# math_expressions

A math library for parsing and evaluating expressions in real, interval and vector contexts. Also supports simplification and differentiation.

It is partly inspired by mathExpr for Java.

Note: This library is still in an early state, the test coverage is not perfect, the performance is not optimized and some features are still unimplemented. Most REAL and basic INTERVAL and VECTOR evaluations should work though. Suggestions and pull requests are always welcome!

## Features

• Parsing, simplification and differentiation of mathematical expressions.
• Evaluation of expressions in various modes (Real, Vector, Interval).
• Supporting most basic functions out of the box.
• Well documented.

### What's not working yet?

• Some evaluations in vector and interval space (especially functions).
• Parser only works for real numbers.
• Complex numbers.

## Documentation

See the DartDocs and the example code. For even more details, have a look into the unit tests.

## Examples

### 1. Expression creation and evaluation

This example shows how to evaluate

$(x^2+cos(y))/3$

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 = new Variable('x'), y = new Variable('y');
Power xSquare = new Power(x, 2);
Cos yCos = new Cos(y);
Number three = new Number(3.0);
Expression exp = (xSquare + yCos) / three;
``````
• Create the expression via the parser:
``````  Parser p = new 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 = new ContextModel();
cm.bindVariable(x, new Number(2.0));
cm.bindVariable(y, new 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

$x*1-(-5)$

• 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
``````

For a CLI evaluator, see cli_evaluator.dart.
For more code, see example.dart.