math_parser 1.3.0

Process math expressions, like formulas or parts of equations, convert them to machine-readable form, and calculate them.

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.

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.

• Set isMinusNegativeFunction to true to interpret minus operator as a sum of two values, right of which will be negative: X - Y turns to X + (-Y)
• Set isImplicitMultiplication to false to disable implicit multiplication

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, others - letters, digits, or underscore. 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
3. Functions (case-sensitive):
   • 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'},
  });

Example for parsing a string and evaluating it with x = 20 and y = 5:

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

More complicated work with variables 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.getPotentialVariableNames.

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

final expr = '2*a+b';
final vars = MathNodeExpression.getPotentialVariableNames(
  expr,
  hideBuiltIns: true,
);

MathNodeExpression.fromString(
  expr,
  variableNames: vars,
  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,
);