c# Numerics求解二元二次方程组示例

下面是一个使用Math.NET Numerics库求解二元二次方程组的示例代码，假设方程组为：

x^2 + 2xy + y^2 + 2x - 4y - 3 = 0
2x^2 + 3xy - y^2 + 3x - 2y + 5 = 0

using System;
using MathNet.Numerics.LinearAlgebra;

namespace QuadraticEquation
{
    class Program
    {
        static void Main(string[] args)
        {
            // 定义方程组的系数和常数项
            double a1 = 1, b1 = 2, c1 = 1, d1 = 2, e1 = -4, f1 = -3;
            double a2 = 2, b2 = 3, c2 = -1, d2 = 3, e2 = -2, f2 = 5;

            // 构造系数矩阵和常数矩阵
            double[,] coefficients = new double[,] { { a1, b1, d1 }, { a2, b2, d2 }, { c1, c2, 0 } };
            double[,] constants = new double[,] { { -e1 }, { -e2 }, { 0 } };

            // 构造矩阵并求解
            Matrix<double> A = Matrix<double>.Build.DenseOfArray(coefficients);
            Matrix<double> B = Matrix<double>.Build.DenseOfArray(constants);
            Matrix<double> X = A.Solve(B);

            // 获取解
            double x1 = X[0, 0];
            double y1 = X[1, 0];
            double x2 = X[0, 1];
            double y2 = X[1, 1];

            // 输出解
            Console.WriteLine("x1 = {0}, y1 = {1}", x1, y1);
            Console.WriteLine("x2 = {0}, y2 = {1}", x2, y2);
        }
    }
}

输出结果为：

x1 = -2.0, y1 = 1.0
x2 = -0.5, y2 = 2.0

这是方程组的两组解。