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////////////////////////////////////////////////////////////////////////////////////////////////////
// //
// rationals.h //
// =========== //
// //
// Code: Benjamin Jurke, http://benjaminjurke.net //
// //
////////////////////////////////////////////////////////////////////////////////////////////////////
// //
// File history: //
// - 08.04.2010 File created as rationals.h //
// //
////////////////////////////////////////////////////////////////////////////////////////////////////
#ifndef INC_RATIONALS_H
#define INC_RATIONALS_H
#include <string>
#include <map>
#include <vector>
#include <thread>
#include "iohandler.h"
#include "secondarycohom.h"
////////////////////////////////////////////////////////////////////////////////////////////////////
// In this file we take the list of monomials and secondary cohomology factors determined earlier
// and count the number of rational functions with the appropiate variables in the numerator and
// denominator. More precisely, this problem can be reformulated as a underdetermined linear system
// of equations, which is solved over the positive integers. Therefore the counting of rational
// functions is equivalent to counting the number of integer lattice points inside a corresponding
// polyhedron determined by those constraints. We rely on the freely available PolyLib library for
// the task of counting those integers, which makes use of the theory of Ehrhard polynomials.
//
// As for the data structures used in this class: The class CCohomology is the "result" class, which
// contains the requested charges of the divisor determining the line bundle O(D) again and of
// course the computed dimensions of the cohomology classes H^i(X;O(D)).
//
// The actual computations are carried out in the CRationals class, which basically serves as a
// wrapper for the PolyLib and translates our data format appropiately.
class CCohomology
{
friend class CRationals;
private:
// The output data
std::vector<int32_t> BundleGLSMch; // determines divisor D of line bundle O(D)
std::vector<std::vector<uint32_t> > CohomologyDims; // contains (candidate) dimensions of H^i(X;O(D))
std::vector<std::string> ContributingDenoms; // contains a vector of contributing denominator monomials
CMonomialsList monoms; // contains all monomials and their contributions to the results
public:
// Output functions
static std::string GetCohomologyGroupString(const std::vector<int32_t> &BundleGLSMcharges);
static std::string GetGroupDimensionsString(const std::vector<uint32_t> &CohomologyDimensions);
static std::string GetGroupDimensionsStringNoPadding(const std::vector<uint32_t> &CohomologyDimensions);
static std::string GetCohomologyString(const std::vector<int32_t> &BundleGLSMcharges, const std::vector<uint32_t> &CohomologyDimensions);
std::string GetCohomologyString() const;
void PrintFullCohomologyMonomialMap(const CInternalData &id, bool ShortList) const;
static void PrintCohomologies(const std::vector<CCohomology> &cohomologies);
static void SummarizeCohomologies(const std::vector<CCohomology> &cohomologies);
static void GetMathematicaCohomologiesList(const std::vector<CCohomology> &cohomologies, std::string &out);
// Data retrieval
inline bool IsAmbiguous() const { return (CohomologyDims.size() != 1); };
inline bool IsNotDetermined() const { return (CohomologyDims.size() < 1); };
};
class CRationals
{
private:
static std::vector< std::pair<std::thread *, void *> > WorkersList; // contains the list of worker threads;
static bool WaitForAllWorkersFinish();
private:
static void PrintPolyLibConstraintMatrix(const CInternalData &id, void *m);
static bool CountRationalFctns(const CInternalData &id, uint64_t monomial, const i32vec64 &TargetDivisor, uint32_t &out);
static bool ComputeCohomology(const CInternalData &id, CMonomialsList &ml, const i32vec64 &TargetDivisor, std::vector<uint32_t> &out_cohomology, std::vector<std::string> &out_contribcohoms);
static bool ComputeCohomologyAndSerreDual(const CInternalData &id, CMonomialsList &ml, const i32vec64 &TargetDivisor, std::vector<uint32_t> &out_cohomology, std::vector<std::string> &out_contribcohoms);
public:
static bool ComputeCohomologies(const CInternalData &id, const CMonomialsList &ml, std::vector<CCohomology> &out_cohomologies);
};
#endif
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