c#中的小数到精确分数转换器

Question

所以我开始了一个项目，我制作了一个二次方程求解器，并且我设法做到了。我的下一步是转换 X₁ 和 X₂ 的值，例如 (X+X₁)(X+X ₂) 精确到分数，如果它们变成小数的话。

所以一个例子是：

12x² + 44x + 21

给我，

X₁ = -3.10262885097732

X₂ = -0.564037815689349

但是我怎么能把它转换成一个精确的分数呢？ 感谢您的帮助！

Answer 1

您可以使用Continued Fractions 解决此问题。

如 cmets 所述，您无法获得完全代表 irrational number 的分数（rational number），但您可以非常接近。

我在一个宠物项目中实现了一次有理数类型。你可以找到它here。查看TryFromDouble 的示例，了解如何使用连续分数获得与任何给定数字最接近的有理数（具有指定精度）。

相关代码的摘录如下（我会 不贴整个类型实现，因为太长了，但代码应该还是挺容易理解的）：

public static bool TryFromDouble(double target, double precision, out Rational result)
{
    //Continued fraction algorithm: http://en.wikipedia.org/wiki/Continued_fraction
    //Implemented recursively. Problem is figuring out when precision is met without unwinding each solution. Haven't figured out how to do that.
    //Current implementation computes rational number approximations for increasing algorithm depths until precision criteria is met, maximum depth is reached (fromDoubleMaxIterations)
    //or an OverflowException is thrown. Efficiency is probably improvable but this method will not be used in any performance critical code. No use in optimizing it unless there is
    //a good reason. Current implementation works reasonably well.

    result = zero;
    int steps = 0;

    while (Math.Abs(target - Rational.ToDouble(result)) > precision)
    {
        if (steps > fromDoubleMaxIterations)
        {
            result = zero;
            return false;
        }

        result = getNearestRationalNumber(target, 0, steps++);
    }

    return true;
}

private static Rational getNearestRationalNumber(double number, int currentStep, int maximumSteps)
{
    var integerPart = (BigInteger)number;
    double fractionalPart = number - Math.Truncate(number);

    while (currentStep < maximumSteps && fractionalPart != 0)
    {
        return integerPart + new Rational(1, getNearestRationalNumber(1 / fractionalPart, ++currentStep, maximumSteps));
    }

    return new Rational(integerPart);
}