libraryDependencies += "io.github.edadma" %%% "numbers" % "0.0.1"

import io.github.edadma.numbers._

// Create rational numbers
val half = Rational(1, 2)
val third = Rational(1, 3)

// Exact arithmetic
val sum = half + third        // 5/6
val product = half * third    // 1/6
val power = half ^ 3          // 1/8

// Automatic reduction
val reduced = Rational(4, 8)  // 1/2

// Convert to decimal
val decimal = half.doubleValue // 0.5

import io.github.edadma.numbers._

// Double precision complex numbers
val z1 = ComplexDouble(3, 4)
val z2 = ComplexDouble(1, 2)

val sum = z1 + z2             // 4+6i
val product = z1 * z2         // -5+10i
val conjugate = z1.conj       // 3-4i
val magnitude = z1.abs        // 5.0

// Mathematical functions
val exponential = z1.exp
val logarithm = z1.ln
val sine = z1.sin

// Rational coefficient complex numbers
val zr = ComplexRational(Rational(1,2), Rational(1,3))

// Arbitrary precision complex numbers
import BigDecimalMath.decimal128._
val zbd = ComplexBigDecimal(BigDecimal("1.23456789"), BigDecimal("2.98765432"))

import io.github.edadma.numbers._

// Create quaternions (a + bi + cj + dk)
val q1 = QuaternionDouble(1, 2, 3, 4)
val q2 = QuaternionDouble(2, 1, 0, 1)

// Quaternion arithmetic
val sum = q1 + q2
val product = q1 * q2         // Non-commutative multiplication
val conjugate = q1.conj       // 1-2i-3j-4k
val norm = q1.abs

// Unit quaternions
val i = QuaternionDouble.i    // 0+1i+0j+0k
val j = QuaternionDouble.j    // 0+0i+1j+0k  
val k = QuaternionDouble.k    // 0+0i+0j+1k

// Rational quaternions for exact arithmetic
val qr = QuaternionRational(Rational(1,2), Rational(1,3), Rational(1,4), Rational(1,5))

import io.github.edadma.numbers._
import BigDecimalMath.decimal128._

// High-precision mathematical constants
val pi = bdmath.Pi.v
val e = bdmath.E.v

// High-precision functions
val sqrt2 = BigDecimalMath.sqrt(BigDecimal(2))
val ln10 = BigDecimalMath.ln(BigDecimal(10))
val sin30 = BigDecimalMath.sin(pi / 6)

// Complex arithmetic with arbitrary precision
val z = ComplexBigDecimal(pi, e)
val result = z.exp

import BigDecimalMath._

// Use different precision contexts
object decimal64 {
  implicit val bdmath = new BigDecimalMath(16) // 16 decimal places
}

object decimal256 {
  implicit val bdmath = new BigDecimalMath(77) // 77 decimal places  
}

import io.github.edadma.numbers._
import ComplexDoubleIsFractional._

val complexNumbers = List(ComplexDouble(1,0), ComplexDouble(2,0), ComplexDouble(3,0))
val sum = complexNumbers.sum              // ComplexDouble(6,0)
val product = complexNumbers.product      // ComplexDouble(6,0)

val rationals = List(Rational(1,2), Rational(1,3), Rational(1,6))
val rationalSum = rationals.sum           // Rational(1,1)

import io.github.edadma.numbers._

// Mandelbrot set iteration
def mandelbrot(c: ComplexDouble, maxIter: Int = 100): Int = {
  var z = ComplexDouble.zero
  var n = 0
  while (z.abs <= 2.0 && n < maxIter) {
    z = z * z + c
    n += 1
  }
  n
}

val point = ComplexDouble(-0.75, 0.1)
val iterations = mandelbrot(point)

import io.github.edadma.numbers._

// Rotation quaternion for 90° around Z-axis
val angle = math.Pi / 4  // 45° in radians, but quaternion uses half-angle
val axis = QuaternionDouble(0, 0, 0, 1) // Z-axis
val rotation = QuaternionDouble(math.cos(angle), 0, 0, math.sin(angle))

// Apply rotation to a point
val point = QuaternionDouble(0, 1, 0, 0) // Point on X-axis
val rotated = rotation * point * rotation.conj

import io.github.edadma.numbers._

// Exact monetary calculations with rational numbers
val price = Rational(1299, 100)      // $12.99
val taxRate = Rational(875, 10000)   // 8.75% tax
val quantity = 3

val subtotal = price * quantity      // $38.97 exactly
val tax = subtotal * taxRate         // Exact tax calculation
val total = subtotal + tax           // Exact total

println(s"Subtotal: $$${subtotal.doubleValue}")
println(s"Tax: $$${tax.doubleValue}")  
println(s"Total: $$${total.doubleValue}")