math_expressions

A library for parsing and evaluating mathematical expressions.

• Performs evaluations in real, vector, and interval contexts.
• Supports expression simplification and differentiation.

math_expressions is inspired by mathExpr for Java and distributed under the MIT license.

Features

• Evaluation of expressions in various modes: Real, Vector and Interval.
• Parsing, simplification and differentiation of mathematical expressions.
• Supporting most basic math functions out of the box.
• Extensible through custom function definitions in code.
• Well documented and tested.

This package contains a very simple command-line interpreter for real numbers:

dart pub run math_expressions:interpreter

What's not working yet?

• Some evaluations in vector and interval space (especially functions).
• N-dimensional vectors. Curently no more than four dimensions are supported.
• The parser only works for real numbers.
• Complex numbers.

Suggestions and pull requests are always welcome!

Usage

Below are two basic examples of how to use this library. There also is some additional example code available.

1. Expression creation and evaluation

This example shows how to evaluate

$\frac{(x^2+\cos y)}{3}$

for $x=2, y=\pi$

Build the expression

You can either create an mathematical expression programmatically or parse a string.

• Create the expression programmatically:

  Variable x = Variable('x'), y = Variable('y');
  Power xSquare = Power(x, 2);
  Cos yCos = Cos(y);
  Number three = Number(3.0);
  Expression exp = (xSquare + yCos) / three;

• Create the expression via the parser:

  Parser p = Parser();
  Expression exp = p.parse("(x^2 + cos(y)) / 3");

Evaluate the expression

• Bind variables and evaluate the expression as real number:

  // Bind variables:
  ContextModel cm = ContextModel();
  cm.bindVariable(x, Number(2.0));
  cm.bindVariable(y, Number(Math.PI));

  // Evaluate expression:
  double eval = exp.evaluate(EvaluationType.REAL, cm);

  print(eval) // = 1.0

2. Expression simplification and differentiation

This example shows how to simplify and differentiate

$x \cdot 1 - (-5)$

• Expressions can be simplified and differentiated with respect to a given variable:

  Expression exp = p.parse("x*1 - (-5)");

  print(exp);            // = ((x * 1.0) - -(5.0))
  print(exp.simplify()); // = (x + 5.0)

  Expression expDerived = exp.derive('x');

  print(expDerived);            // = (((x * 0.0) + (1.0 * 1.0)) - -(0.0))
  print(expDerived.simplify()); // = 1.0

Alternatives

Here are some other Dart libraries that implement similar functionality to math_expression: parsing and evaluating mathematical expressions.

• expressions: an elegant and small library to parse and evaluate simple expressions.
• function_tree: a library for parsing, evaluating and plotting single- and multi-variables numerical functions.

To the author's knowledge math_expressions is currently the only library supporting interval arithmetics.