有理数系的线性代数运算程序(1)有理数类
线性代数主要涉及矩阵的运算，尤其是矩阵中行/列变换，矩阵的秩、行列式、线性方程组、特征值等问题。在开始设计之前，先完成有理数系的运算。我们要将分数形式的数字展现成分数而不是近似小数。
首先添加一个类RationalNumber，表示一个有理数，如果它是整数，则分母为1，如果它是小数，就保存成最简分数。如果是负有理数，保证负号在分子上。这样定义后重载四则运算和判等运算的运算符。
class RationalNumber
{
private int _num, _den;
private int gcd(int x,int y)
{
if(x%y==0)
{
return y;
}
else
{
return gcd(y, x % y);
}
}
public RationalNumber()
{
_num = 0;
_den = 1;
}
public RationalNumber(int x)
{
_num = x;
_den = 1;
}
public RationalNumber(int nn,int dd)
{
int sign = 1;
int g = gcd(Math.Abs(nn), Math.Abs(dd));
if(nn*dd<0)
{
sign = -1;
}
_num = sign*Math.Abs(nn)/g;
_den = Math.Abs(dd)/g;
}
public string ToLaTeX()
{
if (_den == 1)
{
return _num.ToString();
}
else
{
if (_num > 0)
{
return String.Format("\\frac{{{0}}}{{{1}}}", _num, _den);
}
else
{
return String.Format("-\\frac{{{0}}}{{{1}}}", -_num, _den);
}
}
}
public override string ToString()
{
return String.Format("{0}/{1}", _num, _den);
}
public static RationalNumber operator+(RationalNumber self,RationalNumber o)
{
return new RationalNumber(self._num * o._den + self._den * o._num, self._den * o._den);
}
public static RationalNumber operator -(RationalNumber self, RationalNumber o)
{
return new RationalNumber(self._num * o._den - self._den * o._num, self._den * o._den);
}
public static RationalNumber operator *(RationalNumber self, RationalNumber o)
{
return new RationalNumber(self._num * o._num, self._den * o._den);
}
public static RationalNumber operator /(RationalNumber self, RationalNumber o)
{
return new RationalNumber(self._num * o._den, self._den * o._num);
}
public static RationalNumber operator /( int o, RationalNumber self)
{
return new RationalNumber( self._den * o, self._num);
}
public static RationalNumber operator /(RationalNumber self, int o)
{
return new RationalNumber(self._num , self._den *o );
}
public static bool operator ==(RationalNumber self, RationalNumber o)
{
return self._num == o._num && self._den == o._den;
}
public static bool operator !=(RationalNumber self, RationalNumber o)
{
return !(self._num == o._num && self._den == o._den);
}
public static bool operator ==(RationalNumber self, int o)
{
return self._den == 1 && self._num == o;
}
public static bool operator !=(RationalNumber self, int o)
{
return (self._den != 1 || (self._den ==1 && self._num != o));
}
public override bool Equals(Object o)
{
return this is RationalNumber && this == (RationalNumber)o;
}
public override int GetHashCode()
{
return Convert.ToInt32(String.Format("{0}{1}",_num , _den));
}
}