Trait/Object

algebra.ring

Rig

Related Docs: object Rig | package ring

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trait Rig[A] extends Semiring[A] with MultiplicativeMonoid[A]

Rig consists of:

Alternately, a Rig can be thought of as a ring without multiplicative or additive inverses (or as a semiring with a multiplicative identity).

Mnemonic: "Rig is a Ring without 'N'egation."

Linear Supertypes
MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Serializable, Serializable, Any
Known Subclasses
BoolRing, CommutativeRig, CommutativeRing, EuclideanRing, Field, Ring
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. Rig
  2. MultiplicativeMonoid
  3. Semiring
  4. MultiplicativeSemigroup
  5. AdditiveCommutativeMonoid
  6. AdditiveCommutativeSemigroup
  7. AdditiveMonoid
  8. AdditiveSemigroup
  9. Serializable
  10. Serializable
  11. 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 one: A

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    Definition Classes
    MultiplicativeMonoid

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

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    Definition Classes
    AdditiveSemigroup

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

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    Definition Classes
    MultiplicativeSemigroup

  5. 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: CommutativeMonoid[A]

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    Definition Classes
    AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → 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 hashCode(): Int

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    Definition Classes
    Any

  8. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  9. 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

  10. 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

  11. def multiplicative: Monoid[A]

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

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

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

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

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

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

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  15. 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

  16. 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

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

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    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  18. def toString(): String

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    Definition Classes
    Any

  19. 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

  20. 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 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