trait RingAlgebra[V, R] extends Module[V, R] with Rng[V]

A RingAlgebra is a module that is also a Rng. An example is the Gaussian numbers.

Linear Supertypes
Rng[V], Semiring[V], MultiplicativeSemigroup[V], Module[V, R], AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], Any
Known Subclasses
FieldAlgebra, ZAlgebra, PolynomialEuclideanRing, PolynomialRing, PolynomialRng, MapInnerProductSpace, MapRng, MapVectorSpace
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. RingAlgebra
  2. Rng
  3. Semiring
  4. MultiplicativeSemigroup
  5. Module
  6. AdditiveAbGroup
  7. AdditiveCMonoid
  8. AdditiveCSemigroup
  9. AdditiveGroup
  10. AdditiveMonoid
  11. AdditiveSemigroup
  12. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]
    Definition Classes
    Any
  2. abstract def negate(x: V): V
    Definition Classes
    AdditiveGroup
  3. abstract def plus(x: V, y: V): V
    Definition Classes
    AdditiveSemigroup
  4. implicit abstract def scalar: Rng[R]
    Definition Classes
    Module
  5. abstract def times(x: V, y: V): V
    Definition Classes
    MultiplicativeSemigroup
  6. abstract def timesl(r: R, v: V): V
    Definition Classes
    Module
  7. abstract def zero: V
    Definition Classes
    AdditiveMonoid

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  2. final def ##(): Int
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    Any
  4. def additive: AbGroup[V]
    Definition Classes
    AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. def equals(arg0: Any): Boolean
    Definition Classes
    Any
  7. def hashCode(): Int
    Definition Classes
    Any
  8. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  9. def isZero(a: V)(implicit ev: Eq[V]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid
  10. def minus(x: V, y: V): V
    Definition Classes
    AdditiveGroup
  11. def multiplicative: Semigroup[V]
    Definition Classes
    MultiplicativeSemigroup
  12. def pow(a: V, n: Int): V

    Returns a multiplied with itself n times.

    Returns a multiplied with itself n times. For instance, a pow 3 === a * a * a. Since this is a semiring, there is no notion of a multiplicative identity, and so the exponent must be positive.

    Definition Classes
    Semiring
  13. def prodOption(as: TraversableOnce[V]): Option[V]

    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
  14. def prodn(a: V, n: Int): V

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeSemigroup
  15. def prodnAboveOne(a: V, n: Int): V
    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup
  16. def sum(as: TraversableOnce[V]): V

    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
  17. def sumOption(as: TraversableOnce[V]): Option[V]

    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
  18. def sumn(a: V, n: Int): V

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
  19. def sumnAboveOne(a: V, n: Int): V
    Attributes
    protected
    Definition Classes
    AdditiveSemigroup
  20. def timesr(v: V, r: R): V
    Definition Classes
    Module
  21. def toString(): String
    Definition Classes
    Any

Inherited from Rng[V]

Inherited from Semiring[V]

Inherited from MultiplicativeSemigroup[V]

Inherited from Module[V, R]

Inherited from AdditiveAbGroup[V]

Inherited from AdditiveCMonoid[V]

Inherited from AdditiveCSemigroup[V]

Inherited from AdditiveGroup[V]

Inherited from AdditiveMonoid[V]

Inherited from AdditiveSemigroup[V]

Inherited from Any

Ungrouped