// algebra
//
// math.js has support for symbolic computation (CAS). It can parse
// expressions in an expression tree and do algebraic operations like
// simplification and derivation on this tree.

// load math.js (using node.js)
const math = require('../index')

// simplify an expression
console.log('simplify expressions')
console.log(math.simplify('3 + 2 / 4').toString()) // '7 / 2'
console.log(math.simplify('2x + 3x').toString()) // '5 * x'
console.log(math.simplify('2 * 3 * x', {x: 4}).toString()) // '24'
console.log(math.simplify('x^2 + x + 3 + x^2').toString()) // '2 * x ^ 2 + x + 3'
console.log(math.simplify('x * y * -x / (x ^ 2)').toString()) // '-y'

// work with an expression tree, evaluate results
const f = math.parse('2x + x')
const simplified = math.simplify(f)
console.log(simplified.toString()) // '3 * x'
console.log(simplified.eval({x: 4})) // 12
console.log()

// calculate a derivative
console.log('calculate derivatives')
console.log(math.derivative('2x^2 + 3x + 4', 'x').toString()) // '4 * x + 3'
console.log(math.derivative('sin(2x)', 'x').toString()) // '2 * cos(2 * x)'

// work with an expression tree, evaluate results
const h = math.parse('x^2 + x')
const dh = math.derivative(h, 'x')
console.log(dh.toString()) // '2 * x + 1'
console.log(dh.eval({x: 3})) // '7'