Trait

spire.algebra.Field

FieldOfFractionsGCD

Related Doc: package Field

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trait FieldOfFractionsGCD[A, R] extends Field[A]

Field defined as a field of fractions with a default implementation of GCD/LCM such that - gcd(a/b, c/d) = gcd(a, c) / lcm(b, d) - lcm(a/b, c/d) = lcm(a, c) / gcd(b, d) which corresponds to the convention of the GCD domains of SageMath; on rational numbers, it "yields the unique extension of gcd from integers to rationals presuming the natural extension of the divisibility relation from integers to rationals", see http://math.stackexchange.com/a/151431

Linear Supertypes
Field[A], EuclideanRing[A], GCDRing[A], algebra.ring.Field[A], MultiplicativeCommutativeGroup[A], algebra.ring.MultiplicativeGroup[A], CommutativeRing[A], CommutativeRng[A], CommutativeRig[A], MultiplicativeCommutativeMonoid[A], CommutativeSemiring[A], MultiplicativeCommutativeSemigroup[A], algebra.ring.Ring[A], algebra.ring.Rng[A], AdditiveCommutativeGroup[A], algebra.ring.AdditiveGroup[A], algebra.ring.Rig[A], algebra.ring.MultiplicativeMonoid[A], algebra.ring.Semiring[A], algebra.ring.MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], algebra.ring.AdditiveMonoid[A], algebra.ring.AdditiveSemigroup[A], Serializable, Serializable, Any
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Inherited
  1. FieldOfFractionsGCD
  2. Field
  3. EuclideanRing
  4. GCDRing
  5. Field
  6. MultiplicativeCommutativeGroup
  7. MultiplicativeGroup
  8. CommutativeRing
  9. CommutativeRng
  10. CommutativeRig
  11. MultiplicativeCommutativeMonoid
  12. CommutativeSemiring
  13. MultiplicativeCommutativeSemigroup
  14. Ring
  15. Rng
  16. AdditiveCommutativeGroup
  17. AdditiveGroup
  18. Rig
  19. MultiplicativeMonoid
  20. Semiring
  21. MultiplicativeSemigroup
  22. AdditiveCommutativeMonoid
  23. AdditiveCommutativeSemigroup
  24. AdditiveMonoid
  25. AdditiveSemigroup
  26. Serializable
  27. Serializable
  28. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def denominator(a: A): R

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

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    Definition Classes
    MultiplicativeGroup

  3. implicit abstract def eqR: Eq[R]

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  4. abstract def fraction(num: R, den: R): A

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

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    Definition Classes
    Any

  6. abstract def negate(x: A): A

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    Definition Classes
    AdditiveGroup

  7. abstract def numerator(a: A): R

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  8. abstract def one: A

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    Definition Classes
    MultiplicativeMonoid

  9. abstract def plus(x: A, y: A): A

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    Definition Classes
    AdditiveSemigroup

  10. implicit abstract def ringR: GCDRing[R]

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  11. abstract def times(x: A, y: A): A

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    Definition Classes
    MultiplicativeSemigroup

  12. 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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    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → 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 euclideanFunction(a: A): BigInt

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    Definition Classes
    Field → EuclideanRing

  8. def fromBigInt(n: BigInt): A

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    Definition Classes
    Ring

  9. def fromDouble(a: Double): A

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    Definition Classes
    Field

  10. def fromInt(n: Int): A

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    Definition Classes
    Ring

  11. def gcd(x: A, y: A)(implicit ev: Eq[A]): A

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    Definition Classes
    FieldOfFractionsGCD → GCDRing

  12. def hashCode(): Int

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    Definition Classes
    Any

  13. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  14. def isOne(a: A)(implicit ev: algebra.Eq[A]): Boolean

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    Definition Classes
    MultiplicativeMonoid

  15. def isZero(a: A)(implicit ev: algebra.Eq[A]): Boolean

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    Definition Classes
    AdditiveMonoid

  16. def lcm(x: A, y: A)(implicit ev: Eq[A]): A

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    Definition Classes
    FieldOfFractionsGCD → GCDRing

  17. def minus(x: A, y: A): A

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    Definition Classes
    AdditiveGroup

  18. def mod(a: A, b: A): A

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    Definition Classes
    Field → EuclideanRing

  19. def multiplicative: CommutativeGroup[A]

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    Definition Classes
    MultiplicativeCommutativeGroup → MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

  21. def positiveSumN(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  22. def pow(a: A, n: Int): A

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    Definition Classes
    MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

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    Definition Classes
    MultiplicativeMonoid

  24. def quot(a: A, b: A): A

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    Definition Classes
    Field → EuclideanRing

  25. def quotmod(a: A, b: A): (A, A)

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    Definition Classes
    Field → EuclideanRing

  26. def reciprocal(x: A): A

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    Definition Classes
    MultiplicativeGroup

  27. def sum(as: TraversableOnce[A]): A

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    Definition Classes
    AdditiveMonoid

  28. def sumN(a: A, n: Int): A

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    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  29. def toString(): String

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    Definition Classes
    Any

  30. def tryProduct(as: TraversableOnce[A]): Option[A]

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  31. def trySum(as: TraversableOnce[A]): Option[A]

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    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

Inherited from Field[A]

Inherited from EuclideanRing[A]

Inherited from GCDRing[A]

Inherited from algebra.ring.Field[A]

Inherited from MultiplicativeCommutativeGroup[A]

Inherited from algebra.ring.MultiplicativeGroup[A]

Inherited from CommutativeRing[A]

Inherited from CommutativeRng[A]

Inherited from CommutativeRig[A]

Inherited from MultiplicativeCommutativeMonoid[A]

Inherited from CommutativeSemiring[A]

Inherited from MultiplicativeCommutativeSemigroup[A]

Inherited from algebra.ring.Ring[A]

Inherited from algebra.ring.Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from algebra.ring.AdditiveGroup[A]

Inherited from algebra.ring.Rig[A]

Inherited from algebra.ring.MultiplicativeMonoid[A]

Inherited from algebra.ring.Semiring[A]

Inherited from algebra.ring.MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from algebra.ring.AdditiveMonoid[A]

Inherited from algebra.ring.AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped