spire.math

PolynomialEuclideanRing

Related Doc: package math

trait PolynomialEuclideanRing[C] extends PolynomialRing[C] with EuclideanRing[Polynomial[C]] with VectorSpace[Polynomial[C], C]

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Inherited
  1. PolynomialEuclideanRing
  2. VectorSpace
  3. EuclideanRing
  4. CRing
  5. MultiplicativeCMonoid
  6. MultiplicativeCSemigroup
  7. PolynomialRing
  8. Ring
  9. Rig
  10. MultiplicativeMonoid
  11. PolynomialRng
  12. RingAlgebra
  13. Rng
  14. Module
  15. AdditiveAbGroup
  16. AdditiveCMonoid
  17. AdditiveCSemigroup
  18. AdditiveGroup
  19. PolynomialSemiring
  20. Semiring
  21. MultiplicativeSemigroup
  22. AdditiveMonoid
  23. AdditiveSemigroup
  24. AnyRef
  25. Any
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Abstract Value Members

  1. implicit abstract def ct: ClassTag[C]

    Definition Classes
    PolynomialSemiring
  2. implicit abstract def eq: Eq[C]

    Definition Classes
    PolynomialSemiring
  3. implicit abstract val scalar: Field[C]

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  4. def additive: AbGroup[Polynomial[C]]

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  6. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  7. def divr(x: Polynomial[C], k: C): Polynomial[C]

    Definition Classes
    PolynomialEuclideanRingVectorSpace
  8. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  9. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  10. final def euclid(a: Polynomial[C], b: Polynomial[C])(implicit eq: Eq[Polynomial[C]]): Polynomial[C]

    Attributes
    protected[this]
    Definition Classes
    EuclideanRing
    Annotations
    @tailrec()
  11. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  12. def fromInt(n: Int): Polynomial[C]

    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
  13. final def gcd(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialEuclideanRingEuclideanRing
  14. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  16. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  17. def isOne(a: Polynomial[C])(implicit ev: Eq[Polynomial[C]]): Boolean

    Definition Classes
    MultiplicativeMonoid
  18. def isZero(a: Polynomial[C])(implicit ev: Eq[Polynomial[C]]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid
  19. def lcm(a: Polynomial[C], b: Polynomial[C]): Polynomial[C]

    Definition Classes
    EuclideanRing
  20. def minus(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

    Definition Classes
    AdditiveGroup
  21. def mod(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialEuclideanRingEuclideanRing
  22. def multiplicative: CMonoid[Polynomial[C]]

  23. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  24. def negate(x: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialRngAdditiveGroup
  25. final def notify(): Unit

    Definition Classes
    AnyRef
  26. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  27. def one: Polynomial[C]

    Definition Classes
    PolynomialRingMultiplicativeMonoid
  28. def plus(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialSemiringAdditiveSemigroup
  29. def pow(a: Polynomial[C], n: Int): Polynomial[C]

    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
    RigSemiring
  30. def prod(as: TraversableOnce[Polynomial[C]]): Polynomial[C]

    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
  31. def prodOption(as: TraversableOnce[Polynomial[C]]): Option[Polynomial[C]]

    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
  32. def prodn(a: Polynomial[C], n: Int): Polynomial[C]

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes
    MultiplicativeMonoidMultiplicativeSemigroup
  33. def prodnAboveOne(a: Polynomial[C], n: Int): Polynomial[C]

    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup
  34. def quot(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialEuclideanRingEuclideanRing
  35. def quotmod(x: Polynomial[C], y: Polynomial[C]): (Polynomial[C], Polynomial[C])

    Definition Classes
    PolynomialEuclideanRingEuclideanRing
  36. def sum(as: TraversableOnce[Polynomial[C]]): Polynomial[C]

    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
  37. def sumOption(as: TraversableOnce[Polynomial[C]]): Option[Polynomial[C]]

    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
  38. def sumn(a: Polynomial[C], n: Int): Polynomial[C]

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroupAdditiveMonoidAdditiveSemigroup
  39. def sumnAboveOne(a: Polynomial[C], n: Int): Polynomial[C]

    Attributes
    protected
    Definition Classes
    AdditiveSemigroup
  40. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  41. def times(x: Polynomial[C], y: Polynomial[C]): Polynomial[C]

  42. def timesl(r: C, v: Polynomial[C]): Polynomial[C]

    Definition Classes
    PolynomialRngModule
  43. def timesr(v: Polynomial[C], r: C): Polynomial[C]

    Definition Classes
    Module
  44. def toString(): String

    Definition Classes
    AnyRef → Any
  45. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  46. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  47. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  48. def zero: Polynomial[C]

    Definition Classes
    PolynomialSemiringAdditiveMonoid

Inherited from VectorSpace[Polynomial[C], C]

Inherited from EuclideanRing[Polynomial[C]]

Inherited from CRing[Polynomial[C]]

Inherited from MultiplicativeCMonoid[Polynomial[C]]

Inherited from PolynomialRing[C]

Inherited from Ring[Polynomial[C]]

Inherited from Rig[Polynomial[C]]

Inherited from MultiplicativeMonoid[Polynomial[C]]

Inherited from PolynomialRng[C]

Inherited from RingAlgebra[Polynomial[C], C]

Inherited from Rng[Polynomial[C]]

Inherited from Module[Polynomial[C], C]

Inherited from AdditiveAbGroup[Polynomial[C]]

Inherited from AdditiveCMonoid[Polynomial[C]]

Inherited from AdditiveCSemigroup[Polynomial[C]]

Inherited from AdditiveGroup[Polynomial[C]]

Inherited from PolynomialSemiring[C]

Inherited from Semiring[Polynomial[C]]

Inherited from MultiplicativeSemigroup[Polynomial[C]]

Inherited from AdditiveMonoid[Polynomial[C]]

Inherited from AdditiveSemigroup[Polynomial[C]]

Inherited from AnyRef

Inherited from Any

Ungrouped