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Field.scala
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Field.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}
trait Field[@sp(Int, Long, Float, Double) A]
extends Any
with EuclideanRing[A]
with DivisionRing[A]
with CommutativeSemifield[A] {
self =>
// default implementations for GCD
override def gcd(a: A, b: A)(implicit eqA: Eq[A]): A =
if (isZero(a) && isZero(b)) zero else one
override def lcm(a: A, b: A)(implicit eqA: Eq[A]): A = times(a, b)
// default implementations for Euclidean division in a field (as every nonzero element is a unit!)
def euclideanFunction(a: A): BigInt = BigInt(0)
def equot(a: A, b: A): A = div(a, b)
def emod(a: A, b: A): A = zero
override def equotmod(a: A, b: A): (A, A) = (div(a, b), zero)
// needed for bin-compat
override def fromDouble(a: Double): A =
DivisionRing.defaultFromDouble[A](a)(self, self)
}
trait FieldFunctions[F[T] <: Field[T]] extends EuclideanRingFunctions[F] with MultiplicativeGroupFunctions[F] {
def fromDouble[@sp(Int, Long, Float, Double) A](n: Double)(implicit ev: F[A]): A =
ev.fromDouble(n)
}
object Field extends FieldFunctions[Field] {
@inline final def apply[A](implicit ev: Field[A]): Field[A] = ev
}