#ifndef POLYNOMIAL_H_INCLUDED
#define POLYNOMIAL_H_INCLUDED

class Polynomial;
class PolynomialSet;
//class PolynomialSetList;

#include <map>
#include "polynomialring.h"
//#include "linalg.h"
#include "term.h"
#include "termorder.h"


struct TermMapCompare
{
  inline bool operator()(const Monomial &s1, const Monomial &s2) const
  {
    return LexicographicTermOrder()(s1.exponent,s2.exponent);
  }
};

typedef std::map<Monomial,FieldElement,TermMapCompare> TermMap;

class Polynomial
{
  Term marked;
  bool isMarkedBool;
  int sugar;
  PolynomialRing theRing;
 public:
  PolynomialRing const &getRing()const{return theRing;}
  TermMap terms;
  Polynomial(const Term &t);
  Polynomial(PolynomialRing const &r);
  void computeInitialSugar();
  int getSugar()const;
  void madd(const Term &m, const Polynomial &p);
  void operator+=(const Polynomial &p);
  void operator-=(const Polynomial &p);
  friend Polynomial operator+(const Polynomial &p, const Polynomial &q);
  friend Polynomial operator-(const Polynomial &p, const Polynomial &q);
  void operator*=(const Term &p);
  void operator*=(const Monomial &m);
  void operator*=(FieldElement const &c);
  void operator*=(Polynomial const &p);
  friend Polynomial operator*(const Polynomial &p, Term const &t);
  friend Polynomial operator*(const Polynomial &p, Monomial const &m);
  friend Polynomial operator*(const Polynomial &p, FieldElement const &c);
  friend Polynomial operator*(const Polynomial &p, const Polynomial &q);
  int getNumberOfVariables()const;
  void changeNumberOfVariables(int n);
  void mark(class TermOrder const &termOrder);
  void mark(Monomial const &monomial);
  void scaleMarkedCoefficientToOne();
  bool isMonomial() const;
  const Term &getMarked()const{return marked;}
  bool isZero()const;
  int numberOfTerms()const;//linear time in worst case!
  IntegerVector exponentsSum()const;
  int totalDegree()const;
  int64 degree(IntegerVector const &w)const;// evaluateTropically
  Polynomial homogenization(PolynomialRing const &newRing, IntegerVector const *w=0)const;
  /**
     Each variable x_i in the polynomial is substituted by w_ix_i.
   */
  Polynomial torusAct(class FieldVector const &w)const;
  Polynomial derivative()const;//single variable
  Polynomial deHomogenization()const;
  Polynomial deHomogenizationInSameRing()const;
  int numberOfVariablesInRing()const;//by looking at just one monomial
  bool checkMarking(TermOrder const &termOrder)const;
  /**
     Checks wether the polynomial is homogeneous with respect to the
     grading given by the vector.
   */
  bool isHomogeneous(IntegerVector const &v)const;
  void saturate(int variableNum=-1);//default is to saturate with respect to all variables
  bool isMarked()const;
  bool isValid(int numberOfVarialbes=-1)const; //debug testing
  FieldElement evaluate(const FieldElement &x)const;//single variable
  int maximalIndexOfVariableInSupport()const;
  Polynomial embeddedInto(PolynomialRing const &r2, list<int> const *chosenVariables=0)const;
  /* Creates a polynomial in r2 by extending or truncating the
     exponent vectors of the current polynomial appropriately. In
     particular this method can be used for dehomogenization */
  int numberOfVariablesInUseConsecutive()const;
  string toString(bool latex/*, bool mathMode*/)const;
  /**
   * For debugging
   */
  bool checkExponentVectors()const;
};


class PolynomialCompare
{
 public:
  bool operator()(const Polynomial &a, const Polynomial &b)const;
};


class PolynomialCompareMarkedTerms
{
  TermOrder const &termOrder;
 public:
  PolynomialCompareMarkedTerms(TermOrder const &termOrder_);
  bool operator()(const Polynomial &a, const Polynomial &b)const;
};


class PolynomialCompareMarkedTermsReverse
{
  TermOrder const &termOrder;
 public:
  PolynomialCompareMarkedTermsReverse(TermOrder const &termOrder_);
  bool operator()(const Polynomial &a, const Polynomial &b)const;
};


class PolynomialSet : public list<Polynomial>
{
  PolynomialRing theRing;
 public:
  PolynomialSet(PolynomialRing const &r):theRing(r){}
  PolynomialRing const &getRing()const
    {
      return theRing;
    }
  int numberOfVariablesInUseConsecutive()const;
  void changeNumberOfVariables(int n=-1);
  int numberOfVariablesInRing()const;//by looking at just one monomial
  //  Field &
  void scaleMarkedCoefficientsToOne();
  void markAndScale(TermOrder const &termOrder);
  bool checkMarkings(TermOrder const &termOrder)const;
  /**
     The set of vectors inducing the markings of the polynomials in
     the set is an open polyhedral cone (assuming that the markings
     are consistent). This function checks if the vector v is
     contained in the closure of that cone.
   */
  bool containsInClosedGroebnerCone(IntegerVector const &v)const;
  /**
     Checks wether the polynomials are homogeneous with respect to the
     grading given by the vector.
   */
  bool isHomogeneous(IntegerVector const &v)const;
  void unionPolynomial(const Polynomial &p);
  void unionSet(const PolynomialSet &s);
  int totalDegree()const;
  IntegerVector exponentsSum()const;
  void sort_();
  friend bool operator==(PolynomialSet const &a, PolynomialSet const &b); //remember to call sort_ before calling this procedure
  bool isEqualTo(PolynomialSet const &b)const; //remember to call sort_ before calling this procedure
  PolynomialSet markedTermIdeal()const;
  void computeInitialSugar();
  bool isMarked()const;
  PolynomialSet homogenization(PolynomialRing const &newRing, IntegerVector const *w=0)const;
  PolynomialSet torusAct(FieldVector const &w)const;
  PolynomialSet deHomogenization()const;
  PolynomialSet deHomogenizationInSameRing()const;
  PolynomialSet polynomialRingIntersection(PolynomialRing const &newRing)const;//intersect the list of polynomials with a subpolynomial ring

  bool isValid()const; //debug testing
  void saturate(int variableNum=-1);//default is to saturate with respect to all variables
  PolynomialSet embeddedInto(PolynomialRing const &r2, list<int> const *chosenVariables=0)const;
  int totalNumberOfTerms()const;
};

typedef list<PolynomialSet> PolynomialSetList;
/*class PolynomialSetList : public list<PolynomialSet>
{
};*/

#endif