Trait/Object

com.twitter.algebird

Ring

Related Docs: object Ring | package algebird

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trait Ring[T] extends Group[T]

Ring: Group + multiplication (see: http://en.wikipedia.org/wiki/Ring_%28mathematics%29) and the three elements it defines:

Note, if you have distributive property, additive inverses, and multiplicative identity you can prove you have a commutative group under the ring:

  1. (a + 1)*(b + 1) = a(b + 1) + (b + 1) 2. = ab + a + b + 1 3. or: 4. 5. = (a + 1)b + (a + 1) 6. = ab + b + a + 1 7. 8. So: ab + a + b + 1 == ab + b + a + 1 9. using the fact that -(ab) and -1 exist, we get: 10. a + b == b + a
Annotations
@implicitNotFound( ... )
Source
Ring.scala
Linear Supertypes
Group[T], Monoid[T], Semigroup[T], Serializable, AnyRef, Any
Known Subclasses
AbstractField, AbstractRing, AdjoinedUnitRing, ApplicativeField, ApplicativeRing, BigDecimalRing, BigIntRing, BijectedField, BijectedRing, BooleanField, DoubleField, EventuallyRing, Field, FloatField, GenericMapRing, IndexedSeqRing, IntRing, JBoolField, JDoubleField, JFloatField, JIntRing, JLongRing, JShortRing, LongRing, MapRing, MinPlusSemiring, NumericRing, Product10Ring, Product11Ring, Product12Ring, Product13Ring, Product14Ring, Product15Ring, Product16Ring, Product17Ring, Product18Ring, Product19Ring, Product20Ring, Product21Ring, Product22Ring, Product2Ring, Product3Ring, Product4Ring, Product5Ring, Product6Ring, Product7Ring, Product8Ring, Product9Ring, ScMapRing, ShortRing, StatisticsRing, Tuple10Ring, Tuple11Ring, Tuple12Ring, Tuple13Ring, Tuple14Ring, Tuple15Ring, Tuple16Ring, Tuple17Ring, Tuple18Ring, Tuple19Ring, Tuple20Ring, Tuple21Ring, Tuple22Ring, Tuple2Ring, Tuple3Ring, Tuple4Ring, Tuple5Ring, Tuple6Ring, Tuple7Ring, Tuple8Ring, Tuple9Ring
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Ring
  2. Group
  3. Monoid
  4. Semigroup
  5. Serializable
  6. AnyRef
  7. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def one: T

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  2. abstract def plus(l: T, r: T): T

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    Combines two T instances associatively.

    Combines two T instances associatively.

    returns

    result of combining l and r

    Definition Classes
    Semigroup

  3. abstract def times(l: T, r: T): T

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  4. abstract def zero: T

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    Returns the identity element of T for plus.

    Returns the identity element of T for plus.

    Definition Classes
    Monoid

Concrete Value Members

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

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    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any

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

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    Definition Classes
    AnyRef → Any

  4. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  5. def assertNotZero(v: T): Unit

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    Definition Classes
    Monoid

  6. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  7. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef

  8. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  9. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  10. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any

  11. def hashCode(): Int

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    Definition Classes
    AnyRef → Any

  12. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  13. def isNonZero(v: T): Boolean

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    Definition Classes
    Monoid

  14. def minus(l: T, r: T): T

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    Definition Classes
    Group

  15. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef

  16. def negate(v: T): T

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    Definition Classes
    Group

  17. def nonZeroOption(v: T): Option[T]

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    Definition Classes
    Monoid

  18. final def notify(): Unit

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    Definition Classes
    AnyRef

  19. final def notifyAll(): Unit

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    Definition Classes
    AnyRef

  20. def product(iter: TraversableOnce[T]): T

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  21. def sum(vs: TraversableOnce[T]): T

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    Definition Classes
    Monoid

  22. def sumOption(iter: TraversableOnce[T]): Option[T]

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    Returns an instance of T calculated by summing all instances in iter in one pass.

    Returns an instance of T calculated by summing all instances in iter in one pass. Returns None if iter is empty, else Some[T].

    iter

    instances of T to be combined

    returns

    None if iter is empty, else an option value containing the summed T

    Definition Classes
    Semigroup
    Note

    Override if there is a faster way to compute this sum than iter.reduceLeftOption using plus.

  23. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef

  24. def toString(): String

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    Definition Classes
    AnyRef → Any

  25. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  26. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  27. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Group[T]

Inherited from Monoid[T]

Inherited from Semigroup[T]

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

Ungrouped