[81384b] | 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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[58b407] | 14 | #include <Singular/ipid.h> |
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[81384b] | 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() == v.size()); |
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| 43 | assume(c.ambientDimension() == 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() == v.size()); |
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| 56 | assume(c.ambientDimension() == 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() == v.size()); |
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| 69 | assume(c.ambientDimension() == 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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[e44b149] | 166 | if ((v != NULL) && (v->Typ() == BIGINTMAT_CMD)) |
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[81384b] | 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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[e44b149] | 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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[58b407] | 366 | void gitfan_setup(SModulFunctions* p) |
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[81384b] | 367 | { |
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[58b407] | 368 | p->iiAddCproc("","refineCones",FALSE,refineCones); |
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[e44b149] | 369 | p->iiAddCproc("","listOfAfacesToCheck",FALSE,listOfAfacesToCheck); |
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| 370 | p->iiAddCproc("","nextAfaceToCheck",FALSE,nextAfaceToCheck); |
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[81384b] | 371 | } |
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