如何实现 Fractional[Int] 并访问新的算术运算

Question

我正在尝试在 Scala 3 中创建一个

Fractional[Int]

实例，我想将其用于有限域算术。

我有一个类，其实例可以作为

Fractional[Int]

实现：

class IntModp(val p : Int) extends Fractional[Int] {
  def inverse(a : Int) : Int = { 
    // implementation of modular inverse with fast Euclidean algorithm here
  }
  val inverses : Map[Int, Int] = Map.from(
    Range(1, p-1).map(j => (j -> inverse(j))) ++
      Range(-(p-1), -1).map(j => (j -> -inverse(-j)))
  )
  def norm(a: Int): Int = {
    val r : Int = a % p
    return r match {
      case rr : Int if (rr < -(p-1)/2) => rr + p
      case rr : Int if (rr > (p-1)/2) => rr-p
      case rr : Int => rr
    }
  }

  def compare(x: Int, y: Int): Int = Ordering.Int.compare(norm(x), norm(y))
  def div(x: Int, y: Int): Int = times(x, inverses(norm(y)))
  def fromInt(x: Int): Int = norm(x)
  def minus(x: Int, y: Int): Int = norm(x - y)
  def negate(x: Int): Int = norm(-x)
  def parseString(str: String): Option[Int] =
    IntIsIntegral.parseString(str).map(j => norm(j))
  def plus(x: Int, y: Int): Int = norm(x + y)
  def times(x: Int, y: Int): Int = norm(x * y)
  def toDouble(x: Int): Double = IntIsIntegral.toDouble(norm(x))
  def toFloat(x: Int): Float = IntIsIntegral.toFloat(norm(x))
  def toInt(x: Int): Int = IntIsIntegral.toInt(norm(x))
  def toLong(x: Int): Long = IntIsIntegral.toLong(norm(x))
}

根据我对 Scala 3 类型类和

scala.math.Fractional.Implicits

的理解，我现在应该能够执行以下操作：

given IntMod17 : Fractional[Int] = new IntModp(17)
15 + 12 // expect to see -7, instead see 27
15 / 12 // expect to see -3, instead see 1

但是相反，每当我实际使用任何算术运算符时，我都会得到“正常”

Int

行为。我当然可以做类似的事情

given IntMod17 : Fractional[Int] = new IntModp(17)
val fr = summon[Fractional[Int]] // fr is now this IntMod17 object
fr.plus(15, 12) // expect to see -7, and see -7
fr.div(15, 12) // expect to see -3, and see -3