| 1 | /* |
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| 2 | Compute the Groebner fan of an ideal |
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| 3 | $Author: monerjan $ |
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| 4 | $Date: 2009-05-05 15:15:02 $ |
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| 5 | $Header: /exports/cvsroot-2/cvsroot/kernel/gfan.cc,v 1.45 2009-05-05 15:15:02 monerjan Exp $ |
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| 6 | $Id: gfan.cc,v 1.45 2009-05-05 15:15:02 monerjan Exp $ |
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| 7 | */ |
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| 8 | |
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| 9 | #include "mod2.h" |
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| 10 | |
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| 11 | #ifdef HAVE_GFAN |
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| 12 | |
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| 13 | #include "kstd1.h" |
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| 14 | #include "kutil.h" |
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| 15 | #include "intvec.h" |
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| 16 | #include "polys.h" |
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| 17 | #include "ideals.h" |
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| 18 | #include "kmatrix.h" |
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| 19 | #include "fast_maps.h" //Mapping of ideals |
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| 20 | #include "maps.h" |
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| 21 | #include "ring.h" |
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| 22 | #include "prCopy.h" |
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| 23 | #include <iostream.h> //deprecated |
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| 24 | #include <bitset> |
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| 25 | |
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| 26 | /*remove the following at your own risk*/ |
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| 27 | #ifndef GMPRATIONAL |
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| 28 | #define GMPRATIONAL |
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| 29 | #endif |
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| 30 | |
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| 31 | //Hacks for different working places |
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| 32 | #define ITWM |
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| 33 | |
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| 34 | #ifdef UNI |
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| 35 | #include "/users/urmel/alggeom/monerjan/cddlib/include/setoper.h" //Support for cddlib. Dirty hack |
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| 36 | #include "/users/urmel/alggeom/monerjan/cddlib/include/cdd.h" |
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| 37 | #endif |
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| 38 | |
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| 39 | #ifdef HOME |
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| 40 | #include "/home/momo/studium/diplomarbeit/cddlib/include/setoper.h" |
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| 41 | #include "/home/momo/studium/diplomarbeit/cddlib/include/cdd.h" |
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| 42 | #endif |
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| 43 | |
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| 44 | #ifdef ITWM |
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| 45 | #include "/u/slg/monerjan/cddlib/include/setoper.h" |
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| 46 | #include "/u/slg/monerjan/cddlib/include/cdd.h" |
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| 47 | #include "/u/slg/monerjan/cddlib/include/cddmp.h" |
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| 48 | #endif |
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| 49 | |
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| 50 | #ifndef gfan_DEBUG |
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| 51 | #define gfan_DEBUG |
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| 52 | #endif |
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| 53 | |
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| 54 | //#include gcone.h |
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| 55 | |
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| 56 | /** |
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| 57 | *\brief Class facet |
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| 58 | * Implements the facet structure as a linked list |
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| 59 | * |
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| 60 | */ |
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| 61 | class facet |
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| 62 | { |
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| 63 | private: |
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| 64 | /** \brief Inner normal of the facet, describing it uniquely up to isomorphism */ |
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| 65 | intvec *fNormal; |
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| 66 | |
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| 67 | /** \brief The Groebner basis on the other side of a shared facet |
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| 68 | * |
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| 69 | * In order not to have to compute the flipped GB twice we store the basis we already get |
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| 70 | * when identifying search facets. Thus in the next step of the reverse search we can |
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| 71 | * just copy the old cone and update the facet and the gcBasis. |
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| 72 | * facet::flibGB is set via facet::setFlipGB() and printed via facet::printFlipGB |
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| 73 | */ |
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| 74 | ideal flipGB; //The Groebner Basis on the other side, computed via gcone::flip |
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| 75 | |
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| 76 | |
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| 77 | public: |
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| 78 | //bool isFlippable; //flippable facet? Want to have cone->isflippable.facet[i] |
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| 79 | bool isIncoming; //Is the facet incoming or outgoing? |
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| 80 | facet *next; //Pointer to next facet |
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| 81 | |
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| 82 | /** The default constructor. Do I need a constructor of type facet(intvec)? */ |
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| 83 | facet() |
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| 84 | { |
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| 85 | // Pointer to next facet. */ |
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| 86 | /* Defaults to NULL. This way there is no need to check explicitly */ |
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| 87 | this->next=NULL; |
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| 88 | } |
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| 89 | |
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| 90 | /** The default destructor */ |
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| 91 | ~facet(){;} |
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| 92 | |
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| 93 | /** Stores the facet normal \param intvec*/ |
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| 94 | void setFacetNormal(intvec *iv) |
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| 95 | { |
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| 96 | this->fNormal = ivCopy(iv); |
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| 97 | //return; |
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| 98 | } |
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| 99 | |
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| 100 | /** Hopefully returns the facet normal */ |
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| 101 | intvec *getFacetNormal() |
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| 102 | { |
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| 103 | //this->fNormal->show(); cout << endl; |
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| 104 | return this->fNormal; |
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| 105 | } |
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| 106 | |
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| 107 | /** Method to print the facet normal*/ |
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| 108 | void printNormal() |
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| 109 | { |
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| 110 | fNormal->show(); |
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| 111 | } |
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| 112 | |
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| 113 | /** Store the flipped GB*/ |
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| 114 | void setFlipGB(ideal I) |
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| 115 | { |
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| 116 | this->flipGB=I; |
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| 117 | } |
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| 118 | |
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| 119 | /** Return the flipped GB*/ |
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| 120 | ideal getFlipGB() |
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| 121 | { |
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| 122 | return this->flipGB; |
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| 123 | } |
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| 124 | |
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| 125 | /** Print the flipped GB*/ |
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| 126 | void printFlipGB() |
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| 127 | { |
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| 128 | idShow(this->flipGB); |
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| 129 | } |
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| 130 | |
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| 131 | /*bool isFlippable(intvec &load) |
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| 132 | { |
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| 133 | bool res=TRUE; |
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| 134 | int jj; |
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| 135 | for (int jj = 0; jj<load.length(); jj++) |
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| 136 | { |
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| 137 | intvec *ivCanonical = new intvec(load.length()); |
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| 138 | (*ivCanonical)[jj]=1; |
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| 139 | if (ivMult(&load,ivCanonical)<0) |
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| 140 | { |
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| 141 | res=FALSE; |
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| 142 | break; |
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| 143 | } |
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| 144 | } |
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| 145 | return res; |
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| 146 | |
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| 147 | /*while (dotProduct(load,ivCanonical)>=0) |
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| 148 | { |
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| 149 | if (jj!=this->numVars) |
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| 150 | { |
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| 151 | intvec *ivCanonical = new intvec(this->numVars); |
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| 152 | (*ivCanonical)[jj]=1; |
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| 153 | res=TRUE; |
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| 154 | jj += 1; |
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| 155 | } |
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| 156 | } |
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| 157 | if (jj==this->numVars) |
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| 158 | { |
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| 159 | delete ivCanonical; |
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| 160 | return FALSE; |
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| 161 | } |
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| 162 | else |
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| 163 | { |
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| 164 | delete ivCanonical; |
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| 165 | return TRUE; |
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| 166 | }*/ |
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| 167 | }//bool isFlippable(facet &f) |
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| 168 | |
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| 169 | |
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| 170 | friend class gcone; //Bad style |
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| 171 | }; |
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| 172 | |
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| 173 | /** |
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| 174 | *\brief Implements the cone structure |
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| 175 | * |
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| 176 | * A cone is represented by a linked list of facet normals |
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| 177 | * @see facet |
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| 178 | */ |
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| 179 | /*class gcone |
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| 180 | finally this should become s.th. like gconelib.{h,cc} to provide an API |
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| 181 | */ |
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| 182 | class gcone |
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| 183 | { |
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| 184 | private: |
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| 185 | int numFacets; //#of facets of the cone |
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| 186 | ring rootRing; //good to know this -> generic walk |
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| 187 | ideal inputIdeal; //the original |
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| 188 | ring baseRing; //the basering of the cone |
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| 189 | /* TODO in order to save memory use pointers to rootRing and inputIdeal instead */ |
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| 190 | intvec *ivIntPt; //an interior point of the cone |
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| 191 | |
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| 192 | public: |
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| 193 | /** \brief Default constructor. |
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| 194 | * |
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| 195 | * Initialises this->next=NULL and this->facetPtr=NULL |
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| 196 | */ |
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| 197 | gcone() |
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| 198 | { |
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| 199 | this->next=NULL; |
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| 200 | this->facetPtr=NULL; |
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| 201 | this->baseRing=currRing; |
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| 202 | } |
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| 203 | |
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| 204 | /** \brief Constructor with ring and ideal |
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| 205 | * |
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| 206 | * This constructor takes the root ring and the root ideal as parameters and stores |
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| 207 | * them in the private members gcone::rootRing and gcone::inputIdeal |
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| 208 | */ |
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| 209 | gcone(ring r, ideal I) |
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| 210 | { |
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| 211 | this->next=NULL; |
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| 212 | this->facetPtr=NULL; |
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| 213 | this->rootRing=r; |
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| 214 | this->inputIdeal=I; |
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| 215 | this->baseRing=currRing; |
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| 216 | } |
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| 217 | |
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| 218 | /** \brief Copy constructor |
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| 219 | * |
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| 220 | * Copies one cone, sets this->gcBasis to the flipped GB and reverses the |
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| 221 | * direction of the according facet normal |
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| 222 | */ |
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| 223 | gcone(const gcone& gc) |
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| 224 | { |
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| 225 | this->next=NULL; |
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| 226 | this->numVars=gc.numVars; |
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| 227 | facet *fAct= new facet(); |
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| 228 | this->facetPtr=fAct; |
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| 229 | |
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| 230 | intvec *ivtmp = new intvec(this->numVars); |
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| 231 | ivtmp = gc.facetPtr->getFacetNormal(); |
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| 232 | ivtmp->show(); |
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| 233 | |
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| 234 | ideal gb; |
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| 235 | gb=gc.facetPtr->getFlipGB(); |
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| 236 | this->gcBasis=gb;//gc.facetPtr->getFlipGB(); //this cone's GB is the flipped GB |
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| 237 | idShow(this->gcBasis); |
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| 238 | |
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| 239 | /*Reverse direction of the facet normal to make it an inner normal*/ |
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| 240 | for (int ii=0; ii<this->numVars;ii++) |
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| 241 | { |
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| 242 | (*ivtmp)[ii]=-(*ivtmp)[ii]; |
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| 243 | } |
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| 244 | //ivtmp->show(); cout << endl; |
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| 245 | fAct->setFacetNormal(ivtmp); |
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| 246 | //fAct->printNormal();cout << endl; |
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| 247 | //ivtmp->show();cout << endl; |
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| 248 | } |
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| 249 | |
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| 250 | /** \brief Default destructor */ |
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| 251 | ~gcone(){;} //destructor |
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| 252 | |
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| 253 | /** Pointer to the first facet */ |
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| 254 | facet *facetPtr; //Will hold the adress of the first facet; set by gcone::getConeNormals |
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| 255 | |
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| 256 | /** # of variables in the ring */ |
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| 257 | int numVars; //#of variables in the ring |
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| 258 | |
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| 259 | /** Contains the Groebner basis of the cone. Is set by gcone::getGB(ideal I)*/ |
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| 260 | ideal gcBasis; //GB of the cone, set by gcone::getGB(); |
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| 261 | gcone *next; //Pointer to *previous* cone in search tree |
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| 262 | |
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| 263 | /** \brief Set the interior point of a cone */ |
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| 264 | void setIntPoint(intvec *iv) |
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| 265 | { |
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| 266 | this->ivIntPt=ivCopy(iv); |
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| 267 | } |
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| 268 | |
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| 269 | /** \brief Return the interior point */ |
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| 270 | intvec *getIntPoint() |
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| 271 | { |
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| 272 | return this->ivIntPt; |
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| 273 | } |
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| 274 | |
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| 275 | void showIntPoint() |
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| 276 | { |
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| 277 | ivIntPt->show(); |
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| 278 | } |
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| 279 | |
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| 280 | /** \brief Compute the normals of the cone |
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| 281 | * |
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| 282 | * This method computes a representation of the cone in terms of facet normals. It takes an ideal |
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| 283 | * as its input. Redundancies are automatically removed using cddlib's dd_MatrixCanonicalize. |
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| 284 | * Other methods for redundancy checkings might be implemented later. See Anders' diss p.44. |
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| 285 | * 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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| 286 | * each row to represent an inequality of type const+x1+...+xn <= 0. While computing the normals we come across |
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| 287 | * the set \f$ \partial\mathcal{G} \f$ which we might store for later use. C.f p71 of journal |
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| 288 | * As a result of this procedure the pointer facetPtr points to the first facet of the cone. |
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| 289 | * |
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| 290 | * Optionally, if the parameter bool compIntPoint is set to TRUE the method will also compute |
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| 291 | * an interior point of the cone. |
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| 292 | */ |
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| 293 | void getConeNormals(ideal const &I, bool compIntPoint=FALSE) |
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| 294 | { |
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| 295 | #ifdef gfan_DEBUG |
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| 296 | std::cout << "*** Computing Inequalities... ***" << std::endl; |
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| 297 | #endif |
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| 298 | //All variables go here - except ineq matrix and *v, see below |
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| 299 | int lengthGB=IDELEMS(I); // # of polys in the groebner basis |
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| 300 | int pCompCount; // # of terms in a poly |
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| 301 | poly aktpoly; |
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| 302 | int numvar = pVariables; // # of variables in a polynomial (or ring?) |
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| 303 | int leadexp[numvar]; // dirty hack of exp.vects |
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| 304 | int aktexp[numvar]; |
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| 305 | int cols,rows; // will contain the dimensions of the ineq matrix - deprecated by |
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| 306 | dd_rowrange ddrows; |
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| 307 | dd_colrange ddcols; |
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| 308 | dd_rowset ddredrows; // # of redundant rows in ddineq |
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| 309 | dd_rowset ddlinset; // the opposite |
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| 310 | dd_rowindex ddnewpos; // all to make dd_Canonicalize happy |
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| 311 | dd_NumberType ddnumb=dd_Integer; //Number type |
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| 312 | dd_ErrorType dderr=dd_NoError; // |
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| 313 | // End of var declaration |
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| 314 | #ifdef gfan_DEBUG |
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| 315 | cout << "The Groebner basis has " << lengthGB << " elements" << endl; |
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| 316 | cout << "The current ring has " << numvar << " variables" << endl; |
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| 317 | #endif |
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| 318 | cols = numvar; |
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| 319 | |
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| 320 | //Compute the # inequalities i.e. rows of the matrix |
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| 321 | rows=0; //Initialization |
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| 322 | for (int ii=0;ii<IDELEMS(I);ii++) |
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| 323 | { |
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| 324 | aktpoly=(poly)I->m[ii]; |
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| 325 | rows=rows+pLength(aktpoly)-1; |
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| 326 | } |
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| 327 | #ifdef gfan_DEBUG |
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| 328 | cout << "rows=" << rows << endl; |
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| 329 | cout << "Will create a " << rows << " x " << cols << " matrix to store inequalities" << endl; |
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| 330 | #endif |
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| 331 | dd_rowrange aktmatrixrow=0; // needed to store the diffs of the expvects in the rows of ddineq |
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| 332 | dd_set_global_constants(); |
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| 333 | ddrows=rows; |
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| 334 | ddcols=cols; |
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| 335 | dd_MatrixPtr ddineq; //Matrix to store the inequalities |
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| 336 | ddineq=dd_CreateMatrix(ddrows,ddcols+1); //The first col has to be 0 since cddlib checks for additive consts there |
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| 337 | |
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| 338 | // We loop through each g\in GB and compute the resulting inequalities |
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| 339 | for (int i=0; i<IDELEMS(I); i++) |
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| 340 | { |
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| 341 | aktpoly=(poly)I->m[i]; //get aktpoly as i-th component of I |
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| 342 | pCompCount=pLength(aktpoly); //How many terms does aktpoly consist of? |
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| 343 | cout << "Poly No. " << i << " has " << pCompCount << " components" << endl; |
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| 344 | |
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| 345 | int *v=(int *)omAlloc((numvar+1)*sizeof(int)); |
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| 346 | pGetExpV(aktpoly,v); //find the exp.vect in v[1],...,v[n], use pNext(p) |
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| 347 | |
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| 348 | //Store leadexp for aktpoly |
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| 349 | for (int kk=0;kk<numvar;kk++) |
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| 350 | { |
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| 351 | leadexp[kk]=v[kk+1]; |
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| 352 | //Since we need to know the difference of leadexp with the other expvects we do nothing here |
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| 353 | //but compute the diff below |
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| 354 | } |
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| 355 | |
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| 356 | |
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| 357 | while (pNext(aktpoly)!=NULL) //move to next term until NULL |
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| 358 | { |
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| 359 | aktpoly=pNext(aktpoly); |
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| 360 | pSetm(aktpoly); //doesn't seem to help anything |
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| 361 | pGetExpV(aktpoly,v); |
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| 362 | for (int kk=0;kk<numvar;kk++) |
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| 363 | { |
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| 364 | aktexp[kk]=v[kk+1]; |
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| 365 | //ineq[aktmatrixrow][kk]=leadexp[kk]-aktexp[kk]; //dito |
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| 366 | 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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| 367 | } |
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| 368 | aktmatrixrow=aktmatrixrow+1; |
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| 369 | }//while |
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| 370 | |
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| 371 | } //for |
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| 372 | |
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| 373 | //Maybe add another row to contain the constraints of the standard simplex? |
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| 374 | |
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| 375 | #ifdef gfan_DEBUG |
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| 376 | cout << "The inequality matrix is" << endl; |
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| 377 | dd_WriteMatrix(stdout, ddineq); |
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| 378 | #endif |
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| 379 | |
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| 380 | // The inequalities are now stored in ddineq |
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| 381 | // Next we check for superflous rows |
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| 382 | ddredrows = dd_RedundantRows(ddineq, &dderr); |
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| 383 | if (dderr!=dd_NoError) // did an error occur? |
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| 384 | { |
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| 385 | dd_WriteErrorMessages(stderr,dderr); //if so tell us |
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| 386 | } else |
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| 387 | { |
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| 388 | cout << "Redundant rows: "; |
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| 389 | set_fwrite(stdout, ddredrows); //otherwise print the redundant rows |
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| 390 | }//if dd_Error |
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| 391 | |
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| 392 | //Remove reduntant rows here! |
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| 393 | dd_MatrixCanonicalize(&ddineq, &ddlinset, &ddredrows, &ddnewpos, &dderr); |
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| 394 | ddrows = ddineq->rowsize; //Size of the matrix with redundancies removed |
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| 395 | ddcols = ddineq->colsize; |
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| 396 | #ifdef gfan_DEBUG |
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| 397 | cout << "Having removed redundancies, the normals now read:" << endl; |
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| 398 | dd_WriteMatrix(stdout,ddineq); |
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| 399 | cout << "Rows = " << ddrows << endl; |
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| 400 | cout << "Cols = " << ddcols << endl; |
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| 401 | #endif |
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| 402 | |
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| 403 | /*Write the normals into class facet*/ |
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| 404 | #ifdef gfan_DEBUG |
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| 405 | cout << "Creating list of normals" << endl; |
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| 406 | #endif |
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| 407 | /*The pointer *fRoot should be the return value of this function*/ |
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| 408 | facet *fRoot = new facet(); //instantiate new facet |
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| 409 | this->facetPtr = fRoot; //set variable facetPtr of class gcone to first facet |
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| 410 | facet *fAct; //instantiate pointer to active facet |
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| 411 | fAct = fRoot; //Seems to do the trick. fRoot and fAct have to point to the same adress! |
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| 412 | std::cout << "fRoot = " << fRoot << ", fAct = " << fAct << endl; |
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| 413 | for (int kk = 0; kk<ddrows; kk++) |
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| 414 | { |
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| 415 | intvec *load = new intvec(numvar); //intvec to store a single facet normal that will then be stored via setFacetNormal |
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| 416 | for (int jj = 1; jj <ddcols; jj++) |
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| 417 | { |
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| 418 | #ifdef GMPRATIONAL |
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| 419 | double foo; |
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| 420 | foo = mpq_get_d(ddineq->matrix[kk][jj]); |
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| 421 | /*#ifdef gfan_DEBUG |
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| 422 | std::cout << "fAct is " << foo << " at " << fAct << std::endl; |
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| 423 | #endif*/ |
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| 424 | (*load)[jj-1] = (int)foo; //store typecasted entry at pos jj-1 of load |
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| 425 | #endif |
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| 426 | #ifndef GMPRATIONAL |
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| 427 | double *foo; |
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| 428 | foo = (double*)ddineq->matrix[kk][jj]; //get entry from actual position#endif |
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| 429 | /*#ifdef gfan_DEBUG |
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| 430 | std::cout << "fAct is " << *foo << " at " << fAct << std::endl; |
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| 431 | #endif*/ |
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| 432 | (*load)[jj-1] = (int)*foo; //store typecasted entry at pos jj-1 of load |
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| 433 | #endif //GMPRATIONAL |
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| 434 | |
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| 435 | |
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| 436 | //(*load)[jj-1] = (int)foo; //store typecasted entry at pos jj-1 of load |
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| 437 | //check for flipability here |
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| 438 | if (jj<ddcols) //Is this facet NOT the last facet? Writing while instead of if is a really bad idea :) |
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| 439 | { |
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| 440 | //fAct->next = new facet(); //If so: instantiate new facet. Otherwise this->next=NULL due to the constructor |
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| 441 | } |
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| 442 | }//for (int jj = 1; jj <ddcols; jj++) |
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| 443 | /*Quick'n'dirty hack for flippability*/ |
|---|
| 444 | bool isFlippable=FALSE; |
|---|
| 445 | //NOTE BUG HERE |
|---|
| 446 | /* The flippability check is wrong! |
|---|
| 447 | (1,-4) will pass, but (-1,7) will not. |
|---|
| 448 | REWRITE THIS |
|---|
| 449 | */ |
|---|
| 450 | /*for (int jj = 0; jj<this->numVars; jj++) |
|---|
| 451 | { |
|---|
| 452 | intvec *ivCanonical = new intvec(this->numVars); |
|---|
| 453 | (*ivCanonical)[jj]=1; |
|---|
| 454 | if (dotProduct(load,ivCanonical)>=0) |
|---|
| 455 | { |
|---|
| 456 | isFlippable=FALSE; |
|---|
| 457 | } |
|---|
| 458 | else |
|---|
| 459 | { |
|---|
| 460 | isFlippable=TRUE; |
|---|
| 461 | } |
|---|
| 462 | delete ivCanonical; |
|---|
| 463 | }//for (int jj = 0; jj<this->numVars; jj++) |
|---|
| 464 | */ |
|---|
| 465 | for (int jj = 0; jj<load->length(); jj++) |
|---|
| 466 | { |
|---|
| 467 | intvec *ivCanonical = new intvec(load->length()); |
|---|
| 468 | (*ivCanonical)[jj]=1; |
|---|
| 469 | if (dotProduct(load,ivCanonical)<0) |
|---|
| 470 | { |
|---|
| 471 | isFlippable=TRUE; |
|---|
| 472 | break; //URGHS |
|---|
| 473 | } |
|---|
| 474 | } |
|---|
| 475 | if (isFlippable==FALSE) |
|---|
| 476 | { |
|---|
| 477 | cout << "Ignoring facet"; |
|---|
| 478 | load->show(); |
|---|
| 479 | //fAct->next=NULL; |
|---|
| 480 | } |
|---|
| 481 | else |
|---|
| 482 | { /*Now load should be full and we can call setFacetNormal*/ |
|---|
| 483 | fAct->setFacetNormal(load); |
|---|
| 484 | fAct->next = new facet(); |
|---|
| 485 | //fAct->printNormal(); |
|---|
| 486 | fAct=fAct->next; //this should definitely not be called in the above while-loop :D |
|---|
| 487 | }//if (isFlippable==FALSE) |
|---|
| 488 | delete load; |
|---|
| 489 | }//for (int kk = 0; kk<ddrows; kk++) |
|---|
| 490 | /* |
|---|
| 491 | Now we should have a linked list containing the facet normals of those facets that are |
|---|
| 492 | -irredundant |
|---|
| 493 | -flipable |
|---|
| 494 | Adressing is done via *facetPtr |
|---|
| 495 | */ |
|---|
| 496 | |
|---|
| 497 | if (compIntPoint==TRUE) |
|---|
| 498 | { |
|---|
| 499 | intvec *iv = new intvec(this->numVars); |
|---|
| 500 | interiorPoint(ddineq, *iv); |
|---|
| 501 | this->setIntPoint(iv); //stores the interior point in gcone::ivIntPt |
|---|
| 502 | delete iv; |
|---|
| 503 | } |
|---|
| 504 | |
|---|
| 505 | //Clean up but don't delete the return value! (Whatever it will turn out to be) |
|---|
| 506 | |
|---|
| 507 | dd_FreeMatrix(ddineq); |
|---|
| 508 | set_free(ddredrows); |
|---|
| 509 | free(ddnewpos); |
|---|
| 510 | set_free(ddlinset); |
|---|
| 511 | dd_free_global_constants(); |
|---|
| 512 | |
|---|
| 513 | }//method getConeNormals(ideal I) |
|---|
| 514 | |
|---|
| 515 | |
|---|
| 516 | /** \brief Compute the Groebner Basis on the other side of a shared facet |
|---|
| 517 | * |
|---|
| 518 | * Implements algorithm 4.3.2 from Anders' thesis. |
|---|
| 519 | * As shown there it is not necessary to compute an interior point. The knowledge of the facet normal |
|---|
| 520 | * suffices. A term \f$ x^\gamma \f$ of \f$ g \f$ is in \f$ in_\omega(g) \f$ iff \f$ \gamma - leadexp(g)\f$ |
|---|
| 521 | * is parallel to \f$ leadexp(g) \f$ |
|---|
| 522 | * Parallelity is checked using basic linear algebra. See gcone::isParallel. |
|---|
| 523 | * Other possibilities include computing the rank of the matrix consisting of the vectors in question and |
|---|
| 524 | * computing an interior point of the facet and taking all terms having the same weight with respect |
|---|
| 525 | * to this interior point. |
|---|
| 526 | *\param ideal, facet |
|---|
| 527 | * Input: a marked,reduced Groebner basis and a facet |
|---|
| 528 | */ |
|---|
| 529 | void flip(ideal gb, facet *f) //Compute "the other side" |
|---|
| 530 | { |
|---|
| 531 | intvec *fNormal = new intvec(this->numVars); //facet normal, check for parallelity |
|---|
| 532 | fNormal = f->getFacetNormal(); //read this->fNormal; |
|---|
| 533 | #ifdef gfan_DEBUG |
|---|
| 534 | std::cout << "===" << std::endl; |
|---|
| 535 | std::cout << "running gcone::flip" << std::endl; |
|---|
| 536 | std::cout << "fNormal="; |
|---|
| 537 | fNormal->show(); |
|---|
| 538 | std::cout << std::endl; |
|---|
| 539 | #endif |
|---|
| 540 | /*1st step: Compute the initial ideal*/ |
|---|
| 541 | poly initialFormElement[IDELEMS(gb)]; //array of #polys in GB to store initial form |
|---|
| 542 | ideal initialForm=idInit(IDELEMS(gb),this->gcBasis->rank); |
|---|
| 543 | poly aktpoly; |
|---|
| 544 | intvec *check = new intvec(this->numVars); //array to store the difference of LE and v |
|---|
| 545 | |
|---|
| 546 | for (int ii=0;ii<IDELEMS(gb);ii++) |
|---|
| 547 | { |
|---|
| 548 | aktpoly = (poly)gb->m[ii]; |
|---|
| 549 | int *v=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 550 | int *leadExpV=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 551 | pGetExpV(aktpoly,leadExpV); //find the leading exponent in leadExpV[1],...,leadExpV[n], use pNext(p) |
|---|
| 552 | initialFormElement[ii]=pHead(aktpoly); |
|---|
| 553 | |
|---|
| 554 | while(pNext(aktpoly)!=NULL) /*loop trough terms and check for parallelity*/ |
|---|
| 555 | { |
|---|
| 556 | aktpoly=pNext(aktpoly); //next term |
|---|
| 557 | pSetm(aktpoly); |
|---|
| 558 | pGetExpV(aktpoly,v); |
|---|
| 559 | /* Convert (int)v into (intvec)check */ |
|---|
| 560 | for (int jj=0;jj<this->numVars;jj++) |
|---|
| 561 | { |
|---|
| 562 | //cout << "v["<<jj+1<<"]="<<v[jj+1]<<endl; |
|---|
| 563 | //cout << "leadExpV["<<jj+1<<"]="<<leadExpV[jj+1]<<endl; |
|---|
| 564 | (*check)[jj]=v[jj+1]-leadExpV[jj+1]; |
|---|
| 565 | } |
|---|
| 566 | #ifdef gfan_DEBUG |
|---|
| 567 | cout << "check="; |
|---|
| 568 | check->show(); |
|---|
| 569 | cout << endl; |
|---|
| 570 | #endif |
|---|
| 571 | //TODO why not *check, *fNormal???? |
|---|
| 572 | if (isParallel(*check,*fNormal)) //pass *check when |
|---|
| 573 | { |
|---|
| 574 | cout << "Parallel vector found, adding to initialFormElement" << endl; |
|---|
| 575 | initialFormElement[ii] = pAdd(pCopy(initialFormElement[ii]),(poly)pHead(aktpoly)); |
|---|
| 576 | } |
|---|
| 577 | }//while |
|---|
| 578 | #ifdef gfan_DEBUG |
|---|
| 579 | cout << "Initial Form="; |
|---|
| 580 | pWrite(initialFormElement[ii]); |
|---|
| 581 | cout << "---" << endl; |
|---|
| 582 | #endif |
|---|
| 583 | /*Now initialFormElement must be added to (ideal)initialForm */ |
|---|
| 584 | initialForm->m[ii]=initialFormElement[ii]; |
|---|
| 585 | }//for |
|---|
| 586 | //f->setFlipGB(initialForm); //FIXME PROBABLY WRONG TO STORE HERE SINCE INA!=flibGB |
|---|
| 587 | #ifdef gfan_DEBUG |
|---|
| 588 | cout << "Initial ideal is: " << endl; |
|---|
| 589 | idShow(initialForm); |
|---|
| 590 | //f->printFlipGB(); |
|---|
| 591 | cout << "===" << endl; |
|---|
| 592 | #endif |
|---|
| 593 | delete check; |
|---|
| 594 | |
|---|
| 595 | /*2nd step: lift initial ideal to a GB of the neighbouring cone using minus alpha as weight*/ |
|---|
| 596 | /*Substep 2.1 |
|---|
| 597 | compute $G_{-\alpha}(in_v(I)) |
|---|
| 598 | see journal p. 66 |
|---|
| 599 | */ |
|---|
| 600 | ring srcRing=currRing; |
|---|
| 601 | |
|---|
| 602 | /* copied and modified from ring.cc::rAssureSyzComp */ |
|---|
| 603 | //ring tmpRing=rCopyAndChangeWeight(srcRing,fNormal); |
|---|
| 604 | ring tmpRing=rCopy0(srcRing); |
|---|
| 605 | int i=rBlocks(srcRing); |
|---|
| 606 | int j; |
|---|
| 607 | tmpRing->order=(int *)omAlloc((i+1)*sizeof(int)); |
|---|
| 608 | /*NOTE This should probably be set, but as of now crashes Singular*/ |
|---|
| 609 | /*tmpRing->block0=(int *)omAlloc0((i+1)*sizeof(int)); |
|---|
| 610 | tmpRing->block1=(int *)omAlloc0((i+1)*sizeof(int));*/ |
|---|
| 611 | tmpRing->wvhdl[0] =( int *)omAlloc((fNormal->length())*sizeof(int)); //found in Singular/ipshell.cc |
|---|
| 612 | for(j=i;j>0;j--) |
|---|
| 613 | { |
|---|
| 614 | tmpRing->order[j]=srcRing->order[j-1]; |
|---|
| 615 | tmpRing->block0[j]=srcRing->block0[j-1]; |
|---|
| 616 | tmpRing->block1[j]=srcRing->block1[j-1]; |
|---|
| 617 | if (srcRing->wvhdl[j-1] != NULL) |
|---|
| 618 | { |
|---|
| 619 | tmpRing->wvhdl[j] = (int*) omMemDup(srcRing->wvhdl[j-1]); |
|---|
| 620 | } |
|---|
| 621 | } |
|---|
| 622 | tmpRing->order[0]=ringorder_a; |
|---|
| 623 | tmpRing->order[1]=ringorder_dp; |
|---|
| 624 | tmpRing->order[2]=ringorder_C; |
|---|
| 625 | //tmpRing->wvhdl[0] =( int *)omAlloc((fNormal->length())*sizeof(int)); //found in Singular/ipshell.cc |
|---|
| 626 | |
|---|
| 627 | for (int ii=0;ii<this->numVars;ii++) |
|---|
| 628 | { |
|---|
| 629 | tmpRing->wvhdl[0][ii]=-(*fNormal)[ii]; //What exactly am I doing here? |
|---|
| 630 | //cout << tmpring->wvhdl[0][ii] << endl; |
|---|
| 631 | } |
|---|
| 632 | rComplete(tmpRing); |
|---|
| 633 | rChangeCurrRing(tmpRing); |
|---|
| 634 | |
|---|
| 635 | rWrite(currRing); cout << endl; |
|---|
| 636 | ideal ina; |
|---|
| 637 | ina=idrCopyR(initialForm,srcRing); |
|---|
| 638 | #ifdef gfan_DEBUG |
|---|
| 639 | cout << "ina="; |
|---|
| 640 | idShow(ina); cout << endl; |
|---|
| 641 | #endif |
|---|
| 642 | ideal H; |
|---|
| 643 | H=kStd(ina,NULL,isHomog,NULL); //we know it is homogeneous |
|---|
| 644 | idSkipZeroes(H); |
|---|
| 645 | #ifdef gfan_DEBUG |
|---|
| 646 | cout << "H="; idShow(H); cout << endl; |
|---|
| 647 | #endif |
|---|
| 648 | /*Substep 2.2 |
|---|
| 649 | do the lifting and mark according to H |
|---|
| 650 | */ |
|---|
| 651 | rChangeCurrRing(srcRing); |
|---|
| 652 | ideal srcRing_H; |
|---|
| 653 | ideal srcRing_HH; |
|---|
| 654 | srcRing_H=idrCopyR(H,tmpRing); |
|---|
| 655 | #ifdef gfan_DEBUG |
|---|
| 656 | cout << "srcRing_H = "; |
|---|
| 657 | idShow(srcRing_H); cout << endl; |
|---|
| 658 | #endif |
|---|
| 659 | srcRing_HH=ffG(srcRing_H,this->gcBasis); |
|---|
| 660 | #ifdef gfan_DEBUG |
|---|
| 661 | cout << "srcRing_HH = "; |
|---|
| 662 | idShow(srcRing_HH); cout << endl; |
|---|
| 663 | #endif |
|---|
| 664 | /*Substep 2.2.1 |
|---|
| 665 | Mark according to G_-\alpha |
|---|
| 666 | Here we have a minimal basis srcRing_HH. In order to turn this basis into a reduced basis |
|---|
| 667 | we have to compute an interior point of C(srcRing_HH). For this we need to know the cone |
|---|
| 668 | represented by srcRing_HH MARKED ACCORDING TO G_{-\alpha} |
|---|
| 669 | Thus we check whether the leading monomials of srcRing_HH and srcRing_H coincide. If not we |
|---|
| 670 | compute the difference accordingly |
|---|
| 671 | */ |
|---|
| 672 | dd_set_global_constants(); |
|---|
| 673 | bool markingsAreCorrect=FALSE; |
|---|
| 674 | dd_MatrixPtr intPointMatrix; |
|---|
| 675 | int iPMatrixRows=0; |
|---|
| 676 | dd_rowrange aktrow=0; |
|---|
| 677 | for (int ii=0;ii<IDELEMS(srcRing_HH);ii++) |
|---|
| 678 | { |
|---|
| 679 | poly aktpoly=(poly)srcRing_HH->m[ii]; |
|---|
| 680 | iPMatrixRows = iPMatrixRows+pLength(aktpoly)-1; |
|---|
| 681 | } |
|---|
| 682 | /* additionally one row for the standard-simplex and another for a row that becomes 0 during |
|---|
| 683 | construction of the differences |
|---|
| 684 | */ |
|---|
| 685 | intPointMatrix = dd_CreateMatrix(iPMatrixRows+2,this->numVars+1); |
|---|
| 686 | intPointMatrix->numbtype=dd_Integer; //NOTE: DO NOT REMOVE OR CHANGE TO dd_Rational |
|---|
| 687 | |
|---|
| 688 | for (int ii=0;ii<IDELEMS(srcRing_HH);ii++) |
|---|
| 689 | { |
|---|
| 690 | markingsAreCorrect=FALSE; //crucial to initialise here |
|---|
| 691 | poly aktpoly=srcRing_HH->m[ii]; |
|---|
| 692 | /*Comparison of leading monomials is done via exponent vectors*/ |
|---|
| 693 | for (int jj=0;jj<IDELEMS(H);jj++) |
|---|
| 694 | { |
|---|
| 695 | int *src_ExpV = (int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 696 | int *dst_ExpV = (int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 697 | pGetExpV(aktpoly,src_ExpV); |
|---|
| 698 | rChangeCurrRing(tmpRing); //this ring change is crucial! |
|---|
| 699 | pGetExpV(pCopy(H->m[ii]),dst_ExpV); |
|---|
| 700 | rChangeCurrRing(srcRing); |
|---|
| 701 | bool expVAreEqual=TRUE; |
|---|
| 702 | for (int kk=1;kk<=this->numVars;kk++) |
|---|
| 703 | { |
|---|
| 704 | cout << src_ExpV[kk] << "," << dst_ExpV[kk] << endl; |
|---|
| 705 | if (src_ExpV[kk]!=dst_ExpV[kk]) |
|---|
| 706 | { |
|---|
| 707 | expVAreEqual=FALSE; |
|---|
| 708 | } |
|---|
| 709 | } |
|---|
| 710 | //if (*src_ExpV == *dst_ExpV) |
|---|
| 711 | if (expVAreEqual==TRUE) |
|---|
| 712 | { |
|---|
| 713 | markingsAreCorrect=TRUE; //everything is fine |
|---|
| 714 | cout << "correct markings" << endl; |
|---|
| 715 | }//if (pHead(aktpoly)==pHead(H->m[jj]) |
|---|
| 716 | delete src_ExpV; |
|---|
| 717 | delete dst_ExpV; |
|---|
| 718 | }//for (int jj=0;jj<IDELEMS(H);jj++) |
|---|
| 719 | |
|---|
| 720 | int *v=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 721 | int *leadExpV=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 722 | if (markingsAreCorrect==TRUE) |
|---|
| 723 | { |
|---|
| 724 | pGetExpV(aktpoly,leadExpV); |
|---|
| 725 | } |
|---|
| 726 | else |
|---|
| 727 | { |
|---|
| 728 | rChangeCurrRing(tmpRing); |
|---|
| 729 | pGetExpV(pHead(H->m[ii]),leadExpV); //We use H->m[ii] as leading monomial |
|---|
| 730 | rChangeCurrRing(srcRing); |
|---|
| 731 | } |
|---|
| 732 | /*compute differences of the expvects*/ |
|---|
| 733 | while (pNext(aktpoly)!=NULL) |
|---|
| 734 | { |
|---|
| 735 | /*The following if-else-block makes sure the first term (i.e. the wrongly marked term) |
|---|
| 736 | is not omitted when computing the differences*/ |
|---|
| 737 | if(markingsAreCorrect==TRUE) |
|---|
| 738 | { |
|---|
| 739 | aktpoly=pNext(aktpoly); |
|---|
| 740 | pGetExpV(aktpoly,v); |
|---|
| 741 | } |
|---|
| 742 | else |
|---|
| 743 | { |
|---|
| 744 | pGetExpV(pHead(aktpoly),v); |
|---|
| 745 | markingsAreCorrect=TRUE; |
|---|
| 746 | } |
|---|
| 747 | |
|---|
| 748 | for (int jj=0;jj<this->numVars;jj++) |
|---|
| 749 | { |
|---|
| 750 | /*Store into ddMatrix*/ |
|---|
| 751 | dd_set_si(intPointMatrix->matrix[aktrow][jj+1],leadExpV[jj+1]-v[jj+1]); |
|---|
| 752 | } |
|---|
| 753 | aktrow +=1; |
|---|
| 754 | } |
|---|
| 755 | delete v; |
|---|
| 756 | delete leadExpV; |
|---|
| 757 | }//for (int ii=0;ii<IDELEMS(srcRing_HH);ii++) |
|---|
| 758 | /*Now we add the constraint for the standard simplex*/ |
|---|
| 759 | /*NOTE:Might actually work without the standard simplex*/ |
|---|
| 760 | dd_set_si(intPointMatrix->matrix[aktrow][0],-1); |
|---|
| 761 | for (int jj=1;jj<=this->numVars;jj++) |
|---|
| 762 | { |
|---|
| 763 | dd_set_si(intPointMatrix->matrix[aktrow][jj],1); |
|---|
| 764 | } |
|---|
| 765 | dd_WriteMatrix(stdout,intPointMatrix); |
|---|
| 766 | intvec *iv_weight = new intvec(this->numVars); |
|---|
| 767 | interiorPoint(intPointMatrix, *iv_weight); //iv_weight now contains the interior point |
|---|
| 768 | dd_FreeMatrix(intPointMatrix); |
|---|
| 769 | dd_free_global_constants(); |
|---|
| 770 | |
|---|
| 771 | /*Step 3 |
|---|
| 772 | turn the minimal basis into a reduced one |
|---|
| 773 | */ |
|---|
| 774 | ring dstRing=rCopy0(srcRing); |
|---|
| 775 | i=rBlocks(srcRing); |
|---|
| 776 | |
|---|
| 777 | dstRing->order=(int *)omAlloc((i+1)*sizeof(int)); |
|---|
| 778 | for(j=i;j>0;j--) |
|---|
| 779 | { |
|---|
| 780 | dstRing->order[j]=srcRing->order[j-1]; |
|---|
| 781 | dstRing->block0[j]=srcRing->block0[j-1]; |
|---|
| 782 | dstRing->block1[j]=srcRing->block1[j-1]; |
|---|
| 783 | if (srcRing->wvhdl[j-1] != NULL) |
|---|
| 784 | { |
|---|
| 785 | dstRing->wvhdl[j] = (int*) omMemDup(srcRing->wvhdl[j-1]); |
|---|
| 786 | } |
|---|
| 787 | } |
|---|
| 788 | dstRing->order[0]=ringorder_a; |
|---|
| 789 | dstRing->order[1]=ringorder_dp; |
|---|
| 790 | dstRing->order[2]=ringorder_C; |
|---|
| 791 | dstRing->wvhdl[0] =( int *)omAlloc((iv_weight->length())*sizeof(int)); |
|---|
| 792 | |
|---|
| 793 | for (int ii=0;ii<this->numVars;ii++) |
|---|
| 794 | { |
|---|
| 795 | dstRing->wvhdl[0][ii]=(*iv_weight)[ii]; |
|---|
| 796 | } |
|---|
| 797 | rComplete(dstRing); |
|---|
| 798 | rChangeCurrRing(dstRing); |
|---|
| 799 | #ifdef gfan_DEBUG |
|---|
| 800 | rWrite(dstRing); cout << endl; |
|---|
| 801 | #endif |
|---|
| 802 | ideal dstRing_I; |
|---|
| 803 | dstRing_I=idrCopyR(srcRing_HH,srcRing); |
|---|
| 804 | //validOpts<1>=TRUE; |
|---|
| 805 | #ifdef gfan_DEBUG |
|---|
| 806 | idShow(dstRing_I); |
|---|
| 807 | #endif |
|---|
| 808 | BITSET save=test; |
|---|
| 809 | test|=Sy_bit(OPT_REDSB); |
|---|
| 810 | test|=Sy_bit(6); //OPT_DEBUG |
|---|
| 811 | dstRing_I=kStd(idrCopyR(this->inputIdeal,this->rootRing),NULL,testHomog,NULL); |
|---|
| 812 | kInterRed(dstRing_I); |
|---|
| 813 | idSkipZeroes(dstRing_I); |
|---|
| 814 | test=save; |
|---|
| 815 | /*End of step 3 - reduction*/ |
|---|
| 816 | |
|---|
| 817 | f->setFlipGB(dstRing_I);//store the flipped GB |
|---|
| 818 | #ifdef gfan_DEBUG |
|---|
| 819 | cout << "Flipped GB is: " << endl; |
|---|
| 820 | f->printFlipGB(); |
|---|
| 821 | #endif |
|---|
| 822 | }//void flip(ideal gb, facet *f) |
|---|
| 823 | |
|---|
| 824 | /** \brief Compute the remainder of a polynomial by a given ideal |
|---|
| 825 | * |
|---|
| 826 | * Compute \f$ f^{\mathcal{G}} \f$ |
|---|
| 827 | * Algorithm is taken from Cox, Little, O'Shea, IVA 2nd Ed. p 62 |
|---|
| 828 | * However, since we are only interested in the remainder, there is no need to |
|---|
| 829 | * compute the factors \f$ a_i \f$ |
|---|
| 830 | */ |
|---|
| 831 | //NOTE: Should be replaced by kNF or kNF2 |
|---|
| 832 | poly restOfDiv(poly const &f, ideal const &I) |
|---|
| 833 | { |
|---|
| 834 | cout << "Entering restOfDiv" << endl; |
|---|
| 835 | poly p=f; |
|---|
| 836 | pWrite(p); |
|---|
| 837 | //poly r=kCreateZeroPoly(,currRing,currRing); //The 0-polynomial, hopefully |
|---|
| 838 | poly r=NULL; //The zero polynomial |
|---|
| 839 | int ii; |
|---|
| 840 | bool divOccured; |
|---|
| 841 | |
|---|
| 842 | while (p!=NULL) |
|---|
| 843 | { |
|---|
| 844 | ii=1; |
|---|
| 845 | divOccured=FALSE; |
|---|
| 846 | |
|---|
| 847 | while( (ii<=IDELEMS(I) && (divOccured==FALSE) )) |
|---|
| 848 | { |
|---|
| 849 | if (pDivisibleBy(I->m[ii-1],p)) //does LM(I->m[ii]) divide LM(p) ? |
|---|
| 850 | { |
|---|
| 851 | //cout << "TICK 3" << endl; |
|---|
| 852 | poly step1,step2,step3; |
|---|
| 853 | //cout << "dividing "; pWrite(pHead(p));cout << "by ";pWrite(pHead(I->m[ii-1])); cout << endl; |
|---|
| 854 | step1 = pDivideM(pHead(p),pHead(I->m[ii-1])); |
|---|
| 855 | //cout << "LT(p)/LT(f_i)="; pWrite(step1); cout << endl; |
|---|
| 856 | //cout << "TICK 3.1" << endl; |
|---|
| 857 | step2 = ppMult_qq(step1, I->m[ii-1]); |
|---|
| 858 | //cout << "TICK 3.2" << endl; |
|---|
| 859 | step3 = pSub(pCopy(p), step2); |
|---|
| 860 | //p=pSub(p,pMult( pDivide(pHead(p),pHead(I->m[ii])), I->m[ii])); |
|---|
| 861 | //cout << "TICK 4" << endl; |
|---|
| 862 | //pSetm(p); |
|---|
| 863 | pSort(step3); //must be here, otherwise strange behaviour with many +o+o+o+o+ terms |
|---|
| 864 | p=step3; |
|---|
| 865 | pWrite(p); |
|---|
| 866 | divOccured=TRUE; |
|---|
| 867 | } |
|---|
| 868 | else |
|---|
| 869 | { |
|---|
| 870 | ii += 1; |
|---|
| 871 | }//if (pLmDivisibleBy(I->m[ii],p,currRing)) |
|---|
| 872 | }//while( (ii<IDELEMS(I) && (divOccured==FALSE) )) |
|---|
| 873 | if (divOccured==FALSE) |
|---|
| 874 | { |
|---|
| 875 | //cout << "TICK 5" << endl; |
|---|
| 876 | r=pAdd(pCopy(r),pHead(p)); |
|---|
| 877 | pSetm(r); |
|---|
| 878 | pSort(r); |
|---|
| 879 | //cout << "r="; pWrite(r); cout << endl; |
|---|
| 880 | //cout << "TICK 6" << endl; |
|---|
| 881 | if (pLength(p)!=1) |
|---|
| 882 | { |
|---|
| 883 | p=pSub(pCopy(p),pHead(p)); //Here it may occur that p=0 instead of p=NULL |
|---|
| 884 | } |
|---|
| 885 | else |
|---|
| 886 | { |
|---|
| 887 | p=NULL; //Hack to correct this situation |
|---|
| 888 | } |
|---|
| 889 | //cout << "TICK 7" << endl; |
|---|
| 890 | //cout << "p="; pWrite(p); |
|---|
| 891 | }//if (divOccured==FALSE) |
|---|
| 892 | }//while (p!=0) |
|---|
| 893 | return r; |
|---|
| 894 | }//poly restOfDiv(poly const &f, ideal const &I) |
|---|
| 895 | |
|---|
| 896 | /** \brief Compute \f$ f-f^{\mathcal{G}} \f$ |
|---|
| 897 | */ |
|---|
| 898 | //NOTE: use kNF or kNF2 instead of restOfDivision |
|---|
| 899 | ideal ffG(ideal const &H, ideal const &G) |
|---|
| 900 | { |
|---|
| 901 | cout << "Entering ffG" << endl; |
|---|
| 902 | int size=IDELEMS(H); |
|---|
| 903 | ideal res=idInit(size,1); |
|---|
| 904 | poly temp1, temp2, temp3; //polys to temporarily store values for pSub |
|---|
| 905 | for (int ii=0;ii<size;ii++) |
|---|
| 906 | { |
|---|
| 907 | res->m[ii]=restOfDiv(H->m[ii],G); |
|---|
| 908 | //res->m[ii]=kNF(H->m[ii],G); |
|---|
| 909 | temp1=H->m[ii]; |
|---|
| 910 | temp2=res->m[ii]; |
|---|
| 911 | temp3=pSub(temp1, temp2); |
|---|
| 912 | res->m[ii]=temp3; |
|---|
| 913 | //res->m[ii]=pSub(temp1,temp2); //buggy |
|---|
| 914 | //pSort(res->m[ii]); |
|---|
| 915 | //pSetm(res->m[ii]); |
|---|
| 916 | cout << "res->m["<<ii<<"]=";pWrite(res->m[ii]); |
|---|
| 917 | } |
|---|
| 918 | return res; |
|---|
| 919 | } |
|---|
| 920 | |
|---|
| 921 | /** \brief Compute a Groebner Basis |
|---|
| 922 | * |
|---|
| 923 | * Computes the Groebner basis and stores the result in gcone::gcBasis |
|---|
| 924 | *\param ideal |
|---|
| 925 | *\return void |
|---|
| 926 | */ |
|---|
| 927 | void getGB(ideal const &inputIdeal) |
|---|
| 928 | { |
|---|
| 929 | ideal gb; |
|---|
| 930 | gb=kStd(inputIdeal,NULL,testHomog,NULL); |
|---|
| 931 | idSkipZeroes(gb); |
|---|
| 932 | this->gcBasis=gb; //write the GB into gcBasis |
|---|
| 933 | }//void getGB |
|---|
| 934 | |
|---|
| 935 | /** \brief The Generic Groebner Walk due to FJLT |
|---|
| 936 | * Needed for computing the search facet |
|---|
| 937 | */ |
|---|
| 938 | ideal GenGrbWlk(ideal, ideal) |
|---|
| 939 | { |
|---|
| 940 | }//GGW |
|---|
| 941 | |
|---|
| 942 | |
|---|
| 943 | /** \brief Compute the dot product of two intvecs |
|---|
| 944 | * |
|---|
| 945 | */ |
|---|
| 946 | int dotProduct(intvec const &iva, intvec const &ivb) |
|---|
| 947 | { |
|---|
| 948 | //intvec iva=a; |
|---|
| 949 | //intvec ivb=b; |
|---|
| 950 | int res=0; |
|---|
| 951 | for (int i=0;i<this->numVars;i++) |
|---|
| 952 | { |
|---|
| 953 | res = res+(iva[i]*ivb[i]); |
|---|
| 954 | } |
|---|
| 955 | return res; |
|---|
| 956 | }//int dotProduct |
|---|
| 957 | |
|---|
| 958 | /** \brief Check whether two intvecs are parallel |
|---|
| 959 | * |
|---|
| 960 | * \f$ \alpha\parallel\beta\Leftrightarrow\langle\alpha,\beta\rangle^2=\langle\alpha,\alpha\rangle\langle\beta,\beta\rangle \f$ |
|---|
| 961 | */ |
|---|
| 962 | bool isParallel(intvec const &a, intvec const &b) |
|---|
| 963 | { |
|---|
| 964 | int lhs,rhs; |
|---|
| 965 | lhs=dotProduct(a,b)*dotProduct(a,b); |
|---|
| 966 | rhs=dotProduct(a,a)*dotProduct(b,b); |
|---|
| 967 | cout << "LHS="<<lhs<<", RHS="<<rhs<<endl; |
|---|
| 968 | if (lhs==rhs) |
|---|
| 969 | { |
|---|
| 970 | return TRUE; |
|---|
| 971 | } |
|---|
| 972 | else |
|---|
| 973 | { |
|---|
| 974 | return FALSE; |
|---|
| 975 | } |
|---|
| 976 | }//bool isParallel |
|---|
| 977 | |
|---|
| 978 | /** \brief Compute an interior point of a given cone |
|---|
| 979 | */ |
|---|
| 980 | void interiorPoint(dd_MatrixPtr const &M, intvec &iv) //no const &M here since we want to remove redundant rows |
|---|
| 981 | { |
|---|
| 982 | dd_LPPtr lp,lpInt; |
|---|
| 983 | dd_ErrorType err=dd_NoError; |
|---|
| 984 | dd_LPSolverType solver=dd_DualSimplex; |
|---|
| 985 | dd_LPSolutionPtr lpSol=NULL; |
|---|
| 986 | dd_rowset ddlinset,ddredrows; //needed for dd_FindRelativeInterior |
|---|
| 987 | dd_rowindex ddnewpos; |
|---|
| 988 | dd_NumberType numb; |
|---|
| 989 | //M->representation=dd_Inequality; |
|---|
| 990 | //M->objective-dd_LPMin; //Not sure whether this is needed |
|---|
| 991 | dd_set_si(M->rowvec[0],1);dd_set_si(M->rowvec[1],1);dd_set_si(M->rowvec[2],1); |
|---|
| 992 | //cout << "TICK 1" << endl; |
|---|
| 993 | |
|---|
| 994 | //dd_MatrixCanonicalize(&M, &ddlinset, &ddredrows, &ddnewpos, &err); |
|---|
| 995 | //if (err!=dd_NoError){cout << "Error during dd_MatrixCanonicalize" << endl;} |
|---|
| 996 | //cout << "Tick 2" << endl; |
|---|
| 997 | //dd_WriteMatrix(stdout,M); |
|---|
| 998 | |
|---|
| 999 | lp=dd_Matrix2LP(M, &err); |
|---|
| 1000 | if (err!=dd_NoError){cout << "Error during dd_Matrix2LP in gcone::interiorPoint" << endl;} |
|---|
| 1001 | if (lp==NULL){cout << "LP is NULL" << endl;} |
|---|
| 1002 | dd_WriteLP(stdout,lp); |
|---|
| 1003 | //cout << "Tick 3" << endl; |
|---|
| 1004 | |
|---|
| 1005 | lpInt=dd_MakeLPforInteriorFinding(lp); |
|---|
| 1006 | if (err!=dd_NoError){cout << "Error during dd_MakeLPForInteriorFinding in gcone::interiorPoint" << endl;} |
|---|
| 1007 | dd_WriteLP(stdout,lpInt); |
|---|
| 1008 | //cout << "Tick 4" << endl; |
|---|
| 1009 | |
|---|
| 1010 | dd_FindRelativeInterior(M,&ddlinset,&ddredrows,&lpSol,&err); |
|---|
| 1011 | if (err!=dd_NoError) |
|---|
| 1012 | { |
|---|
| 1013 | cout << "Error during dd_FindRelativeInterior in gcone::interiorPoint" << endl; |
|---|
| 1014 | dd_WriteErrorMessages(stdout, err); |
|---|
| 1015 | } |
|---|
| 1016 | |
|---|
| 1017 | //dd_LPSolve(lpInt,solver,&err); //This will not result in a point from the relative interior |
|---|
| 1018 | if (err!=dd_NoError){cout << "Error during dd_LPSolve" << endl;} |
|---|
| 1019 | //cout << "Tick 5" << endl; |
|---|
| 1020 | |
|---|
| 1021 | //lpSol=dd_CopyLPSolution(lpInt); |
|---|
| 1022 | if (err!=dd_NoError){cout << "Error during dd_CopyLPSolution" << endl;} |
|---|
| 1023 | //cout << "Tick 6" << endl; |
|---|
| 1024 | #ifdef gfan_DEBUG |
|---|
| 1025 | cout << "Interior point: "; |
|---|
| 1026 | #endif |
|---|
| 1027 | for (int ii=1; ii<(lpSol->d)-1;ii++) |
|---|
| 1028 | { |
|---|
| 1029 | #ifdef gfan_DEBUG |
|---|
| 1030 | dd_WriteNumber(stdout,lpSol->sol[ii]); |
|---|
| 1031 | #endif |
|---|
| 1032 | /* NOTE This works only as long as gmp returns fractions with the same denominator*/ |
|---|
| 1033 | (iv)[ii-1]=(int)mpz_get_d(mpq_numref(lpSol->sol[ii])); //looks evil, but does the trick |
|---|
| 1034 | } |
|---|
| 1035 | dd_FreeLPSolution(lpSol); |
|---|
| 1036 | dd_FreeLPData(lpInt); |
|---|
| 1037 | dd_FreeLPData(lp); |
|---|
| 1038 | set_free(ddlinset); |
|---|
| 1039 | set_free(ddredrows); |
|---|
| 1040 | |
|---|
| 1041 | }//void interiorPoint(dd_MatrixPtr const &M) |
|---|
| 1042 | |
|---|
| 1043 | ring rCopyAndChangeWeight(ring const r, intvec const *ivw) |
|---|
| 1044 | { |
|---|
| 1045 | ring res=rCopy0(r, FALSE, FALSE); |
|---|
| 1046 | int i=rBlocks(r); |
|---|
| 1047 | int j; |
|---|
| 1048 | |
|---|
| 1049 | res->order=(int *)omAlloc((i+1)*sizeof(int)); |
|---|
| 1050 | /*res->block0=(int *)omAlloc0((i+1)*sizeof(int)); |
|---|
| 1051 | res->block1=(int *)omAlloc0((i+1)*sizeof(int)); |
|---|
| 1052 | int ** wvhdl =(int **)omAlloc0((i+1)*sizeof(int**));*/ |
|---|
| 1053 | for(j=i;j>0;j--) |
|---|
| 1054 | { |
|---|
| 1055 | res->order[j]=r->order[j-1]; |
|---|
| 1056 | res->block0[j]=r->block0[j-1]; |
|---|
| 1057 | res->block1[j]=r->block1[j-1]; |
|---|
| 1058 | if (r->wvhdl[j-1] != NULL) |
|---|
| 1059 | { |
|---|
| 1060 | res->wvhdl[j] = (int*) omMemDup(r->wvhdl[j-1]); |
|---|
| 1061 | } |
|---|
| 1062 | } |
|---|
| 1063 | res->order[0]=ringorder_a; |
|---|
| 1064 | res->order[1]=ringorder_dp; |
|---|
| 1065 | res->order[2]=ringorder_C; |
|---|
| 1066 | //res->wvhdl = wvhdl; |
|---|
| 1067 | |
|---|
| 1068 | res->wvhdl[0] =( int *)omAlloc((ivw->length())*sizeof(int)); |
|---|
| 1069 | for (int ii=0;ii<this->numVars;ii++) |
|---|
| 1070 | { |
|---|
| 1071 | res->wvhdl[0][ii]=(*ivw)[ii]; |
|---|
| 1072 | } |
|---|
| 1073 | |
|---|
| 1074 | rComplete(res); |
|---|
| 1075 | return res; |
|---|
| 1076 | }//rCopyAndChange |
|---|
| 1077 | |
|---|
| 1078 | /** |
|---|
| 1079 | * Determines whether a given facet of a cone is the search facet of a neighbouring cone |
|---|
| 1080 | * This is done in the following way: |
|---|
| 1081 | * We loop through all facets of the cone and find the "smallest" facet, i.e. the unique facet |
|---|
| 1082 | * that is first crossed during the generic walk. |
|---|
| 1083 | * We then check whether the fNormal of this facet is parallel to the fNormal of our testfacet. |
|---|
| 1084 | * If this is the case, then our facet is indeed a search facet and TRUE is retuned. |
|---|
| 1085 | */ |
|---|
| 1086 | bool isSearchFacet(gcone &gcTmp, facet &testfacet) |
|---|
| 1087 | { |
|---|
| 1088 | ring actRing=currRing; |
|---|
| 1089 | facet *facetPtr=(facet*)gcTmp.facetPtr; |
|---|
| 1090 | facet *fMin=new facet(*facetPtr); //Pointer to the "minimal" facet |
|---|
| 1091 | //facet *fMin = new facet(tmpcone.facetPtr); |
|---|
| 1092 | //fMin=tmpcone.facetPtr; //Initialise to first facet of tmpcone |
|---|
| 1093 | facet *fAct; //Ptr to alpha_i |
|---|
| 1094 | facet *fCmp; //Ptr to alpha_j |
|---|
| 1095 | fAct = fMin; |
|---|
| 1096 | fCmp = fMin->next; |
|---|
| 1097 | |
|---|
| 1098 | //cout << endl<< fMin->next << endl; |
|---|
| 1099 | //cout << gcTmp.facetPtr->next << endl; |
|---|
| 1100 | //gcTmp.facetPtr->printNormal(); |
|---|
| 1101 | //fAct=gcTmp.facetPtr->next; |
|---|
| 1102 | //fAct->printNormal(); |
|---|
| 1103 | |
|---|
| 1104 | rChangeCurrRing(this->rootRing); //because we compare the monomials in the rootring |
|---|
| 1105 | poly p=pInit(); |
|---|
| 1106 | poly q=pInit(); |
|---|
| 1107 | intvec *alpha_i = new intvec(this->numVars); |
|---|
| 1108 | intvec *alpha_j = new intvec(this->numVars); |
|---|
| 1109 | intvec *sigma = new intvec(this->numVars); |
|---|
| 1110 | sigma=gcTmp.getIntPoint(); |
|---|
| 1111 | |
|---|
| 1112 | int *u=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 1113 | int *v=(int *)omAlloc((this->numVars+1)*sizeof(int)); |
|---|
| 1114 | u[0]=0; v[0]=0; |
|---|
| 1115 | int weight1,weight2; |
|---|
| 1116 | while(fAct->next->next!=NULL) //NOTE this is ugly. Can it be done without fCmp? |
|---|
| 1117 | { |
|---|
| 1118 | /* Get alpha_i and alpha_{i+1} */ |
|---|
| 1119 | alpha_i=fAct->getFacetNormal(); |
|---|
| 1120 | alpha_j=fCmp->getFacetNormal(); |
|---|
| 1121 | #ifdef gfan_DEBUG |
|---|
| 1122 | alpha_i->show(); |
|---|
| 1123 | alpha_j->show(); |
|---|
| 1124 | #endif |
|---|
| 1125 | /*Compute the dot product of sigma and alpha_{i,j}*/ |
|---|
| 1126 | weight1=dotProduct(sigma,alpha_i); |
|---|
| 1127 | weight2=dotProduct(sigma,alpha_j); |
|---|
| 1128 | #ifdef gfan_DEBUG |
|---|
| 1129 | cout << "weight1=" << weight1 << " " << "weight2=" << weight2 << endl; |
|---|
| 1130 | #endif |
|---|
| 1131 | /*Adjust alpha_i and alpha_i+1 accordingly*/ |
|---|
| 1132 | for(int ii=1;ii<=this->numVars;ii++) |
|---|
| 1133 | { |
|---|
| 1134 | u[ii]=weight1*(*alpha_i)[ii-1]; |
|---|
| 1135 | v[ii]=weight2*(*alpha_j)[ii-1]; |
|---|
| 1136 | } |
|---|
| 1137 | |
|---|
| 1138 | /*Now p_weight and q_weight need to be compared as exponent vectors*/ |
|---|
| 1139 | pSetCoeff0(p,nInit(1)); |
|---|
| 1140 | pSetCoeff0(q,nInit(1)); |
|---|
| 1141 | pSetExpV(p,u); |
|---|
| 1142 | pSetm(p); |
|---|
| 1143 | pSetExpV(q,v); |
|---|
| 1144 | pSetm(q); |
|---|
| 1145 | #ifdef gfan_DEBUG |
|---|
| 1146 | pWrite(p);pWrite(q); |
|---|
| 1147 | #endif |
|---|
| 1148 | /*We want to check whether x^p < x^q |
|---|
| 1149 | => want to check for return value 1 */ |
|---|
| 1150 | if (pLmCmp(p,q)==1) //i.e. x^q is smaller |
|---|
| 1151 | { |
|---|
| 1152 | fMin=fCmp; |
|---|
| 1153 | fAct=fMin; |
|---|
| 1154 | } |
|---|
| 1155 | else |
|---|
| 1156 | { |
|---|
| 1157 | //fAct=fAct->next; |
|---|
| 1158 | if(fCmp->next!=NULL) |
|---|
| 1159 | { |
|---|
| 1160 | fCmp=fCmp->next; |
|---|
| 1161 | } |
|---|
| 1162 | else |
|---|
| 1163 | { |
|---|
| 1164 | fAct=fAct->next; |
|---|
| 1165 | } |
|---|
| 1166 | } |
|---|
| 1167 | //fAct=fAct->next; |
|---|
| 1168 | }//while(fAct.facetPtr->next!=NULL) |
|---|
| 1169 | |
|---|
| 1170 | /*If testfacet was minimal then fMin should still point there */ |
|---|
| 1171 | intvec *alpha_min = new intvec(this->numVars); |
|---|
| 1172 | alpha_min=fMin->getFacetNormal(); |
|---|
| 1173 | intvec *test = new intvec(this->numVars); |
|---|
| 1174 | test=testfacet.getFacetNormal(); |
|---|
| 1175 | if (isParallel(alpha_min,test)) |
|---|
| 1176 | //if (fMin==gcTmp.facetPtr) |
|---|
| 1177 | { |
|---|
| 1178 | rChangeCurrRing(actRing); |
|---|
| 1179 | return TRUE; |
|---|
| 1180 | } |
|---|
| 1181 | else |
|---|
| 1182 | { |
|---|
| 1183 | rChangeCurrRing(actRing); |
|---|
| 1184 | return FALSE; |
|---|
| 1185 | } |
|---|
| 1186 | }//bool isSearchFacet |
|---|
| 1187 | |
|---|
| 1188 | void reverseSearch(gcone *gcAct) //no const possible here since we call gcAct->flip |
|---|
| 1189 | { |
|---|
| 1190 | facet *fAct=new facet(); |
|---|
| 1191 | fAct = gcAct->facetPtr; |
|---|
| 1192 | |
|---|
| 1193 | while(fAct->next!=NULL) //NOTE NOT SURE WHETHER THIS IS RIGHT! Do I reach EVERY facet or only all but the last? |
|---|
| 1194 | { |
|---|
| 1195 | cout << "==========================================================================================="<< endl; |
|---|
| 1196 | gcAct->flip(gcAct->gcBasis,gcAct->facetPtr); |
|---|
| 1197 | gcone *gcTmp = new gcone(*gcAct); |
|---|
| 1198 | idShow(gcTmp->gcBasis); |
|---|
| 1199 | gcTmp->getConeNormals(gcTmp->gcBasis, TRUE); |
|---|
| 1200 | #ifdef gfan_DEBUG |
|---|
| 1201 | facet *f = new facet(); |
|---|
| 1202 | f=gcTmp->facetPtr; |
|---|
| 1203 | while(f->next!=NULL) |
|---|
| 1204 | { |
|---|
| 1205 | f->printNormal(); |
|---|
| 1206 | f=f->next; |
|---|
| 1207 | } |
|---|
| 1208 | #endif |
|---|
| 1209 | gcTmp->showIntPoint(); |
|---|
| 1210 | /*recursive part goes gere*/ |
|---|
| 1211 | if (isSearchFacet(*gcTmp,(facet&)gcAct->facetPtr)) |
|---|
| 1212 | { |
|---|
| 1213 | gcAct->next=gcTmp; |
|---|
| 1214 | cout << "PING"<< endl; |
|---|
| 1215 | reverseSearch(gcTmp); |
|---|
| 1216 | } |
|---|
| 1217 | else |
|---|
| 1218 | { |
|---|
| 1219 | delete gcTmp; |
|---|
| 1220 | /*NOTE remove fAct from linked list. It's no longer needed*/ |
|---|
| 1221 | } |
|---|
| 1222 | /*recursion ends*/ |
|---|
| 1223 | fAct = fAct->next; |
|---|
| 1224 | }//while(fAct->next!=NULL) |
|---|
| 1225 | }//reverseSearch |
|---|
| 1226 | friend class facet; |
|---|
| 1227 | };//class gcone |
|---|
| 1228 | |
|---|
| 1229 | ideal gfan(ideal inputIdeal) |
|---|
| 1230 | { |
|---|
| 1231 | int numvar = pVariables; |
|---|
| 1232 | |
|---|
| 1233 | #ifdef gfan_DEBUG |
|---|
| 1234 | cout << "Now in subroutine gfan" << endl; |
|---|
| 1235 | #endif |
|---|
| 1236 | ring inputRing=currRing; // The ring the user entered |
|---|
| 1237 | ring rootRing; // The ring associated to the target ordering |
|---|
| 1238 | ideal res; |
|---|
| 1239 | facet *fRoot; |
|---|
| 1240 | |
|---|
| 1241 | /* |
|---|
| 1242 | 1. Select target order, say dp. |
|---|
| 1243 | 2. Compute GB of inputIdeal wrt target order -> newRing, setCurrRing etc... |
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| 1244 | 3. getConeNormals |
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| 1245 | */ |
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| 1246 | |
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| 1247 | /* Construct a new ring which will serve as our root |
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| 1248 | Does not yet work as expected. Will work fine with order dp,Dp but otherwise hangs in getGB |
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| 1249 | resolved 07.04.2009 MM |
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| 1250 | */ |
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| 1251 | rootRing=rCopy0(currRing); |
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| 1252 | rootRing->order[0]=ringorder_lp; |
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| 1253 | //NOTE: Build ring accordiing to rCopyAndChangeWeight |
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| 1254 | /*rootRing->order[0]=ringorder_a; |
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| 1255 | rootRing->order[1]=ringorder_lp; |
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| 1256 | rootRing->wvhdl[0] =( int *)omAlloc(numvar*sizeof(int)); |
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| 1257 | rootRing->wvhdl[0][1]=1; |
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| 1258 | rootRing->wvhdl[0][2]=1;*/ |
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| 1259 | rComplete(rootRing); |
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| 1260 | rChangeCurrRing(rootRing); |
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| 1261 | |
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| 1262 | /* Fetch the inputIdeal into our rootRing */ |
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| 1263 | map theMap=(map)idMaxIdeal(1); //evil hack! |
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| 1264 | theMap->preimage=NULL; //neccessary? |
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| 1265 | ideal rootIdeal; |
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| 1266 | rootIdeal=fast_map(inputIdeal,inputRing,(ideal)theMap, currRing); |
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| 1267 | #ifdef gfan_DEBUG |
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| 1268 | cout << "Root ideal is " << endl; |
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| 1269 | idShow(rootIdeal); |
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| 1270 | cout << "The root ring is " << endl; |
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| 1271 | rWrite(rootRing); |
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| 1272 | cout << endl; |
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| 1273 | #endif |
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| 1274 | |
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| 1275 | //gcone *gcRoot = new gcone(); //Instantiate the sink |
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| 1276 | gcone *gcRoot = new gcone(rootRing,rootIdeal); |
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| 1277 | gcone *gcAct; |
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| 1278 | gcAct = gcRoot; |
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| 1279 | gcAct->numVars=pVariables; |
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| 1280 | gcAct->getGB(rootIdeal); //sets gcone::gcBasis |
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| 1281 | idShow(gcAct->gcBasis); |
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| 1282 | gcAct->getConeNormals(gcAct->gcBasis); //hopefully compute the normals |
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| 1283 | //gcAct->flip(gcAct->gcBasis,gcAct->facetPtr); |
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| 1284 | /*Now it is time to compute the search facets, respectively start the reverse search. |
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| 1285 | But since we are in the root all facets should be search facets. IS THIS TRUE? |
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| 1286 | NOTE: Check for flippability is not very sophisticated |
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| 1287 | */ |
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| 1288 | /*facet *fAct=new facet(); |
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| 1289 | fAct=gcAct->facetPtr; |
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| 1290 | while(fAct->next!=NULL) |
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| 1291 | { |
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| 1292 | gcAct->flip(gcAct->gcBasis,gcAct->facetPtr); |
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| 1293 | gcone *gcTmp = new gcone(*gcAct); |
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| 1294 | idShow(gcTmp->gcBasis); |
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| 1295 | gcTmp->getConeNormals(gcTmp->gcBasis, TRUE); |
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| 1296 | gcTmp->getIntPoint(); |
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| 1297 | fAct = fAct->next; |
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| 1298 | }*/ |
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| 1299 | gcAct->reverseSearch(gcAct); |
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| 1300 | /*As of now extra.cc expects gfan to return type ideal. Probably this will change in near future. |
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| 1301 | The return type will then be of type LIST_CMD |
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| 1302 | Assume gfan has finished, thus we have enumerated all the cones |
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| 1303 | Create an array of size of #cones. Let each entry in the array contain a pointer to the respective |
|---|
| 1304 | Groebner Basis and merge this somehow with LIST_CMD |
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| 1305 | => Count the cones! |
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| 1306 | */ |
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| 1307 | rChangeCurrRing(rootRing); |
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| 1308 | //res=gcAct->gcBasis; |
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| 1309 | res=gcRoot->gcBasis; |
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| 1310 | return res; |
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| 1311 | //return GBlist; |
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| 1312 | } |
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| 1313 | /* |
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| 1314 | Since gfan.cc is #included from extra.cc there must not be a int main(){} here |
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| 1315 | */ |
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| 1316 | #endif |
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