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
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@implicitNotFound( ... )
Linear Supertypes
Group[T], Monoid[T], Semigroup[T], Serializable, AnyRef, Any
Known Subclasses
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Inherited
  1. Ring
  2. Group
  3. Monoid
  4. Semigroup
  5. Serializable
  6. AnyRef
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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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    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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    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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    override this if there is a faster way to do this sum than reduceLeftOption on plus

    override this if there is a faster way to do this sum than reduceLeftOption on plus

    Definition Classes
    Semigroup
  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

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