Trait/Object

spire.algebra

Module

Related Docs: object Module | package algebra

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trait Module[V, R] extends AdditiveAbGroup[V]

A module generalizes a vector space by requiring its scalar need only form a ring, rather than a field.

Linear Supertypes
AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], Any
Known Subclasses
ArrayCoordinateSpace, CoordinateSpace, DistInnerProductSpace, DistModule, DistNormedVectorSpace, DistVectorSpace, FieldAlgebra, InnerProductSpace, MapInnerProductSpace, MapRng, MapVectorSpace, NormedVectorSpace, PolynomialEuclideanRing, PolynomialRing, PolynomialRng, RingAlgebra, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqModule, SeqVectorSpace, VectorSpace, ZAlgebra, ZModule
Ordering
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  2. By Inheritance
Inherited
  1. Module
  2. AdditiveAbGroup
  3. AdditiveCMonoid
  4. AdditiveCSemigroup
  5. AdditiveGroup
  6. AdditiveMonoid
  7. AdditiveSemigroup
  8. 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: Rng[R]

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  5. abstract def timesl(r: R, v: V): V

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  6. 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 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 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

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

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    Definition Classes
    AdditiveGroup

  11. 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

  12. 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

  13. 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

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

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    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  15. def timesr(v: V, r: R): V

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  16. def toString(): String

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    Definition Classes
    Any

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