trait DivisionRing[A] extends Ring[A] with Semifield[A]
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- By Inheritance
- DivisionRing
- Semifield
- MultiplicativeGroup
- Ring
- Rng
- AdditiveCommutativeGroup
- AdditiveGroup
- Rig
- MultiplicativeMonoid
- Semiring
- MultiplicativeSemigroup
- AdditiveCommutativeMonoid
- AdditiveCommutativeSemigroup
- AdditiveMonoid
- AdditiveSemigroup
- Serializable
- Any
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- Public
- Protected
Abstract Value Members
- abstract def div(x: A, y: A): A
- Definition Classes
- MultiplicativeGroup
- abstract def getClass(): Class[_ <: AnyRef]
- Definition Classes
- Any
- abstract def negate(x: A): A
- Definition Classes
- AdditiveGroup
- abstract def one: A
- Definition Classes
- MultiplicativeMonoid
- abstract def plus(x: A, y: A): A
- Definition Classes
- AdditiveSemigroup
- abstract def times(x: A, y: A): A
- Definition Classes
- MultiplicativeSemigroup
- abstract def zero: A
- Definition Classes
- AdditiveMonoid
Concrete Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- Any
- final def ##: Int
- Definition Classes
- Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- Any
- def additive: CommutativeGroup[A]
- Definition Classes
- AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def equals(arg0: Any): Boolean
- Definition Classes
- Any
- 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
nrepeated summations of this ring'sone, or-nsummations of-oneifnis negative.Most type class instances should consider overriding this method for performance reasons.
- Definition Classes
- Ring
- def fromDouble(a: Double): A
This is implemented in terms of basic Ring ops.
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.
- 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,
nrepeated summations of this ring'sone, or-nsummations of-oneifnis negative.Most type class instances should consider overriding this method for performance reasons.
- Definition Classes
- Ring
- def hashCode(): Int
- Definition Classes
- Any
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isOne(a: A)(implicit ev: Eq[A]): Boolean
Tests if
ais one.Tests if
ais one.- Definition Classes
- MultiplicativeMonoid
- def isZero(a: A)(implicit ev: Eq[A]): Boolean
Tests if
ais zero.Tests if
ais zero.- Definition Classes
- AdditiveMonoid
- def minus(x: A, y: A): A
- Definition Classes
- AdditiveGroup
- def multiplicative: Group[A]
- Definition Classes
- MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup
- def positivePow(a: A, n: Int): A
- Attributes
- protected[this]
- Definition Classes
- MultiplicativeSemigroup
- def positiveSumN(a: A, n: Int): A
- Attributes
- protected[this]
- Definition Classes
- AdditiveSemigroup
- def pow(a: A, n: Int): A
- Definition Classes
- MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup
- def product(as: TraversableOnce[A]): A
Given a sequence of
as, compute the product.Given a sequence of
as, compute the product.- Definition Classes
- MultiplicativeMonoid
- Annotations
- @nowarn()
- def reciprocal(x: A): A
- Definition Classes
- MultiplicativeGroup
- def sum(as: TraversableOnce[A]): A
Given a sequence of
as, compute the sum.Given a sequence of
as, compute the sum.- Definition Classes
- AdditiveMonoid
- Annotations
- @nowarn()
- def sumN(a: A, n: Int): A
- Definition Classes
- AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
- def toString(): String
- Definition Classes
- Any
- def tryProduct(as: TraversableOnce[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).
- Definition Classes
- MultiplicativeMonoid → MultiplicativeSemigroup
- Annotations
- @nowarn()
- def trySum(as: TraversableOnce[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).
- Definition Classes
- AdditiveMonoid → AdditiveSemigroup
- Annotations
- @nowarn()