// 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 { simplify, parse, derivative } = require('..')

// simplify an expression

console.log('simplify expressions')

console.log(simplify('3 + 2 / 4').toString()) // '7 / 2'

console.log(simplify('2x + 3x').toString()) // '5 * x'

console.log(simplify('2 * 3 * x', { x: 4 }).toString()) // '24'

console.log(simplify('x^2 + x + 3 + x^2').toString()) // '2 * x ^ 2 + x + 3'

console.log(simplify('x * y * -x / (x ^ 2)').toString()) // '-y'

// work with an expression tree, evaluate results

const f = parse('2x + x')

const simplified = simplify(f)

console.log(simplified.toString()) // '3 * x'

console.log(simplified.evaluate({ x: 4 })) // 12

console.log()

// calculate a derivative

console.log('calculate derivatives')

console.log(derivative('2x^2 + 3x + 4', 'x').toString()) // '4 * x + 3'

console.log(derivative('sin(2x)', 'x').toString()) // '2 * cos(2 * x)'

// work with an expression tree, evaluate results

const h = parse('x^2 + x')

const dh = derivative(h, 'x')

console.log(dh.toString()) // '2 * x + 1'

console.log(dh.evaluate({ x: 3 })) // '7'