# math_expressions library

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

The libary supports the three basic data types Number, Interval and Vector. It includes a Parser to create Expressions from Strings.

## Classes

Abs
The absolute value function.
Acos
The arcus cosine function.
AlgorithmicFunction
Asin
The arcus sine function.
Atan
The arcus tangens function.
BinaryOperator
A binary operator takes two expressions and performs an operation on them.
BoundVariable
A bound variable is an anonymous variable, e.g. a variable without name, which is bound to an expression.
Ceil
The ceil function.
CompositeFunction
A composition of two given MathFunctions.
ContextModel
The context model keeps track of all known variables and functions.
Cos
The cosine function. Expects input in `radians`.
CustomFunction
A user-defined MathFunction with an arbitrary expression.
DefaultFunction
A default function is predefined in this library. It contains no expression because the appropriate evaluation method usually uses native Dart math code.
Divide
The divide operator performs a division.
Exponential
The exponential function.
Expression
Any Expression supports basic mathematical operations like addition, subtraction, multiplication, division, power and negate.
Factorial
simple factorial function might be expanded to the Gamma function to allow negative and complex numbers and deriving
Floor
The floor function.
Interval
An Interval is defined by its minimum and maximum values, where min <= max.
IntervalLiteral
An interval literal.
Lexer
The lexer creates tokens (see TokenType and Token) from an input string. The input string is expected to be in infix notation form. The lexer can convert an infix stream into a postfix stream (Reverse Polish Notation) for further processing by a Parser.
Literal
A literal can be a number, a constant or a variable.
Ln
The natural logarithm (log based e).
Log
The logarithm function.
MathFunction
A function with an arbitrary number of arguments.
Minus
The minus operator performs a subtraction.
Modulo
The modulo operator performs a Euclidean modulo operation, as Dart performs it. That is, a % b = a - floor(a / |b|) |b|. For positive integers, this is a remainder.
Number
A number is a constant number literal.
Parser
The Parser creates a mathematical Expression from a given input string.
Plus
The plus operator performs an addition.
Point3
A point in 3-dimensional space, which is a Vector3. This implementation supplies common mathematical operations on points.
Power
The power operator.
Root
The n-th root function. n needs to be a natural number.
Sgn
The sign function.
Sin
The sine function. Expects input in `radians`.
Sqrt
The square root function. A specialisation of Root.
Tan
The tangens function. Expects input in `radians`.
Times
The times operator performs a multiplication.
Token
A Token consists of text and has a TokenType.
TokenType
UnaryMinus
The unary minus negates its argument.
UnaryOperator
A unary operator takes one argument and performs an operation on it.
UnaryPlus
Variable
A variable is a named literal.
Vector
A vector of arbitrary size.

## Enums

EvaluationType
Mathematical expressions must be evaluated under a certain EvaluationType.