DivisionRing

algebra.ring.DivisionRing
See theDivisionRing companion object
trait DivisionRing[A] extends Ring[A] with Semifield[A]

Attributes

Companion:
object
Source:
DivisionRing.scala
Graph
Supertypes
Known subtypes
Self type

Members list

Concise view

Value members

Concrete methods

def fromDouble(a: Double): A

This is implemented in terms of basic Ring ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.

This is implemented in terms of basic Ring ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.

This is possible because a Double is a rational number.

Attributes

Source:
DivisionRing.scala

Inherited methods

def div(x: A, y: A): A

Attributes

Inherited from:
MultiplicativeGroup
Source:
Multiplicative.scala
def fromBigInt(n: BigInt): A

Convert the given BigInt to an instance of A.

Convert the given BigInt to an instance of A.

This is equivalent to n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Inherited from:
Ring
Source:
Ring.scala
def fromInt(n: Int): A

Convert the given integer to an instance of A.

Convert the given integer to an instance of A.

Defined to be equivalent to sumN(one, n).

That is, n repeated summations of this ring's one, or -n summations of -one if n is negative.

Most type class instances should consider overriding this method for performance reasons.

Attributes

Inherited from:
Ring
Source:
Ring.scala
def isOne(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is one.

Tests if a is one.

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def isZero(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is zero.

Tests if a is zero.

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala
def minus(x: A, y: A): A

Attributes

Inherited from:
AdditiveGroup
Source:
Additive.scala
def negate(x: A): A

Attributes

Inherited from:
AdditiveGroup
Source:
Additive.scala
def one: A

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def plus(x: A, y: A): A

Attributes

Inherited from:
AdditiveSemigroup
Source:
Additive.scala
override def pow(a: A, n: Int): A
def product(as: IterableOnce[A]): A

Given a sequence of as, compute the product.

Given a sequence of as, compute the product.

Attributes

Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
def reciprocal(x: A): A

Attributes

Inherited from:
MultiplicativeGroup
Source:
Multiplicative.scala
def sum(as: IterableOnce[A]): A

Given a sequence of as, compute the sum.

Given a sequence of as, compute the sum.

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala
override def sumN(a: A, n: Int): A

Attributes

Definition Classes
Inherited from:
AdditiveGroup
Source:
Additive.scala
def times(x: A, y: A): A

Attributes

Inherited from:
MultiplicativeSemigroup
Source:
Multiplicative.scala
override def tryProduct(as: IterableOnce[A]): Option[A]

Given a sequence of as, combine them and return the total.

Given a sequence of as, combine them and return the total.

If the sequence is empty, returns None. Otherwise, returns Some(total).

Attributes

Definition Classes
Inherited from:
MultiplicativeMonoid
Source:
Multiplicative.scala
override def trySum(as: IterableOnce[A]): Option[A]

Given a sequence of as, combine them and return the total.

Given a sequence of as, combine them and return the total.

If the sequence is empty, returns None. Otherwise, returns Some(total).

Attributes

Definition Classes
Inherited from:
AdditiveMonoid
Source:
Additive.scala
def zero: A

Attributes

Inherited from:
AdditiveMonoid
Source:
Additive.scala