algebra

A javascript algebra engine

import { calculate, simplify } from 'algebra'
calculate('1+1') // => 2
calculate('5(10^2)(12-9)') // => 1500

simplify('16/24') // => '2/3'

Motivation

The goal of this project is to parse and solve algebraic equations. For instance, given 2x-5=10, output x=15/2.

• Why not use eval?

  Similar beahviour could be achieved by simply using eval. But that would:

  • be too easy
  • be incredibly boring
  • prevent implementing more complex behaviours, such as implicit multiplication, exponentiation with the '^' sign, fraction reducing, algebraic variables, etc...

Implementation

The code is written in a functional style. A previous imperative version of the code is available unser the imperative branch, though the algorithm is the same.

There are two core modules:

Lexer

The lexer, defined in src/core/lex/, takes an input string and returns a list of tokens. It identifies numbers, operands, and parentheses. It also handles token transformation based on context. For instance, it differentiates negative numbers from substractions, and handles implicit multiplication (ie 2(2+10) is interpreted as 2*(2+10)).

Parser

The parser, defined in src/core/parse/, takes a list of tokens and produces a syntax tree. It analyses operation precedence, and handles parentheses.

Higher level funcitons

Then, higher level functions, such as calculate, reduce or solve are defined on the parse tree. These are public facing functions that use the core internally.