Algebra - Advanced

The Parser converts a mathematical expression to a tree.

As humans, we read and write math as a line of text. If you were to type a math expression, it would probably look something like this:

You could also just look at that math expression and use your intuition to prioritize where to start simplifying. But a computer will understand the expression best when it’s stored in a tree. These trees can be surprisingly complicated — even a short expression like (1+2)-\left|-3\right|\times x^2 becomes this tree:

          (-)
         /   \
        ( )   (*)
       /     /   \
     (+)    abs   (^)
    /   \    |   /   \
   1     2  -3  x     2

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public class Parser

The Lexer is converting a sequence of characters (mathematical expression) into a sequence of Token

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public class Lexer

The Grouper is the class that will be in charged of converting an array of Token into an array of Group in the process of parsing a mathematical expression.

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public class Grouper

A Group is a intermediate representation object for representing a mathematical expression. This is the object that allows the tokens to be grouped together to convert them into nodes. In particular, it is in charge of recognizing parentheses and preanalysing them before passing the expression to Parser.

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public class Group : NSObject

An entity that helps build a tree when parsing math expressions

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public protocol Node : NSObject

A Node for cell adress such as A2 or $HH$26

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public class CellAddressNode : NSObject, Node

An ExpressionNode is a Node containing 1 or more expression.

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public class ExpressionNode : NSObject, Node

A ParenthesisNode is an ExpressionNode used to treat parenthesis

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public class ParenthesisNode : ExpressionNode

This is a Node object that represents a number as a BigDouble

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public class ConstantNode : NSObject, Node

A Node for mathematical symbols such as x or y

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public class SymbolNode : NSObject, Node

A special Node for string expression (works excusively in table mode)

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public class StringNode : NSObject, Node

A type of Node for representing mathematical operations

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public class OperatorNode : NSObject, Node

A Node that represents a mathematical function

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public class FunctionNode : NSObject, Node

This is a Node object that represents an empty Node

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public class NullNode : NSObject, Node