1 | /*************************************************************** |
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2 | * |
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3 | * File: gitfan.cc |
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4 | * Purpose: Computationally intensive procedures for gitfan.lib, |
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5 | * outsourced to improve the performance. |
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6 | * Authors: Janko Boehm boehm@mathematik.uni-kl.de |
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7 | * Simon Keicher keicher@mail.mathematik.uni-tuebingen.de |
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8 | * Yue Ren ren@mathematik.uni-kl.de |
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9 | * |
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10 | ***************************************************************/ |
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11 | |
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12 | #include <kernel/mod2.h> |
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13 | |
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14 | #include <Singular/ipid.h> |
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15 | #include <Singular/lists.h> |
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16 | #include <Singular/ipshell.h> |
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17 | #include <libpolys/coeffs/bigintmat.h> |
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18 | |
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19 | #include <bbcone.h> |
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20 | #include <bbfan.h> |
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21 | #include <gitfan.h> |
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22 | |
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23 | namespace gitfan |
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24 | { |
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25 | |
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26 | facet::facet(): |
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27 | eta(gfan::ZCone()), |
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28 | interiorPoint(gfan::ZVector()), |
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29 | facetNormal(gfan::ZVector()) |
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30 | { |
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31 | } |
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32 | |
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33 | facet::facet(const gitfan::facet &f): |
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34 | eta(f.eta), |
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35 | interiorPoint(f.interiorPoint), |
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36 | facetNormal(f.facetNormal) |
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37 | { |
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38 | #ifndef NDEBUG |
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39 | gfan::ZCone c = f.eta; |
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40 | gfan::ZVector v = f.interiorPoint; |
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41 | gfan::ZVector w = f.facetNormal; |
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42 | assume(c.ambientDimension() == (int)v.size()); |
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43 | assume(c.ambientDimension() == (int)w.size()); |
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44 | assume(c.contains(v)); |
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45 | assume(!c.contains(w)); |
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46 | #endif |
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47 | } |
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48 | |
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49 | facet::facet(const gfan::ZCone &c, const gfan::ZVector &v, const gfan::ZVector &w): |
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50 | eta(c), |
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51 | interiorPoint(v), |
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52 | facetNormal(w) |
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53 | { |
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54 | #ifndef NDEBUG |
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55 | assume(c.ambientDimension() == (int)v.size()); |
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56 | assume(c.ambientDimension() == (int)w.size()); |
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57 | assume(c.contains(v)); |
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58 | assume(!c.contains(w)); |
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59 | #endif |
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60 | } |
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61 | |
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62 | facet::~facet() |
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63 | { |
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64 | #ifndef NDEBUG |
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65 | gfan::ZCone c = this->eta; |
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66 | gfan::ZVector v = this->interiorPoint; |
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67 | gfan::ZVector w = this->facetNormal; |
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68 | assume(c.ambientDimension() == (int)v.size()); |
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69 | assume(c.ambientDimension() == (int)w.size()); |
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70 | assume(c.contains(v)); |
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71 | assume(!c.contains(w)); |
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72 | #endif |
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73 | } |
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74 | |
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75 | void mergeFacets(facets &F, const facets &newFacets) |
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76 | { |
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77 | std::pair<facets::iterator,bool> check(newFacets.begin(),false); |
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78 | for(facets::iterator p=newFacets.begin(); p!=newFacets.end(); p++) |
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79 | { |
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80 | check = F.insert(*p); |
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81 | if(!check.second) |
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82 | F.erase(check.first); |
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83 | } |
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84 | } |
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85 | |
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86 | } |
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87 | |
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88 | |
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89 | static gfan::ZCone subcone(const lists &cones, const gfan::ZVector &point) |
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90 | { |
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91 | gfan::ZCone sigma = gfan::ZCone(gfan::ZMatrix(1,point.size()), gfan::ZMatrix(1,point.size())); |
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92 | gfan::ZCone* zc; |
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93 | for (int i=0; i<=cones->nr; i++) |
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94 | { |
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95 | zc = (gfan::ZCone*) cones->m[i].Data(); |
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96 | if (zc->contains(point)) |
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97 | sigma = gfan::intersection(sigma,*zc); |
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98 | } |
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99 | return(sigma); |
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100 | } |
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101 | |
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102 | static gitfan::facets interiorFacets(const gfan::ZCone &zc, const gfan::ZCone &bound) |
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103 | { |
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104 | gfan::ZMatrix inequalities = zc.getFacets(); |
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105 | gfan::ZMatrix equations = zc.getImpliedEquations(); |
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106 | int r = inequalities.getHeight(); |
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107 | int c = inequalities.getWidth(); |
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108 | gitfan::facets F; |
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109 | if (r*c == 0) |
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110 | /*** |
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111 | * this is the trivial case where either we are in a zerodimensional ambient space, |
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112 | * or the cone has no facets. |
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113 | **/ |
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114 | return F; |
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115 | |
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116 | // int index = 0; |
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117 | /* next we iterate over each of the r facets, build the respective cone and add it to the list */ |
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118 | /* this is the i=0 case */ |
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119 | gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c); |
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120 | gfan::ZMatrix newEquations = equations; |
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121 | newEquations.appendRow(inequalities[0]); |
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122 | gfan::ZCone eta = gfan::ZCone(newInequalities,newEquations); |
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123 | eta.canonicalize(); |
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124 | gfan::ZVector v = eta.getRelativeInteriorPoint(); |
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125 | gfan::ZVector w = inequalities[0]; |
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126 | |
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127 | if (bound.containsRelatively(v)) |
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128 | F.insert(gitfan::facet(eta,v,w)); |
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129 | |
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130 | /* these are the cases i=1,...,r-2 */ |
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131 | for (int i=1; i<r-1; i++) |
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132 | { |
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133 | newInequalities = inequalities.submatrix(0,0,i,c); |
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134 | newInequalities.append(inequalities.submatrix(i+1,0,r,c)); |
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135 | newEquations = equations; |
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136 | newEquations.appendRow(inequalities[i]); |
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137 | eta = gfan::ZCone(newInequalities,newEquations); |
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138 | eta.canonicalize(); |
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139 | v = eta.getRelativeInteriorPoint(); |
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140 | w = inequalities[i]; |
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141 | if (bound.containsRelatively(v)) |
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142 | F.insert(gitfan::facet(eta,v,w)); |
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143 | } |
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144 | |
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145 | /* this is the i=r-1 case */ |
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146 | newInequalities = inequalities.submatrix(0,0,r-1,c); |
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147 | newEquations = equations; |
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148 | newEquations.appendRow(inequalities[r-1]); |
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149 | eta = gfan::ZCone(newInequalities,newEquations); |
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150 | eta.canonicalize(); |
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151 | |
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152 | v = eta.getRelativeInteriorPoint(); |
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153 | w = inequalities[r-1]; |
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154 | if (bound.containsRelatively(v)) |
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155 | F.insert(gitfan::facet(eta,v,w)); |
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156 | |
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157 | return F; |
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158 | } |
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159 | |
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160 | BOOLEAN refineCones(leftv res, leftv args) |
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161 | { |
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162 | leftv u=args; |
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163 | if ((u != NULL) && (u->Typ() == LIST_CMD)) |
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164 | { |
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165 | leftv v=u->next; |
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166 | if ((v != NULL) && (v->Typ() == BIGINTMAT_CMD)) |
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167 | { |
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168 | lists cones = (lists) u->Data(); |
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169 | bigintmat* bim = (bigintmat*) v->Data(); |
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170 | gfan::ZMatrix* zm = bigintmatToZMatrix(bim->transpose()); |
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171 | gfan::ZCone support = gfan::ZCone::givenByRays(*zm, gfan::ZMatrix(0, zm->getWidth())); |
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172 | delete zm; |
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173 | |
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174 | /*** |
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175 | * Randomly compute a first full-dimensional cone and insert it into the fan. |
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176 | * Compute a list of facets and relative interior points. |
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177 | * The relative interior points are unique, assuming the cone is stored in canonical form, |
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178 | * which is the case in our algorithm, as we supply no redundant inequalities. |
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179 | * Hence we can decide whether a facet need to be traversed by crosschecking |
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180 | * its relative interior point with this list. |
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181 | **/ |
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182 | gfan::ZCone lambda; gfan::ZVector point; |
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183 | do |
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184 | { |
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185 | point = randomPoint(&support); |
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186 | lambda = subcone(cones, point); |
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187 | } |
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188 | while (lambda.dimension() < lambda.ambientDimension()); |
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189 | int iterationNumber = 1; |
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190 | std::cout << "cones found: " << iterationNumber++ << std::endl; |
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191 | |
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192 | lambda.canonicalize(); |
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193 | gfan::ZFan* Sigma = new gfan::ZFan(lambda.ambientDimension()); |
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194 | Sigma->insert(lambda); |
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195 | gitfan::facets F = interiorFacets(lambda, support); |
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196 | if (F.empty()) |
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197 | { |
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198 | res->rtyp = fanID; |
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199 | res->data = (void*) Sigma; |
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200 | return FALSE; |
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201 | } |
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202 | int mu = 1024; |
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203 | |
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204 | gitfan::facet f; |
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205 | gfan::ZCone eta; |
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206 | gfan::ZVector interiorPoint; |
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207 | gfan::ZVector facetNormal; |
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208 | gitfan::facets newFacets; |
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209 | while (!F.empty()) |
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210 | { |
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211 | /*** |
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212 | * Extract a facet to traverse and its relative interior point. |
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213 | **/ |
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214 | f = *(F.begin()); |
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215 | eta = f.getEta(); |
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216 | interiorPoint = f.getInteriorPoint(); |
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217 | facetNormal = f.getFacetNormal(); |
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218 | |
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219 | /*** |
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220 | * construct a point, which lies on the other side of the facet. |
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221 | * make sure it lies in the known support of our fan |
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222 | * and that the cone around the point is maximal, containing eta. |
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223 | **/ |
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224 | point = mu * interiorPoint - facetNormal; |
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225 | while (!support.containsRelatively(point)) |
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226 | { |
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227 | mu = mu * 16; |
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228 | point = mu * interiorPoint - facetNormal; |
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229 | } |
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230 | |
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231 | lambda = subcone(cones,point); |
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232 | while ((lambda.dimension() < lambda.ambientDimension()) && !(lambda.contains(interiorPoint))) |
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233 | { |
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234 | mu = mu * 16; |
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235 | point = mu * interiorPoint - facetNormal; |
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236 | lambda = subcone(cones,point); |
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237 | } |
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238 | std::cout << "cones found: " << iterationNumber++ << std::endl; |
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239 | |
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240 | /*** |
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241 | * insert lambda into Sigma, and create a list of facets of lambda. |
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242 | * merge the two lists of facets |
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243 | **/ |
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244 | lambda.canonicalize(); |
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245 | Sigma->insert(lambda); |
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246 | newFacets = interiorFacets(lambda, support); |
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247 | mergeFacets(F,newFacets); |
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248 | newFacets.clear(); |
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249 | } |
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250 | res->rtyp = fanID; |
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251 | res->data = (void*) Sigma; |
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252 | return FALSE; |
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253 | } |
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254 | } |
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255 | WerrorS("refineCones: unexpected parameters"); |
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256 | return TRUE; |
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257 | } |
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258 | |
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259 | |
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260 | static int binomial(int n, int k) |
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261 | { |
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262 | if (n<k) |
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263 | return(0); |
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264 | gfan::Integer num = 1; |
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265 | gfan::Integer den = 1; |
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266 | for (int i=1; i<=k; i++) |
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267 | den = den*i; |
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268 | for (int j=n-k+1; j<=n; j++) |
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269 | num = num*j; |
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270 | gfan::Integer bin = num/den; |
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271 | return(bin.toInt()); |
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272 | } |
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273 | |
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274 | |
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275 | intvec* intToAface(unsigned int v0, int n, int k) |
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276 | { |
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277 | intvec* v = new intvec(k); |
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278 | int j = 0; |
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279 | for (int i=0; i<n; i++) |
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280 | { |
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281 | if (v0 & (1<<i)) |
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282 | (*v)[j++] = i+1; |
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283 | } |
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284 | return v; |
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285 | } |
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286 | |
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287 | |
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288 | BOOLEAN listOfAfacesToCheck(leftv res, leftv args) |
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289 | { |
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290 | leftv u = args; |
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291 | if ((u != NULL) && (u->Typ() == INT_CMD)) |
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292 | { |
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293 | leftv v = u->next; |
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294 | if ((v != NULL) && (v->Typ() == INT_CMD)) |
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295 | { |
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296 | int n = (int)(long) u->Data(); |
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297 | int k = (int)(long) v->Data(); |
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298 | unsigned int v = 0; |
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299 | for (int i=0; i<k; i++) |
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300 | v |= 1<<i; // sets the first k bits of v as 1 |
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301 | |
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302 | lists L = (lists)omAllocBin(slists_bin); |
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303 | int count = (int) binomial(n,k); L->Init(count); |
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304 | unsigned int t; |
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305 | while (!(v & (1<<n))) |
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306 | { |
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307 | L->m[--count].rtyp = INTVEC_CMD; |
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308 | L->m[count].data = (void*) intToAface(v,n,k); |
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309 | |
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310 | // t gets v's least significant 0 bits set to 1 |
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311 | t = v | (v - 1); |
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312 | // Next set to 1 the most significant bit to change, |
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313 | // set to 0 the least significant ones, and add the necessary 1 bits. |
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314 | v = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1)); |
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315 | } |
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316 | res->rtyp = LIST_CMD; |
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317 | res->data = (void*) L; |
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318 | return FALSE; |
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319 | } |
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320 | } |
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321 | WerrorS("listOfAfacesToCheck: unexpected parameter"); |
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322 | return TRUE; |
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323 | } |
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324 | |
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325 | |
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326 | BOOLEAN nextAfaceToCheck(leftv res, leftv args) |
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327 | { |
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328 | leftv u = args; |
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329 | if ((u != NULL) && (u->Typ() == INTVEC_CMD)) |
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330 | { |
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331 | leftv v = u->next; |
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332 | if ((v != NULL) && (v->Typ() == INT_CMD)) |
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333 | { |
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334 | leftv w = v->next; |
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335 | if ((w != NULL) && (w->Typ() == INT_CMD)) |
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336 | { |
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337 | intvec* aface = (intvec*) u->Data(); |
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338 | int ambientDimension = (int)(long) v->Data(); |
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339 | int dimension = (int)(long) w->Data(); |
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340 | |
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341 | unsigned int af = 0; |
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342 | for (int i=0; i<aface->length(); i++) |
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343 | af |= 1<<((*aface)[i]-1); |
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344 | |
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345 | unsigned int t = af | (af - 1); |
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346 | af = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(af) + 1)); |
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347 | |
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348 | if (af & (1<<ambientDimension)) |
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349 | { |
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350 | res->rtyp = INTVEC_CMD; |
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351 | res->data = (void*) new intvec(1); |
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352 | return FALSE; |
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353 | } |
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354 | |
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355 | res->rtyp = INTVEC_CMD; |
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356 | res->data = (void*) intToAface(af,ambientDimension,dimension); |
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357 | return FALSE; |
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358 | } |
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359 | } |
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360 | } |
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361 | WerrorS("nextAfaceToCheck: unexpected parameter"); |
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362 | return TRUE; |
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363 | } |
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364 | |
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365 | |
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366 | void gitfan_setup(SModulFunctions* p) |
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367 | { |
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368 | p->iiAddCproc("","refineCones",FALSE,refineCones); |
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369 | p->iiAddCproc("","listOfAfacesToCheck",FALSE,listOfAfacesToCheck); |
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370 | p->iiAddCproc("","nextAfaceToCheck",FALSE,nextAfaceToCheck); |
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371 | } |
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