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tropicalTraversal.h File Reference
#include "groebnerCone.h"

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Functions

groebnerCones tropicalTraversalMinimizingFlips (const groebnerCone startingCone)
 
groebnerCones tropicalTraversal (const groebnerCone startingCone)
 
groebnerCones groebnerTraversal (const groebnerCone startingCone)
 

Function Documentation

◆ groebnerTraversal()

groebnerCones groebnerTraversal ( const groebnerCone  startingCone)

Pick a maximal Groebner cone from the working list and compute interior points on its facets as well as outer facet normals

Definition at line 141 of file tropicalTraversal.cc.

142 {
143  const tropicalStrategy* currentStrategy = startingCone.getTropicalStrategy();
144 
146  groebnerCones workingList;
147  workingList.insert(startingCone);
148  std::set<gfan::ZVector> finishedInteriorPoints;
149  bool onlyLowerHalfSpace = !currentStrategy->isValuationTrivial();
150 
151  while(!workingList.empty())
152  {
153  /**
154  * Pick a maximal Groebner cone from the working list
155  * and compute interior points on its facets as well as outer facet normals
156  */
157  groebnerCone sigma=*(workingList.begin());
158  workingList.erase(workingList.begin());
159 
160  std::pair<gfan::ZMatrix,gfan::ZMatrix> interiorPointsAndOuterFacetNormals = interiorPointsAndNormalsOfFacets(sigma.getPolyhedralCone(), finishedInteriorPoints, onlyLowerHalfSpace);
161  gfan::ZMatrix interiorPoints = interiorPointsAndOuterFacetNormals.first;
162  gfan::ZMatrix outerFacetNormals = interiorPointsAndOuterFacetNormals.second;
163  std::vector<bool> needToFlip = checkNecessaryGroebnerFlips(groebnerFan,workingList, interiorPoints);
164 
165  for (int i=0; i<interiorPoints.getHeight(); i++)
166  {
167  gfan::ZVector interiorPoint = interiorPoints[i];
168 
169  if (needToFlip[i]==true)
170  {
171  groebnerCone neighbour = sigma.flipCone(interiorPoint,outerFacetNormals[i]);
172  workingList.insert(neighbour);
173  }
174  finishedInteriorPoints.insert(interiorPoints[i]);
175  }
176 
177  sigma.deletePolynomialData();
178  groebnerFan.insert(sigma);
179  if (printlevel > 0)
180  Print("cones finished: %lu cones in working list: %lu\n",
181  (unsigned long)groebnerFan.size(), (unsigned long)workingList.size());
182  }
183  return groebnerFan;
184 }
std::pair< gfan::ZMatrix, gfan::ZMatrix > interiorPointsAndNormalsOfFacets(const gfan::ZCone zc, const std::set< gfan::ZVector > &exceptThesePoints, const bool onlyLowerHalfSpace)
Definition: bbcone.cc:1853
int i
Definition: cfEzgcd.cc:132
gfan::ZCone getPolyhedralCone() const
Definition: groebnerCone.h:64
const tropicalStrategy * getTropicalStrategy() const
Definition: groebnerCone.h:66
groebnerCone flipCone(const gfan::ZVector &interiorPoint, const gfan::ZVector &facetNormal) const
Given an interior point on the facet and the outer normal factor on the facet, returns the adjacent g...
void deletePolynomialData()
Definition: groebnerCone.h:53
bool isValuationTrivial() const
#define Print
Definition: emacs.cc:80
VAR int printlevel
Definition: febase.cc:36
std::set< groebnerCone, groebnerCone_compare > groebnerCones
Definition: groebnerCone.h:23
gfan::ZFan * groebnerFan(const tropicalStrategy currentStrategy)
Definition: groebnerFan.cc:28
std::vector< bool > checkNecessaryGroebnerFlips(const groebnerCones &groebnerFan, const groebnerCones &workingList, const gfan::ZMatrix &interiorPoints)

◆ tropicalTraversal()

groebnerCones tropicalTraversal ( const groebnerCone  startingCone)

◆ tropicalTraversalMinimizingFlips()

groebnerCones tropicalTraversalMinimizingFlips ( const groebnerCone  startingCone)

Pick an element the working list and compute interior points on its facets

For each interior point, compute the rays of the tropical star in that point

Definition at line 52 of file tropicalTraversal.cc.

53 {
55  if (startingCone.isTrivial())
56  {
57  return tropicalVariety;
58  }
59 
60  groebnerCones workingList;
61  workingList.insert(startingCone);
62  const tropicalStrategy* currentStrategy=startingCone.getTropicalStrategy();
63  std::set<gfan::ZVector> finishedInteriorPoints;
64  while(!workingList.empty())
65  {
66  /**
67  * Pick an element the working list and compute interior points on its facets
68  */
69  groebnerCone sigma=*(workingList.begin());
70  gfan::ZMatrix interiorPoints = interiorPointsOfFacets(sigma.getPolyhedralCone(),finishedInteriorPoints);
71 
72  for (int i=0; i<interiorPoints.getHeight(); i++)
73  {
74  /**
75  * For each interior point, compute the rays of the tropical star in that point
76  */
77  gfan::ZVector interiorPoint = interiorPoints[i];
78  if (!(currentStrategy->restrictToLowerHalfSpace() && interiorPoint[0].sign()==0))
79  {
80  ideal inI = initial(sigma.getPolynomialIdeal(),sigma.getPolynomialRing(),interiorPoint);
81  ideal inISTD = gfanlib_satStd_wrapper(inI,sigma.getPolynomialRing());
82  id_Delete(&inI,sigma.getPolynomialRing());
83  gfan::ZMatrix normalVectors = raysOfTropicalStar(inISTD,
84  sigma.getPolynomialRing(),
85  interiorPoint,
86  sigma.getTropicalStrategy());
87  id_Delete(&inISTD,sigma.getPolynomialRing());
88 
89  std::vector<bool> needToFlip = checkNecessaryTropicalFlips(tropicalVariety,workingList,interiorPoint,normalVectors);
90  for (int j=0; j<normalVectors.getHeight(); j++)
91  {
92  if (needToFlip[j])
93  {
94  groebnerCone neighbour = sigma.flipCone(interiorPoint,normalVectors[j]);
95  workingList.insert(neighbour);
96  }
97  }
98  }
99  finishedInteriorPoints.insert(interiorPoint);
100  }
101 
102  sigma.deletePolynomialData();
103  workingList.erase(sigma);
104  tropicalVariety.insert(sigma);
105  if (printlevel > 0)
106  Print("cones finished: %lu cones in working list: %lu\n",
107  (unsigned long)tropicalVariety.size(), (unsigned long)workingList.size());
108  }
109  return tropicalVariety;
110 }
gfan::ZMatrix interiorPointsOfFacets(const gfan::ZCone &zc, const std::set< gfan::ZVector > &exceptThese)
Definition: bbcone.cc:1799
bool isTrivial() const
Definition: groebnerCone.h:69
ideal getPolynomialIdeal() const
Definition: groebnerCone.h:62
ring getPolynomialRing() const
Definition: groebnerCone.h:63
bool restrictToLowerHalfSpace() const
returns true, if valuation non-trivial, false otherwise
int j
Definition: facHensel.cc:110
poly initial(const poly p, const ring r, const gfan::ZVector &w)
Returns the initial form of p with respect to w.
Definition: initial.cc:30
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ideal gfanlib_satStd_wrapper(ideal I, ring r, tHomog h=testHomog)
Definition: std_wrapper.cc:124
gfan::ZMatrix raysOfTropicalStar(ideal I, const ring r, const gfan::ZVector &u, const tropicalStrategy *currentStrategy)
std::vector< bool > checkNecessaryTropicalFlips(const groebnerCones &tropicalVariety, const groebnerCones &workingList, const gfan::ZVector &interiorPoint, const gfan::ZMatrix &normalVectors)
BOOLEAN tropicalVariety(leftv res, leftv args)