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Semifield.scala
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Semifield.scala
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/*
* Copyright (c) 2015 Typelevel
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
package algebra
package ring
import scala.{specialized => sp}
/**
* Semifield consists of:
*
* - a commutative monoid for addition (+)
* - a group for multiplication (*)
*
* Alternately, a Semifield can be thought of as a DivisionRing without an additive inverse.
*/
trait Semifield[@sp(Int, Long, Float, Double) A] extends Any with Rig[A] with MultiplicativeGroup[A]
object Semifield extends AdditiveMonoidFunctions[Semifield] with MultiplicativeGroupFunctions[Semifield] {
@inline final def apply[A](implicit ev: Semifield[A]): Semifield[A] = ev
}