) |
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296 | { |
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297 | int i,j,k,index=0; |
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298 | poly p; |
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299 | ideal deg0=NULL,reddeg0=NULL; |
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300 | intvec *have_del=NULL,*to_del=NULL; |
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301 | |
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302 | while ((index<length) && (res[index]!=NULL)) |
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303 | { |
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304 | /*---we take out dependend elements from syz---------------------*/ |
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305 | if (res[index+1]!=NULL) |
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306 | { |
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307 | deg0 = id_Jet(res[index+1],0,currRing); |
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308 | reddeg0 = kInterRedOld(deg0); |
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309 | idDelete(°0); |
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310 | have_del = new intvec(IDELEMS(res[index])); |
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311 | for (i=0;i<IDELEMS(reddeg0);i++) |
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312 | { |
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313 | if (reddeg0->m[i]!=NULL) |
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314 | { |
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315 | j = pGetComp(reddeg0->m[i]); |
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316 | pDelete(&(res[index]->m[j-1])); |
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317 | /*res[index]->m[j-1] = NULL;*/ |
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318 | (*have_del)[j-1] = 1; |
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319 | } |
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320 | } |
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321 | idDelete(&reddeg0); |
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322 | } |
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323 | if (index>0) |
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324 | { |
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325 | /*--- we search for units and perform Gaussian elimination------*/ |
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326 | j = to_del->length(); |
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327 | while (j>0) |
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328 | { |
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329 | if ((*to_del)[j-1]==1) |
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330 | { |
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331 | k = 0; |
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332 | while (k<IDELEMS(res[index])) |
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333 | { |
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334 | p = res[index]->m[k]; |
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335 | while ((p!=NULL) && ((!pLmIsConstantComp(p)) || (pGetComp(p)!=(unsigned)j))) |
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336 | pIter(p); |
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337 | if ((p!=NULL) && (pLmIsConstantComp(p)) && (pGetComp(p)==(unsigned)j)) break; |
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338 | k++; |
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339 | } |
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340 | if (k>=IDELEMS(res[index])) |
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341 | { |
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342 | PrintS("out of range\n"); |
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343 | } |
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344 | syGaussForOne(res[index],k,j); |
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345 | if (res[index+1]!=NULL) |
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346 | syDeleteAbove1(res[index+1],k+1); |
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347 | (*to_del)[j-1] = 0; |
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348 | } |
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349 | j--; |
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350 | } |
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351 | } |
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352 | if (to_del!=NULL) delete to_del; |
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353 | to_del = have_del; |
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354 | have_del = NULL; |
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355 | index++; |
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356 | } |
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357 | if (TEST_OPT_PROT) PrintLn(); |
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358 | syKillEmptyEntres(res,length); |
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359 | } |
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360 | |
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361 | void syMinimizeResolvente(resolvente res, int length, int first) |
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362 | { |
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363 | int syzIndex=first; |
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364 | intvec *dummy; |
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365 | |
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366 | if (syzIndex<1) syzIndex=1; |
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367 | if ((syzIndex==1) && (idHomModule(res[0],currQuotient,&dummy)) && (!rIsPluralRing(currRing))) |
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368 | { |
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369 | syMinStep1(res,length); |
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370 | delete dummy; |
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371 | return; |
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372 | } |
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373 | while ((syzIndex<length-1) && (res[syzIndex]!=NULL) && (res[syzIndex+1]!=NULL)) |
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374 | { |
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375 | syMinStep(res[syzIndex-1],res[syzIndex],FALSE,res[syzIndex+1]); |
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376 | syzIndex++; |
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377 | } |
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378 | if (res[syzIndex]!=NULL) |
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379 | syMinStep(res[syzIndex-1],res[syzIndex]); |
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380 | if (!idIs0(res[0])) |
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381 | idMinEmbedding(res[0],TRUE); |
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382 | } |
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383 | |
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384 | /*2 |
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385 | * resolution of ideal/module arg, <=maxlength steps, (r[0..maxlength]) |
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386 | * no limitation in length if maxlength==0 |
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387 | * input:arg |
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388 | * minim: TRUE means mres cmd, FALSE nres cmd. |
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389 | * if *len!=0: module weights: weights[0] |
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390 | * (and weights is defined:weights[0..len-1] |
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391 | * |
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392 | * output:resolvente r[0..length-1], |
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393 | * module weights: weights[0..length-1] |
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394 | */ |
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395 | resolvente syResolvente(ideal arg, int maxlength, int * length, |
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396 | intvec *** weights, BOOLEAN minim) |
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397 | { |
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398 | BITSET save1; |
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399 | SI_SAVE_OPT1(save1); |
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400 | resolvente res; |
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401 | resolvente newres; |
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402 | tHomog hom=isNotHomog; |
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403 | ideal temp=NULL; |
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404 | intvec *w = NULL,**tempW; |
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405 | int i,k,syzIndex = 0,j,rk_arg=si_max(1,(int)id_RankFreeModule(arg,currRing)); |
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406 | int Kstd1_OldDeg=Kstd1_deg; |
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407 | BOOLEAN completeMinim; |
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408 | BOOLEAN oldDegBound=TEST_OPT_DEGBOUND; |
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409 | BOOLEAN setRegularity=TRUE; |
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410 | int wlength=*length; |
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411 | |
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412 | if (maxlength!=-1) *length = maxlength+1; |
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413 | else *length = 5; |
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414 | if ((wlength!=0) && (*length!=wlength)) |
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415 | { |
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416 | intvec **wtmp = (intvec**)omAlloc0((*length)*sizeof(intvec*)); |
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417 | wtmp[0]=(*weights)[0]; |
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418 | omFreeSize((ADDRESS)*weights,wlength*sizeof(intvec*)); |
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419 | *weights=wtmp; |
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420 | } |
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421 | res = (resolvente)omAlloc0((*length)*sizeof(ideal)); |
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422 | |
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423 | /*--- initialize the syzygy-ring -----------------------------*/ |
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424 | ring origR = currRing; |
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425 | ring syz_ring = rAssure_SyzComp(origR, TRUE); // will do rChangeCurrRing if needed |
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426 | rSetSyzComp(rk_arg, syz_ring); |
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427 | |
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428 | if (syz_ring != origR) |
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429 | { |
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430 | rChangeCurrRing(syz_ring); |
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431 | res[0] = idrCopyR_NoSort(arg, origR, syz_ring); |
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432 | } |
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433 | else |
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434 | { |
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435 | res[0] = idCopy(arg); |
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436 | } |
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437 | |
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438 | /*--- creating weights for the module components ---------------*/ |
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439 | if ((weights!=NULL) && (*weights!=NULL)&& ((*weights)[0]!=NULL)) |
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440 | { |
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441 | if (!idTestHomModule(res[0],currQuotient,(*weights)[0])) |
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442 | { |
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443 | WarnS("wrong weights given(1):"); (*weights)[0]->show();PrintLn(); |
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444 | idHomModule(res[0],currQuotient,&w); |
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445 | w->show();PrintLn(); |
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446 | *weights=NULL; |
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447 | } |
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448 | } |
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449 | |
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450 | if ((weights==NULL) || (*weights==NULL) || ((*weights)[0]==NULL)) |
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451 | { |
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452 | hom=(tHomog)idHomModule(res[0],currQuotient,&w); |
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453 | if (hom==isHomog) |
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454 | { |
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455 | *weights = (intvec**)omAlloc0((*length)*sizeof(intvec*)); |
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456 | if (w!=NULL) (*weights)[0] = ivCopy(w); |
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457 | } |
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458 | } |
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459 | else |
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460 | { |
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461 | if ((weights!=NULL) && (*weights!=NULL)&& ((*weights)[0]!=NULL)) |
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462 | { |
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463 | w = ivCopy((*weights)[0]); |
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464 | hom = isHomog; |
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465 | } |
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466 | } |
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467 | |
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468 | #ifdef HAVE_PLURAL |
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469 | if (rIsPluralRing(currRing) && !rIsSCA(currRing) ) |
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470 | { |
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471 | // quick solution; need theory to apply homog GB stuff for G-Algebras |
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472 | hom = isNotHomog; |
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473 | } |
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474 | #endif // HAVE_PLURAL |
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475 | |
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476 | if (hom==isHomog) |
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477 | { |
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478 | intvec *w1 = syPrepareModComp(res[0],&w); |
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479 | if (w!=NULL) { delete w;w=NULL; } |
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480 | w = w1; |
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481 | j = 0; |
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482 | while ((j<IDELEMS(res[0])) && (res[0]->m[j]==NULL)) j++; |
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483 | if (j<IDELEMS(res[0])) |
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484 | { |
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485 | if (p_FDeg(res[0]->m[j],currRing)!=pTotaldegree(res[0]->m[j])) |
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486 | setRegularity = FALSE; |
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487 | } |
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488 | } |
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489 | else |
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490 | { |
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491 | setRegularity = FALSE; |
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492 | } |
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493 | |
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494 | /*--- the main loop --------------------------------------*/ |
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495 | while ((!idIs0(res[syzIndex])) && |
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496 | ((maxlength==-1) || (syzIndex<=maxlength))) |
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497 | // (syzIndex<maxlength+(int)minim))) |
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498 | /*--- compute one step more for minimizing-----------------*/ |
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499 | { |
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500 | if (Kstd1_deg!=0) Kstd1_deg++; |
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501 | if (syzIndex+1==*length) |
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502 | { |
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503 | newres = (resolvente)omAlloc0((*length+5)*sizeof(ideal)); |
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504 | tempW = (intvec**)omAlloc0((*length+5)*sizeof(intvec*)); |
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505 | for (j=0;j<*length;j++) |
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506 | { |
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507 | newres[j] = res[j]; |
---|
508 | if (*weights!=NULL) tempW[j] = (*weights)[j]; |
---|
509 | /*else tempW[j] = NULL;*/ |
---|
510 | } |
---|
511 | omFreeSize((ADDRESS)res,*length*sizeof(ideal)); |
---|
512 | if (*weights != NULL) omFreeSize((ADDRESS)*weights,*length*sizeof(intvec*)); |
---|
513 | *length += 5; |
---|
514 | res=newres; |
---|
515 | *weights = tempW; |
---|
516 | } |
---|
517 | /*--- interreducing first -----------------------------------*/ |
---|
518 | if (syzIndex>0) |
---|
519 | { |
---|
520 | int rkI=id_RankFreeModule(res[syzIndex],currRing); |
---|
521 | rSetSyzComp(rkI, currRing); |
---|
522 | } |
---|
523 | if(! TEST_OPT_NO_SYZ_MINIM ) |
---|
524 | if (minim || (syzIndex!=0)) |
---|
525 | { |
---|
526 | temp = kInterRedOld(res[syzIndex],currQuotient); |
---|
527 | idDelete(&res[syzIndex]); |
---|
528 | idSkipZeroes(temp); |
---|
529 | res[syzIndex] = temp; |
---|
530 | } |
---|
531 | temp = NULL; |
---|
532 | /*--- computing the syzygy modules --------------------------------*/ |
---|
533 | if ((currQuotient==NULL)&&(syzIndex==0)&& (!TEST_OPT_DEGBOUND)) |
---|
534 | { |
---|
535 | res[/*syzIndex+*/1] = idSyzygies(res[0/*syzIndex*/],hom,&w,FALSE,setRegularity,&Kstd1_deg); |
---|
536 | if ((!TEST_OPT_NOTREGULARITY) && (Kstd1_deg>0) |
---|
537 | #ifdef HAVE_RINGS |
---|
538 | && (!rField_is_Ring(currRing)) |
---|
539 | #endif |
---|
540 | ) si_opt_1 |= Sy_bit(OPT_DEGBOUND); |
---|
541 | } |
---|
542 | else |
---|
543 | { |
---|
544 | res[syzIndex+1] = idSyzygies(res[syzIndex],hom,&w,FALSE); |
---|
545 | } |
---|
546 | completeMinim=(syzIndex!=maxlength) || (maxlength ==-1) || (hom!=isHomog); |
---|
547 | syzIndex++; |
---|
548 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
---|
549 | |
---|
550 | if(! TEST_OPT_NO_SYZ_MINIM ) |
---|
551 | { |
---|
552 | if ((minim)||(syzIndex>1)) |
---|
553 | syMinStep(res[syzIndex-1],res[syzIndex],!completeMinim,NULL,hom); |
---|
554 | if (!completeMinim) |
---|
555 | /*minim is TRUE, we are in the module: maxlength, maxlength <>0*/ |
---|
556 | { |
---|
557 | idDelete(&res[syzIndex]); |
---|
558 | } |
---|
559 | } |
---|
560 | /*---creating the iterated weights for module components ---------*/ |
---|
561 | if ((hom == isHomog) && (!idIs0(res[syzIndex]))) |
---|
562 | { |
---|
563 | //Print("die %d Modulegewichte sind:\n",w1->length()); |
---|
564 | //w1->show(); |
---|
565 | //PrintLn(); |
---|
566 | int max_comp = id_RankFreeModule(res[syzIndex],currRing); |
---|
567 | k = max_comp - rGetCurrSyzLimit(currRing); |
---|
568 | assume(w != NULL); |
---|
569 | if (w != NULL) |
---|
570 | w->resize(max_comp+IDELEMS(res[syzIndex])); |
---|
571 | else |
---|
572 | w = new intvec(max_comp+IDELEMS(res[syzIndex])); |
---|
573 | (*weights)[syzIndex] = new intvec(k); |
---|
574 | for (i=0;i<k;i++) |
---|
575 | { |
---|
576 | if (res[syzIndex-1]->m[i]!=NULL) // hs |
---|
577 | { |
---|
578 | (*w)[i + rGetCurrSyzLimit(currRing)] = p_FDeg(res[syzIndex-1]->m[i],currRing); |
---|
579 | if (pGetComp(res[syzIndex-1]->m[i])>0) |
---|
580 | (*w)[i + rGetCurrSyzLimit(currRing)] |
---|
581 | += (*w)[pGetComp(res[syzIndex-1]->m[i])-1]; |
---|
582 | (*((*weights)[syzIndex]))[i] = (*w)[i+rGetCurrSyzLimit(currRing)]; |
---|
583 | } |
---|
584 | } |
---|
585 | for (i=k;i<k+IDELEMS(res[syzIndex]);i++) |
---|
586 | { |
---|
587 | if (res[syzIndex]->m[i-k]!=NULL) |
---|
588 | (*w)[i+rGetCurrSyzLimit(currRing)] = p_FDeg(res[syzIndex]->m[i-k],currRing) |
---|
589 | +(*w)[pGetComp(res[syzIndex]->m[i-k])-1]; |
---|
590 | } |
---|
591 | } |
---|
592 | } |
---|
593 | /*--- end of the main loop --------------------------------------*/ |
---|
594 | /*--- deleting the temporare data structures --------------------*/ |
---|
595 | if ((syzIndex!=0) && (res[syzIndex]!=NULL) && (idIs0(res[syzIndex]))) |
---|
596 | idDelete(&res[syzIndex]); |
---|
597 | if (w !=NULL) delete w; |
---|
598 | |
---|
599 | Kstd1_deg=Kstd1_OldDeg; |
---|
600 | if (!oldDegBound) |
---|
601 | si_opt_1 &= ~Sy_bit(OPT_DEGBOUND); |
---|
602 | |
---|
603 | for (i=1; i<=syzIndex; i++) |
---|
604 | { |
---|
605 | if (! idIs0(res[i])) |
---|
606 | { |
---|
607 | for (j=0; j<IDELEMS(res[i]); j++) |
---|
608 | { |
---|
609 | p_Shift(&res[i]->m[j], -rGetMaxSyzComp(i, currRing),currRing); |
---|
610 | } |
---|
611 | } |
---|
612 | } |
---|
613 | /*--- going back to the original ring -------------------------*/ |
---|
614 | if (origR != syz_ring) |
---|
615 | { |
---|
616 | rChangeCurrRing(origR); // should not be needed now? |
---|
617 | for (i=0; i<=syzIndex; i++) |
---|
618 | { |
---|
619 | res[i] = idrMoveR_NoSort(res[i], syz_ring, origR); |
---|
620 | } |
---|
621 | rDelete(syz_ring); |
---|
622 | } |
---|
623 | SI_RESTORE_OPT1(save1); |
---|
624 | return res; |
---|
625 | } |
---|
626 | |
---|
627 | syStrategy syResolution(ideal arg, int maxlength,intvec * w, BOOLEAN minim) |
---|
628 | { |
---|
629 | |
---|
630 | #ifdef HAVE_PLURAL |
---|
631 | |
---|
632 | const ideal idSaveCurrQuotient = currQuotient; |
---|
633 | const ideal idSaveCurrRingQuotient = currRing->qideal; |
---|
634 | |
---|
635 | if( rIsSCA(currRing) ) |
---|
636 | { |
---|
637 | |
---|
638 | #ifdef RDEBUG |
---|
639 | // rWrite(currRing); |
---|
640 | // rDebugPrint(currRing); |
---|
641 | #endif |
---|
642 | |
---|
643 | if( ncExtensions(TESTSYZSCAMASK) ) |
---|
644 | { |
---|
645 | currQuotient = SCAQuotient(currRing); |
---|
646 | currRing->qideal = currQuotient; |
---|
647 | } |
---|
648 | |
---|
649 | const unsigned int m_iFirstAltVar = scaFirstAltVar(currRing); |
---|
650 | const unsigned int m_iLastAltVar = scaLastAltVar(currRing); |
---|
651 | |
---|
652 | arg = id_KillSquares(arg, m_iFirstAltVar, m_iLastAltVar, currRing, false); // kill suares in input! |
---|
653 | } |
---|
654 | #endif |
---|
655 | |
---|
656 | syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy)); |
---|
657 | |
---|
658 | if ((w!=NULL) && (!idTestHomModule(arg,currQuotient,w))) // is this right in SCA case??? |
---|
659 | { |
---|
660 | WarnS("wrong weights given(2):");w->show();PrintLn(); |
---|
661 | idHomModule(arg,currQuotient,&w); |
---|
662 | w->show();PrintLn(); |
---|
663 | w=NULL; |
---|
664 | } |
---|
665 | if (w!=NULL) |
---|
666 | { |
---|
667 | result->weights = (intvec**)omAlloc0Bin(char_ptr_bin); |
---|
668 | (result->weights)[0] = ivCopy(w); |
---|
669 | result->length = 1; |
---|
670 | } |
---|
671 | resolvente fr = syResolvente(arg,maxlength,&(result->length),&(result->weights),minim),fr1; |
---|
672 | if (minim) |
---|
673 | { |
---|
674 | result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal)); |
---|
675 | fr1 = result->minres; |
---|
676 | } |
---|
677 | else |
---|
678 | { |
---|
679 | result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal)); |
---|
680 | fr1 = result->fullres; |
---|
681 | } |
---|
682 | for (int i=result->length-1;i>=0;i--) |
---|
683 | { |
---|
684 | if (fr[i]!=NULL) |
---|
685 | fr1[i] = fr[i]; |
---|
686 | fr[i] = NULL; |
---|
687 | } |
---|
688 | omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal)); |
---|
689 | |
---|
690 | |
---|
691 | #ifdef HAVE_PLURAL |
---|
692 | if( rIsSCA(currRing) ) |
---|
693 | { |
---|
694 | |
---|
695 | if( ncExtensions(TESTSYZSCAMASK) ) |
---|
696 | { |
---|
697 | currQuotient = idSaveCurrQuotient; |
---|
698 | currRing->qideal = idSaveCurrRingQuotient; |
---|
699 | } |
---|
700 | |
---|
701 | id_Delete(&arg, currRing); |
---|
702 | } |
---|
703 | #endif |
---|
704 | |
---|
705 | |
---|
706 | return result; |
---|
707 | } |
---|
708 | |
---|
709 | static poly sypCopyConstant(poly inp) |
---|
710 | { |
---|
711 | poly outp=NULL,q; |
---|
712 | |
---|
713 | while (inp!=NULL) |
---|
714 | { |
---|
715 | if (pLmIsConstantComp(inp)) |
---|
716 | { |
---|
717 | if (outp==NULL) |
---|
718 | { |
---|
719 | q = outp = pHead(inp); |
---|
720 | } |
---|
721 | else |
---|
722 | { |
---|
723 | pNext(q) = pHead(inp); |
---|
724 | pIter(q); |
---|
725 | } |
---|
726 | } |
---|
727 | pIter(inp); |
---|
728 | } |
---|
729 | return outp; |
---|
730 | } |
---|
731 | int syDetect(ideal id,int index,BOOLEAN homog,int * degrees,int * tocancel) |
---|
732 | { |
---|
733 | int i, j, k, subFromRank=0; |
---|
734 | ideal temp; |
---|
735 | |
---|
736 | if (idIs0(id)) return 0; |
---|
737 | temp = idInit(IDELEMS(id),id->rank); |
---|
738 | for (i=0;i<IDELEMS(id);i++) |
---|
739 | { |
---|
740 | temp->m[i] = sypCopyConstant(id->m[i]); |
---|
741 | } |
---|
742 | i = IDELEMS(id); |
---|
743 | while ((i>0) && (temp->m[i-1]==NULL)) i--; |
---|
744 | if (i==0) |
---|
745 | { |
---|
746 | idDelete(&temp); |
---|
747 | return 0; |
---|
748 | } |
---|
749 | j = 0; |
---|
750 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
751 | while (j<i) |
---|
752 | { |
---|
753 | if (homog) |
---|
754 | { |
---|
755 | if (index==0) k = p_FDeg(temp->m[j],currRing)+degrees[pGetComp(temp->m[j])]; |
---|
756 | else k = degrees[pGetComp(temp->m[j])]; |
---|
757 | if (k>=index) tocancel[k-index]++; |
---|
758 | if ((k>=0) && (index==0)) subFromRank++; |
---|
759 | } |
---|
760 | else |
---|
761 | { |
---|
762 | tocancel[0]--; |
---|
763 | } |
---|
764 | syGaussForOne(temp,j,pGetComp(temp->m[j]),j+1,i); |
---|
765 | j++; |
---|
766 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
767 | } |
---|
768 | idDelete(&temp); |
---|
769 | return subFromRank; |
---|
770 | } |
---|
771 | |
---|
772 | void syDetect(ideal id,int index,int rsmin, BOOLEAN homog, |
---|
773 | intvec * degrees,intvec * tocancel) |
---|
774 | { |
---|
775 | int * deg=NULL; |
---|
776 | int * tocan=(int*) omAlloc0(tocancel->length()*sizeof(int)); |
---|
777 | int i; |
---|
778 | |
---|
779 | if (homog) |
---|
780 | { |
---|
781 | deg = (int*) omAlloc0(degrees->length()*sizeof(int)); |
---|
782 | for (i=degrees->length();i>0;i--) |
---|
783 | deg[i-1] = (*degrees)[i-1]-rsmin; |
---|
784 | } |
---|
785 | syDetect(id,index,homog,deg,tocan); |
---|
786 | for (i=tocancel->length();i>0;i--) |
---|
787 | (*tocancel)[i-1] = tocan[i-1]; |
---|
788 | if (homog) |
---|
789 | omFreeSize((ADDRESS)deg,degrees->length()*sizeof(int)); |
---|
790 | omFreeSize((ADDRESS)tocan,tocancel->length()*sizeof(int)); |
---|
791 | } |
---|
792 | |
---|
793 | /*2 |
---|
794 | * computes the betti numbers from a given resolution |
---|
795 | * of length 'length' (0..length-1), not necessairily minimal, |
---|
796 | * (if weights are given, they are used) |
---|
797 | * returns the int matrix of betti numbers |
---|
798 | * and the regularity |
---|
799 | */ |
---|
800 | intvec * syBetti(resolvente res,int length, int * regularity, |
---|
801 | intvec* weights,BOOLEAN tomin,int * row_shift) |
---|
802 | { |
---|
803 | //#define BETTI_WITH_ZEROS |
---|
804 | //tomin = FALSE; |
---|
805 | int i,j=0,k=0,l,rows,cols,mr; |
---|
806 | int *temp1,*temp2,*temp3;/*used to compute degrees*/ |
---|
807 | int *tocancel; /*(BOOLEAN)tocancel[i]=element is superfluous*/ |
---|
808 | int r0_len; |
---|
809 | |
---|
810 | /*------ compute size --------------*/ |
---|
811 | *regularity = -1; |
---|
812 | cols = length; |
---|
813 | while ((cols>0) |
---|
814 | && ((res[cols-1]==NULL) |
---|
815 | || (idIs0(res[cols-1])))) |
---|
816 | { |
---|
817 | cols--; |
---|
818 | } |
---|
819 | intvec * result; |
---|
820 | if (idIs0(res[0])) |
---|
821 | { |
---|
822 | if (res[0]==NULL) |
---|
823 | result = new intvec(1,1,1); |
---|
824 | else |
---|
825 | result = new intvec(1,1,res[0]->rank); |
---|
826 | return result; |
---|
827 | } |
---|
828 | intvec *w=NULL; |
---|
829 | if (weights!=NULL) |
---|
830 | { |
---|
831 | if (!idTestHomModule(res[0],currQuotient,weights)) |
---|
832 | { |
---|
833 | WarnS("wrong weights given(3):");weights->show();PrintLn(); |
---|
834 | idHomModule(res[0],currQuotient,&w); |
---|
835 | if (w!=NULL) { w->show();PrintLn();} |
---|
836 | weights=NULL; |
---|
837 | } |
---|
838 | } |
---|
839 | #if 0 |
---|
840 | if (idHomModule(res[0],currQuotient,&w)!=isHomog) |
---|
841 | { |
---|
842 | Warn("betti-command: Input is not homogeneous!"); |
---|
843 | weights=NULL; |
---|
844 | } |
---|
845 | #endif |
---|
846 | if (weights==NULL) weights=w; |
---|
847 | else delete w; |
---|
848 | r0_len=IDELEMS(res[0]); |
---|
849 | while ((r0_len>0) && (res[0]->m[r0_len-1]==NULL)) r0_len--; |
---|
850 | #ifdef SHOW_W |
---|
851 | PrintS("weights:");if (weights!=NULL) weights->show(); else Print("NULL"); PrintLn(); |
---|
852 | #endif |
---|
853 | int rkl=l = si_max(id_RankFreeModule(res[0],currRing),res[0]->rank); |
---|
854 | i = 0; |
---|
855 | while ((i<length) && (res[i]!=NULL)) |
---|
856 | { |
---|
857 | if (IDELEMS(res[i])>l) l = IDELEMS(res[i]); |
---|
858 | i++; |
---|
859 | } |
---|
860 | temp1 = (int*)omAlloc0((l+1)*sizeof(int)); |
---|
861 | temp2 = (int*)omAlloc((l+1)*sizeof(int)); |
---|
862 | rows = 1; |
---|
863 | mr = 1; |
---|
864 | cols++; |
---|
865 | for (i=0;i<cols-1;i++) |
---|
866 | { |
---|
867 | if ((i==0) && (weights!=NULL)) p_SetModDeg(weights, currRing); |
---|
868 | memset(temp2,0,(l+1)*sizeof(int)); |
---|
869 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
870 | { |
---|
871 | if (res[i]->m[j]!=NULL) |
---|
872 | { |
---|
873 | if ((pGetComp(res[i]->m[j])>(unsigned)l) |
---|
874 | || ((i>1) && (res[i-1]->m[pGetComp(res[i]->m[j])-1]==NULL))) |
---|
875 | { |
---|
876 | WerrorS("input not a resolvent"); |
---|
877 | omFreeSize((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
878 | omFreeSize((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
879 | return NULL; |
---|
880 | } |
---|
881 | temp2[j+1] = p_FDeg(res[i]->m[j],currRing)+temp1[pGetComp(res[i]->m[j])]; |
---|
882 | if (temp2[j+1]-i>rows) rows = temp2[j+1]-i; |
---|
883 | if (temp2[j+1]-i<mr) mr = temp2[j+1]-i; |
---|
884 | } |
---|
885 | } |
---|
886 | if ((i==0) && (weights!=NULL)) p_SetModDeg(NULL, currRing); |
---|
887 | temp3 = temp1; |
---|
888 | temp1 = temp2; |
---|
889 | temp2 = temp3; |
---|
890 | } |
---|
891 | mr--; |
---|
892 | if (weights!=NULL) |
---|
893 | { |
---|
894 | for(j=0;j<weights->length();j++) |
---|
895 | { |
---|
896 | if (rows <(*weights)[j]+1) rows=(-mr)+(*weights)[j]+1; |
---|
897 | } |
---|
898 | } |
---|
899 | /*------ computation betti numbers --------------*/ |
---|
900 | rows -= mr; |
---|
901 | result = new intvec(rows+1,cols,0); |
---|
902 | if (weights!=NULL) |
---|
903 | { |
---|
904 | for(j=0;j<weights->length();j++) |
---|
905 | { |
---|
906 | IMATELEM((*result),(-mr)+(*weights)[j]+1,1) ++; |
---|
907 | //Print("imat(%d,%d)++ -> %d\n",(-mr)+(*weights)[j]+1, 1, IMATELEM((*result),(-mr)+(*weights)[j]+1,1)); |
---|
908 | } |
---|
909 | } |
---|
910 | else |
---|
911 | { |
---|
912 | (*result)[(-mr)*cols] = /*idRankFreeModule(res[0])*/ rkl; |
---|
913 | if ((!idIs0(res[0])) && ((*result)[(-mr)*cols]==0)) |
---|
914 | (*result)[(-mr)*cols] = 1; |
---|
915 | } |
---|
916 | tocancel = (int*)omAlloc0((rows+1)*sizeof(int)); |
---|
917 | memset(temp1,0,(l+1)*sizeof(int)); |
---|
918 | if (weights!=NULL) |
---|
919 | { |
---|
920 | memset(temp2,0,l*sizeof(int)); |
---|
921 | p_SetModDeg(weights, currRing); |
---|
922 | } |
---|
923 | else |
---|
924 | memset(temp2,0,l*sizeof(int)); |
---|
925 | syDetect(res[0],0,TRUE,temp2,tocancel); |
---|
926 | if (weights!=NULL) p_SetModDeg(NULL, currRing); |
---|
927 | if (tomin) |
---|
928 | { |
---|
929 | //(*result)[(-mr)*cols] -= dummy; |
---|
930 | for(j=0;j<=rows+mr;j++) |
---|
931 | { |
---|
932 | //Print("tocancel[%d]=%d imat(%d,%d)=%d\n",j,tocancel[j],(-mr)+j+1,1,IMATELEM((*result),(-mr)+j+1,1)); |
---|
933 | IMATELEM((*result),(-mr)+j+1,1) -= tocancel[j]; |
---|
934 | } |
---|
935 | } |
---|
936 | for (i=0;i<cols-1;i++) |
---|
937 | { |
---|
938 | if ((i==0) && (weights!=NULL)) p_SetModDeg(weights, currRing); |
---|
939 | memset(temp2,0,l*sizeof(int)); |
---|
940 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
941 | { |
---|
942 | if (res[i]->m[j]!=NULL) |
---|
943 | { |
---|
944 | temp2[j+1] = p_FDeg(res[i]->m[j],currRing)+temp1[pGetComp(res[i]->m[j])]; |
---|
945 | //(*result)[i+1+(temp2[j+1]-i-1)*cols]++; |
---|
946 | //if (temp2[j+1]>i) IMATELEM((*result),temp2[j+1]-i-mr,i+2)++; |
---|
947 | IMATELEM((*result),temp2[j+1]-i-mr,i+2)++; |
---|
948 | } |
---|
949 | else if (i==0) |
---|
950 | { |
---|
951 | if (j<r0_len) IMATELEM((*result),-mr,2)++; |
---|
952 | } |
---|
953 | } |
---|
954 | /*------ computation betti numbers, if res not minimal --------------*/ |
---|
955 | if (tomin) |
---|
956 | { |
---|
957 | for (j=mr;j<rows+mr;j++) |
---|
958 | { |
---|
959 | //(*result)[i+1+j*cols] -= tocancel[j+1]; |
---|
960 | IMATELEM((*result),j+1-mr,i+2) -= tocancel[j+1]; |
---|
961 | } |
---|
962 | if ((i<length-1) && (res[i+1]!=NULL)) |
---|
963 | { |
---|
964 | memset(tocancel,0,(rows+1)*sizeof(int)); |
---|
965 | syDetect(res[i+1],i+1,TRUE,temp2,tocancel); |
---|
966 | for (j=0;j<rows;j++) |
---|
967 | { |
---|
968 | //(*result)[i+1+j*cols] -= tocancel[j]; |
---|
969 | IMATELEM((*result),j+1,i+2) -= tocancel[j]; |
---|
970 | } |
---|
971 | } |
---|
972 | } |
---|
973 | temp3 = temp1; |
---|
974 | temp1 = temp2; |
---|
975 | temp2 = temp3; |
---|
976 | for (j=0;j<=rows;j++) |
---|
977 | { |
---|
978 | // if (((*result)[i+1+j*cols]!=0) && (j>*regularity)) *regularity = j; |
---|
979 | if ((IMATELEM((*result),j+1,i+2)!=0) && (j>*regularity)) *regularity = j; |
---|
980 | } |
---|
981 | if ((i==0) && (weights!=NULL)) p_SetModDeg(NULL, currRing); |
---|
982 | } |
---|
983 | // Print("nach minim:\n"); result->show(); PrintLn(); |
---|
984 | /*------ clean up --------------*/ |
---|
985 | omFreeSize((ADDRESS)tocancel,(rows+1)*sizeof(int)); |
---|
986 | omFreeSize((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
987 | omFreeSize((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
988 | if ((tomin) && (mr<0)) // deletes the first (zero) line |
---|
989 | { |
---|
990 | for (j=1;j<=rows+mr+1;j++) |
---|
991 | { |
---|
992 | for (k=1;k<=cols;k++) |
---|
993 | { |
---|
994 | IMATELEM((*result),j,k) = IMATELEM((*result),j-mr,k); |
---|
995 | } |
---|
996 | } |
---|
997 | for (j=rows+mr+1;j<=rows+1;j++) |
---|
998 | { |
---|
999 | for (k=1;k<=cols;k++) |
---|
1000 | { |
---|
1001 | IMATELEM((*result),j,k) = 0; |
---|
1002 | } |
---|
1003 | } |
---|
1004 | } |
---|
1005 | j = 0; |
---|
1006 | k = 0; |
---|
1007 | for (i=1;i<=result->rows();i++) |
---|
1008 | { |
---|
1009 | for(l=1;l<=result->cols();l++) |
---|
1010 | if (IMATELEM((*result),i,l) != 0) |
---|
1011 | { |
---|
1012 | j = si_max(j, i-1); |
---|
1013 | k = si_max(k, l-1); |
---|
1014 | } |
---|
1015 | } |
---|
1016 | intvec * exactresult=new intvec(j+1,k+1,0); |
---|
1017 | for (i=0;i<exactresult->rows();i++) |
---|
1018 | { |
---|
1019 | for (j=0;j<exactresult->cols();j++) |
---|
1020 | { |
---|
1021 | IMATELEM(*exactresult,i+1,j+1) = IMATELEM(*result,i+1,j+1); |
---|
1022 | } |
---|
1023 | } |
---|
1024 | if (row_shift!=NULL) *row_shift = mr; |
---|
1025 | delete result; |
---|
1026 | return exactresult; |
---|
1027 | } |
---|
1028 | |
---|
1029 | /*2 |
---|
1030 | * minbare via syzygies |
---|
1031 | */ |
---|
1032 | ideal syMinBase(ideal arg) |
---|
1033 | { |
---|
1034 | intvec ** weights=NULL; |
---|
1035 | int leng; |
---|
1036 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
1037 | resolvente res=syResolvente(arg,1,&leng,&weights,TRUE); |
---|
1038 | ideal result=res[0]; |
---|
1039 | omFreeSize((ADDRESS)res,leng*sizeof(ideal)); |
---|
1040 | if (weights!=NULL) |
---|
1041 | { |
---|
1042 | if (*weights!=NULL) |
---|
1043 | { |
---|
1044 | delete (*weights); |
---|
1045 | *weights=NULL; |
---|
1046 | } |
---|
1047 | if ((leng>=1) && (*(weights+1)!=NULL)) |
---|
1048 | { |
---|
1049 | delete *(weights+1); |
---|
1050 | *(weights+1)=NULL; |
---|
1051 | } |
---|
1052 | } |
---|
1053 | idSkipZeroes(result); |
---|
1054 | return result; |
---|
1055 | } |
---|
1056 | |
---|
1057 | #if 0 /* currently used: syBetti */ |
---|
1058 | /*2 |
---|
1059 | * computes Betti-numbers from a resolvente of |
---|
1060 | * (non-)homogeneous objects |
---|
1061 | * the numbers of entrees !=NULL in res and weights must be equal |
---|
1062 | * and < length |
---|
1063 | */ |
---|
1064 | intvec * syNewBetti(resolvente res, intvec ** weights, int length) |
---|
1065 | { |
---|
1066 | intvec * result,*tocancel; |
---|
1067 | int i,j,k,rsmin=0,rsmax=0,rs=0; |
---|
1068 | BOOLEAN homog=TRUE; |
---|
1069 | |
---|
1070 | if (weights!=NULL) //---homogeneous Betti numbers |
---|
1071 | { |
---|
1072 | /*--------------computes size of the field----------------------*/ |
---|
1073 | for (i=1;i<length;i++) |
---|
1074 | { |
---|
1075 | if (weights[i] != NULL) |
---|
1076 | { |
---|
1077 | for (j=1;j<(weights[i])->length();j++) |
---|
1078 | { |
---|
1079 | if ((*(weights[i]))[j]-i<rsmin) rsmin = (*(weights[i]))[j]-i; |
---|
1080 | if ((*(weights[i]))[j]-i>rsmax) rsmax = (*(weights[i]))[j]-i; |
---|
1081 | } |
---|
1082 | } |
---|
1083 | } |
---|
1084 | i = 0; |
---|
1085 | while (weights[i] != NULL) i++; |
---|
1086 | i--; |
---|
1087 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1088 | { |
---|
1089 | if (res[i]->m[j]!=NULL) |
---|
1090 | { |
---|
1091 | k = p_FDeg(res[i]->m[j],currRing)+(*(weights[i]))[pGetComp(res[i]->m[j])]-i-1; |
---|
1092 | if (k>rsmax) rsmax = k; |
---|
1093 | if (k<rsmin) rsmin = k; |
---|
1094 | } |
---|
1095 | } |
---|
1096 | for (j=1;j<(weights[0])->length();j++) |
---|
1097 | { |
---|
1098 | if ((*weights[0])[j]>rsmax) rsmax = (*weights[0])[j]; |
---|
1099 | if ((*weights[0])[j]<rsmin) rsmin = (*weights[0])[j]; |
---|
1100 | } |
---|
1101 | //Print("rsmax = %d\n",rsmax); |
---|
1102 | //Print("rsmin = %d\n",rsmin); |
---|
1103 | rs = rsmax-rsmin+1; |
---|
1104 | result = new intvec(rs,i+2,0); |
---|
1105 | tocancel = new intvec(rs); |
---|
1106 | /*-----------enter the Betti numbers-------------------------------*/ |
---|
1107 | if (/*idRankFreeModule(res[0])*/ res[0]->rank==0) |
---|
1108 | { |
---|
1109 | IMATELEM(*result,1-rsmin,1)=1; |
---|
1110 | } |
---|
1111 | else |
---|
1112 | { |
---|
1113 | for (i=1;i<(weights[0])->length();i++) |
---|
1114 | IMATELEM(*result,(*weights[0])[i]+1-rsmin,1)++; |
---|
1115 | } |
---|
1116 | i = 1; |
---|
1117 | while (weights[i]!=NULL) |
---|
1118 | { |
---|
1119 | for (j=1;j<(weights[i])->length();j++) |
---|
1120 | { |
---|
1121 | IMATELEM(*result,(*(weights[i]))[j]-i+1-rsmin,i+1)++; |
---|
1122 | } |
---|
1123 | i++; |
---|
1124 | } |
---|
1125 | i--; |
---|
1126 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1127 | { |
---|
1128 | if (res[i]->m[j]!=NULL) |
---|
1129 | { |
---|
1130 | k = p_FDeg(res[i]->m[j],currRing)+(*(weights[i]))[pGetComp(res[i]->m[j])]-i; |
---|
1131 | IMATELEM(*result,k-rsmin,i+2)++; |
---|
1132 | } |
---|
1133 | } |
---|
1134 | } |
---|
1135 | else //-----the non-homgeneous case |
---|
1136 | { |
---|
1137 | homog = FALSE; |
---|
1138 | tocancel = new intvec(1); |
---|
1139 | k = length; |
---|
1140 | while ((k>0) && (idIs0(res[k-1]))) k--; |
---|
1141 | result = new intvec(1,k+1,0); |
---|
1142 | (*result)[0] = res[0]->rank; |
---|
1143 | for (i=0;i<length;i++) |
---|
1144 | { |
---|
1145 | if (res[i]!=NULL) |
---|
1146 | { |
---|
1147 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1148 | { |
---|
1149 | if (res[i]->m[j]!=NULL) (*result)[i+1]++; |
---|
1150 | } |
---|
1151 | } |
---|
1152 | } |
---|
1153 | } |
---|
1154 | /*--------computes the Betti numbers for the minimized reolvente----*/ |
---|
1155 | |
---|
1156 | i = 1; |
---|
1157 | while ((res[i]!=NULL) && (weights[i]!=NULL)) |
---|
1158 | { |
---|
1159 | syDetect(res[i],i,rsmin,homog,weights[i],tocancel); |
---|
1160 | if (homog) |
---|
1161 | { |
---|
1162 | for (j=0;j<rs-1;j++) |
---|
1163 | { |
---|
1164 | IMATELEM((*result),j+1,i+1) -= (*tocancel)[j]; |
---|
1165 | IMATELEM((*result),j+1,i+2) -= (*tocancel)[j+1]; |
---|
1166 | } |
---|
1167 | IMATELEM((*result),rs,i+1) -= (*tocancel)[rs-1]; |
---|
1168 | } |
---|
1169 | else |
---|
1170 | { |
---|
1171 | (*result)[i+1] -= (*tocancel)[0]; |
---|
1172 | (*result)[i+2] -= (*tocancel)[0]; |
---|
1173 | } |
---|
1174 | i++; |
---|
1175 | } |
---|
1176 | |
---|
1177 | /*--------print Betti numbers for control---------------------------*/ |
---|
1178 | for(i=rsmin;i<=rsmax;i++) |
---|
1179 | { |
---|
1180 | Print("%2d:",i); |
---|
1181 | for(j=1;j<=result->cols();j++) |
---|
1182 | { |
---|
1183 | Print(" %5d",IMATELEM(*result,i-rsmin+1,j)); |
---|
1184 | } |
---|
1185 | PrintLn(); |
---|
1186 | } |
---|
1187 | return result; |
---|
1188 | } |
---|
1189 | #endif |
---|
1190 | |
---|