1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: ideals.cc,v 1.20 1998-02-27 16:27:58 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT - all basic methods to manipulate ideals |
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7 | */ |
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8 | |
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9 | /* includes */ |
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10 | #include "mod2.h" |
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11 | #include "tok.h" |
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12 | #include "mmemory.h" |
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13 | #include "febase.h" |
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14 | #include "numbers.h" |
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15 | #include "polys.h" |
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16 | #include "ipid.h" |
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17 | #include "ring.h" |
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18 | #include "kstd1.h" |
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19 | #include "matpol.h" |
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20 | #include "weight.h" |
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21 | #include "intvec.h" |
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22 | #include "syz.h" |
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23 | #include "ideals.h" |
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24 | #include "lists.h" |
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25 | |
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26 | |
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27 | static poly * idpower; |
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28 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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29 | static int idpowerpoint; |
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30 | /*index of the actual monomial in idpower*/ |
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31 | static poly * givenideal; |
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32 | /*the ideal from which a power is computed*/ |
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33 | |
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34 | /*0 implementation*/ |
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35 | |
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36 | /*2 |
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37 | * initialise an ideal |
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38 | */ |
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39 | #ifdef MDEBUG |
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40 | ideal idDBInit(int idsize, int rank, char *f, int l) |
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41 | #else |
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42 | ideal idInit(int idsize, int rank) |
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43 | #endif |
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44 | { |
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45 | /*- initialise an ideal -*/ |
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46 | #ifdef MDEBUG |
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47 | ideal hh = (ideal )mmDBAllocBlock(sizeof(*hh),f,l); |
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48 | #else |
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49 | ideal hh = (ideal )Alloc(sizeof(*hh)); |
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50 | #endif |
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51 | hh->nrows = 1; |
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52 | hh->rank = rank; |
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53 | IDELEMS(hh) = idsize; |
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54 | if (idsize>0) |
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55 | { |
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56 | #ifdef MDEBUG |
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57 | hh->m = (poly *)mmDBAllocBlock0(idsize*sizeof(poly),f,l); |
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58 | #else |
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59 | hh->m = (poly *)Alloc0(idsize*sizeof(poly)); |
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60 | #endif |
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61 | } |
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62 | else |
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63 | hh->m=NULL; |
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64 | return hh; |
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65 | } |
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66 | |
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67 | /*2 |
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68 | * initialise the maximal ideal (at 0) |
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69 | */ |
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70 | ideal idMaxIdeal (void) |
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71 | { |
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72 | int l; |
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73 | ideal hh=NULL; |
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74 | |
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75 | hh=idInit(pVariables,1); |
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76 | for (l=0; l<pVariables; l++) |
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77 | { |
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78 | hh->m[l] = pOne(); |
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79 | pSetExp(hh->m[l],l+1,1); |
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80 | pSetm(hh->m[l]); |
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81 | } |
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82 | return hh; |
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83 | } |
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84 | |
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85 | /*2 |
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86 | * deletes an ideal/matrix |
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87 | */ |
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88 | #ifdef MDEBUG |
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89 | void idDBDelete (ideal* h, char *f, int l) |
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90 | #else |
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91 | void idDelete (ideal * h) |
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92 | #endif |
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93 | { |
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94 | int j,elems; |
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95 | if (*h == NULL) |
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96 | return; |
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97 | elems=j=(*h)->nrows*(*h)->ncols; |
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98 | if (j>0) |
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99 | { |
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100 | do |
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101 | { |
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102 | #ifdef MDEBUG |
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103 | pDBDelete(&((*h)->m[--j]),f,l); |
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104 | #else |
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105 | pDelete(&((*h)->m[--j])); |
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106 | #endif |
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107 | } |
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108 | while (j>0); |
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109 | #ifdef MDEBUG |
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110 | mmDBFreeBlock((ADDRESS)((*h)->m),sizeof(poly)*elems,f,l); |
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111 | #else |
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112 | Free((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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113 | #endif |
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114 | } |
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115 | #ifdef MDEBUG |
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116 | mmDBFreeBlock((ADDRESS)(*h),sizeof(**h),f,l); |
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117 | #else |
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118 | Free((ADDRESS)*h,sizeof(**h)); |
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119 | #endif |
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120 | *h=NULL; |
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121 | } |
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122 | |
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123 | /*2 |
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124 | *gives an ideal the minimal possible size |
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125 | */ |
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126 | void idSkipZeroes (ideal ide) |
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127 | { |
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128 | int k; |
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129 | int j = -1; |
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130 | BOOLEAN change=FALSE; |
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131 | for (k=0; k<IDELEMS(ide); k++) |
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132 | { |
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133 | if (ide->m[k] != NULL) |
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134 | { |
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135 | j++; |
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136 | if (change) |
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137 | { |
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138 | ide->m[j] = ide->m[k]; |
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139 | } |
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140 | } |
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141 | else |
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142 | { |
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143 | change=TRUE; |
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144 | } |
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145 | } |
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146 | if (change) |
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147 | { |
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148 | if (j == -1) |
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149 | j = 0; |
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150 | else |
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151 | { |
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152 | for (k=j+1; k<IDELEMS(ide); k++) |
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153 | ide->m[k] = NULL; |
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154 | } |
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155 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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156 | IDELEMS(ide) = j+1; |
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157 | } |
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158 | } |
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159 | |
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160 | /*2 |
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161 | * ideal id = (id[i]) |
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162 | * result is leadcoeff(id[i]) = 1 |
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163 | */ |
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164 | void idNorm(ideal id) |
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165 | { |
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166 | for (int i=0; i<IDELEMS(id); i++) |
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167 | { |
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168 | if (id->m[i] != NULL) |
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169 | { |
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170 | pNorm(id->m[i]); |
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171 | } |
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172 | } |
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173 | } |
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174 | |
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175 | /*2 |
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176 | * ideal id = (id[i]), c any number |
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177 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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178 | */ |
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179 | void idDelMultiples(ideal id) |
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180 | { |
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181 | int i, j, t; |
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182 | int k = IDELEMS(id), l = k; |
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183 | for (i=k-2; i>=0; i--) |
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184 | { |
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185 | if (id->m[i]!=NULL) |
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186 | { |
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187 | for (j=l-1; j>i; j--) |
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188 | { |
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189 | if ((id->m[j]!=NULL) |
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190 | && (pComparePolys(id->m[i], id->m[j]))) |
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191 | { |
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192 | pDelete(&id->m[j]); |
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193 | l--; |
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194 | for(t=j; t<l; t++) |
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195 | { |
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196 | id->m[t] = id->m[t+1]; |
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197 | } |
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198 | } |
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199 | } |
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200 | } |
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201 | } |
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202 | if (l != k) |
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203 | { |
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204 | pEnlargeSet(&id->m, k, l-k); |
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205 | IDELEMS(id) = l; |
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206 | } |
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207 | } |
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208 | |
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209 | /*2 |
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210 | * ideal id = (id[i]) |
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211 | * if id[i] = id[j] then id[j] is deleted for j > i |
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212 | */ |
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213 | void idDelEquals(ideal id) |
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214 | { |
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215 | int i, j, t; |
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216 | int k = IDELEMS(id), l = k; |
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217 | for (i=k-2; i>=0; i--) |
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218 | { |
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219 | for (j=l-1; j>i; j--) |
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220 | { |
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221 | if (pEqualPolys(id->m[i], id->m[j])) |
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222 | { |
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223 | pDelete(&id->m[j]); |
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224 | l--; |
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225 | for(t=j; t<l; t++) |
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226 | { |
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227 | id->m[t] = id->m[t+1]; |
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228 | } |
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229 | } |
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230 | } |
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231 | } |
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232 | if (l != k) |
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233 | { |
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234 | pEnlargeSet(&id->m, k, l-k); |
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235 | IDELEMS(id) = l; |
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236 | } |
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237 | } |
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238 | |
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239 | /*2 |
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240 | * copy an ideal |
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241 | */ |
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242 | #ifdef MDEBUG |
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243 | ideal idDBCopy(ideal h1,char *f,int l) |
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244 | #else |
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245 | ideal idCopy (ideal h1) |
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246 | #endif |
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247 | { |
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248 | int i; |
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249 | ideal h2; |
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250 | |
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251 | //#ifdef TEST |
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252 | if (h1 == NULL) |
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253 | { |
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254 | #ifdef MDEBUG |
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255 | h2=idDBInit(1,1,f,l); |
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256 | #else |
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257 | h2=idInit(1,1); |
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258 | #endif |
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259 | } |
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260 | else |
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261 | //#endif |
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262 | { |
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263 | #ifdef MDEBUG |
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264 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
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265 | #else |
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266 | h2=idInit(IDELEMS(h1),h1->rank); |
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267 | #endif |
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268 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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269 | #ifdef MDEBUG |
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270 | h2->m[i] = pDBCopy(h1->m[i],f,l); |
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271 | #else |
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272 | h2->m[i] = pCopy(h1->m[i]); |
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273 | #endif |
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274 | } |
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275 | return h2; |
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276 | } |
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277 | |
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278 | #ifdef PDEBUG |
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279 | void idDBTest(ideal h1,char *f,int l) |
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280 | { |
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281 | int i; |
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282 | |
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283 | if (h1 != NULL) |
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284 | { |
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285 | #ifdef MDEBUG |
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286 | mmDBTestBlock(h1,sizeof(*h1),f,l); |
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287 | #endif |
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288 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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289 | pDBTest(h1->m[i],f,l); |
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290 | } |
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291 | } |
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292 | #endif |
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293 | |
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294 | /*3 |
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295 | * for idSort: compare a and b revlex inclusive module comp. |
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296 | */ |
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297 | static int pComp_RevLex(poly a, poly b) |
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298 | { |
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299 | int l=pVariables; |
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300 | while ((l>=0) && (pGetExp(a,l)==pGetExp(b,l))) l--; |
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301 | if (l<0) |
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302 | return 0; |
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303 | else if (pGetExp(a,l)>pGetExp(b,l)) |
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304 | return 1; |
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305 | else |
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306 | return -1; |
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307 | } |
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308 | |
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309 | /*2 |
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310 | *sorts the ideal w.r.t. the actual ringordering |
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311 | *uses lex-ordering when nolex = FALSE |
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312 | */ |
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313 | intvec *idSort(ideal id,BOOLEAN nolex) |
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314 | { |
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315 | poly p,q; |
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316 | intvec * result = new intvec(IDELEMS(id)); |
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317 | int i, j, actpos=0, newpos, l; |
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318 | int diff, olddiff, lastcomp, newcomp; |
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319 | BOOLEAN notFound; |
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320 | |
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321 | pCompProc oldComp=pComp0; |
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322 | |
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323 | if (!nolex) pComp0=pComp_RevLex; |
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324 | |
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325 | for (i=0;i<IDELEMS(id);i++) |
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326 | { |
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327 | if (id->m[i]!=NULL) |
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328 | { |
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329 | notFound = TRUE; |
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330 | newpos = actpos / 2; |
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331 | diff = (actpos+1) / 2; |
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332 | diff = (diff+1) / 2; |
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333 | lastcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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334 | if (lastcomp<0) |
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335 | { |
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336 | newpos -= diff; |
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337 | } |
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338 | else if (lastcomp>0) |
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339 | { |
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340 | newpos += diff; |
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341 | } |
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342 | else |
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343 | { |
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344 | notFound = FALSE; |
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345 | } |
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346 | while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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347 | { |
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348 | newcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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349 | olddiff = diff; |
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350 | if (diff>1) |
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351 | { |
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352 | diff = (diff+1) / 2; |
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353 | if ((newcomp==1) |
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354 | && (actpos-newpos>1) |
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355 | && (diff>1) |
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356 | && (newpos+diff>=actpos)) |
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357 | { |
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358 | diff = actpos-newpos-1; |
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359 | } |
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360 | else if ((newcomp==-1) |
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361 | && (diff>1) |
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362 | && (newpos<diff)) |
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363 | { |
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364 | diff = newpos; |
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365 | } |
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366 | } |
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367 | if (newcomp<0) |
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368 | { |
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369 | if ((olddiff==1) && (lastcomp>0)) |
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370 | notFound = FALSE; |
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371 | else |
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372 | newpos -= diff; |
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373 | } |
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374 | else if (newcomp>0) |
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375 | { |
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376 | if ((olddiff==1) && (lastcomp<0)) |
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377 | { |
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378 | notFound = FALSE; |
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379 | newpos++; |
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380 | } |
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381 | else |
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382 | { |
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383 | newpos += diff; |
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384 | } |
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385 | } |
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386 | else |
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387 | { |
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388 | notFound = FALSE; |
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389 | } |
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390 | lastcomp = newcomp; |
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391 | if (diff==0) notFound=FALSE; /*hs*/ |
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392 | } |
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393 | if (newpos<0) newpos = 0; |
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394 | if (newpos>=actpos) |
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395 | { |
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396 | (*result)[actpos] = i; |
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397 | } |
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398 | else |
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399 | { |
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400 | for (j=actpos;j>newpos;j--) |
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401 | { |
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402 | (*result)[j] = (*result)[j-1]; |
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403 | } |
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404 | (*result)[newpos] = i; |
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405 | } |
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406 | actpos++; |
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407 | } |
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408 | } |
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409 | for (j=0;j<actpos;j++) (*result)[j]++; |
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410 | pComp0=oldComp; |
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411 | return result; |
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412 | } |
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413 | |
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414 | /*2 |
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415 | * concat the lists h1 and h2 without zeros |
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416 | */ |
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417 | ideal idSimpleAdd (ideal h1,ideal h2) |
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418 | { |
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419 | int i,j,r,l; |
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420 | ideal result; |
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421 | |
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422 | if (h1==NULL) return idCopy(h2); |
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423 | if (h2==NULL) return idCopy(h1); |
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424 | j = IDELEMS(h1); |
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425 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
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426 | i = IDELEMS(h2); |
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427 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
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428 | if (i+j==0) |
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429 | result = idInit(1,1); |
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430 | else |
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431 | result=idInit(i+j,1); |
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432 | if (h1->rank<h2->rank) |
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433 | result->rank = h2->rank; |
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434 | else |
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435 | result->rank = h1->rank; |
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436 | if (i+j==0) return result; |
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437 | r = 0; |
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438 | for (l=0; l<j; l++) |
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439 | { |
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440 | result->m[r] = pCopy(h1->m[l]); |
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441 | r++; |
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442 | } |
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443 | for (l=0; l<i; l++) |
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444 | { |
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445 | result->m[r] = pCopy(h2->m[l]); |
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446 | r++; |
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447 | } |
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448 | return result; |
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449 | } |
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450 | |
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451 | /*2 |
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452 | * h1 + h2 |
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453 | */ |
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454 | ideal idAdd (ideal h1,ideal h2) |
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455 | { |
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456 | ideal result = idSimpleAdd(h1,h2); |
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457 | ideal tmp = idCompactify(result); |
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458 | |
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459 | idDelete(&result); |
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460 | return tmp; |
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461 | } |
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462 | |
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463 | /*2 |
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464 | * h1 * h2 |
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465 | */ |
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466 | ideal idMult (ideal h1,ideal h2) |
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467 | { |
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468 | int i,j,k; |
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469 | ideal hh; |
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470 | |
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471 | j = IDELEMS(h1); |
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472 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
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473 | i = IDELEMS(h2); |
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474 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
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475 | j = j * i; |
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476 | if (j == 0) |
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477 | hh = idInit(1,1); |
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478 | else |
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479 | hh=idInit(j,1); |
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480 | if (h1->rank<h2->rank) |
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481 | hh->rank = h2->rank; |
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482 | else |
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483 | hh->rank = h1->rank; |
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484 | if (j==0) return hh; |
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485 | k = 0; |
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486 | for (i=0; i<IDELEMS(h1); i++) |
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487 | { |
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488 | if (h1->m[i] != NULL) |
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489 | { |
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490 | for (j=0; j<IDELEMS(h2); j++) |
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491 | { |
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492 | if (h2->m[j] != NULL) |
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493 | { |
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494 | hh->m[k] = pMult(pCopy(h1->m[i]),pCopy(h2->m[j])); |
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495 | k++; |
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496 | } |
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497 | } |
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498 | } |
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499 | } |
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500 | { |
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501 | ideal tmp = idCompactify(hh); |
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502 | idDelete(&hh); |
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503 | return tmp; |
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504 | return hh; |
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505 | } |
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506 | } |
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507 | |
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508 | /*2 |
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509 | *returns true if h is the zero ideal |
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510 | */ |
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511 | BOOLEAN idIs0 (ideal h) |
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512 | { |
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513 | int i; |
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514 | |
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515 | if (h == NULL) return TRUE; |
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516 | i = IDELEMS(h); |
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517 | while ((i > 0) && (h->m[i-1] == NULL)) |
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518 | { |
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519 | i--; |
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520 | } |
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521 | if (i == 0) |
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522 | return TRUE; |
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523 | else |
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524 | return FALSE; |
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525 | } |
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526 | |
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527 | /*2 |
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528 | * return the maximal component number found in any polynomial in s |
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529 | */ |
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530 | int idRankFreeModule (ideal s) |
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531 | { |
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532 | if (s!=NULL) |
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533 | { |
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534 | int j=0; |
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535 | int l=IDELEMS(s); |
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536 | poly *p=s->m; |
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537 | int k; |
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538 | |
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539 | for (; l != 0; l--) |
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540 | { |
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541 | if (*p!=NULL) |
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542 | { |
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543 | k = pMaxComp(*p); |
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544 | if (k>j) j = k; |
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545 | } |
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546 | p++; |
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547 | } |
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548 | return j; |
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549 | } |
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550 | return -1; |
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551 | } |
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552 | |
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553 | /*2 |
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554 | *returns true if id is homogenous with respect to the aktual weights |
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555 | */ |
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556 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
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557 | { |
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558 | int i; |
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559 | BOOLEAN b; |
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560 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
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561 | i = 0; |
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562 | b = TRUE; |
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563 | while ((i < IDELEMS(id)) && b) |
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564 | { |
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565 | b = pIsHomogeneous(id->m[i]); |
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566 | i++; |
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567 | } |
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568 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
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569 | { |
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570 | i=0; |
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571 | while ((i < IDELEMS(Q)) && b) |
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572 | { |
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573 | b = pIsHomogeneous(Q->m[i]); |
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574 | i++; |
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575 | } |
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576 | } |
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577 | return b; |
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578 | } |
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579 | |
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580 | /*2 |
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581 | *returns a minimized set of generators of h1 |
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582 | */ |
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583 | ideal idMinBase (ideal h1) |
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584 | { |
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585 | ideal h2, h3,h4,e; |
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586 | int j,k; |
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587 | int i,l,ll; |
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588 | intvec * wth; |
---|
589 | BOOLEAN homog; |
---|
590 | |
---|
591 | homog = idHomModule(h1,currQuotient,&wth); |
---|
592 | if ((currRing->OrdSgn == 1) && (!homog)) |
---|
593 | { |
---|
594 | Warn("minbase applies only to the local or homogeneous case"); |
---|
595 | e=idCopy(h1); |
---|
596 | return e; |
---|
597 | } |
---|
598 | if ((currRing->OrdSgn == 1) && (homog)) |
---|
599 | { |
---|
600 | lists re=min_std(h1,currQuotient,(tHomog)homog,&wth,NULL,0,2); |
---|
601 | h2 = (ideal)re->m[1].data; |
---|
602 | re->m[1].data = NULL; |
---|
603 | re->m[1].rtyp = NONE; |
---|
604 | re->Clean(); |
---|
605 | return h2; |
---|
606 | } |
---|
607 | e=idInit(1,h1->rank); |
---|
608 | if (idIs0(h1)) |
---|
609 | { |
---|
610 | return e; |
---|
611 | } |
---|
612 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
613 | IDELEMS(e) = 16; |
---|
614 | h2 = std(h1,currQuotient,isNotHomog,NULL); |
---|
615 | h3 = idMaxIdeal(); |
---|
616 | h4=idMult(h2,h3); |
---|
617 | idDelete(&h3); |
---|
618 | h3=std(h4,currQuotient,isNotHomog,NULL); |
---|
619 | k = IDELEMS(h3); |
---|
620 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
621 | j = -1; |
---|
622 | l = IDELEMS(h2); |
---|
623 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
624 | for (i=l-1; i>=0; i--) |
---|
625 | { |
---|
626 | if (h2->m[i] != NULL) |
---|
627 | { |
---|
628 | ll = 0; |
---|
629 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
630 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
631 | ll++; |
---|
632 | if (ll >= k) |
---|
633 | { |
---|
634 | j++; |
---|
635 | if (j > IDELEMS(e)-1) |
---|
636 | { |
---|
637 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
638 | IDELEMS(e) += 16; |
---|
639 | } |
---|
640 | e->m[j] = pCopy(h2->m[i]); |
---|
641 | } |
---|
642 | } |
---|
643 | } |
---|
644 | idDelete(&h2); |
---|
645 | idDelete(&h3); |
---|
646 | idDelete(&h4); |
---|
647 | if (currQuotient!=NULL) |
---|
648 | { |
---|
649 | h3=idInit(1,e->rank); |
---|
650 | h2=kNF(h3,currQuotient,e); |
---|
651 | idDelete(&h3); |
---|
652 | idDelete(&e); |
---|
653 | e=h2; |
---|
654 | } |
---|
655 | idSkipZeroes(e); |
---|
656 | return e; |
---|
657 | } |
---|
658 | |
---|
659 | /*2 |
---|
660 | *the minimal index of used variables - 1 |
---|
661 | */ |
---|
662 | int pLowVar (poly p) |
---|
663 | { |
---|
664 | int k,l,lex; |
---|
665 | |
---|
666 | if (p == NULL) return -1; |
---|
667 | |
---|
668 | k = 32000;/*a very large dummy value*/ |
---|
669 | while (p != NULL) |
---|
670 | { |
---|
671 | l = 1; |
---|
672 | lex = pGetExp(p,l); |
---|
673 | while ((l <= pVariables) && (lex == 0)) |
---|
674 | { |
---|
675 | l++; |
---|
676 | lex = pGetExp(p,l); |
---|
677 | } |
---|
678 | l--; |
---|
679 | if (l < k) k = l; |
---|
680 | pIter(p); |
---|
681 | } |
---|
682 | return k; |
---|
683 | } |
---|
684 | |
---|
685 | /*3 |
---|
686 | *multiplies p with t (!cas) or (t-1) |
---|
687 | *the index of t is:1, so we have to shift all variables |
---|
688 | *p is NOT in the actual ring, it has no t |
---|
689 | */ |
---|
690 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
691 | { |
---|
692 | /*qp is the working pointer in p*/ |
---|
693 | /*result is the result, qresult is the working pointer*/ |
---|
694 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
695 | poly result,qp,pp; |
---|
696 | poly qresult=NULL; |
---|
697 | poly qpp=NULL; |
---|
698 | int i,j,lex; |
---|
699 | number n; |
---|
700 | |
---|
701 | pp = NULL; |
---|
702 | result = NULL; |
---|
703 | qp = p; |
---|
704 | while (qp != NULL) |
---|
705 | { |
---|
706 | i = 0; |
---|
707 | if (result == NULL) |
---|
708 | {/*first monomial*/ |
---|
709 | result = pInit(); |
---|
710 | qresult = result; |
---|
711 | } |
---|
712 | else |
---|
713 | { |
---|
714 | qresult->next = pInit(); |
---|
715 | pIter(qresult); |
---|
716 | } |
---|
717 | for (j=pVariables-1; j>0; j--) |
---|
718 | { |
---|
719 | lex = pGetExp(qp,j); |
---|
720 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
721 | } |
---|
722 | lex = pGetComp(qp); |
---|
723 | pSetComp(qresult,lex); |
---|
724 | n=nCopy(pGetCoeff(qp)); |
---|
725 | pSetCoeff0(qresult,n); |
---|
726 | qresult->next = NULL; |
---|
727 | pSetm(qresult); |
---|
728 | /*qresult is now qp brought into the actual ring*/ |
---|
729 | if (cas) |
---|
730 | { /*case: mult with t-1*/ |
---|
731 | pSetExp(qresult,1,0); |
---|
732 | pSetm(qresult); |
---|
733 | if (pp == NULL) |
---|
734 | { /*first monomial*/ |
---|
735 | pp = pCopy(qresult); |
---|
736 | qpp = pp; |
---|
737 | } |
---|
738 | else |
---|
739 | { |
---|
740 | qpp->next = pCopy(qresult); |
---|
741 | pIter(qpp); |
---|
742 | } |
---|
743 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
744 | /*now qpp contains -1*qp*/ |
---|
745 | } |
---|
746 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
747 | pSetm(qresult); |
---|
748 | pIter(qp); |
---|
749 | } |
---|
750 | /* |
---|
751 | *now p is processed: |
---|
752 | *result contains t*p |
---|
753 | * if cas: pp contains -1*p (in the new ring) |
---|
754 | */ |
---|
755 | if (cas) qresult->next = pp; |
---|
756 | /* else qresult->next = NULL;*/ |
---|
757 | return result; |
---|
758 | } |
---|
759 | |
---|
760 | /*3 |
---|
761 | *deletes the place of t in p (t: variable with index 1) |
---|
762 | *p is NOT in the actual ring: it has pVariables+1 variables |
---|
763 | */ |
---|
764 | static poly pDivByT (poly * p,int size) |
---|
765 | { |
---|
766 | |
---|
767 | poly result=NULL, |
---|
768 | resultp=NULL , /** working pointer in result **/ |
---|
769 | pp; |
---|
770 | int i,j; |
---|
771 | |
---|
772 | while (*p != NULL) |
---|
773 | { |
---|
774 | i = 0; |
---|
775 | if (result == NULL) |
---|
776 | {/*the first monomial*/ |
---|
777 | result = pInit(); |
---|
778 | resultp = result; |
---|
779 | resultp->next = NULL; |
---|
780 | } |
---|
781 | else |
---|
782 | { |
---|
783 | resultp->next = pInit(); |
---|
784 | pIter(resultp); |
---|
785 | resultp->next = NULL; |
---|
786 | } |
---|
787 | for (j=1; j<=pVariables; j++) |
---|
788 | { |
---|
789 | pSetExp(resultp,j,pGetExp(*p,j+1)); |
---|
790 | } |
---|
791 | pSetComp(resultp,pGetComp(*p)); |
---|
792 | pSetCoeff0(resultp,pGetCoeff(*p)); |
---|
793 | pSetm(resultp); |
---|
794 | pp = (*p)->next; |
---|
795 | Free((ADDRESS)*p,size); |
---|
796 | *p = pp; |
---|
797 | } |
---|
798 | return result; |
---|
799 | } |
---|
800 | |
---|
801 | /*2 |
---|
802 | *dehomogenized the generators of the ideal id1 with the leading |
---|
803 | *monomial of p replaced by n |
---|
804 | */ |
---|
805 | ideal idDehomogen (ideal id1,poly p,number n) |
---|
806 | { |
---|
807 | int i; |
---|
808 | ideal result; |
---|
809 | |
---|
810 | if (idIs0(id1)) |
---|
811 | { |
---|
812 | return idInit(1,id1->rank); |
---|
813 | } |
---|
814 | result=idInit(IDELEMS(id1),id1->rank); |
---|
815 | for (i=0; i<IDELEMS(id1); i++) |
---|
816 | { |
---|
817 | result->m[i] = pDehomogen(id1->m[i],p,n); |
---|
818 | } |
---|
819 | return result; |
---|
820 | } |
---|
821 | |
---|
822 | /*2 |
---|
823 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
824 | */ |
---|
825 | void pShift (poly * p,int i) |
---|
826 | { |
---|
827 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
828 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
829 | |
---|
830 | if (j+i < 0) return ; |
---|
831 | while (qp1 != NULL) |
---|
832 | { |
---|
833 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
834 | { |
---|
835 | pSetComp(qp1,pGetComp(qp1)+i); |
---|
836 | qp2 = qp1; |
---|
837 | pIter(qp1); |
---|
838 | } |
---|
839 | else |
---|
840 | { |
---|
841 | if (qp2 == *p) |
---|
842 | { |
---|
843 | pIter(*p); |
---|
844 | qp2->next = NULL; |
---|
845 | pDelete(&qp2); |
---|
846 | qp2 = *p; |
---|
847 | qp1 = *p; |
---|
848 | } |
---|
849 | else |
---|
850 | { |
---|
851 | qp2->next = qp1->next; |
---|
852 | qp1->next = NULL; |
---|
853 | pDelete(&qp1); |
---|
854 | qp1 = qp2->next; |
---|
855 | } |
---|
856 | } |
---|
857 | } |
---|
858 | } |
---|
859 | |
---|
860 | /*2 |
---|
861 | *initialized a field with r numbers between beg and end for the |
---|
862 | *procedure idNextChoise |
---|
863 | */ |
---|
864 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
865 | { |
---|
866 | /*returns the first choise of r numbers between beg and end*/ |
---|
867 | int i; |
---|
868 | for (i=0; i<r; i++) |
---|
869 | { |
---|
870 | choise[i] = 0; |
---|
871 | } |
---|
872 | if (r <= end-beg+1) |
---|
873 | for (i=0; i<r; i++) |
---|
874 | { |
---|
875 | choise[i] = beg+i; |
---|
876 | } |
---|
877 | if (r > end-beg+1) |
---|
878 | *endch = TRUE; |
---|
879 | else |
---|
880 | *endch = FALSE; |
---|
881 | } |
---|
882 | |
---|
883 | /*2 |
---|
884 | *returns the next choise of r numbers between beg and end |
---|
885 | */ |
---|
886 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
887 | { |
---|
888 | int i = r-1,j; |
---|
889 | while ((i >= 0) && (choise[i] == end)) |
---|
890 | { |
---|
891 | i--; |
---|
892 | end--; |
---|
893 | } |
---|
894 | if (i == -1) |
---|
895 | *endch = TRUE; |
---|
896 | else |
---|
897 | { |
---|
898 | choise[i]++; |
---|
899 | for (j=i+1; j<r; j++) |
---|
900 | { |
---|
901 | choise[j] = choise[i]+j-i; |
---|
902 | } |
---|
903 | *endch = FALSE; |
---|
904 | } |
---|
905 | } |
---|
906 | |
---|
907 | /*2 |
---|
908 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
909 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
910 | * w.r.t. the algorithm of construction |
---|
911 | */ |
---|
912 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
913 | { |
---|
914 | int * localchoise,i,result=0; |
---|
915 | BOOLEAN b=FALSE; |
---|
916 | |
---|
917 | if (d<=1) return 1; |
---|
918 | localchoise=(int*)Alloc((d-1)*sizeof(int)); |
---|
919 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
920 | while (!b) |
---|
921 | { |
---|
922 | result++; |
---|
923 | i = 0; |
---|
924 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
925 | if (i>=t) |
---|
926 | { |
---|
927 | i = t+1; |
---|
928 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
929 | if (i>=d) |
---|
930 | { |
---|
931 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
932 | return result; |
---|
933 | } |
---|
934 | } |
---|
935 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
936 | } |
---|
937 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
938 | return 0; |
---|
939 | } |
---|
940 | |
---|
941 | /*2 |
---|
942 | *computes the binomial coefficient |
---|
943 | */ |
---|
944 | int binom (int n,int r) |
---|
945 | { |
---|
946 | int i,result; |
---|
947 | |
---|
948 | if (r==0) return 1; |
---|
949 | if (n-r<r) return binom(n,n-r); |
---|
950 | result = n-r+1; |
---|
951 | for (i=2;i<=r;i++) |
---|
952 | { |
---|
953 | result *= n-r+i; |
---|
954 | result /= i; |
---|
955 | } |
---|
956 | return result; |
---|
957 | } |
---|
958 | |
---|
959 | /*2 |
---|
960 | *the free module of rank i |
---|
961 | */ |
---|
962 | ideal idFreeModule (int i) |
---|
963 | { |
---|
964 | int j; |
---|
965 | ideal h; |
---|
966 | |
---|
967 | h=idInit(i,i); |
---|
968 | for (j=0; j<i; j++) |
---|
969 | { |
---|
970 | h->m[j] = pOne(); |
---|
971 | pSetComp(h->m[j],j+1); |
---|
972 | } |
---|
973 | return h; |
---|
974 | } |
---|
975 | |
---|
976 | /*2 |
---|
977 | * h3 := h1 intersect h2 |
---|
978 | */ |
---|
979 | ideal idSect (ideal h1,ideal h2) |
---|
980 | { |
---|
981 | ideal first=h2,second=h1,temp,temp1,result; |
---|
982 | int i,j,k,flength,slength,length,rank=min(h1->rank,h2->rank); |
---|
983 | intvec *w; |
---|
984 | poly p,q; |
---|
985 | |
---|
986 | if ((idIs0(h1)) && (idIs0(h2))) return idInit(1,rank); |
---|
987 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
988 | { |
---|
989 | first = h1; |
---|
990 | second = h2; |
---|
991 | } |
---|
992 | flength = idRankFreeModule(first); |
---|
993 | slength = idRankFreeModule(second); |
---|
994 | length = max(flength,slength); |
---|
995 | if (length==0) |
---|
996 | { |
---|
997 | length = 1; |
---|
998 | } |
---|
999 | temp = idInit(IDELEMS(first),1); |
---|
1000 | j = IDELEMS(temp); |
---|
1001 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
1002 | k = 0; |
---|
1003 | for (i=0;i<j;i++) |
---|
1004 | { |
---|
1005 | if (first->m[i]!=NULL) |
---|
1006 | { |
---|
1007 | temp->m[k] = pCopy(first->m[i]); |
---|
1008 | q = pOne(); |
---|
1009 | pSetComp(q,i+1+length); |
---|
1010 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
1011 | p = temp->m[k]; |
---|
1012 | while (pNext(p)) pIter(p); |
---|
1013 | pNext(p) = q; |
---|
1014 | k++; |
---|
1015 | } |
---|
1016 | } |
---|
1017 | pEnlargeSet(&(temp->m),IDELEMS(temp),j+IDELEMS(second)-IDELEMS(temp)); |
---|
1018 | IDELEMS(temp) = j+IDELEMS(second); |
---|
1019 | for (i=0;i<IDELEMS(second);i++) |
---|
1020 | { |
---|
1021 | if (second->m[i]!=NULL) |
---|
1022 | { |
---|
1023 | temp->m[k] = pCopy(second->m[i]); |
---|
1024 | if (slength==0) pShift(&(temp->m[k]),1); |
---|
1025 | k++; |
---|
1026 | } |
---|
1027 | } |
---|
1028 | pSetSyzComp(length); |
---|
1029 | temp1 = std(temp,currQuotient,testHomog,&w,NULL,length); |
---|
1030 | if (w!=NULL) delete w; |
---|
1031 | pSetSyzComp(0); |
---|
1032 | idDelete(&temp); |
---|
1033 | result = idInit(IDELEMS(temp1),rank); |
---|
1034 | j = 0; |
---|
1035 | for (i=0;i<IDELEMS(temp1);i++) |
---|
1036 | { |
---|
1037 | if ((temp1->m[i]!=NULL) |
---|
1038 | && (pGetComp(temp1->m[i])>length)) |
---|
1039 | { |
---|
1040 | p = temp1->m[i]; |
---|
1041 | //PrintS("die Syzygie ist: ");pWrite(p); |
---|
1042 | temp1->m[i] = NULL; |
---|
1043 | while (p!=NULL) |
---|
1044 | { |
---|
1045 | q = pNext(p); |
---|
1046 | pNext(p) = NULL; |
---|
1047 | k = pGetComp(p)-1-length; |
---|
1048 | pSetComp(p,0); |
---|
1049 | //PrintS("das %d-te Element: ",k);pWrite(first->m[k]); |
---|
1050 | result->m[j] = pAdd(result->m[j],pMult(pCopy(first->m[k]),p)); |
---|
1051 | p = q; |
---|
1052 | } |
---|
1053 | //PrintS("Generator ist: ");pWrite(result->m[j]); |
---|
1054 | j++; |
---|
1055 | } |
---|
1056 | } |
---|
1057 | idSkipZeroes(result); |
---|
1058 | return result; |
---|
1059 | } |
---|
1060 | |
---|
1061 | /*2 |
---|
1062 | * ideal/module intersection for a list of objects |
---|
1063 | * given as 'resolvente' |
---|
1064 | */ |
---|
1065 | ideal idMultSect(resolvente arg, int length) |
---|
1066 | { |
---|
1067 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
1068 | ideal bigmat,tempstd,result; |
---|
1069 | poly p; |
---|
1070 | int isIdeal=0; |
---|
1071 | intvec * w=NULL; |
---|
1072 | |
---|
1073 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
1074 | for (i=0;i<length;i++) |
---|
1075 | { |
---|
1076 | if (!idIs0(arg[i])) |
---|
1077 | { |
---|
1078 | realrki=idRankFreeModule(arg[i]); |
---|
1079 | k++; |
---|
1080 | j += IDELEMS(arg[i]); |
---|
1081 | if (realrki>maxrk) maxrk = realrki; |
---|
1082 | } |
---|
1083 | else |
---|
1084 | { |
---|
1085 | if (arg[i]!=NULL) |
---|
1086 | { |
---|
1087 | return idInit(1,arg[i]->rank); |
---|
1088 | } |
---|
1089 | } |
---|
1090 | } |
---|
1091 | if (maxrk == 0) |
---|
1092 | { |
---|
1093 | isIdeal = 1; |
---|
1094 | maxrk = 1; |
---|
1095 | } |
---|
1096 | /* init -----------------------------------------------------------*/ |
---|
1097 | j += maxrk; |
---|
1098 | bigmat = idInit(j,(k+1)*maxrk); |
---|
1099 | syzComp = k*maxrk; |
---|
1100 | pSetSyzComp(syzComp); |
---|
1101 | /* create unit matrices ------------------------------------------*/ |
---|
1102 | for (i=0;i<maxrk;i++) |
---|
1103 | { |
---|
1104 | for (j=0;j<=k;j++) |
---|
1105 | { |
---|
1106 | p = pOne(); |
---|
1107 | pSetComp(p,i+1+j*maxrk); |
---|
1108 | pSetm(p); |
---|
1109 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
1110 | } |
---|
1111 | } |
---|
1112 | /* enter given ideals ------------------------------------------*/ |
---|
1113 | i = maxrk; |
---|
1114 | k = 0; |
---|
1115 | for (j=0;j<length;j++) |
---|
1116 | { |
---|
1117 | if (arg[j]!=NULL) |
---|
1118 | { |
---|
1119 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
1120 | { |
---|
1121 | if (arg[j]->m[l]!=NULL) |
---|
1122 | { |
---|
1123 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
1124 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
1125 | i++; |
---|
1126 | } |
---|
1127 | } |
---|
1128 | k++; |
---|
1129 | } |
---|
1130 | } |
---|
1131 | /* std computation --------------------------------------------*/ |
---|
1132 | tempstd = std(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
1133 | if (w!=NULL) delete w; |
---|
1134 | idDelete(&bigmat); |
---|
1135 | pSetSyzComp(0); |
---|
1136 | /* interprete result ----------------------------------------*/ |
---|
1137 | result = idInit(8,maxrk); |
---|
1138 | k = 0; |
---|
1139 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
1140 | { |
---|
1141 | if ((tempstd->m[j]!=NULL) && (pGetComp(tempstd->m[j])>syzComp)) |
---|
1142 | { |
---|
1143 | if (k>=IDELEMS(result)) |
---|
1144 | { |
---|
1145 | pEnlargeSet(&(result->m),IDELEMS(result),8); |
---|
1146 | IDELEMS(result) += 8; |
---|
1147 | } |
---|
1148 | p = tempstd->m[j]; |
---|
1149 | tempstd->m[j] = NULL; |
---|
1150 | pShift(&p,-syzComp-isIdeal); |
---|
1151 | result->m[k] = p; |
---|
1152 | k++; |
---|
1153 | } |
---|
1154 | } |
---|
1155 | /* clean up ----------------------------------------------------*/ |
---|
1156 | idDelete(&tempstd); |
---|
1157 | idSkipZeroes(result); |
---|
1158 | return result; |
---|
1159 | } |
---|
1160 | |
---|
1161 | /*2 |
---|
1162 | *computes the rank of the free module in which h1 embeds |
---|
1163 | */ |
---|
1164 | int lengthFreeModule (ideal h1) |
---|
1165 | { |
---|
1166 | int i,j,k; |
---|
1167 | |
---|
1168 | if (idIs0(h1)) return 0; |
---|
1169 | k = -1; |
---|
1170 | for (i=0; i<IDELEMS(h1); i++) |
---|
1171 | { |
---|
1172 | j = pMaxComp(h1->m[i]); |
---|
1173 | if (j>k) k = j; |
---|
1174 | } |
---|
1175 | return k; |
---|
1176 | } |
---|
1177 | |
---|
1178 | /*2 |
---|
1179 | *computes syzygies of h1, |
---|
1180 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
1181 | */ |
---|
1182 | ideal idPrepare (ideal h1,ideal quot, tHomog h, |
---|
1183 | int* syzcomp, int *quotgen, int *quotdim, intvec **w) |
---|
1184 | { |
---|
1185 | ideal h2, h3; |
---|
1186 | int i; |
---|
1187 | int j,k; |
---|
1188 | poly p,q; |
---|
1189 | BOOLEAN orderChanged=FALSE; |
---|
1190 | |
---|
1191 | if (idIs0(h1)) return NULL; |
---|
1192 | k = lengthFreeModule(h1); |
---|
1193 | if (*syzcomp<k) *syzcomp = k; |
---|
1194 | h2 = NULL; |
---|
1195 | h2=idCopy(h1); |
---|
1196 | i = IDELEMS(h2)-1; |
---|
1197 | //while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
1198 | if (k == 0) |
---|
1199 | { |
---|
1200 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
1201 | *syzcomp = 1; |
---|
1202 | } |
---|
1203 | h2->rank = *syzcomp+i+1; |
---|
1204 | for (j=0; j<=i; j++) |
---|
1205 | { |
---|
1206 | p = h2->m[j]; |
---|
1207 | q = pOne(); |
---|
1208 | #ifdef DRING |
---|
1209 | if (pDRING) { pdDFlag(q)=1; pSetm(q); } |
---|
1210 | #endif |
---|
1211 | pSetComp(q,*syzcomp+1+j); |
---|
1212 | if (p!=NULL) |
---|
1213 | { |
---|
1214 | while (pNext(p)) pIter(p); |
---|
1215 | p->next = q; |
---|
1216 | } |
---|
1217 | else |
---|
1218 | h2->m[j]=q; |
---|
1219 | } |
---|
1220 | if ((pOrdSgn!=1) || (h!=TRUE) || (*syzcomp>1)|| (pLexOrder)) |
---|
1221 | { |
---|
1222 | pSetSyzComp(*syzcomp); |
---|
1223 | orderChanged=TRUE; |
---|
1224 | } |
---|
1225 | else |
---|
1226 | { |
---|
1227 | for(j=0;(j<IDELEMS(h2) && (!orderChanged));j++) |
---|
1228 | { |
---|
1229 | if (h2->m[j] != NULL) |
---|
1230 | { |
---|
1231 | p=h2->m[j]; |
---|
1232 | while ((p!=NULL) |
---|
1233 | && (pGetComp(p)<=*syzcomp)) |
---|
1234 | { |
---|
1235 | if (pIsConstantComp(p)) |
---|
1236 | { |
---|
1237 | pSetSyzComp(*syzcomp); |
---|
1238 | orderChanged=TRUE; |
---|
1239 | break; |
---|
1240 | } |
---|
1241 | pIter(p); |
---|
1242 | } |
---|
1243 | } |
---|
1244 | } |
---|
1245 | } |
---|
1246 | // if (orderChanged) PrintS("order changed\n"); |
---|
1247 | // else PrintS("order not changed\n"); |
---|
1248 | #ifdef PDEBUG |
---|
1249 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
1250 | #endif |
---|
1251 | h3=std(h2,quot,h,w,NULL,*syzcomp); |
---|
1252 | //h3->rank = h2->rank; done by std -> initBuchMora -> initS |
---|
1253 | h3->rank-=*syzcomp; |
---|
1254 | idDelete(&h2); |
---|
1255 | if (orderChanged) pSetSyzComp(0); |
---|
1256 | return h3; |
---|
1257 | } |
---|
1258 | |
---|
1259 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w) |
---|
1260 | { |
---|
1261 | int d; |
---|
1262 | return idSyzygies(h1,quot,h,w,FALSE,d); |
---|
1263 | } |
---|
1264 | |
---|
1265 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1266 | BOOLEAN setRegularity, int °) |
---|
1267 | { |
---|
1268 | ideal e, h3; |
---|
1269 | poly p; |
---|
1270 | int i, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1271 | BOOLEAN isMonomial=TRUE; |
---|
1272 | |
---|
1273 | #ifdef PDEBUG |
---|
1274 | int ii; |
---|
1275 | for(ii=0;ii<IDELEMS(h1);ii++) pTest(h1->m[ii]); |
---|
1276 | if (quot!=NULL) |
---|
1277 | { |
---|
1278 | for(ii=0;ii<IDELEMS(quot);ii++) pTest(quot->m[ii]); |
---|
1279 | } |
---|
1280 | #endif |
---|
1281 | if (idIs0(h1)) |
---|
1282 | return idFreeModule(IDELEMS(h1)); |
---|
1283 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1284 | if (h3==NULL) |
---|
1285 | return idFreeModule(IDELEMS(h1)); |
---|
1286 | i = -1; |
---|
1287 | e=idInit(16,h3->rank); |
---|
1288 | for (j=0; j<IDELEMS(h3); j++) |
---|
1289 | { |
---|
1290 | if (h3->m[j] != NULL) |
---|
1291 | { |
---|
1292 | if (pMinComp(h3->m[j]) > k) |
---|
1293 | { |
---|
1294 | p = h3->m[j]; |
---|
1295 | h3->m[j]=NULL; |
---|
1296 | pShift(&p,-k); |
---|
1297 | if (p!=NULL) |
---|
1298 | { |
---|
1299 | i++; |
---|
1300 | if (i+1 >= IDELEMS(e)) |
---|
1301 | { |
---|
1302 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1303 | IDELEMS(e) += 16; |
---|
1304 | } |
---|
1305 | e->m[i] = p; |
---|
1306 | } |
---|
1307 | } |
---|
1308 | else |
---|
1309 | { |
---|
1310 | isMonomial=isMonomial && (pNext(h3->m[j])==NULL); |
---|
1311 | pDelete(&pNext(h3->m[j])); |
---|
1312 | } |
---|
1313 | } |
---|
1314 | } |
---|
1315 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1316 | { |
---|
1317 | idSkipZeroes(h3); |
---|
1318 | resolvente res = sySchreyerResolvente(h3,-1,&length,TRUE); |
---|
1319 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1320 | deg = reg+2; |
---|
1321 | delete dummy; |
---|
1322 | for (j=0;j<length;j++) |
---|
1323 | { |
---|
1324 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1325 | } |
---|
1326 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1327 | } |
---|
1328 | idDelete(&h3); |
---|
1329 | idSkipZeroes(e); |
---|
1330 | return e; |
---|
1331 | } |
---|
1332 | |
---|
1333 | /*2 |
---|
1334 | * computes syzygies and minimizes the input (h1) |
---|
1335 | * ONLY used in syMinRes |
---|
1336 | */ |
---|
1337 | ideal idSyzMin (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1338 | BOOLEAN setRegularity, int °) |
---|
1339 | { |
---|
1340 | ideal e, h3; |
---|
1341 | poly p; |
---|
1342 | intvec * reord; |
---|
1343 | int i, l=0, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1344 | BOOLEAN isMonomial=TRUE; |
---|
1345 | |
---|
1346 | if (idIs0(h1)) |
---|
1347 | return idFreeModule(1); |
---|
1348 | //PrintS("h1 vorher\n"); |
---|
1349 | //for (i=0;i<IDELEMS(h1);i++) |
---|
1350 | //{ |
---|
1351 | //Print("Element %d: ",i);pWrite(h1->m[i]); |
---|
1352 | //} |
---|
1353 | idSkipZeroes(h1); |
---|
1354 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1355 | //PrintS("h1 nachher\n"); |
---|
1356 | //for (i=0;i<IDELEMS(h3);i++) |
---|
1357 | //{ |
---|
1358 | //Print("Element %d: ",i);pWrite(h3->m[i]); |
---|
1359 | //} |
---|
1360 | if (h3==NULL) |
---|
1361 | return idFreeModule(1); |
---|
1362 | for (i=IDELEMS(h1);i!=0;i--) |
---|
1363 | pDelete(&(h1->m[i-1])); |
---|
1364 | reord = new intvec(IDELEMS(h1)+1); |
---|
1365 | i = -1; |
---|
1366 | e=idInit(16,h3->rank); |
---|
1367 | for (j=0; j<IDELEMS(h3); j++) |
---|
1368 | { |
---|
1369 | if (h3->m[j] != NULL) |
---|
1370 | { |
---|
1371 | p = h3->m[j]; |
---|
1372 | if (pGetComp(p) > k) |
---|
1373 | { |
---|
1374 | h3->m[j]=NULL; |
---|
1375 | pShift(&p,-k); |
---|
1376 | if (p!=NULL) |
---|
1377 | { |
---|
1378 | i++; |
---|
1379 | if (i+1 >= IDELEMS(e)) |
---|
1380 | { |
---|
1381 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1382 | IDELEMS(e) += 16; |
---|
1383 | } |
---|
1384 | e->m[i] = p; |
---|
1385 | } |
---|
1386 | } |
---|
1387 | else |
---|
1388 | { |
---|
1389 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
1390 | if (pIsConstantComp(pNext(p))) |
---|
1391 | { |
---|
1392 | (*reord)[pGetComp(pNext(p))-k] = l+1; |
---|
1393 | //Print("Element %d mit Comp %d: ",j,pGetComp(pNext(p))-k); |
---|
1394 | //pWrite(h3->m[j]); |
---|
1395 | h1->m[l] = h3->m[j]; |
---|
1396 | h3->m[j] = pCopy(h1->m[l]); |
---|
1397 | pDelete(&pNext(p)); |
---|
1398 | l++; |
---|
1399 | } |
---|
1400 | isMonomial=isMonomial && (pGetComp(pNext(h3->m[j]))>k); |
---|
1401 | pDelete(&pNext(h3->m[j])); |
---|
1402 | } |
---|
1403 | } |
---|
1404 | } |
---|
1405 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1406 | { |
---|
1407 | idSkipZeroes(h3); |
---|
1408 | resolvente res = sySchreyerResolvente(h3,0,&length); |
---|
1409 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1410 | deg = reg+2; |
---|
1411 | delete dummy; |
---|
1412 | for (j=0;j<length;j++) |
---|
1413 | { |
---|
1414 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1415 | } |
---|
1416 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1417 | } |
---|
1418 | idDelete(&h3); |
---|
1419 | //PrintS("Komponententransformation: "); |
---|
1420 | //reord->show(); |
---|
1421 | //PrintLn(); |
---|
1422 | for (i=IDELEMS(e);i!=0;i--) |
---|
1423 | { |
---|
1424 | if (e->m[i-1]!=NULL) |
---|
1425 | { |
---|
1426 | p = e->m[i-1]; |
---|
1427 | while (p!=NULL) |
---|
1428 | { |
---|
1429 | j = pGetComp(p); |
---|
1430 | pSetComp(p,(*reord)[j]); |
---|
1431 | pIter(p); |
---|
1432 | } |
---|
1433 | e->m[i-1] = pOrdPolyMerge(e->m[i-1]); |
---|
1434 | } |
---|
1435 | } |
---|
1436 | idSkipZeroes(e); |
---|
1437 | delete reord; |
---|
1438 | return e; |
---|
1439 | } |
---|
1440 | |
---|
1441 | /* |
---|
1442 | *computes a standard basis for h1 and stores the transformation matrix |
---|
1443 | * in ma |
---|
1444 | */ |
---|
1445 | ideal idLiftStd (ideal h1,ideal quot, matrix* ma, tHomog h) |
---|
1446 | { |
---|
1447 | int i, j, k=0, t, quotgen, inputIsIdeal=lengthFreeModule(h1); |
---|
1448 | ideal e, h3; |
---|
1449 | poly p=NULL, q, qq; |
---|
1450 | intvec *w=NULL; |
---|
1451 | |
---|
1452 | idDelete((ideal*)ma); |
---|
1453 | *ma=mpNew(1,0); |
---|
1454 | if (idIs0(h1)) |
---|
1455 | return idInit(1,h1->rank); |
---|
1456 | h3=idPrepare(h1,quot,h,&k,"gen,&i,&w); |
---|
1457 | if (w!=NULL) delete w; |
---|
1458 | i = 0; |
---|
1459 | for (j=0;j<IDELEMS(h3);j++) |
---|
1460 | { |
---|
1461 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1462 | i++; |
---|
1463 | } |
---|
1464 | j = IDELEMS(h1); |
---|
1465 | idDelete((ideal*)ma); |
---|
1466 | *ma = mpNew(j,i); |
---|
1467 | i = -1; |
---|
1468 | e=idInit(16,h1->rank); |
---|
1469 | for (j=0; j<IDELEMS(h3); j++) |
---|
1470 | { |
---|
1471 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1472 | { |
---|
1473 | q = h3->m[j]; |
---|
1474 | qq=q; |
---|
1475 | h3->m[j]=NULL; |
---|
1476 | while (pNext(q) != NULL) |
---|
1477 | { |
---|
1478 | if (pGetComp(pNext(q)) > k) |
---|
1479 | { |
---|
1480 | p = pNext(q); |
---|
1481 | pNext(q) = pNext(pNext(q)); |
---|
1482 | pNext(p) = NULL; |
---|
1483 | t=pGetComp(p); |
---|
1484 | pSetComp(p,0); |
---|
1485 | MATELEM(*ma,t-k,i+2) = pAdd(MATELEM(*ma,t-k,i+2),p); |
---|
1486 | } |
---|
1487 | else |
---|
1488 | { |
---|
1489 | pIter(q); |
---|
1490 | } |
---|
1491 | } |
---|
1492 | if (!inputIsIdeal) pShift(&qq,-1); |
---|
1493 | //if (quotgen != 0) |
---|
1494 | //{ |
---|
1495 | // q = kNF(quot,qq); |
---|
1496 | // pDelete(&qq); |
---|
1497 | //} |
---|
1498 | //else |
---|
1499 | q = qq; |
---|
1500 | if (q !=NULL) |
---|
1501 | { |
---|
1502 | i++; |
---|
1503 | if (i+1 >= IDELEMS(e)) |
---|
1504 | { |
---|
1505 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1506 | IDELEMS(e) += 16; |
---|
1507 | } |
---|
1508 | e->m[i] = q; |
---|
1509 | } |
---|
1510 | } |
---|
1511 | } |
---|
1512 | idDelete(&h3); |
---|
1513 | idSkipZeroes(e); |
---|
1514 | return e; |
---|
1515 | } |
---|
1516 | |
---|
1517 | /*2 |
---|
1518 | *computes a representation of the generators of submod with respect to those |
---|
1519 | * of mod |
---|
1520 | */ |
---|
1521 | ideal idLiftNonStB (ideal mod, ideal submod) |
---|
1522 | { |
---|
1523 | int lsmod =idRankFreeModule(submod), i, j, k, quotgen; |
---|
1524 | ideal result, h3, temp; |
---|
1525 | |
---|
1526 | if (idIs0(mod)) |
---|
1527 | return idInit(1,mod->rank); |
---|
1528 | |
---|
1529 | if ((idRankFreeModule(mod)!=0) && (lsmod==0)) lsmod=1; |
---|
1530 | k=lsmod; |
---|
1531 | //idSkipZeroes(mod); |
---|
1532 | h3=idPrepare(mod,currQuotient,(tHomog)FALSE,&k,"gen,&i,NULL); |
---|
1533 | for (j=0;j<IDELEMS(h3);j++) |
---|
1534 | { |
---|
1535 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) > k)) |
---|
1536 | pDelete(&(h3->m[j])); |
---|
1537 | } |
---|
1538 | idSkipZeroes(h3); |
---|
1539 | if (lsmod==0) |
---|
1540 | { |
---|
1541 | temp = idCopy(submod); |
---|
1542 | for (j=IDELEMS(temp);j>0;j--) |
---|
1543 | { |
---|
1544 | if (temp->m[j-1]!=NULL) |
---|
1545 | pShift(&(temp->m[j-1]),1); |
---|
1546 | } |
---|
1547 | } |
---|
1548 | else |
---|
1549 | { |
---|
1550 | temp = submod; |
---|
1551 | } |
---|
1552 | pSetSyzComp(k); |
---|
1553 | result = kNF(h3,currQuotient,temp,k); |
---|
1554 | result->rank = h3->rank; |
---|
1555 | idDelete(&h3); |
---|
1556 | if (lsmod==0) |
---|
1557 | idDelete(&temp); |
---|
1558 | pSetSyzComp(0); |
---|
1559 | for (j=0;j<IDELEMS(result);j++) |
---|
1560 | { |
---|
1561 | if (result->m[j]!=NULL) |
---|
1562 | { |
---|
1563 | if (pGetComp(result->m[j])<=k) |
---|
1564 | { |
---|
1565 | WerrorS("2nd module lies not in the first"); |
---|
1566 | idDelete(&result); |
---|
1567 | return idInit(1,1); |
---|
1568 | } |
---|
1569 | else |
---|
1570 | { |
---|
1571 | pShift(&(result->m[j]),-k); |
---|
1572 | pNeg(result->m[j]); |
---|
1573 | } |
---|
1574 | } |
---|
1575 | } |
---|
1576 | return result; |
---|
1577 | } |
---|
1578 | |
---|
1579 | /*2 |
---|
1580 | *computes a representation of the generators of submod with respect to those |
---|
1581 | * of mod which is given as standardbasis, |
---|
1582 | * uses currQuotient as the quotient ideal (if not NULL) |
---|
1583 | */ |
---|
1584 | ideal idLift (ideal mod,ideal submod) |
---|
1585 | { |
---|
1586 | ideal temp, result; |
---|
1587 | int j,k; |
---|
1588 | poly p,q; |
---|
1589 | BOOLEAN reported=FALSE; |
---|
1590 | |
---|
1591 | if (idIs0(mod)) return idInit(1,mod->rank); |
---|
1592 | k = lengthFreeModule(mod); |
---|
1593 | temp=idCopy(mod); |
---|
1594 | if (k == 0) |
---|
1595 | { |
---|
1596 | for (j=0; j<IDELEMS(temp); j++) |
---|
1597 | { |
---|
1598 | if (temp->m[j]!=NULL) pSetCompP(temp->m[j],1); |
---|
1599 | } |
---|
1600 | k = 1; |
---|
1601 | } |
---|
1602 | for (j=0; j<IDELEMS(temp); j++) |
---|
1603 | { |
---|
1604 | if (temp->m[j]!=NULL) |
---|
1605 | { |
---|
1606 | p = temp->m[j]; |
---|
1607 | q = pOne(); |
---|
1608 | pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
1609 | pSetComp(q,k+1+j); |
---|
1610 | while (pNext(p)) pIter(p); |
---|
1611 | pNext(p) = q; |
---|
1612 | } |
---|
1613 | } |
---|
1614 | result=idInit(IDELEMS(submod),submod->rank); |
---|
1615 | pSetSyzComp(k); |
---|
1616 | for (j=0; j<IDELEMS(submod); j++) |
---|
1617 | { |
---|
1618 | if (submod->m[j]!=NULL) |
---|
1619 | { |
---|
1620 | p = pCopy(submod->m[j]); |
---|
1621 | if (pGetComp(p)==0) pSetCompP(p,1); |
---|
1622 | q = kNF(temp,currQuotient,p); |
---|
1623 | pDelete(&p); |
---|
1624 | if (q!=NULL) |
---|
1625 | { |
---|
1626 | if (pMinComp(q)<=k) |
---|
1627 | { |
---|
1628 | if (!reported) |
---|
1629 | { |
---|
1630 | Warn("first module not a standardbasis"); |
---|
1631 | Warn("or second not a proper submodule"); |
---|
1632 | reported=TRUE; |
---|
1633 | } |
---|
1634 | pDelete(&q); |
---|
1635 | } |
---|
1636 | else |
---|
1637 | { |
---|
1638 | pShift(&q,-k); |
---|
1639 | result->m[j] = q; |
---|
1640 | } |
---|
1641 | } |
---|
1642 | } |
---|
1643 | } |
---|
1644 | pSetSyzComp(0); |
---|
1645 | //idSkipZeroes(result); |
---|
1646 | idDelete(&temp); |
---|
1647 | return result; |
---|
1648 | } |
---|
1649 | |
---|
1650 | /*2 |
---|
1651 | *computes the quotient of h1,h2 |
---|
1652 | */ |
---|
1653 | #ifdef OLD_QUOT |
---|
1654 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsSB) |
---|
1655 | { |
---|
1656 | int i,j = 0,l,ll,k,kkk,k1,k2,kmax; |
---|
1657 | ideal h3,h4; |
---|
1658 | poly p,q = NULL; |
---|
1659 | BOOLEAN b = FALSE; |
---|
1660 | |
---|
1661 | k1 = lengthFreeModule(h1); |
---|
1662 | k2 = lengthFreeModule(h2); |
---|
1663 | k=max(k1,k2); |
---|
1664 | if (k==0) { k = 1; b=TRUE; } |
---|
1665 | h4 = idInit(1,1); |
---|
1666 | for (i=0; i<IDELEMS(h2); i++) |
---|
1667 | { |
---|
1668 | if (h2->m[i] != NULL) |
---|
1669 | { |
---|
1670 | p = pCopy(h2->m[i]); |
---|
1671 | if (k2 == 0) |
---|
1672 | pShift(&p,j*k+1); |
---|
1673 | else |
---|
1674 | pShift(&p,j*k); |
---|
1675 | q = pAdd(q,p); |
---|
1676 | j++; |
---|
1677 | } |
---|
1678 | } |
---|
1679 | kmax = j*k+1; |
---|
1680 | p = pOne(); |
---|
1681 | pSetComp(p,kmax); |
---|
1682 | pSetSyzComp(kmax-1); |
---|
1683 | q = pAdd(q,p); |
---|
1684 | h4->m[0] = q; |
---|
1685 | if (k2 == 0) |
---|
1686 | { |
---|
1687 | if (k > IDELEMS(h4)) |
---|
1688 | { |
---|
1689 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1690 | IDELEMS(h4) = k; |
---|
1691 | } |
---|
1692 | for (i=1; i<k; i++) |
---|
1693 | { |
---|
1694 | p = pCopy(h4->m[i-1]); |
---|
1695 | pShift(&p,1); |
---|
1696 | h4->m[i] = p; |
---|
1697 | } |
---|
1698 | } |
---|
1699 | kkk = IDELEMS(h4); |
---|
1700 | i = IDELEMS(h1); |
---|
1701 | while (h1->m[i-1] == NULL) i--; |
---|
1702 | for (l=0; l<i; l++) |
---|
1703 | { |
---|
1704 | if(h1->m[l]!=NULL) |
---|
1705 | { |
---|
1706 | for (ll=0; ll<j; ll++) |
---|
1707 | { |
---|
1708 | p = pCopy(h1->m[l]); |
---|
1709 | if (k1 == 0) |
---|
1710 | pShift(&p,ll*k+1); |
---|
1711 | else |
---|
1712 | pShift(&p,ll*k); |
---|
1713 | if (kkk >= IDELEMS(h4)) |
---|
1714 | { |
---|
1715 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1716 | IDELEMS(h4) += 16; |
---|
1717 | } |
---|
1718 | h4->m[kkk] = p; |
---|
1719 | kkk++; |
---|
1720 | } |
---|
1721 | } |
---|
1722 | } |
---|
1723 | h3 = std(h4,currQuotient,(tHomog)FALSE,NULL,NULL,kmax-1); |
---|
1724 | pSetSyzComp(0); |
---|
1725 | idDelete(&h4); |
---|
1726 | for (i=0;i<IDELEMS(h3);i++) |
---|
1727 | { |
---|
1728 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1729 | { |
---|
1730 | if (b) |
---|
1731 | pShift(&h3->m[i],-kmax); |
---|
1732 | else |
---|
1733 | pShift(&h3->m[i],-kmax+1); |
---|
1734 | } |
---|
1735 | else |
---|
1736 | pDelete(&h3->m[i]); |
---|
1737 | } |
---|
1738 | if (b) |
---|
1739 | h3->rank = 1; |
---|
1740 | else |
---|
1741 | h3->rank = h1->rank; |
---|
1742 | h4=idCompactify(h3); |
---|
1743 | idDelete(&h3); |
---|
1744 | return h4; |
---|
1745 | } |
---|
1746 | #else |
---|
1747 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb) |
---|
1748 | { |
---|
1749 | int i,j = 0,l,ll,k,kkk,k1,k2,kmax; |
---|
1750 | intvec * weights,* weights1; |
---|
1751 | ideal h3,h4,temph1; |
---|
1752 | poly p,q = NULL; |
---|
1753 | BOOLEAN resultIsIdeal = FALSE,addOnlyOne=TRUE; |
---|
1754 | tHomog hom=isNotHomog; |
---|
1755 | BITSET old_test=test; |
---|
1756 | |
---|
1757 | k1 = lengthFreeModule(h1); |
---|
1758 | k2 = lengthFreeModule(h2); |
---|
1759 | if (idIs0(h2)) |
---|
1760 | { |
---|
1761 | if (k1==0) |
---|
1762 | { |
---|
1763 | h3 = idInit(1,1); |
---|
1764 | h3->m[0] = pOne(); |
---|
1765 | } |
---|
1766 | else |
---|
1767 | h3 = idFreeModule(h1->rank); |
---|
1768 | return h3; |
---|
1769 | } |
---|
1770 | k=max(k1,k2); |
---|
1771 | if (k==0) |
---|
1772 | { |
---|
1773 | k = 1; |
---|
1774 | resultIsIdeal=TRUE; |
---|
1775 | } |
---|
1776 | else if ((k1>0)&&(k2>0)) |
---|
1777 | { |
---|
1778 | resultIsIdeal=TRUE; |
---|
1779 | } |
---|
1780 | hom = (tHomog)idHomModule(h1,currQuotient,&weights) ; |
---|
1781 | h4 = idInit(1,1); |
---|
1782 | for (i=0; i<IDELEMS(h2); i++) |
---|
1783 | { |
---|
1784 | if (h2->m[i] != NULL) |
---|
1785 | { |
---|
1786 | p = pCopy(h2->m[i]); |
---|
1787 | if (k2 == 0) |
---|
1788 | pShift(&p,j*k+1); |
---|
1789 | else |
---|
1790 | pShift(&p,j*k); |
---|
1791 | q = pAdd(q,p); |
---|
1792 | j++; |
---|
1793 | } |
---|
1794 | } |
---|
1795 | kmax = j*k+1; |
---|
1796 | p = pOne(); |
---|
1797 | pSetComp(p,kmax); |
---|
1798 | pSetSyzComp(kmax-1); |
---|
1799 | q = pAdd(q,p); |
---|
1800 | h4->m[0] = q; |
---|
1801 | if (k2 == 0) |
---|
1802 | { |
---|
1803 | if (k > IDELEMS(h4)) |
---|
1804 | { |
---|
1805 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1806 | IDELEMS(h4) = k; |
---|
1807 | } |
---|
1808 | if (k>1) addOnlyOne = FALSE; |
---|
1809 | for (i=1; i<k; i++) |
---|
1810 | { |
---|
1811 | p = pCopy(h4->m[i-1]); |
---|
1812 | pShift(&p,1); |
---|
1813 | h4->m[i] = p; |
---|
1814 | } |
---|
1815 | } |
---|
1816 | kkk = IDELEMS(h4); |
---|
1817 | if (addOnlyOne && (!h1IsStb)) |
---|
1818 | temph1 = std(h1,currQuotient,hom,&weights,NULL); |
---|
1819 | else |
---|
1820 | temph1 = h1; |
---|
1821 | idTest(temph1); |
---|
1822 | i = IDELEMS(temph1); |
---|
1823 | while ((i>0) && (temph1->m[i-1]==NULL)) i--; |
---|
1824 | for (l=0; l<i; l++) |
---|
1825 | { |
---|
1826 | if(temph1->m[l]!=NULL) |
---|
1827 | { |
---|
1828 | for (ll=0; ll<j; ll++) |
---|
1829 | { |
---|
1830 | p = pCopy(temph1->m[l]); |
---|
1831 | if (k1 == 0) |
---|
1832 | pShift(&p,ll*k+1); |
---|
1833 | else |
---|
1834 | pShift(&p,ll*k); |
---|
1835 | if (kkk >= IDELEMS(h4)) |
---|
1836 | { |
---|
1837 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1838 | IDELEMS(h4) += 16; |
---|
1839 | } |
---|
1840 | h4->m[kkk] = p; |
---|
1841 | kkk++; |
---|
1842 | } |
---|
1843 | } |
---|
1844 | } |
---|
1845 | idTest(h4); |
---|
1846 | if (addOnlyOne) |
---|
1847 | { |
---|
1848 | p = h4->m[0]; |
---|
1849 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
1850 | { |
---|
1851 | h4->m[i] = h4->m[i+1]; |
---|
1852 | } |
---|
1853 | h4->m[IDELEMS(h4)-1] = p; |
---|
1854 | idSkipZeroes(h4); |
---|
1855 | test |= Sy_bit(OPT_SB_1); |
---|
1856 | } |
---|
1857 | idTest(h4); |
---|
1858 | hom = (tHomog)idHomModule(h4,currQuotient,&weights1); |
---|
1859 | if (addOnlyOne) |
---|
1860 | { |
---|
1861 | h3 = std(h4,currQuotient,hom,&weights1,NULL,kmax-1,IDELEMS(h4)-1); |
---|
1862 | } |
---|
1863 | else |
---|
1864 | { |
---|
1865 | h3 = std(h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
1866 | } |
---|
1867 | idTest(h3); |
---|
1868 | idDelete(&h4); |
---|
1869 | pSetSyzComp(0); |
---|
1870 | for (i=0;i<IDELEMS(h3);i++) |
---|
1871 | { |
---|
1872 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1873 | { |
---|
1874 | if (resultIsIdeal) |
---|
1875 | pShift(&h3->m[i],-kmax); |
---|
1876 | else |
---|
1877 | pShift(&h3->m[i],-kmax+1); |
---|
1878 | } |
---|
1879 | else |
---|
1880 | pDelete(&h3->m[i]); |
---|
1881 | } |
---|
1882 | if (resultIsIdeal) |
---|
1883 | h3->rank = 1; |
---|
1884 | else |
---|
1885 | h3->rank = h1->rank; |
---|
1886 | idTest(h3); |
---|
1887 | idSkipZeroes(h3); |
---|
1888 | //h4=idCompactify(h3); |
---|
1889 | //idDelete(&h3); |
---|
1890 | if ((addOnlyOne) && (!h1IsStb)) |
---|
1891 | idDelete(&temph1); |
---|
1892 | if (weights!=NULL) delete weights; |
---|
1893 | if (weights1!=NULL) delete weights1; |
---|
1894 | test = old_test; |
---|
1895 | return h3; |
---|
1896 | } |
---|
1897 | #endif |
---|
1898 | |
---|
1899 | /*2 |
---|
1900 | *computes recursively all monomials of a certain degree |
---|
1901 | *in every step the actvar-th entry in the exponential |
---|
1902 | *vector is incremented and the other variables are |
---|
1903 | *computed by recursive calls of makemonoms |
---|
1904 | *if the last variable is reached, the difference to the |
---|
1905 | *degree is computed directly |
---|
1906 | *vars is the number variables |
---|
1907 | *actvar is the actual variable to handle |
---|
1908 | *deg is the degree of the monomials to compute |
---|
1909 | *monomdeg is the actual degree of the monomial in consideration |
---|
1910 | */ |
---|
1911 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
1912 | { |
---|
1913 | poly p; |
---|
1914 | int i=0; |
---|
1915 | |
---|
1916 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
1917 | { |
---|
1918 | idpower[idpowerpoint] = pOne(); |
---|
1919 | monomdeg = 0; |
---|
1920 | } |
---|
1921 | while (i<=deg) |
---|
1922 | { |
---|
1923 | if (deg == monomdeg) |
---|
1924 | { |
---|
1925 | pSetm(idpower[idpowerpoint]); |
---|
1926 | idpowerpoint++; |
---|
1927 | return; |
---|
1928 | } |
---|
1929 | if (actvar == vars) |
---|
1930 | { |
---|
1931 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
1932 | pSetm(idpower[idpowerpoint]); |
---|
1933 | idpowerpoint++; |
---|
1934 | return; |
---|
1935 | } |
---|
1936 | else |
---|
1937 | { |
---|
1938 | p = pCopy(idpower[idpowerpoint]); |
---|
1939 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
1940 | idpower[idpowerpoint] = p; |
---|
1941 | } |
---|
1942 | monomdeg++; |
---|
1943 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
1944 | pSetm(idpower[idpowerpoint]); |
---|
1945 | i++; |
---|
1946 | } |
---|
1947 | } |
---|
1948 | |
---|
1949 | /*2 |
---|
1950 | *returns the deg-th power of the maximal ideal of 0 |
---|
1951 | */ |
---|
1952 | ideal idMaxIdeal(int deg) |
---|
1953 | { |
---|
1954 | if (deg < 0) |
---|
1955 | { |
---|
1956 | WarnS("maxideal: power must be non-negative"); |
---|
1957 | } |
---|
1958 | if (deg < 1) |
---|
1959 | { |
---|
1960 | ideal I=idInit(1,1); |
---|
1961 | I->m[0]=pOne(); |
---|
1962 | return I; |
---|
1963 | } |
---|
1964 | if (deg == 1) |
---|
1965 | { |
---|
1966 | return idMaxIdeal(); |
---|
1967 | } |
---|
1968 | |
---|
1969 | int vars = currRing->N; |
---|
1970 | int i = binom(vars+deg-1,deg); |
---|
1971 | ideal id=idInit(i,1); |
---|
1972 | idpower = id->m; |
---|
1973 | idpowerpoint = 0; |
---|
1974 | makemonoms(vars,1,deg,0); |
---|
1975 | idpower = NULL; |
---|
1976 | idpowerpoint = 0; |
---|
1977 | return id; |
---|
1978 | } |
---|
1979 | |
---|
1980 | /*2 |
---|
1981 | *computes recursively all generators of a certain degree |
---|
1982 | *of the ideal "givenideal" |
---|
1983 | *elms is the number elements in the given ideal |
---|
1984 | *actelm is the actual element to handle |
---|
1985 | *deg is the degree of the power to compute |
---|
1986 | *gendeg is the actual degree of the generator in consideration |
---|
1987 | */ |
---|
1988 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
1989 | { |
---|
1990 | poly p; |
---|
1991 | int i=0; |
---|
1992 | |
---|
1993 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
1994 | { |
---|
1995 | idpower[idpowerpoint] = pOne(); |
---|
1996 | gendeg = 0; |
---|
1997 | } |
---|
1998 | while (i<=deg) |
---|
1999 | { |
---|
2000 | if (deg == gendeg) |
---|
2001 | { |
---|
2002 | idpowerpoint++; |
---|
2003 | return; |
---|
2004 | } |
---|
2005 | if (actelm == elms) |
---|
2006 | { |
---|
2007 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
2008 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
2009 | idpowerpoint++; |
---|
2010 | return; |
---|
2011 | } |
---|
2012 | else |
---|
2013 | { |
---|
2014 | p = pCopy(idpower[idpowerpoint]); |
---|
2015 | makepotence(elms,actelm+1,deg,gendeg); |
---|
2016 | idpower[idpowerpoint] = p; |
---|
2017 | } |
---|
2018 | gendeg++; |
---|
2019 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
2020 | i++; |
---|
2021 | } |
---|
2022 | } |
---|
2023 | |
---|
2024 | /*2 |
---|
2025 | *returns the deg-th power of the ideal gid |
---|
2026 | */ |
---|
2027 | //ideal idPower(ideal gid,int deg) |
---|
2028 | //{ |
---|
2029 | // int i; |
---|
2030 | // ideal id; |
---|
2031 | // |
---|
2032 | // if (deg < 1) deg = 1; |
---|
2033 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
2034 | // id=idInit(i,1); |
---|
2035 | // idpower = id->m; |
---|
2036 | // givenideal = gid->m; |
---|
2037 | // idpowerpoint = 0; |
---|
2038 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
2039 | // idpower = NULL; |
---|
2040 | // givenideal = NULL; |
---|
2041 | // idpowerpoint = 0; |
---|
2042 | // return id; |
---|
2043 | //} |
---|
2044 | static void idNextPotence(ideal given, ideal result, |
---|
2045 | int begin, int end, int deg, int restdeg, poly ap) |
---|
2046 | { |
---|
2047 | poly p; |
---|
2048 | int i; |
---|
2049 | |
---|
2050 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
2051 | i = result->nrows; |
---|
2052 | result->m[i] = pMult(pCopy(ap),p); |
---|
2053 | //PrintS("."); |
---|
2054 | (result->nrows)++; |
---|
2055 | if (result->nrows >= IDELEMS(result)) |
---|
2056 | { |
---|
2057 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
2058 | IDELEMS(result) += 16; |
---|
2059 | } |
---|
2060 | if (begin == end) return; |
---|
2061 | for (i=restdeg-1;i>=0;i--) |
---|
2062 | { |
---|
2063 | p = pPower(pCopy(given->m[begin]),i); |
---|
2064 | p = pMult(pCopy(ap),p); |
---|
2065 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
2066 | pDelete(&p); |
---|
2067 | } |
---|
2068 | } |
---|
2069 | |
---|
2070 | ideal idPower(ideal given,int exp) |
---|
2071 | { |
---|
2072 | ideal result,temp; |
---|
2073 | poly p1; |
---|
2074 | int i; |
---|
2075 | |
---|
2076 | if (idIs0(given)) return idInit(1,1); |
---|
2077 | temp = idCopy(given); |
---|
2078 | idSkipZeroes(temp); |
---|
2079 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
2080 | result = idInit(i,1); |
---|
2081 | result->nrows = 0; |
---|
2082 | //Print("ideal contains %d elements\n",i); |
---|
2083 | p1=pOne(); |
---|
2084 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
2085 | pDelete(&p1); |
---|
2086 | idDelete(&temp); |
---|
2087 | idSkipZeroes(result); |
---|
2088 | result->nrows = 1; |
---|
2089 | return result; |
---|
2090 | } |
---|
2091 | |
---|
2092 | /*2 |
---|
2093 | * eliminate delVar (product of vars) in h1 |
---|
2094 | */ |
---|
2095 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
2096 | { |
---|
2097 | int i,j=0,k,l; |
---|
2098 | ideal h,hh, h3; |
---|
2099 | int *ord,*block0,*block1; |
---|
2100 | int ordersize=2; |
---|
2101 | short **wv; |
---|
2102 | tHomog hom; |
---|
2103 | intvec * w; |
---|
2104 | sip_sring tmpR; |
---|
2105 | ring origR = currRing; |
---|
2106 | |
---|
2107 | if (delVar==NULL) |
---|
2108 | { |
---|
2109 | return idCopy(h1); |
---|
2110 | } |
---|
2111 | if (currQuotient!=NULL) |
---|
2112 | { |
---|
2113 | WerrorS("cannot eliminate in a qring"); |
---|
2114 | return idCopy(h1); |
---|
2115 | } |
---|
2116 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
2117 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
2118 | h3=idInit(16,h1->rank); |
---|
2119 | for (k=0;; k++) |
---|
2120 | { |
---|
2121 | if (currRing->order[k]!=0) ordersize++; |
---|
2122 | else break; |
---|
2123 | } |
---|
2124 | ord=(int*)Alloc0(ordersize*sizeof(int)); |
---|
2125 | block0=(int*)Alloc(ordersize*sizeof(int)); |
---|
2126 | block1=(int*)Alloc(ordersize*sizeof(int)); |
---|
2127 | for (k=0;; k++) |
---|
2128 | { |
---|
2129 | if (currRing->order[k]!=0) |
---|
2130 | { |
---|
2131 | block0[k+1] = currRing->block0[k]; |
---|
2132 | block1[k+1] = currRing->block1[k]; |
---|
2133 | ord[k+1] = currRing->order[k]; |
---|
2134 | } |
---|
2135 | else |
---|
2136 | break; |
---|
2137 | } |
---|
2138 | block0[0] = 1; |
---|
2139 | block1[0] = pVariables; |
---|
2140 | wv=(short**) Alloc0(ordersize*sizeof(short**)); |
---|
2141 | memcpy4(wv+1,currRing->wvhdl,(ordersize-1)*sizeof(short**)); |
---|
2142 | wv[0]=(short*)Alloc0((pVariables+1)*sizeof(short)); |
---|
2143 | for (j=0;j<pVariables;j++) |
---|
2144 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
2145 | ord[0] = ringorder_a; |
---|
2146 | |
---|
2147 | // fill in tmp ring to get back the data later on |
---|
2148 | tmpR = *origR; |
---|
2149 | tmpR.order = ord; |
---|
2150 | tmpR.block0 = block0; |
---|
2151 | tmpR.block1 = block1; |
---|
2152 | tmpR.wvhdl = wv; |
---|
2153 | rComplete(&tmpR); |
---|
2154 | |
---|
2155 | // change into the new ring |
---|
2156 | pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
2157 | // rChangeCurrRing(&tmpR, FALSE); |
---|
2158 | currRing = &tmpR; |
---|
2159 | h = idInit(IDELEMS(h1),1); |
---|
2160 | // fetch data from the old ring |
---|
2161 | for (k=0;k<IDELEMS(h1);k++) h->m[k] = pFetchCopy(origR, h1->m[k]); |
---|
2162 | // compute std |
---|
2163 | hh = std(h,NULL,hom,&w,hilb); |
---|
2164 | idDelete(&h); |
---|
2165 | |
---|
2166 | // go back to the original ring |
---|
2167 | rChangeCurrRing(origR,FALSE); |
---|
2168 | i = IDELEMS(hh)-1; |
---|
2169 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
2170 | j = -1; |
---|
2171 | // fetch data from temp ring |
---|
2172 | for (k=0; k<=i; k++) |
---|
2173 | { |
---|
2174 | l=pVariables; |
---|
2175 | while ((l>0) && (pRingGetExp(&tmpR, hh->m[k],l)*pGetExp(delVar,l)==0)) l--; |
---|
2176 | if (l==0) |
---|
2177 | { |
---|
2178 | j++; |
---|
2179 | if (j >= IDELEMS(h3)) |
---|
2180 | { |
---|
2181 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
2182 | IDELEMS(h3) += 16; |
---|
2183 | } |
---|
2184 | h3->m[j] = pFetchCopy(&tmpR, hh->m[k]); |
---|
2185 | } |
---|
2186 | } |
---|
2187 | idDelete(&hh); |
---|
2188 | idSkipZeroes(h3); |
---|
2189 | Free((ADDRESS)wv[0],(pVariables+1)*sizeof(short)); |
---|
2190 | Free((ADDRESS)wv,ordersize*sizeof(short**)); |
---|
2191 | Free((ADDRESS)ord,ordersize*sizeof(int)); |
---|
2192 | Free((ADDRESS)block0,ordersize*sizeof(int)); |
---|
2193 | Free((ADDRESS)block1,ordersize*sizeof(int)); |
---|
2194 | if (w!=NULL) |
---|
2195 | delete w; |
---|
2196 | return h3; |
---|
2197 | } |
---|
2198 | |
---|
2199 | /*2 |
---|
2200 | * compute all ar-minors of the matrix a |
---|
2201 | */ |
---|
2202 | ideal idMinors(matrix a, int ar) |
---|
2203 | { |
---|
2204 | if(ar<=0) |
---|
2205 | { |
---|
2206 | Werror("%d-th minor ",ar); |
---|
2207 | return NULL; |
---|
2208 | } |
---|
2209 | int i,j,k,size; |
---|
2210 | int *rowchoise,*colchoise; |
---|
2211 | BOOLEAN rowch,colch; |
---|
2212 | ideal result; |
---|
2213 | matrix tmp; |
---|
2214 | poly p; |
---|
2215 | |
---|
2216 | i = binom(a->rows(),ar); |
---|
2217 | j = binom(a->cols(),ar); |
---|
2218 | |
---|
2219 | rowchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2220 | colchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2221 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
2222 | else size=i*j; |
---|
2223 | result=idInit(size,1); |
---|
2224 | tmp=mpNew(ar,ar); |
---|
2225 | k = 0; /* the index in result*/ |
---|
2226 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
2227 | while (!rowch) |
---|
2228 | { |
---|
2229 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
2230 | while (!colch) |
---|
2231 | { |
---|
2232 | for (i=1; i<=ar; i++) |
---|
2233 | { |
---|
2234 | for (j=1; j<=ar; j++) |
---|
2235 | { |
---|
2236 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
2237 | } |
---|
2238 | } |
---|
2239 | p = mpDet(tmp); |
---|
2240 | if (p!=NULL) |
---|
2241 | { |
---|
2242 | if (k>=size) |
---|
2243 | { |
---|
2244 | pEnlargeSet(&result->m,size,32); |
---|
2245 | size += 32; |
---|
2246 | } |
---|
2247 | result->m[k] = p; |
---|
2248 | k++; |
---|
2249 | } |
---|
2250 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
2251 | } |
---|
2252 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
2253 | } |
---|
2254 | /*delete the matrix tmp*/ |
---|
2255 | for (i=1; i<=ar; i++) |
---|
2256 | { |
---|
2257 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
2258 | } |
---|
2259 | idDelete((ideal*)&tmp); |
---|
2260 | if (k==0) |
---|
2261 | { |
---|
2262 | k=1; |
---|
2263 | result->m[0]=NULL; |
---|
2264 | } |
---|
2265 | Free((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
2266 | Free((ADDRESS)colchoise,ar*sizeof(int)); |
---|
2267 | pEnlargeSet(&result->m,size,k-size); |
---|
2268 | IDELEMS(result) = k; |
---|
2269 | return (result); |
---|
2270 | } |
---|
2271 | |
---|
2272 | /*3 |
---|
2273 | * produces recursively the ideal of all arxar-minors of a |
---|
2274 | */ |
---|
2275 | static void idRecMin(matrix a,int ar,poly *barDiv,ideal result, |
---|
2276 | int * nextPlace, intvec * pfRows, intvec * iv) |
---|
2277 | { |
---|
2278 | //Print("Level: %d\n",ar); |
---|
2279 | /*--- there is no non-zero minor coming from a------------*/ |
---|
2280 | if((ar<0) || (ar>min(a->ncols,a->nrows)-1)) |
---|
2281 | { |
---|
2282 | return; |
---|
2283 | } |
---|
2284 | |
---|
2285 | /*--- initializing temporary structures-------------------*/ |
---|
2286 | int i,j,r,c,newi,newp,k; |
---|
2287 | poly p=NULL,pp; |
---|
2288 | BOOLEAN justChosen=FALSE; |
---|
2289 | |
---|
2290 | if (ar==0) |
---|
2291 | { |
---|
2292 | /*--- ar is 0, the matrix-entres are minors---------------*/ |
---|
2293 | for (i=a->nrows;i>0;i--) |
---|
2294 | { |
---|
2295 | for (j=a->ncols;j>0;j--) |
---|
2296 | { |
---|
2297 | p = MATELEM(a,i,j); |
---|
2298 | if (p!=NULL) |
---|
2299 | { |
---|
2300 | if (*nextPlace>=IDELEMS(result)) |
---|
2301 | { |
---|
2302 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
2303 | IDELEMS(result) += 16; |
---|
2304 | } |
---|
2305 | MATELEM(a,i,j) = NULL; |
---|
2306 | //if ((*nextPlace==21) || (*nextPlace==37)) |
---|
2307 | //{ |
---|
2308 | // Print("Hier sind sie!\n"); |
---|
2309 | //} |
---|
2310 | //pWrite(p); |
---|
2311 | result->m[*nextPlace] = p; |
---|
2312 | (*nextPlace)++; |
---|
2313 | } |
---|
2314 | } |
---|
2315 | } |
---|
2316 | idDelete((ideal*)&a); |
---|
2317 | return; |
---|
2318 | } |
---|
2319 | /*--- ar>0, we perform one step of the Bareiss algorithm--*/ |
---|
2320 | p = pCopy(*barDiv); //we had to store barDiv for the remaining loops |
---|
2321 | pp = pCopy(p); //we had to store barDiv for the remaining loops |
---|
2322 | matrix nextStep = mpOneStepBareiss(a,barDiv,&r,&c); |
---|
2323 | /*--- we compute the row-index of the chosen row r -------*/ |
---|
2324 | newi = 0; |
---|
2325 | while ((newi<iv->length()) && ((*iv)[newi]!=0)) newi++; |
---|
2326 | k = (*iv)[newi] = r; |
---|
2327 | for (j=newi-1;j>0;j--) |
---|
2328 | { |
---|
2329 | if (k>=(*iv)[j]) k++; |
---|
2330 | } |
---|
2331 | newp = 0; |
---|
2332 | while ((newp<pfRows->length()) && ((*pfRows)[newp]!=0)) |
---|
2333 | { |
---|
2334 | if ((*pfRows)[newp]==k) |
---|
2335 | { |
---|
2336 | justChosen = TRUE; |
---|
2337 | //Print("just chosen\n"); |
---|
2338 | break; |
---|
2339 | } |
---|
2340 | newp++; |
---|
2341 | } |
---|
2342 | if (!justChosen) (*pfRows)[newp] = k; |
---|
2343 | //Print("Chosen: ");pfRows->show();PrintLn(); |
---|
2344 | //Print("Deleted: ");iv->show();PrintLn(); |
---|
2345 | /*--- we read out the r-1 x c-1 matrix for the next step--*/ |
---|
2346 | if ((a->nrows-1)*(a->ncols-1)>0) |
---|
2347 | { |
---|
2348 | matrix next = mpNew(a->nrows-1,a->ncols-1); |
---|
2349 | for (i=a->nrows-1;i>0;i--) |
---|
2350 | { |
---|
2351 | for (j=a->ncols-1;j>0;j--) |
---|
2352 | { |
---|
2353 | MATELEM(next,i,j) = MATELEM(nextStep,i,j); |
---|
2354 | MATELEM(nextStep,i,j) =NULL; |
---|
2355 | } |
---|
2356 | } |
---|
2357 | idDelete((ideal*)&nextStep); |
---|
2358 | /*--- we call the next Step------------------------------*/ |
---|
2359 | idRecMin(next,ar-1,barDiv,result,nextPlace,pfRows,iv); |
---|
2360 | next = NULL; |
---|
2361 | } |
---|
2362 | /*--- now we have to take out the r-th row...------------*/ |
---|
2363 | //Print("back for rows on Level: %d\n",ar); |
---|
2364 | //Print("The actual row was %d\n",k); |
---|
2365 | //Print("Chosen: ");pfRows->show();PrintLn(); |
---|
2366 | //Print("Deleted: ");iv->show();PrintLn(); |
---|
2367 | if (((a->nrows)>1) && (!justChosen)) |
---|
2368 | { |
---|
2369 | nextStep = mpNew(a->nrows-1,a->ncols); |
---|
2370 | for (i=r-1;i>0;i--) |
---|
2371 | { |
---|
2372 | for (j=a->ncols;j>0;j--) |
---|
2373 | { |
---|
2374 | MATELEM(nextStep,i,j) = pCopy(MATELEM(a,i,j)); |
---|
2375 | } |
---|
2376 | } |
---|
2377 | for (i=a->nrows;i>r;i--) |
---|
2378 | { |
---|
2379 | for (j=a->ncols;j>0;j--) |
---|
2380 | { |
---|
2381 | MATELEM(nextStep,i-1,j) = pCopy(MATELEM(a,i,j)); |
---|
2382 | } |
---|
2383 | } |
---|
2384 | /*--- and to perform the algorithm with the rest---------*/ |
---|
2385 | idRecMin(nextStep,ar,&p,result,nextPlace,pfRows,iv); |
---|
2386 | nextStep = NULL; |
---|
2387 | } |
---|
2388 | /*--- now we have to take out the c-th col...------------*/ |
---|
2389 | //Print("back for cols on Level: %d\n",ar); |
---|
2390 | //Print("Chosen: ");pfRows->show();PrintLn(); |
---|
2391 | //Print("Deleted: ");iv->show();PrintLn(); |
---|
2392 | if ((a->nrows)>1) |
---|
2393 | { |
---|
2394 | nextStep = mpNew(a->nrows,a->ncols-1); |
---|
2395 | for (i=a->nrows;i>0;i--) |
---|
2396 | { |
---|
2397 | for (j=c-1;j>0;j--) |
---|
2398 | { |
---|
2399 | MATELEM(nextStep,i,j) = MATELEM(a,i,j); |
---|
2400 | MATELEM(a,i,j) = NULL; |
---|
2401 | } |
---|
2402 | } |
---|
2403 | for (i=a->nrows;i>0;i--) |
---|
2404 | { |
---|
2405 | for (j=a->ncols;j>c;j--) |
---|
2406 | { |
---|
2407 | MATELEM(nextStep,i,j-1) = MATELEM(a,i,j); |
---|
2408 | MATELEM(a,i,j) = NULL; |
---|
2409 | } |
---|
2410 | } |
---|
2411 | idDelete((ideal*)&a); |
---|
2412 | /*--- and to perform the algorithm with the rest---------*/ |
---|
2413 | (*iv)[newi] = 0; |
---|
2414 | idRecMin(nextStep,ar,&p,result,nextPlace,pfRows,iv); |
---|
2415 | nextStep = NULL; |
---|
2416 | } |
---|
2417 | /*--- deleting temporary structures and returns----------*/ |
---|
2418 | if (!justChosen) (*pfRows)[newp] = 0; |
---|
2419 | pDelete(barDiv); |
---|
2420 | pDelete(&p); |
---|
2421 | pDelete(&pp); |
---|
2422 | return; |
---|
2423 | } |
---|
2424 | |
---|
2425 | /*2 |
---|
2426 | * compute all ar-minors of the matrix a |
---|
2427 | * the caller of idRecMin |
---|
2428 | */ |
---|
2429 | ideal idMinors1(matrix a, int ar) |
---|
2430 | { |
---|
2431 | if((ar<=0) || (ar>min(a->ncols,a->nrows))) |
---|
2432 | { |
---|
2433 | Werror("%d-th minor ",ar); |
---|
2434 | return NULL; |
---|
2435 | } |
---|
2436 | int i=0; |
---|
2437 | intvec * iv=new intvec(a->nrows+1); |
---|
2438 | intvec * pv=new intvec(a->nrows+1); |
---|
2439 | poly barDiv=NULL; |
---|
2440 | ideal result=idInit(16,0); |
---|
2441 | |
---|
2442 | idRecMin(mpCopy(a),ar-1,&barDiv,result,&i,pv,iv); |
---|
2443 | idSkipZeroes(result); |
---|
2444 | delete iv; |
---|
2445 | delete pv; |
---|
2446 | return result; |
---|
2447 | } |
---|
2448 | |
---|
2449 | /*2 |
---|
2450 | *returns TRUE if p is a unit element in the current ring |
---|
2451 | */ |
---|
2452 | BOOLEAN pIsUnit(poly p) |
---|
2453 | { |
---|
2454 | int i; |
---|
2455 | |
---|
2456 | if (p == NULL) return FALSE; |
---|
2457 | i = 1; |
---|
2458 | while (i<=pVariables && pGetExp(p,i) == 0) i++; |
---|
2459 | if (i > pVariables && (pGetComp(p) == 0)) |
---|
2460 | { |
---|
2461 | if (currRing->OrdSgn == 1 && pNext(p) !=NULL) return FALSE; |
---|
2462 | return TRUE; |
---|
2463 | } |
---|
2464 | return FALSE; |
---|
2465 | } |
---|
2466 | |
---|
2467 | /*2 |
---|
2468 | *skips all zeroes and double elements, searches also for units |
---|
2469 | */ |
---|
2470 | ideal idCompactify(ideal id) |
---|
2471 | { |
---|
2472 | ideal result = NULL; |
---|
2473 | int i,j; |
---|
2474 | BOOLEAN b=FALSE; |
---|
2475 | |
---|
2476 | result=idCopy(id); |
---|
2477 | i = 0; |
---|
2478 | while ((! b) && (i<IDELEMS(result))) |
---|
2479 | { |
---|
2480 | b=pIsUnit(result->m[i]); |
---|
2481 | i++; |
---|
2482 | } |
---|
2483 | if (b) |
---|
2484 | { |
---|
2485 | for (i=0;i<IDELEMS(result);i++) |
---|
2486 | pDelete(&result->m[i]); |
---|
2487 | result->m[0]=pOne(); |
---|
2488 | } |
---|
2489 | else |
---|
2490 | { |
---|
2491 | for (i=1;i<IDELEMS(result);i++) |
---|
2492 | { |
---|
2493 | if (result->m[i]!=NULL) |
---|
2494 | { |
---|
2495 | for (j=0;j<i;j++) |
---|
2496 | { |
---|
2497 | if ((result->m[j]!=NULL) |
---|
2498 | && (pComparePolys(result->m[i],result->m[j]))) |
---|
2499 | { |
---|
2500 | pDelete(&(result->m[j])); |
---|
2501 | } |
---|
2502 | } |
---|
2503 | } |
---|
2504 | } |
---|
2505 | } |
---|
2506 | idSkipZeroes(result); |
---|
2507 | return result; |
---|
2508 | } |
---|
2509 | |
---|
2510 | /*2 |
---|
2511 | *returns TRUE if id1 is a submodule of id2 |
---|
2512 | */ |
---|
2513 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
2514 | { |
---|
2515 | int i; |
---|
2516 | poly p; |
---|
2517 | |
---|
2518 | if (idIs0(id1)) return TRUE; |
---|
2519 | for (i=0;i<IDELEMS(id1);i++) |
---|
2520 | { |
---|
2521 | if (id1->m[i] != NULL) |
---|
2522 | { |
---|
2523 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
2524 | if (p != NULL) |
---|
2525 | { |
---|
2526 | pDelete(&p); |
---|
2527 | return FALSE; |
---|
2528 | } |
---|
2529 | } |
---|
2530 | } |
---|
2531 | return TRUE; |
---|
2532 | } |
---|
2533 | |
---|
2534 | /*2 |
---|
2535 | * returns the ideals of initial terms |
---|
2536 | */ |
---|
2537 | ideal idHead(ideal h) |
---|
2538 | { |
---|
2539 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2540 | int i; |
---|
2541 | |
---|
2542 | for (i=0; i< IDELEMS(h); i++) |
---|
2543 | { |
---|
2544 | if (h->m[i]) m->m[i]=pHead(h->m[i]); |
---|
2545 | } |
---|
2546 | return m; |
---|
2547 | } |
---|
2548 | |
---|
2549 | ideal idHomogen(ideal h, int varnum) |
---|
2550 | { |
---|
2551 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2552 | int i; |
---|
2553 | |
---|
2554 | for (i=0; i< IDELEMS(h); i++) |
---|
2555 | { |
---|
2556 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
2557 | } |
---|
2558 | return m; |
---|
2559 | } |
---|
2560 | |
---|
2561 | /*------------------type conversions----------------*/ |
---|
2562 | ideal idVec2Ideal(poly vec) |
---|
2563 | { |
---|
2564 | ideal result=idInit(1,1); |
---|
2565 | Free((ADDRESS)result->m,sizeof(poly)); |
---|
2566 | result->m=NULL; // remove later |
---|
2567 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
2568 | return result; |
---|
2569 | } |
---|
2570 | |
---|
2571 | ideal idMatrix2Module(matrix mat) |
---|
2572 | { |
---|
2573 | ideal result = idInit(MATCOLS(mat),MATROWS(mat)); |
---|
2574 | int i,j; |
---|
2575 | poly h; |
---|
2576 | #ifdef DRING |
---|
2577 | poly p; |
---|
2578 | #endif |
---|
2579 | |
---|
2580 | for(j=0;j<MATCOLS(mat);j++) /* j is also index in result->m */ |
---|
2581 | { |
---|
2582 | for (i=1;i<=MATROWS(mat);i++) |
---|
2583 | { |
---|
2584 | h = MATELEM(mat,i,j+1); |
---|
2585 | if (h!=NULL) |
---|
2586 | { |
---|
2587 | MATELEM(mat,i,j+1)=NULL; |
---|
2588 | pSetCompP(h,i); |
---|
2589 | #ifdef DRING |
---|
2590 | pdSetDFlag(h,0); |
---|
2591 | #endif |
---|
2592 | result->m[j] = pAdd(result->m[j],h); |
---|
2593 | } |
---|
2594 | } |
---|
2595 | } |
---|
2596 | return result; |
---|
2597 | } |
---|
2598 | |
---|
2599 | /*2 |
---|
2600 | * converts a module into a matrix, destroyes the input |
---|
2601 | */ |
---|
2602 | matrix idModule2Matrix(ideal mod) |
---|
2603 | { |
---|
2604 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
2605 | int i,cp; |
---|
2606 | poly p,h; |
---|
2607 | |
---|
2608 | for(i=0;i<IDELEMS(mod);i++) |
---|
2609 | { |
---|
2610 | p=mod->m[i]; |
---|
2611 | mod->m[i]=NULL; |
---|
2612 | while (p!=NULL) |
---|
2613 | { |
---|
2614 | h=p; |
---|
2615 | pIter(p); |
---|
2616 | pNext(h)=NULL; |
---|
2617 | // cp = max(1,pGetComp(h)); // if used for ideals too |
---|
2618 | cp = pGetComp(h); |
---|
2619 | pSetComp(h,0); |
---|
2620 | #ifdef TEST |
---|
2621 | if (cp>mod->rank) |
---|
2622 | { |
---|
2623 | Print("## inv. rank %d -> %d\n",mod->rank,cp); |
---|
2624 | int k,l,o=mod->rank; |
---|
2625 | mod->rank=cp; |
---|
2626 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
2627 | for (l=1; l<=o; l++) |
---|
2628 | { |
---|
2629 | for (k=1; k<=IDELEMS(mod); k++) |
---|
2630 | { |
---|
2631 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
2632 | MATELEM(result,l,k)=NULL; |
---|
2633 | } |
---|
2634 | } |
---|
2635 | idDelete((ideal *)&result); |
---|
2636 | result=d; |
---|
2637 | } |
---|
2638 | #endif |
---|
2639 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2640 | } |
---|
2641 | } |
---|
2642 | return result; |
---|
2643 | } |
---|
2644 | |
---|
2645 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
2646 | { |
---|
2647 | matrix result = mpNew(rows,cols); |
---|
2648 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
2649 | poly p,h; |
---|
2650 | |
---|
2651 | if (r>rows) r = rows; |
---|
2652 | if (c>cols) c = cols; |
---|
2653 | for(i=0;i<c;i++) |
---|
2654 | { |
---|
2655 | p=mod->m[i]; |
---|
2656 | mod->m[i]=NULL; |
---|
2657 | while (p!=NULL) |
---|
2658 | { |
---|
2659 | h=p; |
---|
2660 | pIter(p); |
---|
2661 | pNext(h)=NULL; |
---|
2662 | cp = pGetComp(h); |
---|
2663 | if (cp<=r) |
---|
2664 | { |
---|
2665 | pSetComp(h,0); |
---|
2666 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2667 | } |
---|
2668 | else |
---|
2669 | pDelete(&h); |
---|
2670 | } |
---|
2671 | } |
---|
2672 | idDelete(&mod); |
---|
2673 | return result; |
---|
2674 | } |
---|
2675 | |
---|
2676 | /*2 |
---|
2677 | * substitute the n-th variable by the monomial e in id |
---|
2678 | * destroy id |
---|
2679 | */ |
---|
2680 | ideal idSubst(ideal id, int n, poly e) |
---|
2681 | { |
---|
2682 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
2683 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
2684 | |
---|
2685 | res->rank = id->rank; |
---|
2686 | for(k--;k>=0;k--) |
---|
2687 | { |
---|
2688 | res->m[k]=pSubst(id->m[k],n,e); |
---|
2689 | id->m[k]=NULL; |
---|
2690 | } |
---|
2691 | idDelete(&id); |
---|
2692 | return res; |
---|
2693 | } |
---|
2694 | |
---|
2695 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
2696 | { |
---|
2697 | if (w!=NULL) *w=NULL; |
---|
2698 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
2699 | if (idIs0(m)) return TRUE; |
---|
2700 | |
---|
2701 | int i,j,cmax=2,order=0,ord,* diff,* iscom,diffmin=32000; |
---|
2702 | poly p=NULL; |
---|
2703 | int length=IDELEMS(m); |
---|
2704 | polyset P=m->m; |
---|
2705 | polyset F=(polyset)Alloc(length*sizeof(poly)); |
---|
2706 | for (i=length-1;i>=0;i--) |
---|
2707 | { |
---|
2708 | p=F[i]=P[i]; |
---|
2709 | cmax=max(cmax,pMaxComp(p)+1); |
---|
2710 | } |
---|
2711 | diff = (int *)Alloc0(cmax*sizeof(int)); |
---|
2712 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
2713 | iscom = (int *)Alloc0(cmax*sizeof(int)); |
---|
2714 | i=0; |
---|
2715 | while (i<=length) |
---|
2716 | { |
---|
2717 | if (i<length) |
---|
2718 | { |
---|
2719 | p=F[i]; |
---|
2720 | while ((p!=NULL) && (!iscom[pGetComp(p)])) pIter(p); |
---|
2721 | } |
---|
2722 | if ((p==NULL) && (i<length)) |
---|
2723 | { |
---|
2724 | i++; |
---|
2725 | } |
---|
2726 | else |
---|
2727 | { |
---|
2728 | if (p==NULL) |
---|
2729 | { |
---|
2730 | i=0; |
---|
2731 | while ((i<length) && (F[i]==NULL)) i++; |
---|
2732 | if (i>=length) break; |
---|
2733 | p = F[i]; |
---|
2734 | } |
---|
2735 | if (pLexOrder) |
---|
2736 | order=pTotaldegree(p); |
---|
2737 | else |
---|
2738 | // order = p->order; |
---|
2739 | order = pFDeg(p); |
---|
2740 | order += diff[pGetComp(p)]; |
---|
2741 | p = F[i]; |
---|
2742 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
2743 | F[i] = NULL; |
---|
2744 | i=0; |
---|
2745 | } |
---|
2746 | while (p!=NULL) |
---|
2747 | { |
---|
2748 | //if (pLexOrder) |
---|
2749 | // ord=pTotaldegree(p); |
---|
2750 | //else |
---|
2751 | // ord = p->order; |
---|
2752 | ord = pFDeg(p); |
---|
2753 | if (!iscom[pGetComp(p)]) |
---|
2754 | { |
---|
2755 | diff[pGetComp(p)] = order-ord; |
---|
2756 | iscom[pGetComp(p)] = 1; |
---|
2757 | /* |
---|
2758 | *PrintS("new diff: "); |
---|
2759 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2760 | *PrintLn(); |
---|
2761 | *PrintS("new iscom: "); |
---|
2762 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
2763 | *PrintLn(); |
---|
2764 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
2765 | */ |
---|
2766 | } |
---|
2767 | else |
---|
2768 | { |
---|
2769 | /* |
---|
2770 | *PrintS("new diff: "); |
---|
2771 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2772 | *PrintLn(); |
---|
2773 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
2774 | */ |
---|
2775 | if (order != ord+diff[pGetComp(p)]) |
---|
2776 | { |
---|
2777 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2778 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2779 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2780 | delete *w;*w=NULL; |
---|
2781 | return FALSE; |
---|
2782 | } |
---|
2783 | } |
---|
2784 | pIter(p); |
---|
2785 | } |
---|
2786 | } |
---|
2787 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2788 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2789 | for (i=1;i<cmax;i++) (**w)[i-1]=diff[i]; |
---|
2790 | for (i=1;i<cmax;i++) |
---|
2791 | { |
---|
2792 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
2793 | } |
---|
2794 | for (i=1;i<cmax;i++) |
---|
2795 | { |
---|
2796 | (**w)[i-1]=diff[i]-diffmin; |
---|
2797 | } |
---|
2798 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2799 | return TRUE; |
---|
2800 | } |
---|
2801 | |
---|
2802 | ideal idJet(ideal i,int d) |
---|
2803 | { |
---|
2804 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
2805 | int k; |
---|
2806 | for(k=0; k<IDELEMS(i); k++) |
---|
2807 | { |
---|
2808 | r->m[k]=pJet(i->m[k],d); |
---|
2809 | } |
---|
2810 | return r; |
---|
2811 | } |
---|
2812 | |
---|
2813 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
2814 | { |
---|
2815 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
2816 | if (ecartWeights!=NULL) |
---|
2817 | { |
---|
2818 | WerrorS("cannot compute weighted jets now"); |
---|
2819 | } |
---|
2820 | else |
---|
2821 | { |
---|
2822 | short *w=iv2array(iv); |
---|
2823 | int k; |
---|
2824 | for(k=0; k<IDELEMS(i); k++) |
---|
2825 | { |
---|
2826 | r->m[k]=pJetW(i->m[k],d,w); |
---|
2827 | } |
---|
2828 | Free((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
2829 | } |
---|
2830 | return r; |
---|
2831 | } |
---|
2832 | |
---|
2833 | matrix idDiff(matrix i, int k) |
---|
2834 | { |
---|
2835 | int e=MATCOLS(i)*MATROWS(i); |
---|
2836 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2837 | int j; |
---|
2838 | for(j=0; j<e; j++) |
---|
2839 | { |
---|
2840 | r->m[j]=pDiff(i->m[j],k); |
---|
2841 | } |
---|
2842 | return r; |
---|
2843 | } |
---|
2844 | |
---|
2845 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2846 | { |
---|
2847 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2848 | int i,j; |
---|
2849 | for(i=0; i<IDELEMS(I); i++) |
---|
2850 | { |
---|
2851 | for(j=0; j<IDELEMS(J); j++) |
---|
2852 | { |
---|
2853 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2854 | } |
---|
2855 | } |
---|
2856 | return r; |
---|
2857 | } |
---|
2858 | |
---|
2859 | /*2 |
---|
2860 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
2861 | */ |
---|
2862 | ideal idModulo (ideal h2,ideal h1) |
---|
2863 | { |
---|
2864 | ideal temp,temp1; |
---|
2865 | int i,j,k,rk,flength=0,slength,length; |
---|
2866 | intvec * w; |
---|
2867 | poly p,q; |
---|
2868 | |
---|
2869 | if (idIs0(h2)) |
---|
2870 | return idFreeModule(max(1,h2->ncols)); |
---|
2871 | if (!idIs0(h1)) |
---|
2872 | flength = idRankFreeModule(h1); |
---|
2873 | slength = idRankFreeModule(h2); |
---|
2874 | length = max(flength,slength); |
---|
2875 | if (length==0) |
---|
2876 | { |
---|
2877 | length = 1; |
---|
2878 | } |
---|
2879 | temp = idInit(IDELEMS(h2),1); |
---|
2880 | for (i=0;i<IDELEMS(h2);i++) |
---|
2881 | { |
---|
2882 | temp->m[i] = pCopy(h2->m[i]); |
---|
2883 | q = pOne(); |
---|
2884 | pSetComp(q,i+1+length); |
---|
2885 | if(temp->m[i]!=NULL) |
---|
2886 | { |
---|
2887 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
2888 | p = temp->m[i]; |
---|
2889 | while (pNext(p)!=NULL) pIter(p); |
---|
2890 | pNext(p) = q; |
---|
2891 | } |
---|
2892 | else |
---|
2893 | temp->m[i]=q; |
---|
2894 | } |
---|
2895 | rk = k = IDELEMS(h2); |
---|
2896 | if (!idIs0(h1)) |
---|
2897 | { |
---|
2898 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
2899 | IDELEMS(temp) += IDELEMS(h1); |
---|
2900 | for (i=0;i<IDELEMS(h1);i++) |
---|
2901 | { |
---|
2902 | if (h1->m[i]!=NULL) |
---|
2903 | { |
---|
2904 | temp->m[k] = pCopy(h1->m[i]); |
---|
2905 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
2906 | k++; |
---|
2907 | } |
---|
2908 | } |
---|
2909 | } |
---|
2910 | pSetSyzComp(length); |
---|
2911 | temp1 = std(temp,currQuotient,testHomog,&w,NULL,length); |
---|
2912 | pSetSyzComp(0); |
---|
2913 | idDelete(&temp); |
---|
2914 | if (w!=NULL) delete w; |
---|
2915 | for (i=0;i<IDELEMS(temp1);i++) |
---|
2916 | { |
---|
2917 | if ((temp1->m[i]!=NULL) |
---|
2918 | && (pGetComp(temp1->m[i])<=length)) |
---|
2919 | { |
---|
2920 | pDelete(&(temp1->m[i])); |
---|
2921 | } |
---|
2922 | else |
---|
2923 | { |
---|
2924 | pShift(&(temp1->m[i]),-length); |
---|
2925 | } |
---|
2926 | } |
---|
2927 | idSkipZeroes(temp1); |
---|
2928 | temp1->rank = rk; |
---|
2929 | return temp1; |
---|
2930 | } |
---|
2931 | |
---|
2932 | int idElem(ideal F) |
---|
2933 | { |
---|
2934 | int i=0,j=0; |
---|
2935 | |
---|
2936 | while(j<IDELEMS(F)) |
---|
2937 | { |
---|
2938 | if ((F->m)[j]!=NULL) i++; |
---|
2939 | j++; |
---|
2940 | } |
---|
2941 | return i; |
---|
2942 | } |
---|
2943 | |
---|
2944 | /* |
---|
2945 | *computes module-weights for liftings of homogeneous modules |
---|
2946 | */ |
---|
2947 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2948 | { |
---|
2949 | if (idIs0(mod)) return new intvec(2); |
---|
2950 | int i=IDELEMS(mod); |
---|
2951 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2952 | intvec *result = new intvec(i+1); |
---|
2953 | while (i>0) |
---|
2954 | { |
---|
2955 | (*result)[i]=pFDeg(mod->m[i])+(*weights)[pGetComp(mod->m[i])]; |
---|
2956 | } |
---|
2957 | return result; |
---|
2958 | } |
---|
2959 | |
---|
2960 | /*2 |
---|
2961 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2962 | *with x_max,...,x_1) |
---|
2963 | */ |
---|
2964 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2965 | { |
---|
2966 | int i; |
---|
2967 | ideal result; |
---|
2968 | |
---|
2969 | if (idIs0(kBase)) return NULL; |
---|
2970 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2971 | *convert = idSort(kBase,FALSE); |
---|
2972 | for (i=0;i<(*convert)->length();i++) |
---|
2973 | { |
---|
2974 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2975 | } |
---|
2976 | return result; |
---|
2977 | } |
---|
2978 | |
---|
2979 | /*2 |
---|
2980 | *returns the index of a given monom in the list of the special kbase |
---|
2981 | */ |
---|
2982 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2983 | { |
---|
2984 | int j=IDELEMS(kbase); |
---|
2985 | |
---|
2986 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2987 | if (j==0) return -1; |
---|
2988 | int i=pVariables; |
---|
2989 | while (i>=0) |
---|
2990 | { |
---|
2991 | while ((j>0) && (pGetExp(monom,i)<pGetExp(kbase->m[j-1],i))) j--; |
---|
2992 | if ((j==0) || (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i))) return -1; |
---|
2993 | if (i==0) |
---|
2994 | return j-1; |
---|
2995 | else |
---|
2996 | i--; |
---|
2997 | } |
---|
2998 | return -1; |
---|
2999 | } |
---|
3000 | |
---|
3001 | /*2 |
---|
3002 | *decomposes the monom in a part of coefficients described by the |
---|
3003 | *complement of how and a monom in variables occuring in how, the |
---|
3004 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
3005 | *exists) |
---|
3006 | */ |
---|
3007 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
3008 | { |
---|
3009 | int i; |
---|
3010 | poly coeff=pOne(), base=pOne(); |
---|
3011 | |
---|
3012 | for (i=1;i<=pVariables;i++) |
---|
3013 | { |
---|
3014 | if (pGetExp(how,i)>0) |
---|
3015 | { |
---|
3016 | pSetExp(base,i,pGetExp(monom,i)); |
---|
3017 | } |
---|
3018 | else |
---|
3019 | { |
---|
3020 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
3021 | } |
---|
3022 | } |
---|
3023 | pSetComp(base,pGetComp(monom)); |
---|
3024 | pSetm(base); |
---|
3025 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
3026 | pSetm(coeff); |
---|
3027 | *pos = idIndexOfKBase(base,kbase); |
---|
3028 | if (*pos<0) |
---|
3029 | pDelete(&coeff); |
---|
3030 | pDelete(&base); |
---|
3031 | return coeff; |
---|
3032 | } |
---|
3033 | |
---|
3034 | /*2 |
---|
3035 | *returns a matrix A of coefficients with kbase*A=arg |
---|
3036 | *if all monomials in variables of how occur in kbase |
---|
3037 | *the other are deleted |
---|
3038 | */ |
---|
3039 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
3040 | { |
---|
3041 | matrix result; |
---|
3042 | ideal tempKbase; |
---|
3043 | poly p,q; |
---|
3044 | intvec * convert; |
---|
3045 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
3046 | |
---|
3047 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
3048 | if (idIs0(arg)) |
---|
3049 | return mpNew(i,1); |
---|
3050 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
3051 | result = mpNew(i,j); |
---|
3052 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
3053 | for (k=0;k<j;k++) |
---|
3054 | { |
---|
3055 | p = arg->m[k]; |
---|
3056 | while (p!=NULL) |
---|
3057 | { |
---|
3058 | q = idDecompose(p,how,tempKbase,&pos); |
---|
3059 | if (pos>=0) |
---|
3060 | { |
---|
3061 | MATELEM(result,(*convert)[pos],k+1) = |
---|
3062 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
3063 | } |
---|
3064 | else |
---|
3065 | pDelete(&q); |
---|
3066 | p = pIter(p); |
---|
3067 | } |
---|
3068 | } |
---|
3069 | idDelete(&tempKbase); |
---|
3070 | return result; |
---|
3071 | } |
---|
3072 | |
---|
3073 | intvec * idQHomWeights(ideal id) |
---|
3074 | { |
---|
3075 | intvec * imat=new intvec(2*pVariables,pVariables,0); |
---|
3076 | poly actHead=NULL,wPoint=NULL; |
---|
3077 | int actIndex,i=-1,j=1,k; |
---|
3078 | BOOLEAN notReady=TRUE; |
---|
3079 | |
---|
3080 | while (notReady) |
---|
3081 | { |
---|
3082 | if (wPoint==NULL) |
---|
3083 | { |
---|
3084 | i++; |
---|
3085 | while ((i<IDELEMS(id)) |
---|
3086 | && ((id->m[i]==NULL) || (pNext(id->m[i])==NULL))) |
---|
3087 | i++; |
---|
3088 | if (i<IDELEMS(id)) |
---|
3089 | { |
---|
3090 | actHead = id->m[i]; |
---|
3091 | wPoint = pNext(actHead); |
---|
3092 | } |
---|
3093 | } |
---|
3094 | while ((wPoint!=NULL) && (j<=2*pVariables)) |
---|
3095 | { |
---|
3096 | for (k=1;k<=pVariables;k++) |
---|
3097 | IMATELEM(*imat,j,k) += pGetExp(actHead,k)-pGetExp(wPoint,k); |
---|
3098 | pIter(wPoint); |
---|
3099 | j++; |
---|
3100 | } |
---|
3101 | if ((i>=IDELEMS(id)) || (j>2*pVariables)) |
---|
3102 | { |
---|
3103 | ivTriangMat(imat,1,1); |
---|
3104 | j = ivFirstEmptyRow(imat); |
---|
3105 | if ((i>=IDELEMS(id)) || (j>pVariables)) notReady=FALSE; |
---|
3106 | } |
---|
3107 | } |
---|
3108 | intvec *result=NULL; |
---|
3109 | if (j<=pVariables) |
---|
3110 | { |
---|
3111 | result=ivSolveIntMat(imat); |
---|
3112 | } |
---|
3113 | //else |
---|
3114 | //{ |
---|
3115 | // WerrorS("not homogeneous"); |
---|
3116 | //} |
---|
3117 | delete imat; |
---|
3118 | return result; |
---|
3119 | } |
---|
3120 | |
---|
3121 | /*2 |
---|
3122 | * returns the presentation of an isomorphic, minimally |
---|
3123 | * embedded module |
---|
3124 | */ |
---|
3125 | ideal idMinEmbedding(ideal arg) |
---|
3126 | { |
---|
3127 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
3128 | |
---|
3129 | int i,j,k,pC; |
---|
3130 | poly p,q; |
---|
3131 | int rg=arg->rank; |
---|
3132 | ideal res = idCopy(arg); |
---|
3133 | intvec *indexMap=new intvec(rg+1); |
---|
3134 | intvec *toKill=new intvec(rg+1); |
---|
3135 | |
---|
3136 | loop |
---|
3137 | { |
---|
3138 | k = 0; |
---|
3139 | for (i=indexMap->length()-1;i>0;i--) |
---|
3140 | { |
---|
3141 | (*indexMap)[i] = i; |
---|
3142 | (*toKill)[i] = 0; |
---|
3143 | } |
---|
3144 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
3145 | { |
---|
3146 | if ((res->m[j]!=NULL) && (pIsConstantComp(res->m[j])) && |
---|
3147 | (pNext(res->m[j])==NULL)) |
---|
3148 | { |
---|
3149 | pC = pGetComp(res->m[j]); |
---|
3150 | if ((*toKill)[pC]==0) |
---|
3151 | { |
---|
3152 | rg--; |
---|
3153 | (*toKill)[pC] = 1; |
---|
3154 | for (i=indexMap->length()-1;i>=pC;i--) |
---|
3155 | (*indexMap)[i]--; |
---|
3156 | } |
---|
3157 | pDelete(&(res->m[j])); |
---|
3158 | k++; |
---|
3159 | } |
---|
3160 | } |
---|
3161 | idSkipZeroes(res); |
---|
3162 | if (k==0) break; |
---|
3163 | if (rg>0) |
---|
3164 | { |
---|
3165 | res->rank=rg; |
---|
3166 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
3167 | { |
---|
3168 | while ((res->m[j]!=NULL) && ((*toKill)[pGetComp(res->m[j])]==1)) |
---|
3169 | pDelete1(&res->m[j]); |
---|
3170 | p = res->m[j]; |
---|
3171 | while ((p!=NULL) && (pNext(p)!=NULL)) |
---|
3172 | { |
---|
3173 | pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
3174 | while ((pNext(p)!=NULL) && ((*toKill)[pGetComp(pNext(p))]==1)) |
---|
3175 | pDelete1(&pNext(p)); |
---|
3176 | pIter(p); |
---|
3177 | } |
---|
3178 | if (p!=NULL) pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
3179 | } |
---|
3180 | idSkipZeroes(res); |
---|
3181 | } |
---|
3182 | else |
---|
3183 | { |
---|
3184 | idDelete(&res); |
---|
3185 | res=idFreeModule(1); |
---|
3186 | break; |
---|
3187 | } |
---|
3188 | } |
---|
3189 | delete toKill; |
---|
3190 | delete indexMap; |
---|
3191 | return res; |
---|
3192 | } |
---|