t

spire.algebra

ZAlgebra

trait ZAlgebra[V] extends RingAlgebra[V, Int] with Ring[V]

Given any Ring[A] we can construct a RingAlgebra[A, Int]. This is possible since we can define fromInt on Ring generally.

Linear Supertypes
Ring[V], Rig[V], MultiplicativeMonoid[V], RingAlgebra[V, Int], Rng[V], Semiring[V], MultiplicativeSemigroup[V], Module[V, Int], AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ZAlgebra
  2. Ring
  3. Rig
  4. MultiplicativeMonoid
  5. RingAlgebra
  6. Rng
  7. Semiring
  8. MultiplicativeSemigroup
  9. Module
  10. AdditiveAbGroup
  11. AdditiveCMonoid
  12. AdditiveCSemigroup
  13. AdditiveGroup
  14. AdditiveMonoid
  15. AdditiveSemigroup
  16. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]
    Definition Classes
    Any
  2. implicit abstract def scalar: Ring[Int]
    Definition Classes
    ZAlgebra → Module
  3. implicit abstract def vector: Ring[V]

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 fromInt(n: Int): V

    Defined to be equivalent to additive.sumn(one, n).

    Defined to be equivalent to additive.sumn(one, n). That is, n repeated summations of this ring's one, or -one if n is negative.

    Definition Classes
    ZAlgebra → Ring
  8. def hashCode(): Int
    Definition Classes
    Any
  9. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  10. def isOne(a: V)(implicit ev: Eq[V]): Boolean
    Definition Classes
    MultiplicativeMonoid
  11. def isZero(a: V)(implicit ev: Eq[V]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid
  12. def minus(v: V, w: V): V
    Definition Classes
    ZAlgebra → AdditiveGroup
  13. def multiplicative: Monoid[V]
    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup
  14. def negate(v: V): V
    Definition Classes
    ZAlgebra → AdditiveGroup
  15. def one: V
    Definition Classes
    ZAlgebra → MultiplicativeMonoid
  16. def plus(v: V, w: V): V
    Definition Classes
    ZAlgebra → AdditiveSemigroup
  17. def pow(a: V, n: Int): V

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    Definition Classes
    Rig → Semiring
  18. def prod(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
    MultiplicativeMonoid
  19. 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
  20. def prodn(a: V, n: Int): V

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup
  21. def prodnAboveOne(a: V, n: Int): V
    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup
  22. 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
  23. 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
  24. 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
  25. def sumnAboveOne(a: V, n: Int): V
    Attributes
    protected
    Definition Classes
    AdditiveSemigroup
  26. def times(v: V, w: V): V
    Definition Classes
    ZAlgebra → MultiplicativeSemigroup
  27. def timesl(r: Int, v: V): V
    Definition Classes
    ZAlgebra → Module
  28. def timesr(v: V, r: Int): V
    Definition Classes
    Module
  29. def toString(): String
    Definition Classes
    Any
  30. def zero: V
    Definition Classes
    ZAlgebra → AdditiveMonoid

Inherited from Ring[V]

Inherited from Rig[V]

Inherited from MultiplicativeMonoid[V]

Inherited from RingAlgebra[V, Int]

Inherited from Rng[V]

Inherited from Semiring[V]

Inherited from MultiplicativeSemigroup[V]

Inherited from Module[V, Int]

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