RationalNumber.hpp

#ifndef _BPAS_RATIONAL_NUMBER_H_
#define _BPAS_RATIONAL_NUMBER_H_

#include "BPASField.hpp"
#include <gmpxx.h>
#include <iostream>

//forward declarations
class Integer;
class ComplexRationalNumber;
class SmallPrimeField;
class BigPrimeField;
class GeneralizedFermatPrimeField;
class DenseUnivariateIntegerPolynomial;
class DenseUnivariateRationalPolynomial;
template <class Ring>
class SparseUnivariatePolynomial;
class SparseMultivariateRationalPolynomial;

/**
 * An arbitrary-precision rational number.
 */
class RationalNumber : public BPASField<RationalNumber> {
    private:
        mpq_class _m;
    
    public:
        static mpz_class characteristic;
        static RingProperties properties;

        // static bool isPrimeField;
        // static bool isSmallPrimeField;
        // static bool isComplexField;

        RationalNumber ();

        RationalNumber (int a, int b = 1);
        
        RationalNumber (const std::string& digits, int base = 10); 

        RationalNumber (const mpq_t& q);

        RationalNumber (const mpq_class& a);

        RationalNumber (const mpz_class& a, const mpz_class& b = mpz_class(1));

        RationalNumber (const RationalNumber& a);

        explicit RationalNumber (const Integer& a);

        explicit RationalNumber (const ComplexRationalNumber& a);

        explicit RationalNumber (const SmallPrimeField& a);

        explicit RationalNumber (const BigPrimeField& a);
        
        explicit RationalNumber (const GeneralizedFermatPrimeField& a);

        explicit RationalNumber (const DenseUnivariateIntegerPolynomial& a);

        explicit RationalNumber (const DenseUnivariateRationalPolynomial& a);

        explicit RationalNumber (const SparseUnivariatePolynomial<Integer>& a);

        explicit RationalNumber (const SparseUnivariatePolynomial<RationalNumber>& a);

        explicit RationalNumber (const SparseUnivariatePolynomial<ComplexRationalNumber>& a);

        explicit RationalNumber (const SparseMultivariateRationalPolynomial& a);

        template <class Ring>
        explicit RationalNumber (const SparseUnivariatePolynomial<Ring>& a);

        RationalNumber* RNpointer(RationalNumber* a);

        RationalNumber* RNpointer(SmallPrimeField* a);

        RationalNumber* RNpointer(BigPrimeField* a);

        RationalNumber* RNpointer(GeneralizedFermatPrimeField* a);

        RationalNumber& set (int a, int b);

        inline mpq_class get_mpq() const {
            return _m;
        }

        inline mpq_class& get_mpq_ref() {
            return _m;
        }

        inline const mpq_class& get_mpq_ref() const {
            return _m;
        }

        inline mpq_ptr get_mpq_t() {
            return _m.get_mpq_t();
        }

        inline mpq_srcptr get_mpq_t() const {
            return _m.get_mpq_t();
        }

        inline Integer get_num() const {
            return Integer(_m.get_num());
        }

        double get_d() const {
            return _m.get_d();
        }

        inline Integer get_den() const {
            return Integer(_m.get_den());
        }

        /**
         * Is a zero
         *
         * @param
         **/
        inline bool isZero() const {
            return (_m == 0);
        }

        /**
         * Assign to zero
         *
         * @param
         **/ 
        inline void zero() {
            _m = 0;
        }
    
        /**
         * Is a 1
         *
         * @param
         **/
        inline bool isOne() const {
            return (_m == 1);
        }
    
        /**
         * Assign to one
         *
         * @param
         **/ 
        inline void one() {
            _m = 1;
        }
    
        /**
         * Is a -1
         *
         * @param
         **/
        inline bool isNegativeOne() const {
            return (_m == -1);
        }
    
        /**
         * Assign to negative one
         *
         * @param
         **/
        inline void negativeOne() {
            _m = -1;
        }
    
        /**
         * Is a constant
         *
         * @param
         **/
        inline int isConstant() const {
            if (_m >= 0)
                return 1;
            else { return -1; }
        }

        /**
         * Obtain the unit normal (a.k.a canonical associate) of an element. 
         * If either parameters u, v, are non-NULL then the units are returned such that 
         * b = ua, v = u^-1. Where b is the unit normal of a, and is the returned value.
         */
        RationalNumber unitCanonical(RationalNumber* u = NULL, RationalNumber* v = NULL) const;

        /**
         * Copy assignment.
         */
        RationalNumber& operator= (const RationalNumber& a);

        /**
         * Addition.
         */
        inline RationalNumber operator+ (const RationalNumber& i) const {
            RationalNumber ret = *this;
            ret += i;
            return ret;
        }

        /**
         * Addition assignment.
         */
        inline RationalNumber& operator+= (const RationalNumber& i) {
            _m += i._m;
            return *this;
        }
        
        /**
         * Subtraction.
         */
        inline RationalNumber operator- (const RationalNumber& i) const {
            RationalNumber ret = *this;
            ret -= i;
            return ret;
        }
        
        /**
         * Subtraction assignment.
         */
        inline RationalNumber& operator-= (const RationalNumber& i) {
            _m -= i._m;
            return *this;
        }

        /**
         * Negation.
         */
        inline RationalNumber operator- () const {
            RationalNumber ret;
            mpq_neg(ret._m.get_mpq_t(), (*this)._m.get_mpq_t());
            return ret;
        }

        /**
         * Multiplication.
         */
        inline RationalNumber operator* (const RationalNumber& i) const {
            RationalNumber ret = *this;
            ret *= i;
            return ret;
        }

        /**
         * Multiplication assignment.
         */
        inline RationalNumber& operator*= (const RationalNumber& i) {
            _m *= i._m;
            return *this;
        }
        
        /**
         * Equality test,
         *
         * returns true iff equal
         */
        inline bool operator== (const RationalNumber& i) const {
            return (_m == i._m); 
        }

        /**
         * Inequality test,
         *
         * returns true iff not equal.
         */
        inline bool operator!= (const RationalNumber& i) const {
            return (_m != i._m); 
        }

        inline ExpressionTree convertToExpressionTree() const {
            return ExpressionTree(new ExprTreeNode(_m));
        }

        /**
         * Exact division.
         */
        inline RationalNumber operator/ (const RationalNumber& i) const {
            //TODO ensure this is exact and not rounded
            RationalNumber ret = *this;
            ret /= i;
            return ret;
        }

        /**
         * Exact division assignment.
         */
        inline RationalNumber& operator/= (const RationalNumber& i) {
            _m /= i._m;
            return *this;
        }

        inline bool operator< (const RationalNumber& r) const {
            return _m < r._m;
        }

        inline bool operator<= (const RationalNumber& r) const {
            return _m <= r._m;
        }

        inline bool operator> (const RationalNumber& r) const {
            return _m > r._m;
        }

        inline bool operator>= (const RationalNumber& r) const {
            return _m >= r._m;
        }

        /**
         * GCD(a, b)
         *
         * @param b: The other rational number
         **/
        inline RationalNumber gcd (const RationalNumber& b) const {
            RationalNumber c;
            if (this->isZero() && b.isZero())
                c = 0;
            else
                c = 1;
            return c;
        }
        
        /**
         * Compute squarefree factorization of *this
         */
        inline Factors<RationalNumber> squareFree() const {
            std::vector<RationalNumber> ret;
            ret.push_back(*this);
            return ret;
        }
    
        /** 
         * Get the euclidean size of *this.
         */
        inline RationalNumber euclideanSize() const {
            std::cerr << "RationalNumber::euclideanSize NOT YET IMPLMENETED" << std::endl;
            exit(1);
            return *this;
        }
        
        /**
         * Perform the eucldiean division of *this and b. Returns the 
         * remainder. If q is not NULL, then returns the quotient in q. 
         */ 
        RationalNumber euclideanDivision(const RationalNumber& b, RationalNumber* q = NULL) const;

        /**
         * Perform the extended euclidean division on *this and b. 
         * Returns the GCD. If s and t are not NULL, returns the bezout coefficients in them.
         */
        RationalNumber extendedEuclidean(const RationalNumber& b, RationalNumber* s = NULL, RationalNumber* t = NULL) const;
        
        /**
         * Get the quotient of *this and b.
         */
        RationalNumber quotient(const RationalNumber& b) const;

        /** 
         * Get the remainder of *this and b.
         */
        RationalNumber remainder(const RationalNumber& b) const;


        /**
         * Overload operator ^
         * replace xor operation by exponentiation
         *
         * @param e: The exponentiation
         **/
        inline RationalNumber operator^ (long long int e) const {
            RationalNumber r;
            mpz_pow_ui(r._m.get_num_mpz_t(), _m.get_num_mpz_t(), (unsigned long int) e);
            mpz_pow_ui(r._m.get_den_mpz_t(), _m.get_den_mpz_t(), (unsigned long int) e);
            return r;
        }

        inline RationalNumber& operator^= (long long int e) {
            *this = *this ^ e;
            return *this;
        }
        
        inline RationalNumber operator% (const RationalNumber& r) const {
            return 0;
        }

        inline RationalNumber& operator%= (const RationalNumber& r) {
            *this = 0;
            return *this;
        }

        inline RationalNumber inverse() const {
            RationalNumber ret;
            mpz_set(ret._m.get_den_mpz_t(), _m.get_num_mpz_t());
            mpz_set(ret._m.get_num_mpz_t(), _m.get_den_mpz_t());
            ret._m.canonicalize();
            return ret;
        }



        //Friend functions

        inline friend RationalNumber operator+(int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) + r._m);
        }

        inline friend RationalNumber operator-(int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) - r._m);
        }

        inline friend RationalNumber operator*(int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) * r._m);
        }

        inline friend RationalNumber operator/(int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) / r._m);
        }

        inline friend RationalNumber operator+(long int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) + r._m);
        }

        inline friend RationalNumber operator-(long int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) - r._m);
        }

        inline friend RationalNumber operator*(long int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) * r._m);
        }

        inline friend RationalNumber operator/(long int a, const RationalNumber& r) {
            return RationalNumber(mpq_class(a) / r._m);
        }

        inline friend RationalNumber abs(const RationalNumber& i) {
            return RationalNumber(abs(i._m));
        }





};

#endif