// (2 * m2)! / [ (1 + m2)! * m2! ]

function R(m2) {

  let num = 1, den = 1

  for(let n = 2 * m2 ; n >= m2 + 2 ; n--) {

    num = num * n

  }

  for(let d = m2 ; d >= 2 ; d--) {

    den = den * d

  }

  return num / den

}

​

// Power series with Catalan number coefficients

// sum from m2=0 to deg of R(m2) * t2 ^ m2

function F(t2, deg) {

  let sum = new Fraction(1)

  let t22 = t2.mul(1)

  for(let m2 = 1 ; m2 <= deg ; m2++) {

    sum = sum.add( new Fraction(R(m2)) .mul(t22) )

    t22 = t22.mul(t2)

  }

  return sum

}

​

function Y(c0, c1, c2, deg) {

  let d0 = c0.mul(1), d1 = c1.mul(1), d2 = new Fraction(1)

  let sum = d0.div(d1)

  for(let m = 1 ; m <= deg ; m++) {

    d0 = d0.mul(c0)

    d1 = d1.mul(c0).mul(c0)

    d2 = d2.mul(c2)

    sum = sum.add( new Fraction(R(m)) .mul(d0).mul(d2).div(d1)  )    

  }

  return [sum, c1.div(c2).sub(sum)]

}

​

function Q(c0, c1, c2) {

  return [ 1/(2*c2) * (c1 + sqrt(c1*c1 - 4*c0*c2)) ,

           1/(2*c2) * (c1 - sqrt(c1*c1 - 4*c0*c2)) ]

}

​

function setup() {

  noLoop()

  print( Q(2, 3, 0.5) )

  let c0 = new Fraction(2),

      c1 = new Fraction(3),

      c2 = new Fraction(1,2)

  let t2 = c0.mul(c2).div(c1).div(c1)

  let x1 = c0.div(c1).mul(F(t2, 5))

  let x2 = c1.div(c2) .sub(x1)

  print(x1.flt(), x2.flt())

  print( Q(3, 7, 2) )

  c0 = new Fraction(3)

  c1 = new Fraction(7)

  c2 = new Fraction(2)

  t2 = c0.mul(c2).div(c1).div(c1)

  x1 = c0.div(c1).mul(F(t2, 3))

  x2 = c1.div(c2) .sub(x1)

  print(x1.flt(), x2.flt())

  print(x1.str(), x2.str())

}

​

function draw() {

}