计算多项式的系数作为抽象类数

我正在努力添加代表适当数学对象的类Natural, Rational, Complex的操作。我需要它来计算x的多项式

所有类继承抽象类Number。把所有系数放在一个数字数组中，我想计算多项式。要做到这一点，我需要乘以2倍的运算(x是2倍)x被转化为有理并相乘。这很好。我的问题是如何添加抽象类型的类数?

我不能使它工作。所有我得到的是在Number::add(Number)中永不结束的递归(它调用自己而不是调用其他类型的Natural, Rational, Complex的方法)。

# include# include# include# include# include# include# include使用命名空间std;

class Natural;class Rational;class Complex;
class Number {
public:
  virtual string toString() const = 0;
  virtual Number *operator*(const Rational) const = 0;
  virtual Number *add(const Natural*) const = 0;
  virtual Number *add(const Rational*) const = 0;
  virtual Number *add(const Complex*) const = 0;
  virtual Number *add(const Number *n) const {
    n->add(this);
  }
};
class Natural : public Number {
  friend class Complex;
  int n;
public:
  Natural(const Natural &s) {
    n = s.n;
  }
  Natural(int number) : n(number) {}
  string toString() const {
    stringstream ss;
    ss << n;
    return ss.str();
  }
  operator Rational() const;
  operator Complex() const;
  operator int() const {
    return n;
  }
  Number *operator*(const Rational r) const;
  Number *add(const Natural* number) const {
    return new Natural(n + number->n);
  }
  Number *add(const Rational*) const;
  Number *add(const Complex*) const;
};
class Rational : public Number {
  friend class Natural;
  int numerator, denominator;
  void divideByGCD() {
    int a = numerator, b = denominator;
    //cout << a << ' ' << b << ' ';
    if(a < b) {
      int temp = a;
      a = b;
      b = temp;
    }
    while (b > 0) {
      int r = a % b;
      a = b; b = r;
      //cout << r << endl;
    }
    numerator /= a;
    denominator /= a;
    //cout << a << endl;
  }
public:
  Rational() {}
  Rational(const Rational &s) {
    numerator = s.numerator;
    denominator = s.denominator;
  }
  Rational(int n, int d) {
    if(d == 0) throw new runtime_error("denominator equals 0");
    if(d < 0) {
      numerator = -n;
      denominator = -d;
    } else {
      numerator = n;
      denominator = d;
    }
    divideByGCD();
  }
  Rational(double d) {
    int i = 0, mul = 1;
    int r = d-floor(d);;
    while(r!=0) {
      i++; mul *= 10;
      r = 10*r-floor(10*r);
    }
    numerator = (int)mul*d;
    denominator = mul;
    divideByGCD();
  }
  string toString() const {
    stringstream ss;
    ss << numerator;
    if(denominator > 1) ss << '/' << denominator;
    return ss.str();
  }
  operator const Complex() const;
  operator const double() const {
    return (double)numerator/denominator;
  }
  Number *operator*(const Rational r) const {
    return new Rational(numerator*r.numerator, denominator*r.denominator);
  }
  Number *add(const Rational* r) const {
    return new Rational(numerator*r->denominator+r->numerator*denominator, denominator*r->denominator);
  }
  Number *add(const Natural*) const;
  Number *add(const Complex*) const;
};
class Complex : public Number {
  friend class Rational;
  double real, imaginary;
  static const double radius = 10;
public:
  Complex() {}
  Complex(const Complex &s) {
    real = s.real;
    imaginary = s.imaginary;
  }
  Complex(const double r, const double im) : real(r), imaginary(im) {}
  string toString() const {
    stringstream ss;
    ss << real;
    if(imaginary != 0) ss << '+' << imaginary << 'i';
    return ss.str();
  }
  Number *operator*(const Rational r) const;
  Number *add(const Complex* c) const {
    return new Complex(real + c->real, imaginary + c->imaginary);
  }
  Number *add(const Natural*) const;
  Number *add(const Rational*) const;
};
Natural::operator Rational() const {
  return Rational(n,1);
}
Natural::operator Complex() const {
  return Complex(n, 0);
}
Rational::operator const Complex() const {
  return Complex((double)numerator/denominator, 0);
}
Number *Natural::operator*(const Rational r) const {
  return new Rational(n*r.numerator, r.denominator);
}
Number *Complex::operator*(const Rational r) const {
  return new Complex(real*(double)r, imaginary*(double)r);
}
Number *Natural::add(const Rational *r) const {
  if(r->denominator == 1) return new Natural(n+r->numerator);
  else return new Rational(n*r->denominator,r->denominator);
}
Number *Natural::add(const Complex *c) const {
  return c->add(this);
}
Number *Rational::add(const Natural *n) const {
  return n->add(this);
}
Number *Rational::add(const Complex *c) const {
  return new Complex(c->real+(double)*this, c->imaginary);
}
Number *Complex::add(const Natural *number) const {
  return new Complex(real+number->n, imaginary);
}
Number *Complex::add(const Rational *r) const {
  return r->add(this);
}
Number *poly(double x, Number *a[], unsigned int size) {
  if(size == 1) return a[0];
  else return a[0]->add((*poly(x, a+1, size-1))*Rational(x));
}
int main() {
  cout << (Natural(5)*(Rational)2.0)->toString() << endl;
  Number *coefs[] = {new Natural(5), new Natural(6)};
  cout <<  poly(2, coefs, 2) << endl;
}

我应该如何修复Number::add(Number)，以便在调用类型为Number的对象上的add时，程序本身可以确定选择哪种虚拟方法add ?