Trait/Object

algebra.ring

Field

Related Docs: object Field | package ring

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trait Field[A] extends EuclideanRing[A] with MultiplicativeCommutativeGroup[A]

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Inherited
  1. Field
  2. MultiplicativeCommutativeGroup
  3. MultiplicativeGroup
  4. EuclideanRing
  5. CommutativeRing
  6. CommutativeRig
  7. MultiplicativeCommutativeMonoid
  8. MultiplicativeCommutativeSemigroup
  9. Ring
  10. Rng
  11. AdditiveCommutativeGroup
  12. AdditiveGroup
  13. Rig
  14. MultiplicativeMonoid
  15. Semiring
  16. MultiplicativeSemigroup
  17. AdditiveCommutativeMonoid
  18. AdditiveCommutativeSemigroup
  19. AdditiveMonoid
  20. AdditiveSemigroup
  21. Serializable
  22. Serializable
  23. Any
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Visibility
  1. Public
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Abstract Value Members

  1. abstract def div(x: A, y: A): A

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    Definition Classes
    MultiplicativeGroup
  2. abstract def getClass(): Class[_]

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    Definition Classes
    Any
  3. abstract def mod(a: A, b: A): A

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    Definition Classes
    EuclideanRing
  4. abstract def negate(x: A): A

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    Definition Classes
    AdditiveGroup
  5. abstract def one: A

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    Definition Classes
    MultiplicativeMonoid
  6. abstract def plus(x: A, y: A): A

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    Definition Classes
    AdditiveSemigroup
  7. abstract def quot(a: A, b: A): A

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    Definition Classes
    EuclideanRing
  8. abstract def times(x: A, y: A): A

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    Definition Classes
    MultiplicativeSemigroup
  9. abstract def zero: A

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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: CommutativeGroup[A]

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  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 fromDouble(a: Double): A

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    This is implemented in terms of basic Field ops.

    This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method be overriden.

    This is possible because a Double is a rational number.

  8. def fromInt(n: Int): A

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    Convert the given integer to an instance of A.

    Convert the given integer to an instance of A.

    Defined to be equivalent to sumN(one, n).

    That is, n repeated summations of this ring's one, or -n summations of -one if n is negative.

    Most type class instances should consider overriding this method for performance reasons.

    Definition Classes
    Ring
  9. def hashCode(): Int

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    Definition Classes
    Any
  10. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  11. def isOne(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is one.

    Tests if a is one.

    Definition Classes
    MultiplicativeMonoid
  12. def isZero(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid
  13. def minus(x: A, y: A): A

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    Definition Classes
    AdditiveGroup
  14. def multiplicative: CommutativeGroup[A]

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  15. def positivePow(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup
  16. def positiveSumN(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup
  17. def pow(a: A, n: Int): A

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  18. def product(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the product.

    Given a sequence of as, compute the product.

    Definition Classes
    MultiplicativeMonoid
  19. def quotmod(a: A, b: A): (A, A)

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    Definition Classes
    EuclideanRing
  20. def reciprocal(x: A): A

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    Definition Classes
    MultiplicativeGroup
  21. def sum(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the sum.

    Given a sequence of as, compute the sum.

    Definition Classes
    AdditiveMonoid
  22. def sumN(a: A, n: Int): A

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  23. def toString(): String

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    Definition Classes
    Any
  24. def tryProduct(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    MultiplicativeSemigroup
  25. def trySum(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    AdditiveSemigroup

Inherited from MultiplicativeCommutativeGroup[A]

Inherited from MultiplicativeGroup[A]

Inherited from EuclideanRing[A]

Inherited from CommutativeRing[A]

Inherited from CommutativeRig[A]

Inherited from Ring[A]

Inherited from Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

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