1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: syz.cc,v 1.15 1999-03-08 17:30:53 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT: resolutions |
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8 | */ |
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9 | |
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10 | |
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11 | #include "mod2.h" |
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12 | #include "tok.h" |
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13 | #include "mmemory.h" |
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14 | #include "polys.h" |
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15 | #include "febase.h" |
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16 | #include "kstd1.h" |
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17 | #include "kutil.h" |
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18 | #include "spolys.h" |
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19 | #include "stairc.h" |
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20 | #include "ipid.h" |
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21 | #include "cntrlc.h" |
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22 | #include "ipid.h" |
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23 | #include "intvec.h" |
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24 | #include "ipshell.h" |
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25 | #include "numbers.h" |
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26 | #include "ideals.h" |
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27 | #include "intvec.h" |
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28 | #include "ring.h" |
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29 | #include "syz.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] = pFDeg(arg->m[i-maxxx]); |
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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=idJet(syz,0); |
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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 | while (searchUnit) |
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125 | { |
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126 | i=0; |
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127 | j=IDELEMS(syz); |
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128 | while ((j>0) && (syz->m[j-1]==NULL)) j--; |
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129 | existsUnit = FALSE; |
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130 | if (currRing->OrdSgn == 1) |
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131 | { |
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132 | while ((i<j) && (!existsUnit)) |
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133 | { |
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134 | existsUnit = pVectorHasUnitB(syz->m[i],&ModComp); |
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135 | i++; |
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136 | } |
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137 | } |
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138 | else |
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139 | { |
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140 | int I=0; |
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141 | l = 0; |
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142 | len=0; |
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143 | for (i=0;i<IDELEMS(syz);i++) |
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144 | { |
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145 | if (syz->m[i]!=NULL) |
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146 | { |
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147 | pVectorHasUnit(syz->m[i],&m, &l); |
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148 | if ((len==0) ||((l>0) && (l<len))) |
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149 | { |
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150 | len = l; |
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151 | ModComp = m; |
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152 | I = i; |
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153 | } |
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154 | } |
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155 | } |
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156 | //Print("Laenge ist: %d\n",len); |
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157 | if (len>0) existsUnit = TRUE; |
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158 | i = I+1; |
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159 | } |
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160 | if (existsUnit) |
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161 | { |
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162 | i--; |
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163 | //--takes out the founded syzygy-- |
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164 | if (TEST_OPT_PROT) PrintS("f"); |
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165 | actWith = syz->m[i]; |
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166 | if (!rField_has_simple_inverse()) pCleardenom(actWith); |
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167 | //Print("actWith: ");pWrite(actWith); |
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168 | syz->m[i] = NULL; |
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169 | for (k=i;k<j-1;k++) syz->m[k] = syz->m[k+1]; |
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170 | syz->m[j-1] = NULL; |
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171 | syDeleteAbove(up,i); |
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172 | j--; |
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173 | //--makes Gauss alg. for the column ModComp-- |
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174 | Unit1 = pTakeOutComp(&(actWith), ModComp); |
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175 | //PrintS("actWith now: ");pWrite(actWith); |
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176 | //Print("Unit1: ");pWrite(Unit1); |
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177 | k=0; |
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178 | //Print("j= %d",j); |
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179 | while (k<j) |
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180 | { |
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181 | if (syz->m[k]!=NULL) |
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182 | { |
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183 | Unit2 = pTakeOutComp(&(syz->m[k]), ModComp); |
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184 | //Print("element %d: ",k);pWrite(syz->m[k]); |
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185 | //PrintS("Unit2: ");pWrite(Unit2); |
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186 | syz->m[k] = pMult(syz->m[k],pCopy(Unit1)); |
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187 | syz->m[k] = pSub(syz->m[k], |
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188 | pMult(pCopy(actWith),Unit2)); |
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189 | if (syz->m[k]==NULL) |
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190 | { |
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191 | for (l=k;l<j-1;l++) |
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192 | syz->m[l] = syz->m[l+1]; |
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193 | syz->m[j-1] = NULL; |
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194 | j--; |
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195 | syDeleteAbove(up,k); |
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196 | k--; |
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197 | } |
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198 | } |
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199 | k++; |
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200 | } |
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201 | pDelete(&actWith); |
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202 | pDelete(&Unit1); |
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203 | //--deletes superfluous elements from the module below--- |
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204 | pDelete(&(mod->m[ModComp-1])); |
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205 | for (k=ModComp-1;k<IDELEMS(mod)-1;k++) |
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206 | mod->m[k] = mod->m[k+1]; |
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207 | mod->m[IDELEMS(mod)-1] = NULL; |
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208 | } |
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209 | else |
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210 | searchUnit = FALSE; |
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211 | } |
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212 | if (TEST_OPT_PROT) PrintLn(); |
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213 | idSkipZeroes(mod); |
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214 | idSkipZeroes(syz); |
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215 | if (deg0!=NULL) |
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216 | idDelete(°0); |
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217 | } |
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218 | |
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219 | /*2 |
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220 | * make Gauss for one element |
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221 | */ |
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222 | static void syGaussForOne(ideal syz, int elnum, int ModComp) |
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223 | { |
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224 | int k,j,i; |
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225 | poly unit1,unit2; |
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226 | poly actWith=syz->m[elnum]; |
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227 | |
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228 | syz->m[elnum] = NULL; |
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229 | if (!rField_has_simple_inverse()) pCleardenom(actWith); |
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230 | /*--makes Gauss alg. for the column ModComp--*/ |
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231 | unit1 = pTakeOutComp1(&(actWith), ModComp); |
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232 | k=0; |
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233 | while (k<IDELEMS(syz)) |
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234 | { |
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235 | if (syz->m[k]!=NULL) |
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236 | { |
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237 | unit2 = pTakeOutComp1(&(syz->m[k]), ModComp); |
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238 | syz->m[k] = pMult(syz->m[k],pCopy(unit1)); |
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239 | syz->m[k] = pSub(syz->m[k], |
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240 | pMult(pCopy(actWith),unit2)); |
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241 | if (syz->m[k]==NULL) |
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242 | { |
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243 | PrintS("Hier muss noch was gemacht werden\n"); |
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244 | } |
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245 | } |
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246 | k++; |
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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 | pp = pNext(p); |
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262 | pNext(p) = NULL; |
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263 | pDelete(&p); |
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264 | p = pp; |
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265 | } |
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266 | up->m[i] = p; |
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267 | if (p!=NULL) |
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268 | { |
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269 | while (pNext(p)!=NULL) |
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270 | { |
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271 | if (pGetComp(pNext(p))==k) |
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272 | { |
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273 | pp = pNext(pNext(p)); |
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274 | pNext(pNext(p)) = NULL; |
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275 | pDelete(&pNext(p)); |
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276 | pNext(p) = pp; |
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277 | } |
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278 | else |
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279 | pIter(p); |
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280 | } |
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281 | } |
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282 | } |
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283 | } |
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284 | } |
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285 | /*2 |
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286 | *minimizes the resolution res |
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287 | *assumes homogeneous or local case |
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288 | */ |
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289 | static void syMinStep1(resolvente res, int length) |
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290 | { |
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291 | int i,j,k,l,index=0; |
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292 | poly p; |
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293 | ideal deg0=NULL,reddeg0=NULL; |
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294 | intvec *have_del=NULL,*to_del=NULL; |
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295 | |
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296 | while ((index<length) && (res[index]!=NULL)) |
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297 | { |
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298 | /*---we take out dependend elements from syz---------------------*/ |
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299 | if (res[index+1]!=NULL) |
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300 | { |
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301 | deg0 = idJet(res[index+1],0); |
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302 | reddeg0 = kInterRed(deg0); |
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303 | idDelete(°0); |
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304 | have_del = new intvec(IDELEMS(res[index])); |
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305 | for (i=0;i<IDELEMS(reddeg0);i++) |
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306 | { |
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307 | if (reddeg0->m[i]!=NULL) |
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308 | { |
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309 | j = pGetComp(reddeg0->m[i]); |
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310 | pDelete(&(res[index]->m[j-1])); |
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311 | res[index]->m[j-1] = NULL; |
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312 | (*have_del)[j-1] = 1; |
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313 | } |
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314 | } |
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315 | idDelete(&reddeg0); |
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316 | } |
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317 | if (index>0) |
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318 | { |
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319 | /*--- we search for units and perform Gaussian elimination------*/ |
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320 | j = to_del->length(); |
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321 | while (j>0) |
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322 | { |
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323 | if ((*to_del)[j-1]==1) |
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324 | { |
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325 | k = 0; |
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326 | while (k<IDELEMS(res[index])) |
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327 | { |
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328 | p = res[index]->m[k]; |
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329 | while ((p!=NULL) && ((!pIsConstantComp(p)) || (pGetComp(p)!=j))) |
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330 | pIter(p); |
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331 | if ((p!=NULL) && (pIsConstantComp(p)) && (pGetComp(p)==j)) break; |
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332 | k++; |
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333 | } |
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334 | if (k>=IDELEMS(res[index])) |
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335 | { |
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336 | PrintS("out of range\n"); |
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337 | } |
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338 | syGaussForOne(res[index],k,j); |
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339 | if (res[index+1]!=NULL) |
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340 | syDeleteAbove1(res[index+1],k+1); |
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341 | (*to_del)[j-1] = 0; |
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342 | } |
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343 | j--; |
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344 | } |
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345 | } |
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346 | if (to_del!=NULL) delete to_del; |
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347 | to_del = have_del; |
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348 | have_del = NULL; |
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349 | index++; |
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350 | } |
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351 | PrintLn(); |
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352 | syKillEmptyEntres(res,length); |
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353 | } |
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354 | |
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355 | void syMinimizeResolvente(resolvente res, int length, int first) |
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356 | { |
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357 | int syzIndex=first; |
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358 | intvec *dummy; |
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359 | |
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360 | if (syzIndex<1) syzIndex=1; |
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361 | if ((syzIndex==1) && (idHomModule(res[0],currQuotient,&dummy))) |
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362 | { |
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363 | syMinStep1(res,length); |
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364 | delete dummy; |
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365 | return; |
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366 | } |
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367 | while ((syzIndex<length-1) && (res[syzIndex]!=NULL) && (res[syzIndex+1]!=NULL)) |
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368 | { |
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369 | syMinStep(res[syzIndex-1],res[syzIndex],FALSE,res[syzIndex+1]); |
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370 | syzIndex++; |
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371 | } |
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372 | if (res[syzIndex]!=NULL) |
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373 | syMinStep(res[syzIndex-1],res[syzIndex]); |
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374 | } |
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375 | |
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376 | /*2 |
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377 | * resolution of ideal/module arg, <=maxlength steps, (r[0..maxlength]) |
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378 | * no limitation in length if maxlength==0 |
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379 | * input:arg |
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380 | * minim: TRUE means mres cmd, FALSE res cmd. |
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381 | * if *len!=0: modul weights: weights[0] |
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382 | * (and weights is defined:weights[0..len-1] |
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383 | * |
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384 | * output:resolvente r[0..length-1], |
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385 | * modul weights: weights[0..length-1] |
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386 | */ |
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387 | resolvente syResolvente(ideal arg, int maxlength, int * length, |
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388 | intvec *** weights, BOOLEAN minim) |
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389 | { |
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390 | resolvente res; |
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391 | resolvente newres; |
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392 | tHomog hom=isNotHomog; |
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393 | ideal temp=NULL; |
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394 | intvec *w,*w1=NULL,**tempW; |
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395 | int i,k,syzIndex = 0,j; |
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396 | int Kstd1_OldDeg=Kstd1_deg; |
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397 | BOOLEAN completeMinim; |
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398 | BOOLEAN oldDegBound=TEST_OPT_DEGBOUND; |
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399 | int wlength=*length; |
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400 | |
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401 | if (maxlength!=-1) *length = maxlength+1; |
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402 | else *length = 5; |
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403 | if ((wlength!=0) && (*length!=wlength)) |
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404 | { |
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405 | intvec **wtmp = (intvec**)Alloc0((*length)*sizeof(intvec*)); |
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406 | wtmp[0]=(*weights)[0]; |
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407 | Free((ADDRESS)*weights,wlength*sizeof(intvec*)); |
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408 | *weights=wtmp; |
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409 | } |
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410 | res = (resolvente)Alloc0((*length)*sizeof(ideal)); |
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411 | res[0] = idCopy(arg); |
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412 | if ((weights==NULL) || (*weights==NULL) || ((*weights)[0]==NULL)) |
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413 | { |
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414 | hom=(tHomog)idHomModule(res[0],currQuotient,&w); |
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415 | if (hom==isHomog) |
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416 | { |
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417 | *weights = (intvec**)Alloc0((*length)*sizeof(intvec*)); |
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418 | if (w!=NULL) (*weights)[0] = ivCopy(w); |
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419 | //Print("die %d Modulegewichte sind:\n",w->length()); |
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420 | //w->show(); |
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421 | //PrintLn(); |
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422 | } |
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423 | } |
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424 | else |
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425 | { |
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426 | if ((weights!=NULL) && (*weights!=NULL)&& ((*weights)[0]!=NULL)) |
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427 | { |
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428 | w = ivCopy((*weights)[0]); |
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429 | hom = isHomog; |
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430 | } |
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431 | } |
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432 | if (hom==isHomog) |
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433 | { |
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434 | w1 = syPrepareModComp(res[0],&w); |
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435 | if (w!=NULL) { delete w;w=NULL; } |
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436 | } |
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437 | while ((!idIs0(res[syzIndex])) && |
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438 | ((maxlength==-1) || (syzIndex<=maxlength))) |
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439 | // (syzIndex<maxlength+(int)minim))) |
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440 | /*compute one step more for minimizing*/ |
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441 | { |
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442 | if (Kstd1_deg!=0) Kstd1_deg++; |
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443 | if (syzIndex+1==*length) |
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444 | { |
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445 | newres = (resolvente)Alloc0((*length+5)*sizeof(ideal)); |
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446 | tempW = (intvec**)Alloc0((*length+5)*sizeof(intvec*)); |
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447 | for (j=0;j<*length;j++) |
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448 | { |
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449 | newres[j] = res[j]; |
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450 | if (*weights!=NULL) tempW[j] = (*weights)[j]; |
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451 | /*else tempW[j] = NULL;*/ |
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452 | } |
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453 | Free((ADDRESS)res,*length*sizeof(ideal)); |
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454 | Free((ADDRESS)*weights,*length*sizeof(intvec*)); |
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455 | *length += 5; |
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456 | res=newres; |
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457 | *weights = tempW; |
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458 | } |
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459 | if (minim || (syzIndex!=0)) |
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460 | { |
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461 | temp = kInterRed(res[syzIndex],currQuotient); |
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462 | idDelete(&res[syzIndex]); |
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463 | idSkipZeroes(temp); |
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464 | res[syzIndex] = temp; |
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465 | } |
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466 | temp = NULL; |
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467 | if ((currQuotient==NULL)&&(syzIndex==0)&& (!TEST_OPT_DEGBOUND)) |
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468 | { |
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469 | res[/*syzIndex+*/1] = idSyzygies(res[0/*syzIndex*/], |
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470 | NULL/*currQuotient*/,hom,&w1,TRUE,Kstd1_deg); |
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471 | if ((!TEST_OPT_NOTREGULARITY) && (Kstd1_deg>0)) test |= Sy_bit(OPT_DEGBOUND); |
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472 | } |
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473 | else |
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474 | res[syzIndex+1] = idSyzygies(res[syzIndex],currQuotient,hom,&w1); |
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475 | completeMinim=(syzIndex!=maxlength) || (maxlength ==-1) || (hom!=isHomog); |
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476 | syzIndex++; |
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477 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
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478 | if ((minim)||(syzIndex>1)) |
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479 | syMinStep(res[syzIndex-1],res[syzIndex],!completeMinim,NULL,hom); |
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480 | if (!completeMinim) |
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481 | /*minim is TRUE, we are in the module: maxlength, maxlength <>0*/ |
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482 | { |
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483 | idDelete(&res[syzIndex]); |
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484 | } |
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485 | if ((hom == isHomog) && (!idIs0(res[syzIndex]))) |
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486 | { |
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487 | //Print("die %d Modulegewichte sind:\n",w1->length()); |
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488 | //w1->show(); |
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489 | //PrintLn(); |
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490 | k = idRankFreeModule(res[syzIndex]); |
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491 | w = new intvec(k+IDELEMS(res[syzIndex])); |
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492 | (*weights)[syzIndex] = new intvec(k); |
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493 | for (i=0;i<k;i++) |
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494 | { |
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495 | if (res[syzIndex-1]->m[i]!=NULL) // hs |
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496 | { |
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497 | (*w)[i] = pFDeg(res[syzIndex-1]->m[i]); |
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498 | if (pGetComp(res[syzIndex-1]->m[i])>0) |
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499 | (*w)[i] += (*w1)[pGetComp(res[syzIndex-1]->m[i])-1]; |
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500 | (*((*weights)[syzIndex]))[i] = (*w)[i]; |
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501 | } |
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502 | } |
---|
503 | for (i=k;i<k+IDELEMS(res[syzIndex]);i++) |
---|
504 | { |
---|
505 | if (res[syzIndex]->m[i-k]!=NULL) |
---|
506 | (*w)[i] = pFDeg(res[syzIndex]->m[i-k]) |
---|
507 | +(*w)[pGetComp(res[syzIndex]->m[i-k])-1]; |
---|
508 | } |
---|
509 | delete w1; |
---|
510 | w1 = w; |
---|
511 | w = NULL; |
---|
512 | } |
---|
513 | } |
---|
514 | if ((syzIndex!=0) && (res[syzIndex]!=NULL) && (idIs0(res[syzIndex]))) |
---|
515 | idDelete(&res[syzIndex]); |
---|
516 | if (w1!=NULL) delete w1; |
---|
517 | //if ((maxlength!=-1) && (!minim)) |
---|
518 | //{ |
---|
519 | // while (syzIndex<=maxlength) |
---|
520 | // { |
---|
521 | // res[syzIndex]=idInit(1,1); |
---|
522 | // syzIndex++; |
---|
523 | // if (syzIndex<=maxlength) |
---|
524 | // { |
---|
525 | // res[syzIndex]=idFreeModule(1); |
---|
526 | // syzIndex++; |
---|
527 | // } |
---|
528 | // } |
---|
529 | //} |
---|
530 | Kstd1_deg=Kstd1_OldDeg; |
---|
531 | if (!oldDegBound) |
---|
532 | test &= ~Sy_bit(OPT_DEGBOUND); |
---|
533 | return res; |
---|
534 | } |
---|
535 | |
---|
536 | syStrategy syResolution(ideal arg, int maxlength,intvec * w, BOOLEAN minim) |
---|
537 | { |
---|
538 | int typ0; |
---|
539 | syStrategy result=(syStrategy)Alloc0(sizeof(ssyStrategy)); |
---|
540 | |
---|
541 | if (w!=NULL) |
---|
542 | { |
---|
543 | result->weights = (intvec**)Alloc0(sizeof(intvec*)); |
---|
544 | (result->weights)[0] = ivCopy(w); |
---|
545 | result->length = 1; |
---|
546 | } |
---|
547 | resolvente fr = syResolvente(arg,maxlength,&(result->length),&(result->weights),minim),fr1; |
---|
548 | if (minim) |
---|
549 | { |
---|
550 | result->minres = (resolvente)Alloc0((result->length+1)*sizeof(ideal)); |
---|
551 | fr1 = result->minres; |
---|
552 | } |
---|
553 | else |
---|
554 | { |
---|
555 | result->fullres = (resolvente)Alloc0((result->length+1)*sizeof(ideal)); |
---|
556 | fr1 = result->fullres; |
---|
557 | } |
---|
558 | for (int i=result->length-1;i>=0;i--) |
---|
559 | { |
---|
560 | if (fr[i]!=NULL) |
---|
561 | fr1[i] = fr[i]; |
---|
562 | fr[i] = NULL; |
---|
563 | } |
---|
564 | Free((ADDRESS)fr,(result->length)*sizeof(ideal)); |
---|
565 | return result; |
---|
566 | } |
---|
567 | |
---|
568 | |
---|
569 | resolvente syMinRes(ideal arg, int maxlength, int * length, BOOLEAN minim) |
---|
570 | { |
---|
571 | resolvente res; |
---|
572 | resolvente newres; |
---|
573 | tHomog hom; |
---|
574 | ideal temp=NULL; |
---|
575 | intvec *w,*w1=NULL; |
---|
576 | int i,k,syzIndex = 0,j; |
---|
577 | int Kstd1_OldDeg=Kstd1_deg; |
---|
578 | BOOLEAN isIdeal=FALSE,oldDegBound=TEST_OPT_DEGBOUND; |
---|
579 | |
---|
580 | if (maxlength!=-1) *length = maxlength+1; |
---|
581 | else *length = 4; |
---|
582 | res = (resolvente)Alloc0((*length)*sizeof(ideal)); |
---|
583 | res[0] = idCopy(arg); |
---|
584 | hom=(tHomog)idHomModule(res[0],currQuotient,&w); |
---|
585 | //Print("die %d Modulegewichte sind:\n",w->length()); |
---|
586 | //w->show(); |
---|
587 | //PrintLn(); |
---|
588 | if (hom==isHomog) |
---|
589 | { |
---|
590 | //if (w!=NULL) |
---|
591 | //{ |
---|
592 | // w->show(); |
---|
593 | // PrintLn(); |
---|
594 | // if (res[0]!=NULL) jjPRINT_MA0(idModule2Matrix(idCopy(res[0])),NULL); |
---|
595 | //} |
---|
596 | int maxxx = 0; |
---|
597 | if (w!=NULL) maxxx = w->length(); |
---|
598 | if (maxxx==1) |
---|
599 | { |
---|
600 | maxxx = 2; |
---|
601 | isIdeal = TRUE; |
---|
602 | } |
---|
603 | w1 = new intvec(maxxx+IDELEMS(arg)); |
---|
604 | if (!isIdeal) |
---|
605 | { |
---|
606 | for (i=0;i<maxxx;i++) |
---|
607 | { |
---|
608 | (*w1)[i] = (*w)[i]; |
---|
609 | } |
---|
610 | } |
---|
611 | for (i=maxxx;i<maxxx+IDELEMS(arg);i++) |
---|
612 | { |
---|
613 | if (res[0]->m[i-maxxx]!=0) |
---|
614 | (*w1)[i] = pFDeg(res[0]->m[i-maxxx])+(*w)[pGetComp(res[0]->m[i-maxxx])]; |
---|
615 | } |
---|
616 | if (w!=NULL) {delete w;w=NULL;} |
---|
617 | } |
---|
618 | while ((!idIs0(res[syzIndex])) |
---|
619 | && ((maxlength==-1) |
---|
620 | || (syzIndex<maxlength))) |
---|
621 | // (syzIndex<maxlength+(int)minim))) |
---|
622 | /*compute one step more for minimizing*/ |
---|
623 | { |
---|
624 | if (Kstd1_deg!=0) Kstd1_deg++; |
---|
625 | if (syzIndex+1==*length) |
---|
626 | { |
---|
627 | newres = (resolvente)Alloc0((*length+4)*sizeof(ideal)); |
---|
628 | for (j=0;j<*length;j++) newres[j] = res[j]; |
---|
629 | Free((ADDRESS)res,*length*sizeof(ideal)); |
---|
630 | *length += 4; |
---|
631 | res=newres; |
---|
632 | } |
---|
633 | if (minim || (syzIndex!=0)) |
---|
634 | { |
---|
635 | temp = kInterRed(res[syzIndex],currQuotient); |
---|
636 | idDelete(&res[syzIndex]); |
---|
637 | res[syzIndex] = temp; |
---|
638 | } |
---|
639 | temp = NULL; |
---|
640 | if ((hom==isHomog) && (currRing->OrdSgn==1)) |
---|
641 | { |
---|
642 | //PrintS("Input: "); |
---|
643 | //for (i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
644 | //{ |
---|
645 | //Print("Element %d: ",i);pWrite(res[syzIndex]->m[i]); |
---|
646 | //} |
---|
647 | if ((currQuotient==NULL)&&(syzIndex==0)&& (!TEST_OPT_DEGBOUND)) |
---|
648 | { |
---|
649 | res[/*syzIndex+*/1] = idSyzMin(res[0/*syzIndex*/], |
---|
650 | NULL/*currQuotient*/,hom,&w1,TRUE,Kstd1_deg); |
---|
651 | if ((!TEST_OPT_NOTREGULARITY) && (Kstd1_deg>0)) test |= Sy_bit(OPT_DEGBOUND); |
---|
652 | //Print("Regularity is %d \n",Kstd1_deg); |
---|
653 | } |
---|
654 | else |
---|
655 | res[syzIndex+1] = idSyzMin(res[syzIndex], |
---|
656 | currQuotient,hom,&w1,FALSE,Kstd1_deg); |
---|
657 | //PrintS("Input: "); |
---|
658 | //for (i=0;i<IDELEMS(res[syzIndex+1]);i++) |
---|
659 | //{ |
---|
660 | //Print("Element %d: ",i);pWrite(res[syzIndex+1]->m[i]); |
---|
661 | //} |
---|
662 | } |
---|
663 | else |
---|
664 | res[syzIndex+1] = idSyzygies(res[syzIndex],currQuotient,hom,&w1); |
---|
665 | //Print("im %d-ten Syzygienmodul: \n",syzIndex+1); |
---|
666 | //for (i=0;i<IDELEMS(res[syzIndex+1]);i++) |
---|
667 | //{ |
---|
668 | //Print("El %d: ",i);pWrite(res[syzIndex+1]->m[i]); |
---|
669 | //} |
---|
670 | syzIndex++; |
---|
671 | if ((maxlength!=-1) && (syzIndex==maxlength)) idDelete(&res[syzIndex]); |
---|
672 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
---|
673 | if ((hom==isHomog) && (res[syzIndex]!=NULL)) |
---|
674 | { |
---|
675 | //Print("die %d Modulegewichte sind:\n",w1->length()); |
---|
676 | //w1->show(); |
---|
677 | //PrintLn(); |
---|
678 | k = idRankFreeModule(res[syzIndex]); |
---|
679 | w = new intvec(k+IDELEMS(res[syzIndex])+1); |
---|
680 | for (i=1;i<=k;i++) |
---|
681 | { |
---|
682 | (*w)[i] = pFDeg(res[syzIndex-1]->m[i-1]) |
---|
683 | +(*w1)[pGetComp(res[syzIndex-1]->m[i-1])]; |
---|
684 | } |
---|
685 | for (i=k+1;i<k+1+IDELEMS(res[syzIndex]);i++) |
---|
686 | { |
---|
687 | if (res[syzIndex]->m[i-k-1]!=NULL) |
---|
688 | (*w)[i] = pFDeg(res[syzIndex]->m[i-k-1]) |
---|
689 | +(*w)[pGetComp(res[syzIndex]->m[i-k-1])]; |
---|
690 | } |
---|
691 | delete w1; |
---|
692 | w1 = w; |
---|
693 | w = NULL; |
---|
694 | } |
---|
695 | } |
---|
696 | if (w1!=NULL) delete w1; |
---|
697 | if (maxlength!=-1) |
---|
698 | { |
---|
699 | if ((syzIndex<maxlength-1) && (res[syzIndex]!=NULL)) syzIndex++; |
---|
700 | while (syzIndex<maxlength) |
---|
701 | { |
---|
702 | res[syzIndex]=idInit(1,1); |
---|
703 | syzIndex++; |
---|
704 | } |
---|
705 | } |
---|
706 | Kstd1_deg=Kstd1_OldDeg; |
---|
707 | if (!oldDegBound) |
---|
708 | test &= ~Sy_bit(OPT_DEGBOUND); |
---|
709 | return res; |
---|
710 | } |
---|
711 | |
---|
712 | void syDetect(ideal id,int index,BOOLEAN homog,int * degrees,int * tocancel) |
---|
713 | { |
---|
714 | int i, j, k, ModComp; |
---|
715 | poly p, q, qq, Unit1, Unit2; |
---|
716 | ideal temp; |
---|
717 | |
---|
718 | if (idIs0(id)) return; |
---|
719 | temp = idInit(IDELEMS(id),id->rank); |
---|
720 | for (i=0;i<IDELEMS(id);i++) |
---|
721 | { |
---|
722 | p = id->m[i]; |
---|
723 | while (p!=NULL) |
---|
724 | { |
---|
725 | if (pIsConstantComp(p)) |
---|
726 | { |
---|
727 | if (temp->m[i]==NULL) |
---|
728 | { |
---|
729 | temp->m[i] = pHead(p); |
---|
730 | q = temp->m[i]; |
---|
731 | } |
---|
732 | else |
---|
733 | { |
---|
734 | pNext(q) = pHead(p); |
---|
735 | pIter(q); |
---|
736 | } |
---|
737 | } |
---|
738 | pIter(p); |
---|
739 | } |
---|
740 | } |
---|
741 | i = IDELEMS(id); |
---|
742 | while ((i>0) && (temp->m[i-1]==NULL)) i--; |
---|
743 | if (i==0) |
---|
744 | { |
---|
745 | idDelete(&temp); |
---|
746 | return; |
---|
747 | } |
---|
748 | j = 0; |
---|
749 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
750 | if (j<i) |
---|
751 | { |
---|
752 | p = temp->m[j]; |
---|
753 | temp->m[j] = NULL; |
---|
754 | } |
---|
755 | else |
---|
756 | { |
---|
757 | p = NULL; |
---|
758 | } |
---|
759 | while (p!=NULL) |
---|
760 | { |
---|
761 | if (homog) |
---|
762 | { |
---|
763 | k = pFDeg(id->m[j])+degrees[pGetComp(id->m[j])]; |
---|
764 | if (k>=index) tocancel[k-index]++; |
---|
765 | } |
---|
766 | else |
---|
767 | { |
---|
768 | tocancel[0]--; |
---|
769 | } |
---|
770 | ModComp = pGetComp(p); |
---|
771 | //Print("Element %d: ",j);pWrite(p); |
---|
772 | Unit1 = pTakeOutComp1(&p,ModComp); |
---|
773 | pSetComp(Unit1,0); |
---|
774 | for (k=j+1;k<i;k++) |
---|
775 | { |
---|
776 | if (temp->m[k]!=NULL) |
---|
777 | { |
---|
778 | //Print("erst %d: ",k);pWrite(temp->m[k]); |
---|
779 | Unit2 = pTakeOutComp1(&(temp->m[k]),ModComp); |
---|
780 | if (Unit2!=NULL) |
---|
781 | { |
---|
782 | number tmp=nCopy(pGetCoeff(Unit2)); |
---|
783 | tmp=nNeg(tmp); |
---|
784 | qq = pCopy(p); |
---|
785 | pMultN(qq,tmp); |
---|
786 | nDelete(&tmp); |
---|
787 | pMultN(temp->m[k],pGetCoeff(Unit1)); |
---|
788 | temp->m[k] = pAdd(temp->m[k],qq); |
---|
789 | //Print("dann %d: ",k);pWrite(temp->m[k]); |
---|
790 | pDelete(&Unit2); |
---|
791 | } |
---|
792 | } |
---|
793 | } |
---|
794 | //PrintLn(); |
---|
795 | pDelete(&Unit1); |
---|
796 | pDelete(&p); |
---|
797 | j++; |
---|
798 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
799 | if (j>=i) |
---|
800 | { |
---|
801 | idDelete(&temp); |
---|
802 | return; |
---|
803 | } |
---|
804 | p = temp->m[j]; |
---|
805 | temp->m[j] = NULL; |
---|
806 | } |
---|
807 | idDelete(&temp); |
---|
808 | } |
---|
809 | |
---|
810 | void syDetect(ideal id,int index,int rsmin, BOOLEAN homog, |
---|
811 | intvec * degrees,intvec * tocancel) |
---|
812 | { |
---|
813 | int * deg=NULL; |
---|
814 | int * tocan=(int*) Alloc0(tocancel->length()*sizeof(int)); |
---|
815 | int i; |
---|
816 | |
---|
817 | if (homog) |
---|
818 | { |
---|
819 | deg = (int*) Alloc0(degrees->length()*sizeof(int)); |
---|
820 | for (i=degrees->length();i>0;i--) |
---|
821 | deg[i-1] = (*degrees)[i-1]-rsmin; |
---|
822 | } |
---|
823 | syDetect(id,index,homog,deg,tocan); |
---|
824 | for (i=tocancel->length();i>0;i--) |
---|
825 | (*tocancel)[i-1] = tocan[i-1]; |
---|
826 | if (homog) |
---|
827 | Free((ADDRESS)deg,degrees->length()*sizeof(int)); |
---|
828 | Free((ADDRESS)tocan,tocancel->length()*sizeof(int)); |
---|
829 | } |
---|
830 | |
---|
831 | /*2 |
---|
832 | * computes the betti numbers from a given resolution |
---|
833 | * of length 'length' (0..length-1), not necessairily minimal, |
---|
834 | * (if weights are given, they are used) |
---|
835 | * returns the int matrix of betti numbers |
---|
836 | * and the regularity |
---|
837 | */ |
---|
838 | intvec * syBetti(resolvente res,int length, int * regularity, |
---|
839 | intvec* weights) |
---|
840 | { |
---|
841 | int i,j=0,k=0,l,rows,cols; |
---|
842 | int *temp1,*temp2,*temp3;/*used to compute degrees*/ |
---|
843 | int *tocancel; /*(BOOLEAN)tocancel[i]=element is superfluous*/ |
---|
844 | |
---|
845 | /*------ compute size --------------*/ |
---|
846 | *regularity = -1; |
---|
847 | cols = length; |
---|
848 | while ((cols>0) |
---|
849 | && ((res[cols-1]==NULL) |
---|
850 | || (idIs0(res[cols-1])))) |
---|
851 | { |
---|
852 | cols--; |
---|
853 | } |
---|
854 | intvec * result; |
---|
855 | if (idIs0(res[0])) |
---|
856 | { |
---|
857 | if (res[0]==NULL) |
---|
858 | result = new intvec(1,1,1); |
---|
859 | else |
---|
860 | result = new intvec(1,1,res[0]->rank); |
---|
861 | return result; |
---|
862 | } |
---|
863 | intvec *w=NULL; |
---|
864 | if (idHomModule(res[0],currQuotient,&w)!=isHomog) |
---|
865 | { |
---|
866 | Warn("betti-command: Input is not homogeneous!"); |
---|
867 | } |
---|
868 | delete w; |
---|
869 | l = max(idRankFreeModule(res[0]),res[0]->rank); |
---|
870 | i = 0; |
---|
871 | while ((i<length) && (res[i]!=NULL)) |
---|
872 | { |
---|
873 | if (IDELEMS(res[i])>l) l = IDELEMS(res[i]); |
---|
874 | i++; |
---|
875 | } |
---|
876 | temp1 = (int*)Alloc0((l+1)*sizeof(int)); |
---|
877 | temp2 = (int*)Alloc((l+1)*sizeof(int)); |
---|
878 | rows = 1; |
---|
879 | cols++; |
---|
880 | for (i=0;i<cols-1;i++) |
---|
881 | { |
---|
882 | if ((i==0) && (weights!=NULL)) pSetModDeg(weights); |
---|
883 | memset(temp2,0,(l+1)*sizeof(int)); |
---|
884 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
885 | { |
---|
886 | if (res[i]->m[j]!=NULL) |
---|
887 | { |
---|
888 | if ((pGetComp(res[i]->m[j])>l) |
---|
889 | || ((i>1) && (res[i-1]->m[pGetComp(res[i]->m[j])-1]==NULL))) |
---|
890 | { |
---|
891 | WerrorS("input not a resolvent"); |
---|
892 | Free((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
893 | Free((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
894 | return NULL; |
---|
895 | } |
---|
896 | temp2[j+1] = pFDeg(res[i]->m[j])+temp1[pGetComp(res[i]->m[j])]; |
---|
897 | if (temp2[j+1]-i>rows) rows = temp2[j+1]-i; |
---|
898 | } |
---|
899 | } |
---|
900 | if ((i==0) && (weights!=NULL)) pSetModDeg(NULL); |
---|
901 | temp3 = temp1; |
---|
902 | temp1 = temp2; |
---|
903 | temp2 = temp3; |
---|
904 | } |
---|
905 | /*------ computation betti numbers --------------*/ |
---|
906 | result = new intvec(rows,cols,0); |
---|
907 | (*result)[0] = /*idRankFreeModule(res[0])*/ res[0]->rank; |
---|
908 | if ((!idIs0(res[0])) && ((*result)[0]==0)) (*result)[0] = 1; |
---|
909 | tocancel = (int*)Alloc0((rows+1)*sizeof(int)); |
---|
910 | memset(temp2,0,l*sizeof(int)); |
---|
911 | memset(temp1,0,(l+1)*sizeof(int)); |
---|
912 | syDetect(res[0],0,TRUE,temp2,tocancel); |
---|
913 | (*result)[0] -= tocancel[0]; |
---|
914 | for (i=0;i<cols-1;i++) |
---|
915 | { |
---|
916 | if ((i==0) && (weights!=NULL)) pSetModDeg(weights); |
---|
917 | memset(temp2,0,l*sizeof(int)); |
---|
918 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
919 | { |
---|
920 | if (res[i]->m[j]!=NULL) |
---|
921 | { |
---|
922 | temp2[j+1] = pFDeg(res[i]->m[j])+temp1[pGetComp(res[i]->m[j])]; |
---|
923 | //(*result)[i+1+(temp2[j+1]-i-1)*cols]++; |
---|
924 | if (temp2[j+1]>i) IMATELEM((*result),temp2[j+1]-i,i+2)++; |
---|
925 | } |
---|
926 | } |
---|
927 | /*------ computation betti numbers, if res not minimal --------------*/ |
---|
928 | for (j=0;j<rows-1;j++) |
---|
929 | { |
---|
930 | //(*result)[i+1+j*cols] -= tocancel[j+1]; |
---|
931 | IMATELEM((*result),j+1,i+2) -= tocancel[j+1]; |
---|
932 | } |
---|
933 | if ((i<length-1) && (res[i+1]!=NULL)) |
---|
934 | { |
---|
935 | memset(tocancel,0,(rows+1)*sizeof(int)); |
---|
936 | syDetect(res[i+1],i+1,TRUE,temp2,tocancel); |
---|
937 | for (j=0;j<rows;j++) |
---|
938 | { |
---|
939 | //(*result)[i+1+j*cols] -= tocancel[j]; |
---|
940 | IMATELEM((*result),j+1,i+2) -= tocancel[j]; |
---|
941 | } |
---|
942 | } |
---|
943 | temp3 = temp1; |
---|
944 | temp1 = temp2; |
---|
945 | temp2 = temp3; |
---|
946 | for (j=0;j<rows;j++) |
---|
947 | { |
---|
948 | // if (((*result)[i+1+j*cols]!=0) && (j>*regularity)) *regularity = j; |
---|
949 | if ((IMATELEM((*result),j+1,i+2)!=0) && (j>*regularity)) *regularity = j; |
---|
950 | } |
---|
951 | if ((i==0) && (weights!=NULL)) pSetModDeg(NULL); |
---|
952 | } |
---|
953 | /*------ clean up --------------*/ |
---|
954 | Free((ADDRESS)tocancel,(rows+1)*sizeof(int)); |
---|
955 | Free((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
956 | Free((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
957 | j = 0; |
---|
958 | k = 0; |
---|
959 | for (i=0;i<rows*cols;i++) |
---|
960 | { |
---|
961 | if ((*result)[i] != 0) |
---|
962 | { |
---|
963 | j = i/cols; |
---|
964 | if (i>k+j*cols) k = i-j*cols; |
---|
965 | } |
---|
966 | } |
---|
967 | intvec * exactresult=new intvec(j+1,k+1,0); |
---|
968 | for (i=0;i<exactresult->rows();i++) |
---|
969 | { |
---|
970 | for (j=0;j<exactresult->cols();j++) |
---|
971 | { |
---|
972 | IMATELEM(*exactresult,i+1,j+1) = IMATELEM(*result,i+1,j+1); |
---|
973 | } |
---|
974 | } |
---|
975 | delete result; |
---|
976 | return exactresult; |
---|
977 | } |
---|
978 | |
---|
979 | /*2 |
---|
980 | * minbare via syzygies |
---|
981 | */ |
---|
982 | ideal syMinBase(ideal arg) |
---|
983 | { |
---|
984 | intvec ** weights=NULL; |
---|
985 | int leng; |
---|
986 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
987 | resolvente res=syResolvente(arg,1,&leng,&weights,TRUE); |
---|
988 | ideal result=res[0]; |
---|
989 | Free((ADDRESS)res,leng*sizeof(ideal)); |
---|
990 | if (weights!=NULL) |
---|
991 | { |
---|
992 | if (*weights!=NULL) |
---|
993 | { |
---|
994 | delete (*weights); |
---|
995 | *weights=NULL; |
---|
996 | } |
---|
997 | if ((leng>=1) && (*(weights+1)!=NULL)) |
---|
998 | { |
---|
999 | delete *(weights+1); |
---|
1000 | *(weights+1)=NULL; |
---|
1001 | } |
---|
1002 | } |
---|
1003 | idSkipZeroes(result); |
---|
1004 | return result; |
---|
1005 | } |
---|
1006 | |
---|
1007 | /*2 |
---|
1008 | * computes Betti-numbers from a resolvente of |
---|
1009 | * (non-)homogeneous objects |
---|
1010 | * the numbers of entrees !=NULL in res and weights must be equal |
---|
1011 | * and < length |
---|
1012 | */ |
---|
1013 | intvec * syNewBetti(resolvente res, intvec ** weights, int length) |
---|
1014 | { |
---|
1015 | intvec * result,*tocancel; |
---|
1016 | int i,j,k,rsmin=0,rsmax=0,rs=0; |
---|
1017 | BOOLEAN homog=TRUE; |
---|
1018 | |
---|
1019 | if (weights!=NULL) //---homogeneous Betti numbers |
---|
1020 | { |
---|
1021 | /*--------------computes size of the field----------------------*/ |
---|
1022 | for (i=1;i<length;i++) |
---|
1023 | { |
---|
1024 | if (weights[i] != NULL) |
---|
1025 | { |
---|
1026 | for (j=1;j<(weights[i])->length();j++) |
---|
1027 | { |
---|
1028 | if ((*(weights[i]))[j]-i<rsmin) rsmin = (*(weights[i]))[j]-i; |
---|
1029 | if ((*(weights[i]))[j]-i>rsmax) rsmax = (*(weights[i]))[j]-i; |
---|
1030 | } |
---|
1031 | } |
---|
1032 | } |
---|
1033 | i = 0; |
---|
1034 | while (weights[i] != NULL) i++; |
---|
1035 | i--; |
---|
1036 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1037 | { |
---|
1038 | if (res[i]->m[j]!=NULL) |
---|
1039 | { |
---|
1040 | k = pFDeg(res[i]->m[j])+(*(weights[i]))[pGetComp(res[i]->m[j])]-i-1; |
---|
1041 | if (k>rsmax) rsmax = k; |
---|
1042 | if (k<rsmin) rsmin = k; |
---|
1043 | } |
---|
1044 | } |
---|
1045 | for (j=1;j<(weights[0])->length();j++) |
---|
1046 | { |
---|
1047 | if ((*weights[0])[j]>rsmax) rsmax = (*weights[0])[j]; |
---|
1048 | if ((*weights[0])[j]<rsmin) rsmin = (*weights[0])[j]; |
---|
1049 | } |
---|
1050 | //Print("rsmax = %d\n",rsmax); |
---|
1051 | //Print("rsmin = %d\n",rsmin); |
---|
1052 | rs = rsmax-rsmin+1; |
---|
1053 | result = new intvec(rs,i+2,0); |
---|
1054 | tocancel = new intvec(rs); |
---|
1055 | /*-----------enter the Betti numbers-------------------------------*/ |
---|
1056 | if (/*idRankFreeModule(res[0])*/ res[0]->rank==0) |
---|
1057 | { |
---|
1058 | IMATELEM(*result,1-rsmin,1)=1; |
---|
1059 | } |
---|
1060 | else |
---|
1061 | { |
---|
1062 | for (i=1;i<(weights[0])->length();i++) |
---|
1063 | IMATELEM(*result,(*weights[0])[i]+1-rsmin,1)++; |
---|
1064 | } |
---|
1065 | i = 1; |
---|
1066 | while (weights[i]!=NULL) |
---|
1067 | { |
---|
1068 | for (j=1;j<(weights[i])->length();j++) |
---|
1069 | { |
---|
1070 | IMATELEM(*result,(*(weights[i]))[j]-i+1-rsmin,i+1)++; |
---|
1071 | } |
---|
1072 | i++; |
---|
1073 | } |
---|
1074 | i--; |
---|
1075 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1076 | { |
---|
1077 | if (res[i]->m[j]!=NULL) |
---|
1078 | { |
---|
1079 | k = pFDeg(res[i]->m[j])+(*(weights[i]))[pGetComp(res[i]->m[j])]-i; |
---|
1080 | IMATELEM(*result,k-rsmin,i+2)++; |
---|
1081 | } |
---|
1082 | } |
---|
1083 | } |
---|
1084 | else //-----the non-homgeneous case |
---|
1085 | { |
---|
1086 | homog = FALSE; |
---|
1087 | tocancel = new intvec(1); |
---|
1088 | k = length; |
---|
1089 | while ((k>0) && (idIs0(res[k-1]))) k--; |
---|
1090 | result = new intvec (1,k+1,0); |
---|
1091 | (*result)[0] = res[0]->rank; |
---|
1092 | for (i=0;i<length;i++) |
---|
1093 | { |
---|
1094 | if (res[i]!=NULL) |
---|
1095 | { |
---|
1096 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
1097 | { |
---|
1098 | if (res[i]->m[j]!=NULL) (*result)[i+1]++; |
---|
1099 | } |
---|
1100 | } |
---|
1101 | } |
---|
1102 | } |
---|
1103 | /*--------computes the Betti numbers for the minimized reolvente----*/ |
---|
1104 | |
---|
1105 | i = 1; |
---|
1106 | while ((res[i]!=NULL) && (weights[i]!=NULL)) |
---|
1107 | { |
---|
1108 | syDetect(res[i],i,rsmin,homog,weights[i],tocancel); |
---|
1109 | if (homog) |
---|
1110 | { |
---|
1111 | for (j=0;j<rs-1;j++) |
---|
1112 | { |
---|
1113 | IMATELEM((*result),j+1,i+1) -= (*tocancel)[j]; |
---|
1114 | IMATELEM((*result),j+1,i+2) -= (*tocancel)[j+1]; |
---|
1115 | } |
---|
1116 | IMATELEM((*result),rs,i+1) -= (*tocancel)[rs-1]; |
---|
1117 | } |
---|
1118 | else |
---|
1119 | { |
---|
1120 | (*result)[i+1] -= (*tocancel)[0]; |
---|
1121 | (*result)[i+2] -= (*tocancel)[0]; |
---|
1122 | } |
---|
1123 | i++; |
---|
1124 | } |
---|
1125 | |
---|
1126 | /*--------print Betti numbers for control---------------------------*/ |
---|
1127 | for(i=rsmin;i<=rsmax;i++) |
---|
1128 | { |
---|
1129 | Print("%2d:",i); |
---|
1130 | for(j=1;j<=result->cols();j++) |
---|
1131 | { |
---|
1132 | Print(" %5d",IMATELEM(*result,i-rsmin+1,j)); |
---|
1133 | } |
---|
1134 | PrintLn(); |
---|
1135 | } |
---|
1136 | return result; |
---|
1137 | } |
---|
1138 | |
---|
1139 | /*2 |
---|
1140 | * is looking for the minimal minimized module of a resolvente |
---|
1141 | * i.e. returns 0 if res comes from a mres-command and 1 in the |
---|
1142 | * case of res-commands |
---|
1143 | */ |
---|
1144 | int syIsMinimizedFrom(resolvente res,int length) |
---|
1145 | { |
---|
1146 | poly p; |
---|
1147 | int i,j=length; |
---|
1148 | |
---|
1149 | while ((j>0) && (res[j-1]==NULL)) j--; |
---|
1150 | while (j>0) |
---|
1151 | { |
---|
1152 | for (i=0;i<IDELEMS(res[j-1]);i++) |
---|
1153 | { |
---|
1154 | p = res[j-1]->m[i]; |
---|
1155 | while (p!=NULL) |
---|
1156 | { |
---|
1157 | if (pIsConstantComp(p)) return j; |
---|
1158 | p = pNext(p); |
---|
1159 | } |
---|
1160 | } |
---|
1161 | j--; |
---|
1162 | } |
---|
1163 | return j; |
---|
1164 | } |
---|