equations 1.0.1
equations: ^1.0.1

Dart native js
Flutter Android iOS web

An equation solving library written in Dart. It also works with complex numbers and fractions!

dart_equations logo

An equation solving library written purely in Dart.


Thanks to dart_equations you're able to easily solve polynomial (algebraic) and nonlinear equations with ease. It's been written in Dart and it has no dependency on any framework: it can be directly used with Flutter for web, desktop and mobile. Here's a summary of the contents of the package:

  • subclasses of Algebraic can be used to solve algebraic/polynomial equations;
  • subclasses of Nonlinear can be used to solve nonlinear equations;
  • Complex is used to easily handle complex number along with many useful methods

This package also depends on fraction in order to easily work with fractions.

Algebraic equations #

Use one of the following classes to find the roots of a specific type of polynomial. You can use complex numbers and fractions.

Solver nameEquationField
Constantf(x) = aa ∈ C
Linearf(x) = ax + ba, b ∈ C
Quadraticf(x) = ax2 + bx + ca, b, c ∈ C
Cubicf(x) = ax3 + bx2 + cx + da, b, c, d ∈ C
Quarticf(x) = ax4 + bx3 + cx2 + dx + ea, b, c, d, e ∈ C

When solving a polynomial up to the fourth degree, prefer using one of these classes rather than guessing the roots with a root-finding algorithm (see below). Here's a simple example of how you can solve polynomial equations:

// 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)
);

final degree = equation.degree; // 3
final isReal = equation.isRealEquation; // false
final discr = equation.discriminant(); // -31299.688 + 27460.192i

// f(x) = (2 - 3i)x^3 + 1.2ix^2 + (5 - 1i)x + (-9 - 6i)
print("$equation");
// f(x) = (2 - 3i)x^3 + 6/5ix^2 + (5 - 1i)x + (-9 - 6i)
print("${equation.toStringWithFractions()}");

/*
 * Prints the roots of the equation:
 *
 *  x1 = 0.348906207844 - 1.734303423032i
 *  x2 = -1.083892638909 + 0.961044482775
 *  x3 = 1.011909507988 + 0.588643555642
 * */
for (final root in equation.solutions()) print(root);
  print(root);

Nonlinear equations #

Use one of the following classes, representing a root-finding algorithm, to find the roots of an equation. Only real numbers are allowed.

Method name
Bisection
Chords
Newton
Secant
Steffensen

Expressions are parsed using math_expressions, a very nice library that supports most of mathematical operators such as sine, cosine, tangent, logarithm and so on. Here's a simple example of how you can find the roots of an equation:

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

final steps = newton.maxSteps; // 5
final tol = newton.tolerance; // 1.0e-10
final fx = newton.function; // 2*x+cos(x)
final guess = newton.x0; // -1

final solutions = await newton.solve();

final convergence = solutions.convergence.round(); // 2
final solutions = solutions.efficiency.round() // 1

/*
 * The getter `solutions.guesses` returns the list of values computed by the algorithm
 *
 * -0.4862880170389824
 * -0.45041860473199363
 * -0.45018362150211116
 * -0.4501836112948736
 * -0.45018361129487355
 */
final guesses = solutions.guesses;
9
likes
110
pub points
42%
popularity

Publisher

fluttercompletereference.com

An equation solving library written in Dart. It also works with complex numbers and fractions!

Homepage
Repository (GitHub)
View/report issues

Documentation

API reference

License

MIT (LICENSE)

Dependencies

collection, fraction, math_expressions

More

Packages that depend on equations