spire.algebra

FieldAlgebra

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
Ordering
  1. Alphabetic
  2. By inheritance
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
  1. Hide All
  2. Show all
Learn more about member selection
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: Field[F]

    Definition Classes
    VectorSpace → Module

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

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    VectorSpace

  7. def equals(arg0: Any): Boolean

    Definition Classes
    Any

  8. def hashCode(): Int

    Definition Classes
    Any

  9. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

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

    Definition Classes
    AdditiveGroup

  12. def multiplicative: Semigroup[V]

    Definition Classes
    MultiplicativeSemigroup

  13. 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

  14. 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

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

    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

    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

  17. 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

  18. 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

  19. 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

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

    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

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

    Definition Classes
    Module

  22. def toString(): String

    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