Trait

spire.algebra

FieldAlgebra

Related Doc: package algebra

Permalink

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], algebra.ring.Rng[V], algebra.ring.Semiring[V], algebra.ring.MultiplicativeSemigroup[V], Module[V, F], AdditiveCommutativeGroup[V], AdditiveCommutativeMonoid[V], AdditiveCommutativeSemigroup[V], algebra.ring.AdditiveGroup[V], algebra.ring.AdditiveMonoid[V], algebra.ring.AdditiveSemigroup[V], Serializable, Serializable, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. FieldAlgebra
  2. VectorSpace
  3. RingAlgebra
  4. Rng
  5. Semiring
  6. MultiplicativeSemigroup
  7. Module
  8. AdditiveCommutativeGroup
  9. AdditiveCommutativeMonoid
  10. AdditiveCommutativeSemigroup
  11. AdditiveGroup
  12. AdditiveMonoid
  13. AdditiveSemigroup
  14. Serializable
  15. Serializable
  16. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]

    Permalink
    Definition Classes
    Any

  2. abstract def negate(x: V): V

    Permalink
    Definition Classes
    AdditiveGroup

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

    Permalink
    Definition Classes
    AdditiveSemigroup

  4. implicit abstract def scalar: Field[F]

    Permalink
    Definition Classes
    VectorSpace → Module

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

    Permalink
    Definition Classes
    MultiplicativeSemigroup

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

    Permalink
    Definition Classes
    Module

  7. abstract def zero: V

    Permalink
    Definition Classes
    AdditiveMonoid

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

    Permalink
    Definition Classes
    Any

  2. final def ##(): Int

    Permalink
    Definition Classes
    Any

  3. final def ==(arg0: Any): Boolean

    Permalink
    Definition Classes
    Any

  4. def additive: CommutativeGroup[V]

    Permalink
    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any

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

    Permalink
    Definition Classes
    VectorSpace

  7. def equals(arg0: Any): Boolean

    Permalink
    Definition Classes
    Any

  8. def hashCode(): Int

    Permalink
    Definition Classes
    Any

  9. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any

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

    Permalink
    Definition Classes
    AdditiveMonoid

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

    Permalink
    Definition Classes
    AdditiveGroup

  12. def multiplicative: algebra.Semigroup[V]

    Permalink
    Definition Classes
    MultiplicativeSemigroup

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

    Permalink
    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

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

    Permalink
    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

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

    Permalink
    Definition Classes
    MultiplicativeSemigroup

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

    Permalink
    Definition Classes
    AdditiveMonoid

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

    Permalink
    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

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

    Permalink
    Definition Classes
    Module

  19. def toString(): String

    Permalink
    Definition Classes
    Any

  20. def tryProduct(as: TraversableOnce[V]): Option[V]

    Permalink
    Definition Classes
    MultiplicativeSemigroup

  21. def trySum(as: TraversableOnce[V]): Option[V]

    Permalink
    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

Inherited from VectorSpace[V, F]

Inherited from RingAlgebra[V, F]

Inherited from algebra.ring.Rng[V]

Inherited from algebra.ring.Semiring[V]

Inherited from algebra.ring.MultiplicativeSemigroup[V]

Inherited from Module[V, F]

Inherited from AdditiveCommutativeGroup[V]

Inherited from AdditiveCommutativeMonoid[V]

Inherited from AdditiveCommutativeSemigroup[V]

Inherited from algebra.ring.AdditiveGroup[V]

Inherited from algebra.ring.AdditiveMonoid[V]

Inherited from algebra.ring.AdditiveSemigroup[V]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped