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• Rng.scala

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algebra.ring.Rng.scala Maven / Gradle / Ivy

package algebra
package ring

import annotation.tailrec
import scala.{specialized => sp}

/**
 * Rng (pronounced "Rung") consists of:
 *
 *  - a commutative group for addition (+)
 *  - a semigroup for multiplication (*)
 *
 * Alternately, a Rng can be thought of as a ring without a
 * multiplicative identity (or as a semiring with an additive
 * inverse).
 *
 * Mnemonic: "Rng is a Ring without multiplicative 'I'dentity."
 */
trait Rng[@sp(Int, Long, Float, Double) A] extends Any with Semiring[A] with AdditiveCommutativeGroup[A]

object Rng extends AdditiveGroupFunctions[Rng] with MultiplicativeSemigroupFunctions[Rng] {
  @inline final def apply[A](implicit ev: Rng[A]): Rng[A] = ev
}