1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /*************************************************************** |
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5 | * File: fast_maps.cc |
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6 | * Purpose: implementation of fast maps |
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7 | * Author: obachman (Olaf Bachmann) |
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8 | * Created: 02/01 |
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9 | * Version: $Id: fast_maps.cc,v 1.10 2002-01-19 13:08:46 obachman Exp $ |
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10 | *******************************************************************/ |
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11 | #include "mod2.h" |
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12 | #include <omalloc.h> |
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13 | #include "p_polys.h" |
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14 | #include "prCopy.h" |
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15 | #include "ideals.h" |
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16 | #include "ring.h" |
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17 | #include "febase.h" |
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18 | #include "fast_maps.h" |
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19 | |
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20 | #if 0 |
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21 | // paste into extra.cc |
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22 | if(strcmp(sys_cmd,"map")==0) |
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23 | { |
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24 | ring image_r = currRing; |
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25 | map theMap = (map)h->Data(); |
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26 | ideal image_id = (ideal) theMap; |
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27 | ring map_r = IDRING(idroot->get(theMap->preimage, myynest)); |
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28 | ideal map_id = IDIDEAL(map_r->idroot->get(h->Next()->Name(), myynest)); |
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29 | |
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30 | ring src_r, dest_r; |
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31 | maMap_CreateRings(map_id, map_r, image_id, image_r, src_r, dest_r); |
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32 | mapoly mp; |
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33 | maideal mideal; |
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34 | |
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35 | maMap_CreatePolyIdeal(map_id, map_r, src_r, dest_r, mp, mideal); |
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36 | maPoly_Out(mp, src_r); |
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37 | return FALSE; |
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38 | } |
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39 | |
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40 | // use as Singular source template |
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41 | ring map_r = 32003, (a, b, c), Dp; |
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42 | ideal map_id = a, ab, c3 + ab, a2b + ab; |
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43 | |
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44 | |
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45 | ring image_r; |
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46 | ideal image_id = x2y3, y, z+x6; |
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47 | |
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48 | map Phi = map_r, image_id; |
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49 | |
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50 | |
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51 | system("map", Phi, map_id); |
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52 | |
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53 | #endif |
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54 | /******************************************************************************* |
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55 | ** |
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56 | *F debugging stuff |
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57 | */ |
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58 | void maMonomial_Out(mapoly monomial, ring src_r, ring dest_r = NULL) |
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59 | { |
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60 | p_wrp(monomial->src, src_r); |
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61 | printf(" ref:%d", monomial->ref); |
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62 | if (dest_r != NULL) |
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63 | { |
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64 | printf(" dest:"); |
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65 | p_wrp(monomial->dest, dest_r); |
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66 | } |
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67 | printf("\n"); |
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68 | fflush(stdout); |
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69 | } |
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70 | |
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71 | void maPoly_Out(mapoly mpoly, ring src_r, ring dest_r = NULL) |
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72 | { |
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73 | while (mpoly != NULL) |
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74 | { |
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75 | maMonomial_Out(mpoly, src_r, dest_r); |
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76 | mpoly = mpoly->next; |
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77 | } |
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78 | } |
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79 | |
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80 | |
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81 | /******************************************************************************* |
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82 | ** |
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83 | *F mapolyCreate . . . . . . . . . . . . . . . Creates mapoly |
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84 | */ |
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85 | static omBin mapolyBin = omGetSpecBin(sizeof(mapoly_s)); |
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86 | static omBin macoeffBin = omGetSpecBin(sizeof(macoeff_s)); |
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87 | |
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88 | mapoly maMonomial_Create(poly p, ring r_p, sBucket_pt bucket = NULL) |
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89 | { |
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90 | mapoly mp = (mapoly) omAlloc0Bin(mapolyBin); |
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91 | mp->src = p; |
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92 | p->next = NULL; |
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93 | |
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94 | if (bucket != NULL) |
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95 | { |
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96 | mp->coeff = (macoeff) omAlloc0Bin(macoeffBin); |
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97 | mp->coeff->bucket = bucket; |
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98 | mp->coeff->n = pGetCoeff(p); |
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99 | } |
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100 | mp->ref = 1; |
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101 | return mp; |
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102 | } |
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103 | |
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104 | void maMonomial_Destroy(mapoly mp, ring src_r, ring dest_r = NULL) |
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105 | { |
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106 | if (mp != NULL) |
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107 | { |
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108 | p_LmFree(mp->src, src_r); |
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109 | if (mp->coeff != NULL) |
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110 | { |
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111 | macoeff coeff, next = mp->coeff; |
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112 | do |
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113 | { |
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114 | coeff = next; |
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115 | next = coeff->next; |
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116 | omFreeBin(coeff, macoeffBin); |
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117 | } |
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118 | while (next != NULL); |
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119 | if (mp->dest != NULL) |
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120 | { |
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121 | assume(dest_r != NULL); |
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122 | p_Delete(&(mp->dest), dest_r); |
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123 | } |
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124 | omFreeBin(mp, mapolyBin); |
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125 | } |
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126 | } |
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127 | } |
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128 | |
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129 | /******************************************************************************* |
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130 | ** |
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131 | *F maPoly_InsertMonomial . . . . . . . . .insertion of a monomial into mapoly |
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132 | */ |
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133 | mapoly maPoly_InsertMonomial(mapoly into, mapoly what, ring src_r) |
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134 | { |
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135 | if (into == NULL) |
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136 | { |
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137 | into = what; |
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138 | return what; |
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139 | } |
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140 | |
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141 | mapoly iter = into; |
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142 | mapoly prev = NULL; |
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143 | |
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144 | Top: |
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145 | p_LmCmpAction(iter->src, what->src, src_r, goto Equal, goto Greater, goto Smaller); |
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146 | |
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147 | |
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148 | Greater: |
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149 | if (iter->next == NULL) |
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150 | { |
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151 | iter->next = what; |
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152 | return into; |
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153 | } |
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154 | prev = iter; |
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155 | iter = iter->next; |
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156 | goto Top; |
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157 | |
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158 | Smaller: |
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159 | if (prev == NULL) |
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160 | { |
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161 | what->next = iter; |
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162 | return what; |
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163 | } |
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164 | prev->next = what; |
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165 | what->next = iter; |
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166 | return into; |
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167 | |
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168 | Equal: |
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169 | iter->ref += what->ref; |
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170 | macoeff coeff = what->coeff; |
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171 | if (coeff != NULL) |
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172 | { |
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173 | while (coeff->next != NULL) coeff = coeff->next; |
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174 | coeff->next = iter->coeff; |
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175 | iter->coeff = what->coeff; |
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176 | what->coeff = NULL; |
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177 | } |
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178 | maMonomial_Free(what, src_r); |
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179 | return into; |
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180 | } |
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181 | |
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182 | mapoly maPoly_InsertMonomial(mapoly into, poly p, ring src_r, sBucket_pt bucket = NULL) |
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183 | { |
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184 | return maPoly_InsertMonomial(into, maMonomial_Create(p, src_r, bucket), src_r); |
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185 | } |
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186 | |
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187 | static mapoly maPoly_InsertPoly(mapoly into, poly what, ring src_r, sBucket_pt bucket) |
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188 | { |
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189 | poly next; |
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190 | |
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191 | while (what != NULL) |
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192 | { |
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193 | next = what->next; |
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194 | into = maPoly_InsertMonomial(into, what, src_r, bucket); |
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195 | what = next; |
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196 | } |
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197 | return into; |
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198 | } |
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199 | |
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200 | void maMap_CreatePolyIdeal(ideal map_id, ring map_r, ring src_r, ring dest_r, |
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201 | mapoly &mp, maideal &mideal) |
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202 | { |
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203 | mideal = (maideal) omAlloc0(sizeof(maideal_s)); |
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204 | mideal->n = IDELEMS(map_id); |
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205 | mideal->buckets = (sBucket_pt*) omAlloc0(mideal->n*sizeof(sBucket_pt)); |
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206 | int i; |
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207 | mp = NULL; |
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208 | |
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209 | for (i=0; i<mideal->n; i++) |
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210 | { |
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211 | if (map_id->m[i] != NULL) |
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212 | { |
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213 | mideal->buckets[i] = sBucketCreate(dest_r); |
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214 | mp = maPoly_InsertPoly(mp, |
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215 | prShallowCopyR_NoSort(map_id->m[i], map_r, src_r), |
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216 | src_r, |
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217 | mideal->buckets[i]); |
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218 | } |
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219 | } |
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220 | } |
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221 | |
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222 | void maMap_CreateRings(ideal map_id, ring map_r, |
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223 | ideal image_id, ring image_r, |
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224 | ring &src_r, ring &dest_r) |
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225 | { |
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226 | src_r = map_r; |
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227 | dest_r = image_r; |
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228 | } |
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229 | |
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230 | |
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231 | ideal maIdeal_2_Ideal(maideal m_id, ring dest_r) |
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232 | { |
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233 | ideal res = idInit(m_id->n, 1); |
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234 | int l; |
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235 | |
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236 | for (int i= 0; i < m_id->n; i++) |
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237 | { |
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238 | sBucketDestroyMerge(m_id->buckets[i], &(res->m[i]), &l); |
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239 | } |
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240 | return res; |
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241 | } |
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242 | |
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243 | #if 0 |
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244 | |
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245 | /******************************************************************************* |
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246 | ** |
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247 | *F maMaxExp . . . . . . . . . . . . returns maximal exponent of result of map |
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248 | */ |
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249 | |
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250 | // return maximal monomial if max_map_monomials are substituted into pi_m |
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251 | static poly maGetMaxExpP(poly* max_map_monomials, |
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252 | int n_max_map_monomials, ring map_r, |
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253 | poly pi_m, ring pi_r) |
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254 | { |
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255 | int n = min(pi_r->N, n_max_map_monomials); |
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256 | int i, j; |
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257 | Exponent_t e_i, e_j; |
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258 | poly m_i, map_j = p_Init(map_r); |
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259 | |
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260 | for (i=1; i <= n; i++) |
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261 | { |
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262 | e_i = p_GetExp(pi_m, i, pi_r); |
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263 | m_i = max_map_monomials[i-1]; |
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264 | if (e_i > 0 && m_i != NULL && ! p_IsConstantComp(m_i, map_r)) |
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265 | { |
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266 | for (j = 1; j<= map_r->N; j++) |
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267 | { |
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268 | e_j = p_GetExp(m_i, j, map_r); |
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269 | if (e_j > 0) |
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270 | { |
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271 | p_AddExp(map_j, j, e_j*e_i, map_r); |
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272 | } |
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273 | } |
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274 | } |
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275 | } |
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276 | return map_j; |
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277 | } |
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278 | |
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279 | // returns maximal monomial if map_id is applied to pi_id |
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280 | static poly maGetMaxExpP(ideal map_id, ring map_r, ideal pi_id, ring pi_r) |
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281 | { |
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282 | poly* max_map_monomials = (poly*) omAlloc(IDELEMS(map_id)*sizeof(poly)); |
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283 | poly max_pi_i, max_map_i; |
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284 | poly max_map = p_Init(map_r); |
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285 | |
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286 | int i, j; |
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287 | for (i=0; i<IDELEMS(map_id); i++) |
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288 | { |
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289 | max_map_monomials[i] = p_GetMaxExpP(map_id->m[i], map_r); |
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290 | } |
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291 | |
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292 | for (i=0; i<IDELEMS(pi_id); i++) |
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293 | { |
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294 | max_pi_i = p_GetMaxExpP(pi_id->m[i], pi_r); |
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295 | max_map_i = maGetMaxExpP(max_map_monomials, IDELEMS(map_id), map_r, |
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296 | max_pi_i, pi_r); |
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297 | // get maximum |
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298 | for (j = 1; j<= map_r->N; j++) |
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299 | { |
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300 | if (p_GetExp(max_map, j, map_r) < p_GetExp(max_map_i, j, map_r)) |
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301 | p_SetExp(max_map, j, p_GetExp(max_map_i, j, map_r), map_r); |
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302 | } |
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303 | p_LmFree(max_pi_i, pi_r); |
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304 | p_LmFree(max_map_i, map_r); |
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305 | } |
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306 | return max_map; |
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307 | } |
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308 | |
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309 | // returns maximal exponent if map_id is applied to pi_id |
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310 | static Exponent_t maGetMaxExp(ideal map_id, ring map_r, ideal pi_id, ring pi_r) |
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311 | { |
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312 | poly p = maGetMaxExpP(map_id, map_r, pi_id, pi_r); |
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313 | Exponent_t max = p_GetMaxExp(p, map_r); |
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314 | p_LmFree(p, map_r); |
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315 | return max; |
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316 | } |
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317 | |
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318 | // construct ring/map ideal in/with which we perform computations |
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319 | // return TRUE if ordering changed (not yet implemented), false, otherwise |
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320 | static BOOLEAN maGetCompIdealRing(ideal map_id, ring map_r, ideal pi_id, |
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321 | ring pi_r, ideal &comp_map_id, ring &comp_r) |
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322 | { |
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323 | Exponent_t max_exp = maGetMaxExp(map_id, map_r, pi_id, pi_r); |
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324 | |
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325 | comp_r = rModifyRing(map_r, FALSE, !idIsModule(pi_id, pi_r), max_exp); |
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326 | if (comp_r != map_r) |
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327 | { |
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328 | if (TEST_OPT_PROT) |
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329 | Print("[%d:%d]", (long) comp_r->bitmask, comp_r->ExpL_Size); |
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330 | comp_map_id = idrShallowCopyR_NoSort(map_id, map_r, comp_r); |
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331 | } |
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332 | else |
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333 | comp_map_id = map_id; |
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334 | |
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335 | return FALSE; |
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336 | } |
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337 | |
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338 | static void maDestroyCompIdealRing(ideal map_id, ring map_r, |
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339 | ideal comp_map_id, ring &comp_r, |
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340 | ideal &result, BOOLEAN sort=FALSE) |
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341 | { |
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342 | if (map_r != comp_r) |
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343 | { |
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344 | result = idrMoveR(result, comp_r, map_r); |
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345 | id_ShallowDelete(&comp_map_id, comp_r); |
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346 | rKillModifiedRing(comp_r); |
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347 | } |
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348 | } |
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349 | |
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350 | /******************************************************************************* |
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351 | ** |
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352 | *F maEggt . . . . . . . . . . . . . . . . . . . . . . . . returns extended ggt |
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353 | */ |
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354 | // return NULL if deg(ggt(m1, m2)) < 2 |
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355 | // else return m = ggT(m1, m2) and q1, q2 such that m1 = q1*m m2 = q2*m |
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356 | static poly maEggT(const poly m1, const poly m2, poly &q1, poly &q2,const ring r) |
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357 | { |
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358 | int i; |
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359 | int dg = 0; |
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360 | poly ggt = NULL; |
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361 | for (i=1; i<=r->N; i++) |
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362 | { |
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363 | Exponent_t e1 = p_GetExp(m1, i, r); |
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364 | Exponent_t e2 = p_GetExp(m2, i, r); |
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365 | if (e1 > 0 && e2 > 0) |
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366 | { |
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367 | Exponent_t em = (e1 > e2 ? e2 : e1); |
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368 | if (dg < 2) |
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369 | { |
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370 | ggt = p_Init(r); |
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371 | q1 = p_Init(r); |
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372 | q2 = p_Init(r); |
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373 | } |
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374 | dg += em; |
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375 | p_SetExp(ggt, i, em, r); |
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376 | p_SetExp(q1, i, e1 - em, r); |
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377 | p_SetExp(q2, i, e2 - em, r); |
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378 | } |
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379 | } |
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380 | if (ggt != NULL) |
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381 | { |
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382 | p_Setm(ggt, r); |
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383 | p_Setm(q1, r); |
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384 | p_Setm(q2, r); |
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385 | } |
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386 | return ggt; |
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387 | } |
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388 | |
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389 | /******************************************************************************* |
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390 | ** |
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391 | *F maGetMapRing . . . . . . . . . . . . gets ring and ideal with which we work |
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392 | */ |
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393 | static ring maGetWeightedRing(ideal theMap, ring map_r) |
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394 | { |
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395 | // we work in a ring with ordering Deg,WeightedDegree,vars |
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396 | // First, construct weighted degrees |
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397 | int* weights = (int*) omAlloc0(map_r->N); |
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398 | int i; |
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399 | int n = min(map_r->N, IDELEMS(theMap)); |
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400 | |
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401 | for (i=0; i<n; i++) |
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402 | { |
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403 | weights[i] = pLength(theMap->m[i]); |
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404 | } |
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405 | return rModifyRing_Wp(map_r, weights); |
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406 | } |
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407 | static void maDestroyWeightedRing(ring r) |
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408 | { |
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409 | rKillModified_Wp_Ring(r); |
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410 | } |
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411 | |
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412 | |
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413 | |
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414 | |
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415 | |
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416 | static void maMap_2_maPoly(ideal source_id, ring source_r, ring weight_r, ring comp_r, |
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417 | mapoly &mp, maideal &mideal) |
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418 | { |
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419 | mideal = (maideal) omAlloc0(sizeof(maideal_s)); |
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420 | mideal->n = IDELEMS(source_id); |
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421 | mideal->buckets = (sBucket_pt*) omAlloc0(mideal->n*sizeof(sBucket_pt)); |
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422 | int i; |
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423 | mp = NULL; |
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424 | |
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425 | for (i=0; i<mideal->n; i++) |
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426 | { |
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427 | if (source_id->m[i] != NULL) |
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428 | { |
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429 | mideal->buckets[i] = sBucketCreate(comp_r); |
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430 | mapInsertPoly(mp, |
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431 | prShallowCopyR_NoSort(source_id->m[i], source_r, weight_r), |
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432 | weight_r, |
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433 | mideal->buckets[i]); |
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434 | } |
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435 | maPoly_Out(mp, source_r); |
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436 | } |
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437 | } |
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438 | |
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439 | |
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440 | |
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441 | |
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442 | |
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443 | static mapoly maFindBestggT(mapoly mp, mapoly in, poly ggT, poly fp, poly fq) |
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444 | { |
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445 | int ggt_deg = 0; |
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446 | poly p = mp->src; |
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447 | mapoly mq = NULL; |
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448 | |
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449 | ggT = NULL; |
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450 | fp = NULL; |
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451 | fq = NULL; |
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452 | while (in != NULL && in->factors > 1 && pFDeg(in->src) > ggt_deg) |
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453 | { |
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454 | poly q1, q2, q; |
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455 | // q = maEggT(p, in->src, q1, q2); |
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456 | if (q != NULL) |
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457 | { |
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458 | if (pFDeg(q) > fft_deg) |
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459 | { |
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460 | if (ggT != NULL) |
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461 | { |
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462 | p_LmFree(ggT); |
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463 | p_LmFree(fp); |
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464 | p_LmFree(fq); |
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465 | } |
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466 | ggT = q; |
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467 | fp = q1; |
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468 | fq = q2; |
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469 | } |
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470 | else |
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471 | { |
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472 | p_LmFree(q); |
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473 | p_LmFree(q1); |
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474 | p_LmFree(q2); |
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475 | } |
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476 | } |
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477 | } |
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478 | } |
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479 | |
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480 | |
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481 | static mapoly maPrepareEval(mapoly mp, ring r) |
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482 | { |
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483 | mapoly res = NULL; |
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484 | mapoly next = mp; |
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485 | |
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486 | while (mp != NULL) |
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487 | { |
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488 | next = mp->next; |
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489 | mp->next = res; |
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490 | res = mp; |
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491 | if (mp->factors > 1 && mp->f1 == NULL && mp->f2 == NULL) |
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492 | { |
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493 | poly fp, fq, ggT; |
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494 | mapoly mq = maFindBestggT(mp, next, ggT, fp, fq); |
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495 | if (mq != NULL) |
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496 | { |
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497 | assume(fp != NULL); |
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498 | mp->f1 = maInsertMonomial(next, fp, r, NULL); |
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499 | |
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500 | if (ggT != NULL) |
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501 | { |
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502 | assume(fq != NULL); |
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503 | mapoly mggT = maInsertMonomial(next, ggT, r, NULL); |
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504 | mq->f1 = maInsertMonomial(next, fq, r, NULL); |
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505 | mq->f2 = mggT; |
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506 | mp->f2 = mggT; |
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507 | mggT->ref++; |
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508 | } |
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509 | else |
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510 | { |
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511 | assume(fq == NULL); |
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512 | mp->f2 = mq; |
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513 | mq->ref++; |
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514 | } |
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515 | } |
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516 | } |
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517 | mp = next; |
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518 | } |
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519 | return res; |
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520 | } |
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521 | /******************************************************************************* |
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522 | ** |
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523 | *F ideal_2_maideal . . . . . . . . . . . . . . . . . converts ideal to maideal |
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524 | */ |
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525 | mapoly ideal_2_maideal(ideal id, ring r, maideal mid, ring mr, ring comp_ring, |
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526 | nMapFunc nMap) |
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527 | { |
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528 | mid->n = IDELEMS(id); |
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529 | mid->buckets = (sBucket_pt*)omAlloc(mid->n*sizeof(sBucket_pt)); |
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530 | mapoly mpoly = NULL; |
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531 | |
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532 | for (int i=0; i<mid->n; i++) |
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533 | { |
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534 | mid->buckets[i] = sBucketCreate(comp_ring); |
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535 | mapoly mpoly_i = poly_2_mapoly(id->m[i], mid, nMap, mid->buckets[i]); |
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536 | mpoly = mapAdd(mpoly, mpoly_i); |
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537 | } |
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538 | return mpoly; |
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539 | } |
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540 | |
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541 | ideal maideal_2_ideal(ideal orig_id, |
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542 | maideal mideal, ring comp_ring, ring dest_ring) |
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543 | { |
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544 | ideal id = idInit(IDELEMS(orig_id), orig_id->rank); |
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545 | for (int i=0; i<mid->n; i++) |
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546 | { |
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547 | sBucketDestroyAdd(mid->buckets[i], &(id->m[i]), &dummy); |
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548 | } |
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549 | |
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550 | if (comp_ring != dest_ring) |
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551 | id = idrMoveR_NoSort(id, comp_ring); |
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552 | |
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553 | return id; |
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554 | } |
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555 | |
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556 | #endif |
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557 | |
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