Trait/Object

spire.algebra

Ring

Related Docs: object Ring | package algebra

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

Ring represents a set (A) that is a group over addition (+) and a monoid over multiplication (*). Aside from this, the 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], AdditiveAbGroup[A], AdditiveCMonoid[A], AdditiveCSemigroup[A], AdditiveGroup[A], Rig[A], MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Any
Known Subclasses
BigDecimalAlgebra, BigDecimalIsField, BigIntAlgebra, BigIntIsEuclideanRing, BigIntegerAlgebra, BigIntegerIsEuclideanRing, ByteAlgebra, ByteIsEuclideanRing, CRing, ComplexIsNumeric, DistEuclideanRing, DistField, DistRing, DoubleAlgebra, DoubleIsField, EuclideanRing, Field, FloatAlgebra, FloatIsField, Fractional, IntAlgebra, IntIsEuclideanRing, Integral, LongAlgebra, LongIsEuclideanRing, Numeric, PolynomialEuclideanRing, PolynomialRing, RealAlgebra, RealIsFractional, ShortAlgebra, ShortIsEuclideanRing, ZAlgebra
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Inherited
  1. Ring
  2. Rng
  3. AdditiveAbGroup
  4. AdditiveCMonoid
  5. AdditiveCSemigroup
  6. AdditiveGroup
  7. Rig
  8. MultiplicativeMonoid
  9. Semiring
  10. MultiplicativeSemigroup
  11. AdditiveMonoid
  12. AdditiveSemigroup
  13. 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: AbGroup[A]

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    Definition Classes
    AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → 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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    Defined to be equivalent to additive.sumn(one, n).

    Defined to be equivalent to additive.sumn(one, n). That is, n repeated summations of this ring's one, or -one if n is negative.

  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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    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 pow(a: A, n: Int): A

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    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    Definition Classes
    Rig → Semiring

  15. def prod(as: TraversableOnce[A]): A

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    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    MultiplicativeMonoid

  16. def prodOption(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

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

    Definition Classes
    MultiplicativeSemigroup

  17. def prodn(a: A, n: Int): A

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    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  18. def prodnAboveOne(a: A, n: Int): A

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    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

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

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    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    AdditiveMonoid

  20. def sumOption(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

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

    Definition Classes
    AdditiveSemigroup

  21. def sumn(a: A, n: Int): A

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    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  22. def sumnAboveOne(a: A, n: Int): A

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    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  23. def toString(): String

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    Definition Classes
    Any

Inherited from Rng[A]

Inherited from AdditiveAbGroup[A]

Inherited from AdditiveCMonoid[A]

Inherited from AdditiveCSemigroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Any

Ungrouped