Math Parser for Dart

Process math expressions, convert them to machine-readable form, and calculate them.

This package is aimed to help you to work with formulas, parts of equations and other forms of simple math expressions in your projects. This package supports custom variables too.

Features: In Short

For more details about these features, refer to documentation, this readme or example file. All public API elements are documented.

  • Parse mathematical expressions using MathNodeExpression.fromString or equations using MathNodeExpression.fromStringExtended.
  • Define custom variables and functions by passing variableNames and customFunctions parameters. To define a custom function, you'll have to implement the MathDefinitionFunctionFreeformImplemented interface for each such function.
  • Automatically detect possible variable and function names used in an expression, but this works reliably only with implicit multiplication off.

Math Tree

The library provides a family of MathExpression and MathNode classes, most of them have subnodes that are being calculated recursively.

There are such types of MathNode:

  • MathFunction (and MathFunctionWithTwoArguments subclass)
  • MathValue
  • MathOperator

Types of MathExpression:

  • MathComparison

All the child classes names begin with the family they belong to.

Evaluation

You can evaluate a MathNode and its subnodes recursively by calling MathNode.calc(MathVariableValues values) and passing custom variable values.

Example: Calculate x + 3, where x = 5.

MathOperatorAddition(
    MathVariable('x'),
    const MathValue(3),
).calc(MathVariableValues.x(5));

You can also evaluate MathExpression.calc, but this method doesn't guarantee numeric result, so it may return null.

Parsing String to MathNode

The library can parse general mathematical expressions strings and return them as a machine-readable MathNode using MathNodeExpression.fromString method.

Define custom variables with variableNames parameter. Don't forget to define the variable value in MathExpression.calc when calling it.

Define custom functions using customFunctions argument. You can use either MathCustomFunctions class, which plainly declares the functions, or MathCustomFunctionsImplemented, which also requires to implement the function. When you use MathCustomFunctionsImplemented during parsing, you don't need to redeclare the function in MathExpression.calc.

Parse priority:

  1. Parentheses () []
  2. Variables: e, pi (π) and custom ones. x is being interpreted as a var by default, but you can override this behavior with the variableNames parameter. You can rewrite e and pi by defining it in variableNames and mentioning it during the calc call. First character must be a letter or _, others - letters, digits, period, or underscore. Last symbol can't be a period. Letters may be latin or Greek, both lower or capital case. You can't use built-in function names like sin, cos, etc. Variable names are case-sensitive. Custom functions have the same requirements, except they can override built-in functions.
  3. Functions (case-sensitive):
    • Custom functions
    • sin, cos, tan (tg), cot (ctg)
    • sqrt (√) (interpreted as power of 1/2), complex numbers not supported
    • ln (base=E), lg (base=2), log[base](x)
    • asin (arcsin), acos (arccos), atan (arctg), acot (arcctg)
  4. Unary minus (-) at the beginning of a block
  5. Power (x^y)
  6. Implicit multiplication (two MathNodes put near without operator between)
  7. Division (/) & Multiplication (*)
  8. Subtraction (-) & Addition (+)
MathNode fromString(
    /// The expression to convert
    String expression, {

    /// Converts all X - Y to X + (-Y)
    bool isMinusNegativeFunction = false,

    /// Allows skipping the multiplication (*) operator
    bool isImplicitMultiplication = true,

    /// Expressions which should be marked as variables
    Set<String> variableNames = const {'x'},

    /// Expressions which should be marked as functions
    MathCustomFunctions customFunctions = const MathCustomFunctions({}),
  });

Example for parsing a string and evaluating it with x = 20:

final expression = MathNodeExpression.fromString(
  '(2x)^(e^3 + 4) + x',
).calc(
  MathVariableValues({'x': 20}),
);

More complicated work with variables and functions is shown off in example.

You can also parse equations with MathNodeExpression.fromStringExtended, refer to example for this.

Detect used variable names

You can detect possible variable names used in a string math expression using MathNodeExpression.getPotentialDefinable.

Detecting variable names works properly only when implicit multiplication is disabled.

final expr = '2*a+b';

final definable = MathNodeExpression.getPotentialDefinable(
  expr,
  hideBuiltIns: true,
);

MathNodeExpression.fromString(
  expr,
  variableNames: definable.variables,
  isImplicitMultiplication: false,
);

Other Features

Numerical methods for Definite Integrals

You can calculate a given node as a definite integral using the MathNodeDefiniteIntegral extension. All methods have the same interface:

num definiteIntegralByLeftRectangles(
    /// Precision
    int n,
    num lowerLimit,
    num upperLimit,
);

Libraries

math_parser
Parse and evaluate mathematical expressions
math_parser_integrate
Numerical methods for integrating extension