Algebraic Engine (Fraction)

Why write this engine？

The reason is I coded a supercalculator last year in Appstore, which is based on one more completed parser.

This parser is just a simplified prototype. It calculates not only fraction but normal expression, so you can enrich this library in normal calculation. Detail illustration will be added in the near future.

Parser Process:

For example：1+2*（3-4） parsing process：

1. Tokenizer: Tokens：1, +, 2, *, (, 3, -, 4, ）

2. Interpreter： Specify the vague tokens，i.e '+' means add or positive ，the same as '-'.

3. Parser

AST(抽象树)：

In fact, the math expression is parsed into one custom nested cluster in coding，and then resolve sub-expression on each level from inside to outside one.

Tips：

1. adjust number, which is regarded as fraction through process，such as

   2 convert to 2/1 ; 0.2 convert to 2/10; 0.9998 convert to 9998/10000

2. because of object-c without function operator,we need to convert operators to function name, i.e @"+" to "add"

Todo ：processing more symbol