[b3e45f] | 1 | /* |
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[6623f3] | 2 | Compute the Groebner fan of an ideal |
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[fc4f9a] | 3 | $Author: monerjan $ |
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[798f721] | 4 | $Date: 2009-03-31 09:59:14 $ |
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| 5 | $Header: /exports/cvsroot-2/cvsroot/kernel/gfan.cc,v 1.25 2009-03-31 09:59:14 monerjan Exp $ |
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| 6 | $Id: gfan.cc,v 1.25 2009-03-31 09:59:14 monerjan Exp $ |
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[b3e45f] | 7 | */ |
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| 8 | |
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[d3398c] | 9 | #include "mod2.h" |
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[34fcf8] | 10 | |
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| 11 | #ifdef HAVE_GFAN |
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| 12 | |
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[d3398c] | 13 | #include "kstd1.h" |
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[50ab25a] | 14 | #include "intvec.h" |
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[2c6535] | 15 | #include "polys.h" |
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| 16 | #include "ideals.h" |
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[198a339] | 17 | #include "kmatrix.h" |
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[90adba8] | 18 | #include "fast_maps.h" //Mapping of ideals |
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[798f721] | 19 | #include "maps.h" |
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[aba53c] | 20 | #include "iostream.h" //deprecated |
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[fc4f9a] | 21 | |
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| 22 | //Hacks for different working places |
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[54248e] | 23 | #define ITWM |
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[fc4f9a] | 24 | |
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| 25 | #ifdef UNI |
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[c5d8dd] | 26 | #include "/users/urmel/alggeom/monerjan/cddlib/include/setoper.h" //Support for cddlib. Dirty hack |
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| 27 | #include "/users/urmel/alggeom/monerjan/cddlib/include/cdd.h" |
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[fc4f9a] | 28 | #endif |
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| 29 | |
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| 30 | #ifdef HOME |
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| 31 | #include "/home/momo/studium/diplomarbeit/cddlib/include/setoper.h" |
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| 32 | #include "/home/momo/studium/diplomarbeit/cddlib/include/cdd.h" |
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| 33 | #endif |
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| 34 | |
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| 35 | #ifdef ITWM |
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[aba53c] | 36 | #include "/u/slg/monerjan/cddlib/include/setoper.h" |
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| 37 | #include "/u/slg/monerjan/cddlib/include/cdd.h" |
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[fc4f9a] | 38 | #endif |
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[d3398c] | 39 | |
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[b3e45f] | 40 | #ifndef gfan_DEBUG |
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| 41 | #define gfan_DEBUG |
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| 42 | #endif |
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[9f9b142] | 43 | |
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| 44 | //#include gcone.h |
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| 45 | |
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[fe919c] | 46 | /** |
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| 47 | *\brief Class facet |
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[53e33d9] | 48 | * Implements the facet structure as a linked list |
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[fe919c] | 49 | * |
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| 50 | */ |
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[8bdaab] | 51 | class facet |
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| 52 | { |
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| 53 | private: |
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[90adba8] | 54 | /** inner normal, describing the facet uniquely up to isomorphism */ |
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[54248e] | 55 | intvec *fNormal; |
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[8bdaab] | 56 | public: |
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[fe919c] | 57 | /** The default constructor. Do I need a constructor of type facet(intvec)? */ |
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| 58 | facet() |
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[fc4f9a] | 59 | { |
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[fe919c] | 60 | // Pointer to next facet. */ |
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| 61 | /* Defaults to NULL. This way there is no need to check explicitly */ |
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| 62 | this->next=NULL; |
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[fc4f9a] | 63 | } |
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| 64 | |
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[fe919c] | 65 | /** The default destructor */ |
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| 66 | ~facet(){;} |
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| 67 | |
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[54248e] | 68 | /** Stores the facet normal \param intvec*/ |
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| 69 | void setFacetNormal(intvec *iv){ |
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[aba53c] | 70 | fNormal = iv; |
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[54248e] | 71 | //return; |
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| 72 | } |
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| 73 | |
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| 74 | /** Method to print the facet normal*/ |
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| 75 | void printNormal() |
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| 76 | { |
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| 77 | fNormal->show(); |
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[fc4f9a] | 78 | } |
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| 79 | |
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[798f721] | 80 | /** \brief The Groebner basis on the other side of a shared facet |
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| 81 | * |
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| 82 | * In order not to have to compute the flipped GB twice we store the basis we already get |
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| 83 | * when identifying search facets. Thus in the next step of the reverse search we can |
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| 84 | * just copy the old cone and update the facet and the gcBasis |
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| 85 | */ |
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| 86 | ideal flibGB; //The Groebner Basis on the other side, computed via gcone::flip |
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| 87 | |
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[18765e] | 88 | bool isFlippable; //flippable facet? Want to have cone->isflippable.facet[i] |
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| 89 | bool isIncoming; //Is the facet incoming or outgoing? |
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[aba53c] | 90 | facet *next; //Pointer to next facet |
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[8bdaab] | 91 | }; |
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| 92 | |
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[fe919c] | 93 | /** |
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[90adba8] | 94 | *\brief Implements the cone structure |
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| 95 | * |
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| 96 | * A cone is represented by a linked list of facet normals |
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| 97 | * @see facet |
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[fe919c] | 98 | */ |
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[8bdaab] | 99 | /*class gcone |
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| 100 | finally this should become s.th. like gconelib.{h,cc} to provide an API |
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| 101 | */ |
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| 102 | class gcone |
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| 103 | { |
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[18765e] | 104 | private: |
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| 105 | int numFacets; //#of facets of the cone |
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| 106 | |
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| 107 | public: |
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[90adba8] | 108 | /** \brief Default constructor. |
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| 109 | * |
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| 110 | * Initialises this->next=NULL and this->facetPtr=NULL |
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| 111 | */ |
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[54248e] | 112 | gcone() |
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| 113 | { |
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| 114 | this->next=NULL; |
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| 115 | this->facetPtr=NULL; |
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| 116 | } |
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[fc4f9a] | 117 | ~gcone(); //destructor |
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[53e33d9] | 118 | /** Pointer to the first facet */ |
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[54248e] | 119 | facet *facetPtr; //Will hold the adress of the first facet |
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[aba53c] | 120 | poly gcMarkedTerm; //marked terms of the cone's Groebner basis |
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[18765e] | 121 | ideal gcBasis; //GB of the cone |
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| 122 | gcone *next; //Pointer to *previous* cone in search tree |
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[90adba8] | 123 | /** \brief Compute the normals of the cone |
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| 124 | * |
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| 125 | * This method computes a representation of the cone in terms of facet normals. It takes an ideal |
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| 126 | * as its input. Redundancies are automatically removed using cddlib's dd_MatrixCanonicalize. |
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| 127 | * Other methods for redundancy checkings might be implemented later. See Anders' diss p.44. |
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| 128 | * Note that in order to use cddlib a 0-th column has to be added to the matrix since cddlib expects |
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| 129 | * each row to represent an inequality of type const+x1+...+xn <= 0 |
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| 130 | * As a result of this procedure the pointer facetPtr points to the first facet of the cone. |
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| 131 | */ |
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| 132 | void getConeNormals(ideal I) |
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[03de21] | 133 | { |
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[90adba8] | 134 | #ifdef gfan_DEBUG |
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| 135 | cout << "*** Computing Inequalities... ***" << endl; |
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| 136 | #endif |
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| 137 | //All variables go here - except ineq matrix and *v, see below |
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| 138 | int lengthGB=IDELEMS(I); // # of polys in the groebner basis |
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| 139 | int pCompCount; // # of terms in a poly |
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| 140 | poly aktpoly; |
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| 141 | int numvar = pVariables; // # of variables in a polynomial (or ring?) |
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| 142 | int leadexp[numvar]; // dirty hack of exp.vects |
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| 143 | int aktexp[numvar]; |
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| 144 | int cols,rows; // will contain the dimensions of the ineq matrix - deprecated by |
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| 145 | dd_rowrange ddrows; |
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| 146 | dd_colrange ddcols; |
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| 147 | dd_rowset ddredrows; // # of redundant rows in ddineq |
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| 148 | dd_rowset ddlinset; // the opposite |
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| 149 | dd_rowindex ddnewpos; // all to make dd_Canonicalize happy |
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| 150 | dd_NumberType ddnumb=dd_Real; //Number type |
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| 151 | dd_ErrorType dderr=dd_NoError; // |
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| 152 | // End of var declaration |
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| 153 | #ifdef gfan_DEBUG |
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| 154 | cout << "The Groebner basis has " << lengthGB << " elements" << endl; |
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| 155 | cout << "The current ring has " << numvar << " variables" << endl; |
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| 156 | #endif |
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| 157 | cols = numvar; |
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[198a339] | 158 | |
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[90adba8] | 159 | //Compute the # inequalities i.e. rows of the matrix |
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| 160 | rows=0; //Initialization |
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| 161 | for (int ii=0;ii<IDELEMS(I);ii++) |
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[03de21] | 162 | { |
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[90adba8] | 163 | aktpoly=(poly)I->m[ii]; |
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| 164 | rows=rows+pLength(aktpoly)-1; |
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[03de21] | 165 | } |
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[90adba8] | 166 | #ifdef gfan_DEBUG |
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| 167 | cout << "rows=" << rows << endl; |
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| 168 | cout << "Will create a " << rows << " x " << cols << " matrix to store inequalities" << endl; |
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| 169 | #endif |
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| 170 | dd_rowrange aktmatrixrow=0; // needed to store the diffs of the expvects in the rows of ddineq |
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| 171 | dd_set_global_constants(); |
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| 172 | ddrows=rows; |
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| 173 | ddcols=cols; |
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| 174 | dd_MatrixPtr ddineq; //Matrix to store the inequalities |
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| 175 | ddineq=dd_CreateMatrix(ddrows,ddcols+1); //The first col has to be 0 since cddlib checks for additive consts there |
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| 176 | |
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| 177 | // We loop through each g\in GB and compute the resulting inequalities |
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| 178 | for (int i=0; i<IDELEMS(I); i++) |
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| 179 | { |
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| 180 | aktpoly=(poly)I->m[i]; //get aktpoly as i-th component of I |
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| 181 | pCompCount=pLength(aktpoly); //How many terms does aktpoly consist of? |
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| 182 | cout << "Poly No. " << i << " has " << pCompCount << " components" << endl; |
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| 183 | |
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| 184 | int *v=(int *)omAlloc((numvar+1)*sizeof(int)); |
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| 185 | pGetExpV(aktpoly,v); //find the exp.vect in v[1],...,v[n], use pNext(p) |
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| 186 | |
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| 187 | //Store leadexp for aktpoly |
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| 188 | for (int kk=0;kk<numvar;kk++) |
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| 189 | { |
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| 190 | leadexp[kk]=v[kk+1]; |
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| 191 | //Since we need to know the difference of leadexp with the other expvects we do nothing here |
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| 192 | //but compute the diff below |
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| 193 | } |
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| 194 | |
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| 195 | |
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| 196 | while (pNext(aktpoly)!=NULL) //move to next term until NULL |
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| 197 | { |
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| 198 | aktpoly=pNext(aktpoly); |
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| 199 | pSetm(aktpoly); //doesn't seem to help anything |
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| 200 | pGetExpV(aktpoly,v); |
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| 201 | for (int kk=0;kk<numvar;kk++) |
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| 202 | { |
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| 203 | aktexp[kk]=v[kk+1]; |
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| 204 | //ineq[aktmatrixrow][kk]=leadexp[kk]-aktexp[kk]; //dito |
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| 205 | dd_set_si(ddineq->matrix[(dd_rowrange)aktmatrixrow][kk+1],leadexp[kk]-aktexp[kk]); //because of the 1st col being const 0 |
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| 206 | } |
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| 207 | aktmatrixrow=aktmatrixrow+1; |
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| 208 | }//while |
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| 209 | |
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| 210 | } //for |
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| 211 | |
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| 212 | //Maybe add another row to contain the constraints of the standard simplex? |
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[c5d8dd] | 213 | |
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[90adba8] | 214 | #ifdef gfan_DEBUG |
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| 215 | cout << "The inequality matrix is" << endl; |
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| 216 | dd_WriteMatrix(stdout, ddineq); |
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| 217 | #endif |
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[e2fb7a] | 218 | |
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[90adba8] | 219 | // The inequalities are now stored in ddineq |
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| 220 | // Next we check for superflous rows |
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| 221 | ddredrows = dd_RedundantRows(ddineq, &dderr); |
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| 222 | if (dderr!=dd_NoError) // did an error occur? |
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| 223 | { |
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| 224 | dd_WriteErrorMessages(stderr,dderr); //if so tell us |
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| 225 | } else |
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| 226 | { |
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| 227 | cout << "Redundant rows: "; |
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| 228 | set_fwrite(stdout, ddredrows); //otherwise print the redundant rows |
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| 229 | }//if dd_Error |
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| 230 | |
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| 231 | //Remove reduntant rows here! |
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| 232 | dd_MatrixCanonicalize(&ddineq, &ddlinset, &ddredrows, &ddnewpos, &dderr); |
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| 233 | ddrows = ddineq->rowsize; //Size of the matrix with redundancies removed |
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| 234 | ddcols = ddineq->colsize; |
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[aba53c] | 235 | #ifdef gfan_DEBUG |
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[90adba8] | 236 | cout << "Having removed redundancies, the normals now read:" << endl; |
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| 237 | dd_WriteMatrix(stdout,ddineq); |
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| 238 | cout << "Rows = " << ddrows << endl; |
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| 239 | cout << "Cols = " << ddcols << endl; |
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[aba53c] | 240 | #endif |
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[90adba8] | 241 | /*Write the normals into class facet*/ |
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| 242 | #ifdef gfan_DEBUG |
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| 243 | cout << "Creating list of normals" << endl; |
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| 244 | #endif |
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| 245 | /*The pointer *fRoot should be the return value of this function*/ |
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| 246 | facet *fRoot = new facet(); //instantiate new facet with intvec with numvar rows, one column and initial values all 0 |
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| 247 | facetPtr = fRoot; //set variable facetPtr of class gcone to first facet |
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| 248 | facet *fAct; //instantiate pointer to active facet |
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| 249 | fAct = fRoot; //This does not seem to do the trick. fRoot and fAct have to point to the same adress! |
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| 250 | std::cout << "fRoot = " << fRoot << ", fAct = " << fAct << endl; |
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| 251 | for (int kk = 0; kk<ddrows; kk++) |
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[aba53c] | 252 | { |
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[90adba8] | 253 | intvec *load = new intvec(numvar); //intvec to store a single facet normal that will then be stored via setFacetNormal |
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| 254 | for (int jj = 1; jj <ddcols; jj++) |
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| 255 | { |
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| 256 | double *foo; |
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| 257 | foo = (double*)ddineq->matrix[kk][jj]; //get entry from actual position |
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| 258 | #ifdef gfan_DEBUG |
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| 259 | std::cout << "fAct is " << *foo << " at " << fAct << std::endl; |
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| 260 | #endif |
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| 261 | (*load)[jj-1] = (int)*foo; //store typecasted entry at pos jj-1 of load |
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| 262 | //check for flipability here |
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| 263 | if (jj<ddcols) //Is this facet NOT the last facet? Writing while instead of if is a really bad idea :) |
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| 264 | { |
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| 265 | fAct->next = new facet(); //If so: instantiate new facet. Otherwise this->next=NULL due to the constructor |
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| 266 | fAct = fAct->next; //scary :) |
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| 267 | } |
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| 268 | }//for jj<ddcols |
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| 269 | /*Now load should be full and we can call setFacetNormal*/ |
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| 270 | fAct->setFacetNormal(load); |
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| 271 | fAct->printNormal(); |
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[aba53c] | 272 | } |
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[90adba8] | 273 | /* |
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| 274 | Now we should have a linked list containing the facet normals of those facets that are |
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| 275 | -irredundant |
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| 276 | -flipable |
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| 277 | Adressing is done via *facetPtr |
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| 278 | */ |
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| 279 | |
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| 280 | //Clean up but don't delete the return value! (Whatever it will turn out to be) |
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| 281 | dd_FreeMatrix(ddineq); |
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| 282 | set_free(ddredrows); |
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| 283 | free(ddnewpos); |
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| 284 | set_free(ddlinset); |
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| 285 | dd_free_global_constants(); |
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| 286 | |
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| 287 | }//method getConeNormals(ideal I) |
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| 288 | |
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[798f721] | 289 | /** \brief Compute the Groebner Basis on the other side of a shared facet |
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| 290 | * |
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| 291 | * Implements algorithm 4.3.2 from Anders' thesis. |
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| 292 | * As shown there it is not necessary to compute an interior point. The knowledge of the facet normal |
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| 293 | * suffices. A term \f$ x^\gamma \f$ of \f$ g \f$ is in \f$ in_\omega(g) \f$ iff \f$ \gamma - leadexp(g)\f$ |
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| 294 | * is parallel to \f$ leadexp(g) \f$ |
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| 295 | * Checking for parallelity is done by computing the rank of the matrix consisting of the vectors in question. |
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| 296 | * Another possibility would be to compute an interior point of the facet and taking all terms having the same |
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| 297 | * weight with respect to this interior point. |
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| 298 | *\param ideal, facet |
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| 299 | */ |
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| 300 | void flip(ideal I, facet *f) //Compute "the other side" |
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| 301 | { |
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| 302 | /*1st step: Compute the initial ideal*/ |
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| 303 | map mapping; |
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| 304 | idhdl h; |
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| 305 | ideal image; |
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| 306 | mapping=IDMAP(h); |
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| 307 | image=idInit(1,1); |
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| 308 | image=maGetPreimage(currRing,mapping,image); |
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| 309 | } |
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[90adba8] | 310 | |
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| 311 | /** \brief Compute a Groebner Basis |
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| 312 | * |
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| 313 | * Computes the Groebner basis and stores the result in this->gcBasis |
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| 314 | *\param ideal |
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| 315 | *\return void |
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| 316 | */ |
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| 317 | void getGB(ideal inputIdeal) |
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| 318 | { |
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| 319 | ideal gb; |
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| 320 | gb=kStd(inputIdeal,NULL,testHomog,NULL); |
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| 321 | idSkipZeroes(gb); |
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| 322 | this->gcBasis=gb; //write the GB into gcBasis |
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| 323 | } |
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| 324 | |
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| 325 | ideal GenGrbWlk(ideal, ideal); //Implementation of the Generic Groebner Walk. Needed for a) Computing the sink and b) finding search facets |
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| 326 | |
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[e2fb7a] | 327 | |
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[90adba8] | 328 | };//class gcone |
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| 329 | |
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| 330 | /* |
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| 331 | function getGB incorporated into class gcone with rev 1.24 |
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| 332 | */ |
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| 333 | |
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| 334 | //DEPRECATED since rev 1.24 with existence of gcone::getConeNormals(ideal I); |
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| 335 | //Kept for unknown reasons ;) |
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| 336 | facet *getConeNormals(ideal I) |
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| 337 | { |
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| 338 | return NULL; |
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[2c6535] | 339 | } |
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| 340 | |
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| 341 | ideal gfan(ideal inputIdeal) |
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| 342 | { |
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[54248e] | 343 | int numvar = pVariables; |
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| 344 | |
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[b3e45f] | 345 | #ifdef gfan_DEBUG |
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[fc4f9a] | 346 | cout << "Now in subroutine gfan" << endl; |
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[b3e45f] | 347 | #endif |
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[90adba8] | 348 | ring inputRing=currRing; // The ring the user entered |
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| 349 | ring rootRing; // The ring associated to the target ordering |
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[b3e45f] | 350 | ideal res; |
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[90adba8] | 351 | //matrix ineq; //Matrix containing the boundary inequalities |
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[9f9b142] | 352 | facet *fRoot; |
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| 353 | |
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[90adba8] | 354 | /* |
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| 355 | 1. Select target order, say dp. |
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| 356 | 2. Compute GB of inputIdeal wrt target order -> newRing, setCurrRing etc... |
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| 357 | 3. getConeNormals |
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| 358 | */ |
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| 359 | |
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[9f9b142] | 360 | |
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[90adba8] | 361 | /* Construct a new ring which will serve as our root |
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| 362 | Does not yet work as expected. Will work fine with order dp,Dp but otherwise hangs in getGB |
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| 363 | */ |
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[9f9b142] | 364 | rootRing=rCopy0(currRing); |
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[53e33d9] | 365 | rootRing->order[0]=ringorder_dp; |
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[9f9b142] | 366 | rComplete(rootRing); |
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| 367 | rChangeCurrRing(rootRing); |
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[90adba8] | 368 | ideal rootIdeal; |
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| 369 | /* Fetch the inputIdeal into our rootRing */ |
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| 370 | map m=(map)idInit(IDELEMS(inputIdeal),0); |
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| 371 | rootIdeal=fast_map(inputIdeal,inputRing,(ideal)m, currRing); |
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| 372 | #ifdef gfan_DEBUG |
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| 373 | cout << "Root ideal is " << endl; |
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| 374 | idPrint(rootIdeal); |
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[9f9b142] | 375 | cout << "The current ring is " << endl; |
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| 376 | rWrite(rootRing); |
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[90adba8] | 377 | cout << endl; |
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| 378 | #endif |
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| 379 | |
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[9f9b142] | 380 | gcone *gcRoot = new gcone(); //Instantiate the sink |
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| 381 | gcone *gcAct; |
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| 382 | gcAct = gcRoot; |
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[90adba8] | 383 | gcAct->getGB(inputIdeal); |
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| 384 | gcAct->getConeNormals(gcAct->gcBasis); //hopefully compute the normals |
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[798f721] | 385 | |
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[90adba8] | 386 | /*Now it is time to compute the search facets, respectively start the reverse search. |
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[798f721] | 387 | But since we are in the root all facets should be search facets. IS THIS TRUE? |
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[90adba8] | 388 | MIND: AS OF NOW, THE LIST OF FACETS IS NOT PURGED OF NON-FLIPPAPLE FACETS |
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| 389 | */ |
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[9f9b142] | 390 | |
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[90adba8] | 391 | /*As of now extra.cc expects gfan to return type ideal. Probably this will change in near future. |
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| 392 | The return type will then be of type LIST_CMD |
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| 393 | Assume gfan has finished, thus we have enumerated all the cones |
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| 394 | Create an array of size of #cones. Let each entry in the array contain a pointer to the respective |
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| 395 | Groebner Basis and merge this somehow with LIST_CMD |
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| 396 | => Count the cones! |
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[fc4f9a] | 397 | */ |
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[90adba8] | 398 | |
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| 399 | res=gcAct->gcBasis; |
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| 400 | //cout << fRoot << endl; |
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[b3e45f] | 401 | return res; |
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[90adba8] | 402 | //return GBlist; |
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[d3398c] | 403 | } |
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[9f9b142] | 404 | /* |
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| 405 | Since gfan.cc is #included from extra.cc there must not be a int main(){} here |
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| 406 | */ |
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[34fcf8] | 407 | #endif |
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