example/README.md

Examples #

Here is a quick overview of the main features of the equations package. For more information about solving equations and examples on how to use the classes from this package, see the articles on the repository's Wiki pages:

• Algebraic equations, for solving polynomial equations;
• Nonlinear equations, for solving nonlinear equations;
• Systems of equations, for solving systems of equations;
• Utilities, for working with matrices, evaluating integrals, interpolating data, and more.

Algebraic (Polynomial) equations #

// f(x) = ix^3 + (-2 + 5i)x + 7
final equation = Cubic(
  a: const Complex.i(),
  c: const Complex(-2, 5),
  d: const Complex.fromReal(7),
);
final solutions = equation.solutions();

/// -1.0447245173314328 + 1.7792977920746025i 
/// 0.3113353509227148 - 2.7574534545940717i
/// 0.733389166408717 + 0.9781556625194701i
print(solutions);

Nonlinear equations #

// f(x) = x^e - cos(x)
final newtonRaphson = Newton(function: 'x^e-cos(x)', x0: 0.5)
final result = newtonRaphson.solve();

// 0.856055...
print(result.guesses.last);

Systems of equations #

// [1.0, 0.0, 1.0 | 6.0]
// [0.0, 2.0, 0.0 | 5.0]
// [1.0, 0.0, 3.0 | -2.0]
final solver = LUSolver(
  matrix: RealMatrix.fromData(
    rows: 3,
    columns: 3,
    data: const [
      [1, 0, 1],
      [0, 2, 0],
      [1, 0, 3],
    ],
  ),
  knownValues: [6, 5, -2],
);
final solutions = solver.solve();

// 10.0
// 2.5
// -4.0
print(solutions);