Trait

spire.algebra

FieldAlgebra

Related Doc: package algebra

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trait FieldAlgebra[V, F] extends RingAlgebra[V, F] with VectorSpace[V, F]

A FieldAlgebra is a vector space that is also a Ring. An example is the complex numbers.

Linear Supertypes
VectorSpace[V, F], RingAlgebra[V, F], Rng[V], Semiring[V], MultiplicativeSemigroup[V], Module[V, F], AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], Any
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Inherited
  1. FieldAlgebra
  2. VectorSpace
  3. RingAlgebra
  4. Rng
  5. Semiring
  6. MultiplicativeSemigroup
  7. Module
  8. AdditiveAbGroup
  9. AdditiveCMonoid
  10. AdditiveCSemigroup
  11. AdditiveGroup
  12. AdditiveMonoid
  13. AdditiveSemigroup
  14. 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: V): V

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    Definition Classes
    AdditiveGroup

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

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    Definition Classes
    AdditiveSemigroup

  4. implicit abstract def scalar: Field[F]

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    Definition Classes
    VectorSpace → Module

  5. abstract def times(x: V, y: V): V

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    Definition Classes
    MultiplicativeSemigroup

  6. abstract def timesl(r: F, v: V): V

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    Definition Classes
    Module

  7. abstract def zero: V

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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[V]

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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 divr(v: V, f: F): V

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    Definition Classes
    VectorSpace

  7. def equals(arg0: Any): Boolean

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    Definition Classes
    Any

  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 isZero(a: V)(implicit ev: Eq[V]): Boolean

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    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

  11. def minus(x: V, y: V): V

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    Definition Classes
    AdditiveGroup

  12. def multiplicative: Semigroup[V]

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    Definition Classes
    MultiplicativeSemigroup

  13. def pow(a: V, n: Int): V

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    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

  14. def prodOption(as: TraversableOnce[V]): Option[V]

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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

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

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    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeSemigroup

  16. def prodnAboveOne(a: V, n: Int): V

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    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

  17. def sum(as: TraversableOnce[V]): V

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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

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

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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

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

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    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  20. def sumnAboveOne(a: V, n: Int): V

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    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  21. def timesr(v: V, r: F): V

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    Definition Classes
    Module

  22. def toString(): String

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    Definition Classes
    Any

Inherited from VectorSpace[V, F]

Inherited from RingAlgebra[V, F]

Inherited from Rng[V]

Inherited from Semiring[V]

Inherited from MultiplicativeSemigroup[V]

Inherited from Module[V, F]

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