spire.algebra

EuclideanRing

trait EuclideanRing[A] extends CRing[A]

Linear Supertypes
CRing[A], MultiplicativeCMonoid[A], MultiplicativeCSemigroup[A], Ring[A], Rng[A], AdditiveAbGroup[A], AdditiveCMonoid[A], AdditiveCSemigroup[A], AdditiveGroup[A], Rig[A], MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Any
Known Subclasses
AlgebraicAlgebra, BigDecimalAlgebra, BigDecimalIsField, BigIntAlgebra, BigIntIsEuclideanRing, BigIntegerAlgebra, BigIntegerIsEuclideanRing, ByteAlgebra, ByteIsEuclideanRing, ComplexIsNumeric, DistEuclideanRing, DistField, DoubleAlgebra, DoubleIsField, Field, FloatAlgebra, FloatIsField, Fractional, IntAlgebra, IntIsEuclideanRing, Integral, LongAlgebra, LongIsEuclideanRing, NumberAlgebra, PolynomialEuclideanRing, RationalAlgebra, RealAlgebra, RealIsFractional, SafeLongAlgebra, ShortAlgebra, ShortIsEuclideanRing
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Inherited
  1. EuclideanRing
  2. CRing
  3. MultiplicativeCMonoid
  4. MultiplicativeCSemigroup
  5. Ring
  6. Rng
  7. AdditiveAbGroup
  8. AdditiveCMonoid
  9. AdditiveCSemigroup
  10. AdditiveGroup
  11. Rig
  12. MultiplicativeMonoid
  13. Semiring
  14. MultiplicativeSemigroup
  15. AdditiveMonoid
  16. AdditiveSemigroup
  17. Any
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  1. Public
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Abstract Value Members

  1. abstract def gcd(a: A, b: A): A

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

    Definition Classes
    Any

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

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

    Definition Classes
    AdditiveGroup

  5. abstract def one: A

    Definition Classes
    MultiplicativeMonoid

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

    Definition Classes
    AdditiveSemigroup

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

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

    Definition Classes
    MultiplicativeSemigroup

  9. abstract def zero: A

    Definition Classes
    AdditiveMonoid

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[A]

    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. final def euclid(a: A, b: A)(implicit eq: Eq[A]): A

    Attributes
    protected[this]
    Annotations
    @tailrec()

  8. def fromInt(n: Int): A

    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
    Ring

  9. def hashCode(): Int

    Definition Classes
    Any

  10. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    MultiplicativeMonoid

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

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

  13. def lcm(a: A, b: A): A

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

    Definition Classes
    AdditiveGroup

  15. def multiplicative: CMonoid[A]

    Definition Classes
    MultiplicativeCMonoid → MultiplicativeCSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

    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

  17. def prod(as: TraversableOnce[A]): A

    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

  18. def prodOption(as: TraversableOnce[A]): Option[A]

    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

  19. def prodn(a: A, n: Int): A

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

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

    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

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

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

    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[A]): Option[A]

    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: A, n: Int): A

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  25. def sumnAboveOne(a: A, n: Int): A

    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  26. def toString(): String

    Definition Classes
    Any

Inherited from CRing[A]

Inherited from MultiplicativeCMonoid[A]

Inherited from MultiplicativeCSemigroup[A]

Inherited from Ring[A]

Inherited from Rng[A]

Inherited from AdditiveAbGroup[A]

Inherited from AdditiveCMonoid[A]

Inherited from AdditiveCSemigroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Any

Ungrouped