使用 Math.NET 符号求解线性方程

Question

我尝试修改给定的代码来求解 x 值的线性方程。比如

(3*x+7)/3+(2*x)/9=6/10

首先将它分成左右两个表达式，然后使用 "SolveSimpleRoot"，它给出了 x 的值。但是如果把线性方程写成

的形式

(3+2*x)/(5*x-2)=7，你可以通过 (5*x-2) 多次遍历它并且确实是线性的然后代码在

// extract coefficients, solve known forms of order up to 1
MathNet.Symbolics.Expression[] coeff = MathNet.Symbolics.Polynomial.Coefficients(variable, simple);

错误为：

The input sequence was empty.Parameter name: source

如果表达式类似于 (2x+7)/x=2，它也无法解决，它仍然扩展为线性。

知道为什么吗？

代码基本上是：

    public void solveForX()
    {
        string eqn = "(3*x+7)/3+(2*x)/9=6/10"

        string[] expString = eqn.Split('=');

        var x = MathNet.Symbolics.Expression.Symbol("x");

        MathNet.Symbolics.Expression aleft = MathNet.Symbolics.Infix.ParseOrThrow(expString[0]);
        MathNet.Symbolics.Expression aright = MathNet.Symbolics.Infix.ParseOrThrow(expString[1]);


        ans = SolveSimpleRoot(x, aleft - aright);
        SelectionInsertText(MathNet.Symbolics.Infix.Print(cx));
    }

    private MathNet.Symbolics.Expression SolveSimpleRoot(MathNet.Symbolics.Expression variable, MathNet.Symbolics.Expression expr)
    {
        // try to bring expression into polynomial form
        MathNet.Symbolics.Expression simple = MathNet.Symbolics.Algebraic.Expand(MathNet.Symbolics.Rational.Simplify(variable, expr));

        // extract coefficients, solve known forms of order up to 1
        MathNet.Symbolics.Expression[] coeff = MathNet.Symbolics.Polynomial.Coefficients(variable, simple);
        switch (coeff.Length)
        {
            case 1: return variable;
            case 2: return MathNet.Symbolics.Rational.Simplify(variable, MathNet.Symbolics.Algebraic.Expand(-coeff[0] / coeff[1]));
            default: return MathNet.Symbolics.Expression.Undefined;
        }
    }

Answer 1

您可以通过将两边与分母相乘来扩展它以支持这种有理数情况（因此有效地只取分子，Rational.Numerator）：

private Expr SolveSimpleRoot(Expr variable, Expr expr)
{
    // try to bring expression into polynomial form
    Expr simple = Algebraic.Expand(Rational.Numerator(Rational.Simplify(variable, expr)));

    // extract coefficients, solve known forms of order up to 1
    Expr[] coeff = Polynomial.Coefficients(variable, simple);
    switch (coeff.Length)
    {
        case 1: return Expr.Zero.Equals(coeff[0]) ? variable : Expr.Undefined;
        case 2: return Rational.Simplify(variable, Algebraic.Expand(-coeff[0] / coeff[1]));
        default: return Expr.Undefined;
    }
}

这样也可以处理(3+2*x)/(5*x-2)=7。如果在这种情况下系数不等于零，我还将情况 1 固定为 return 未定义，因此另一个示例 (2*x+7)/x=2 的解决方案将按预期未定义。

当然，这仍然是一个非常简单的例程，无法处理任何高阶问题。

使用 Math.NET 符号求解线性方程

Solving linear equation using Math.NET Symbolics

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math.net