Flutter数学方程渲染插件equations的使用

简介

equations 包是一个用纯 Dart 编写的用于解决数值分析问题的库。它可以在 Dart CLI 项目或 Flutter 跨平台应用程序中使用。以下是该包的主要功能：

• 解决多项式方程
• 解决非线性方程
• 解决线性方程组
• 计算积分
• 插值数据点

此外，还提供了处理实数和复数矩阵、复数、分数的功能。

安装

在 pubspec.yaml 文件中添加依赖：

dependencies:
  equations: ^latest_version

替换 latest_version 为最新版本号，可以通过 pub.dev 查找。

示例代码

多项式方程求解

使用 Cubic 类求解三次方程

import 'package:equations/equations.dart';

void main() {
  // f(x) = (2-3i)x^3 + 6/5ix^2 - (-5+i)x - (9+6i)
  final equation = Cubic(
    a: Complex(2, -3),
    b: Complex.fromImaginaryFraction(Fraction(6, 5)),
    c: Complex(5, -1),
    d: Complex(-9, -6)
  );

  print('Degree: ${equation.degree}');
  print('Is Real Equation: ${equation.isRealEquation}');
  print('Discriminant: ${equation.discriminant()}');
  print('Equation: $equation');
  print('Equation with fractions: ${equation.toStringWithFractions()}');

  print('Roots:');
  for (final root in equation.solutions()) {
    print(root);
  }
}

使用 DurandKerner 类求解相同方程

import 'package:equations/equations.dart';

void main() {
  // f(x) = (2-3i)x^3 + 6/5ix^2 - (-5+i)x - (9+6i)
  final equation = DurandKerner(
    coefficients: [
      Complex(2, -3),
      Complex.fromImaginaryFraction(Fraction(6, 5)),
      Complex(5, -1),
      Complex(-9, -6),
    ]
  );

  print('Roots:');
  for (final root in equation.solutions()) {
    print(root);
  }
}

非线性方程求解

使用 Newton 类求解非线性方程

import 'package:equations/equations.dart';

void main() {
  final newton = Newton("2*x+cos(x)", -1, maxSteps: 5);

  print('Max Steps: ${newton.maxSteps}');
  print('Tolerance: ${newton.tolerance}');
  print('Function: ${newton.function}');
  print('Initial Guess: ${newton.x0}');

  final solutions = newton.solve();
  print('Convergence: ${solutions.convergence.round()}');
  print('Efficiency: ${solutions.efficiency.round()}');

  print('Guesses:');
  for (final guess in solutions.guesses) {
    print(guess);
  }
}

线性方程组求解

使用 LUSolver 类求解线性方程组

import 'package:equations/equations.dart';

void main() {
  final luSolver = LUSolver(
    equations: const [
      [7, -2, 1],
      [14, -7, -3],
      [-7, 11, 18]
    ],
    constants: const [12, 17, 5]
  );

  print('Solutions: ${luSolver.solve()}');
  print('Determinant: ${luSolver.determinant()}');
}

数值积分

使用 SimpsonRule 类进行数值积分

import 'package:equations/equations.dart';

void main() {
  const simpson = SimpsonRule(
    function: 'sin(x)*e^x',
    lowerBound: 2,
    upperBound: 4,
  );

  final results = simpson.integrate();
  print('Integral Result: ${results.result.toStringAsFixed(3)}');
  print('Number of Guesses: ${results.guesses.length}');
}

插值

使用 NewtonInterpolation 类进行牛顿插值

import 'package:equations/equations.dart';

void main() {
  const newton = NewtonInterpolation(
    nodes: [
      InterpolationNode(x: 45, y: 0.7071),
      InterpolationNode(x: 50, y: 0.7660),
      InterpolationNode(x: 55, y: 0.8192),
      InterpolationNode(x: 60, y: 0.8660),
    ],
  );

  print('Interpolated Value at x=52: ${newton.compute(52).toStringAsFixed(3)}');
  print('Forward Difference Table:\n${newton.forwardDifferenceTable()}');
}

表达式解析

使用 ExpressionParser 类解析表达式

import 'package:equations/equations.dart';

void main() {
  const parser = ExpressionParser();

  print(parser.evaluate('5*3-4')); // 11
  print(parser.evaluate('sqrt(49)+10')); // 17
  print(parser.evaluate('pi')); // 3.1415926535

  print(parser.evaluateOn('6*x + 4', 3)); // 22
  print(parser.evaluateOn('sqrt(x) - 3', 81)); // 6
}

通过以上示例代码，您可以快速上手 equations 包，解决各种数学问题。更多详细信息可以参考 官方文档。