Trait/Object

algebra.ring

Ring

Related Docs: object Ring | package ring

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trait Ring[A] extends Rig[A] with Rng[A]

Ring consists of:

Additionally, multiplication must distribute over addition.

Ring implements some methods (for example fromInt) in terms of other more fundamental methods (zero, one and plus). Where possible, these methods should be overridden by more efficient implementations.

Linear Supertypes
Rng[A], AdditiveCommutativeGroup[A], AdditiveGroup[A], Rig[A], MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Serializable, Serializable, Any
Known Subclasses
BoolRing, CommutativeRing, EuclideanRing, Field
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. Ring
  2. Rng
  3. AdditiveCommutativeGroup
  4. AdditiveGroup
  5. Rig
  6. MultiplicativeMonoid
  7. Semiring
  8. MultiplicativeSemigroup
  9. AdditiveCommutativeMonoid
  10. AdditiveCommutativeSemigroup
  11. AdditiveMonoid
  12. AdditiveSemigroup
  13. Serializable
  14. Serializable
  15. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]

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    Definition Classes
    Any

  2. abstract def negate(x: A): A

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    Definition Classes
    AdditiveGroup

  3. abstract def one: A

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    Definition Classes
    MultiplicativeMonoid

  4. abstract def plus(x: A, y: A): A

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    Definition Classes
    AdditiveSemigroup

  5. abstract def times(x: A, y: A): A

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    Definition Classes
    MultiplicativeSemigroup

  6. abstract def zero: A

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    Definition Classes
    AdditiveMonoid

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    Any

  2. final def ##(): Int

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    Definition Classes
    Any

  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    Any

  4. def additive: CommutativeGroup[A]

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    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  6. def equals(arg0: Any): Boolean

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    Definition Classes
    Any

  7. def fromInt(n: Int): A

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    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.

  8. def hashCode(): Int

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    Definition Classes
    Any

  9. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  10. def isOne(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is one.

    Tests if a is one.

    Definition Classes
    MultiplicativeMonoid

  11. def isZero(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

  12. def minus(x: A, y: A): A

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    Definition Classes
    AdditiveGroup

  13. def multiplicative: Monoid[A]

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  14. def positivePow(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

  15. def positiveSumN(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  16. def pow(a: A, n: Int): A

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  17. def product(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the product.

    Given a sequence of as, compute the product.

    Definition Classes
    MultiplicativeMonoid

  18. def sum(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the sum.

    Given a sequence of as, compute the sum.

    Definition Classes
    AdditiveMonoid

  19. def sumN(a: A, n: Int): A

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    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  20. def toString(): String

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    Definition Classes
    Any

  21. def tryProduct(as: TraversableOnce[A]): Option[A]

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    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
    MultiplicativeSemigroup

  22. def trySum(as: TraversableOnce[A]): Option[A]

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    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
    AdditiveSemigroup

Inherited from Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped