p

cc.redberry.rings

scaladsl

package scaladsl

Since

1.0

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Type Members

  1. type AMonomial[E <: poly.multivar.AMonomial[E]] = poly.multivar.AMonomial[E]
  2. type AMultivariatePolynomial[T <: poly.multivar.AMonomial[T], P <: poly.multivar.AMultivariatePolynomial[T, P]] = poly.multivar.AMultivariatePolynomial[T, P]
  3. final case class AlgebraicNumberField [E](theRing: poly.AlgebraicNumberField[UnivariatePolynomial[E]], variable: String, _cfRing: Ring[E] = null) extends AUnivariateRing[E] with SimpleFieldExtension[UnivariatePolynomial[E], E] with Product with Serializable

    Algebraic number field represented as simple field extension

    Algebraic number field represented as simple field extension

    theRing

    the rings.poly.FiniteField

    variable

    the variable that represent extension generator

  4. class CfOps [E, Poly <: IPolynomial[Poly]] extends AnyRef
  5. trait CfSyntax extends AnyRef
  6. type Coder[E] = io.Coder[E, _, _]
  7. type DegreeVector = poly.multivar.DegreeVector
  8. final case class Frac [E](ring: Ring[E]) extends Ring[Rational[E]] with Product with Serializable

    Ring of rationals

  9. final case class GaloisField [E](theRing: FiniteField[UnivariatePolynomial[E]], variable: String, _cfRing: Ring[E] = null) extends AUnivariateRing[E] with SimpleFieldExtension[UnivariatePolynomial[E], E] with Product with Serializable

    Galois field with arbitrary prime base

    Galois field with arbitrary prime base

    theRing

    the rings.poly.FiniteField

    variable

    the variable of univariate polynomials representing this Galois field

  10. final case class GaloisField64 (theRing: FiniteField[UnivariatePolynomialZp64], variable: String) extends AUnivariateRingZp64 with SimpleFieldExtension[UnivariatePolynomialZp64, Long] with Product with Serializable

    Galois field with prime base in a range of (0, 2^63)

    Galois field with prime base in a range of (0, 2^63)

    theRing

    the rings.poly.FiniteField

    variable

    the variable of univariate polynomials representing this Galois field

  11. sealed abstract class IMultivariateRing [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E] extends IPolynomialRing[Poly, E]

    Ring of multivariate polynomials

  12. type IPolynomial[P <: poly.IPolynomial[P]] = poly.IPolynomial[P]
  13. abstract class IPolynomialRing [Poly <: IPolynomial[Poly], E] extends Ring[Poly]

    Base class for polynomial rings

    Base class for polynomial rings

    E

    coefficient type

  14. type IUnivariatePolynomial[P <: poly.univar.IUnivariatePolynomial[P]] = poly.univar.IUnivariatePolynomial[P]
  15. sealed abstract class IUnivariateRing [Poly <: IUnivariatePolynomial[Poly], E] extends IPolynomialRing[Poly, E]

    Ring of univariate polynomials

  16. final case class Ideal [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ring: IMultivariateRing[Term, Poly, E], theIdeal: poly.multivar.Ideal[Term, Poly]) extends Product with Serializable

    Ideal in multivariate polynomial ring

  17. type IntZ = BigInteger
  18. class IntegerOps [E] extends AnyRef
  19. trait IntegerSyntax extends AnyRef
  20. type Monomial[E] = poly.multivar.Monomial[E]
  21. type MonomialZp64 = poly.multivar.MonomialZp64
  22. final case class MultipleFieldExtension [Term <: AMonomial[Term], mPoly <: AMultivariatePolynomial[Term, mPoly], sPoly <: IUnivariatePolynomial[sPoly], E](theRing: poly.MultipleFieldExtension[Term, mPoly, sPoly], variables: Array[String]) extends MultivariateRingWrapper[Term, mPoly, E] with Product with Serializable
  23. class MultivariateCfOps [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E] extends AnyRef
  24. trait MultivariateCfSyntax extends AnyRef
  25. class MultivariateOps [Poly <: AMultivariatePolynomial[_, Poly]] extends AnyRef
  26. type MultivariatePolynomial[E] = poly.multivar.MultivariatePolynomial[E]
  27. type MultivariatePolynomialZp64 = poly.multivar.MultivariatePolynomialZp64
  28. final case class MultivariateRing [E](coefficientDomain: Ring[E], variables: Array[String], ordering: Ordering) extends IMultivariateRing[Monomial[E], MultivariatePolynomial[E], E] with Product with Serializable

    Ring of multivariate polynomials over generic domains

    Ring of multivariate polynomials over generic domains

    coefficientDomain

    coefficient ring

  29. final case class MultivariateRingZp64 (coefficientDomain: IntegersZp64, variables: Array[String], ordering: Ordering) extends IMultivariateRing[MonomialZp64, MultivariatePolynomialZp64, Long] with Product with Serializable

    Zp[variables] with specified modulus

    Zp[variables] with specified modulus

    coefficientDomain

    coefficient ring

  30. trait MultivariateSyntax extends AnyRef
  31. class MultivariateTermOps [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly]] extends AnyRef
  32. type Ordering = Comparator[DegreeVector]
  33. class PolynomialCfOps [Poly <: IPolynomial[Poly], E] extends AnyRef
  34. trait PolynomialCfSyntax extends AnyRef
  35. type PolynomialFactorDecomposition[P <: IPolynomial[P]] = poly.PolynomialFactorDecomposition[P]
  36. class PolynomialSetOps [Poly <: IPolynomial[Poly]] extends AnyRef
  37. trait PolynomialSetSyntax extends AnyRef
  38. type PrecomputedInverse[Poly <: IUnivariatePolynomial[Poly]] = InverseModMonomial[Poly]
  39. final case class QuotientRing [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](baseRing: IMultivariateRing[Term, Poly, E], ideal: Ideal[Term, Poly, E]) extends MultivariateRingWrapper[Term, Poly, E] with Product with Serializable

    Multivariate quotient ring

  40. type Rational[E] = rings.Rational[E]
  41. final class RichArrayTuple[Poly] extends AnyRef
    Definition Classes
    Predef
  42. sealed class Ring [E] extends Stringifiable[E] with IParser[E] with RingSupport[E] with Serializable

    Simple wrapper around Ring used to unify IPolynomialRing and Ring

  43. class RingOps [E] extends AnyRef
  44. trait RingSupport [E] extends AnyRef
  45. trait RingSyntax extends AnyRef
  46. sealed trait SimpleFieldExtension [E <: IUnivariatePolynomial[E], C] extends IPolynomialRing[E, C]
  47. class UnivariateCfOps [Poly <: IUnivariatePolynomial[Poly], E] extends AnyRef
  48. trait UnivariateCfSyntax extends AnyRef
  49. class UnivariateOps [Poly <: IUnivariatePolynomial[Poly]] extends AnyRef
  50. type UnivariatePolynomial[E] = poly.univar.UnivariatePolynomial[E]
  51. type UnivariatePolynomialZp64 = poly.univar.UnivariatePolynomialZp64
  52. final case class UnivariateRing [E](cfRing: Ring[E], variable: String) extends AUnivariateRing[E] with Product with Serializable

    Ring of univariate polynomials over generic domains

    Ring of univariate polynomials over generic domains

    cfRing

    coefficient ring

    variable

    variable

  53. final case class UnivariateRingZp64 (cfRingZp64: IntegersZp64, variable: String) extends AUnivariateRingZp64 with Product with Serializable

    Ring of Zp[x] polynomials

    Ring of Zp[x] polynomials

    cfRingZp64

    coefficient ring

    variable

    variable

  54. trait UnivariateSyntax extends AnyRef

Value Members

  1. def GaussianIntegers(imaginaryUnit: String = "i"): AlgebraicNumberField[IntZ]

    Ring of Gaussian integers (integer complex numbers).

    Ring of Gaussian integers (integer complex numbers).

    Definition Classes
    Predef
  2. lazy val GaussianIntegers: AlgebraicNumberField[IntZ]

    Ring of Gaussian integers (integer complex numbers).

    Ring of Gaussian integers (integer complex numbers).

    Definition Classes
    Predef
  3. def GaussianNumbers[E](ring: Ring[E], imaginaryUnit: String = "i"): AlgebraicNumberField[E]

    Gaussian numbers for a given ring (that is ring adjoined with imaginary unit)

    Gaussian numbers for a given ring (that is ring adjoined with imaginary unit)

    Definition Classes
    Predef
  4. def GaussianRationals(imaginaryUnit: String): AlgebraicNumberField[Rational[IntZ]]

    Field of Gaussian rationals (rational complex numbers).

    Field of Gaussian rationals (rational complex numbers).

    Definition Classes
    Predef
  5. lazy val GaussianRationals: AlgebraicNumberField[Rational[IntZ]]

    Field of Gaussian rationals (rational complex numbers).

    Field of Gaussian rationals (rational complex numbers).

    Definition Classes
    Predef
  6. val Q: Ring[rings.Rational[BigInteger]]

    Field of rationals (Q)

    Field of rationals (Q)

    Definition Classes
    Predef
  7. def SplittingField[E](poly: UnivariatePolynomial[E], variables: Array[String]): MultipleFieldExtension[Monomial[E], MultivariatePolynomial[E], UnivariatePolynomial[E], E]

    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef
  8. def SplittingField[Term <: AMonomial[Term], mPoly <: AMultivariatePolynomial[Term, mPoly], sPoly <: IUnivariatePolynomial[sPoly], E](poly: sPoly, variables: Array[String]): MultipleFieldExtension[Term, mPoly, sPoly, E]

    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef
  9. def SplittingFieldZp64(poly: UnivariatePolynomialZp64, variables: Array[String]): MultipleFieldExtension[MonomialZp64, MultivariatePolynomialZp64, UnivariatePolynomialZp64, Long]

    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef
  10. val Z: Ring[BigInteger]

    Ring of integers (Z)

    Ring of integers (Z)

    Definition Classes
    Predef
  11. def Zp(modulus: BigInt): Ring[BigInteger]

    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef
  12. def Zp(modulus: BigInteger): Ring[BigInteger]

    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef
  13. def Zp(modulus: Long): Ring[BigInteger]

    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef
  14. def Zp64(modulus: Long): IntegersZp64

    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef
  15. implicit def arrayToTuple[Poly](arr: Array[Poly]): RichArrayTuple[Poly]
    Definition Classes
    Predef
  16. implicit def asBigInteger(v: Long): IntZ
    Definition Classes
    Predef
  17. implicit def asBigInteger(v: Int): IntZ
    Definition Classes
    Predef
  18. implicit def asBigInteger(v: BigInteger): IntZ
    Definition Classes
    Predef
  19. implicit def asBigInteger(v: BigInt): IntZ
    Definition Classes
    Predef
  20. implicit def asIdeal[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ideal: poly.multivar.Ideal[Term, Poly]): Ideal[Term, Poly, E]

    Implicitly convert rings.poly.multivar.Ideal to Ideal

    Implicitly convert rings.poly.multivar.Ideal to Ideal

    Definition Classes
    Predef
  21. implicit def asRandomGenerator(rnd: Random): RandomGenerator
    Definition Classes
    Predef
  22. implicit def asRing(ring: IntegersZp64): Ring[Long]

    Implicitly convert IntegersZp64 to Ring

    Implicitly convert IntegersZp64 to Ring

    Definition Classes
    Predef
  23. implicit def asRing[E](ring: rings.Ring[E]): Ring[E]

    Implicitly convert rings.Ring to Ring

    Implicitly convert rings.Ring to Ring

    Definition Classes
    Predef
  24. implicit def asRingElement[E](v: Long)(implicit ring: Ring[E]): E
    Definition Classes
    Predef
  25. implicit def asRingElement[E](v: Int)(implicit ring: Ring[E]): E
    Definition Classes
    Predef
  26. implicit def factors2Seq[E](factors: FactorDecomposition[E]): Seq[(E, Int)]
    Definition Classes
    Predef
  27. implicit def idealMethods[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ideal: Ideal[Term, Poly, E]): poly.multivar.Ideal[Term, Poly]

    Delegate Ideal methods for Ideal

    Delegate Ideal methods for Ideal

    Definition Classes
    Predef
  28. implicit def ringMethods[E](ring: Ring[E]): rings.Ring[E]

    Delegate rings.Ring methods for Ring

    Delegate rings.Ring methods for Ring

    Definition Classes
    Predef
  29. implicit def ringMethods[E](ring: GaloisField[E]): FiniteField[UnivariatePolynomial[E]]

    Delegate FiniteField methods fo GaloisField64

    Delegate FiniteField methods fo GaloisField64

    Definition Classes
    Predef
  30. implicit def ringMethods(ring: GaloisField64): FiniteField[UnivariatePolynomialZp64]

    Delegate FiniteField methods fo GaloisField64

    Delegate FiniteField methods fo GaloisField64

    Definition Classes
    Predef
  31. implicit def ringMethods(ring: MultivariateRingZp64): poly.MultivariateRing[MultivariatePolynomialZp64]

    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef
  32. implicit def ringMethods[E](ring: MultivariateRing[E]): poly.MultivariateRing[MultivariatePolynomial[E]]

    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef
  33. implicit def ringMethods(ring: UnivariateRingZp64): poly.UnivariateRing[UnivariatePolynomialZp64]

    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef
  34. implicit def ringMethods[E](ring: UnivariateRing[E]): poly.UnivariateRing[UnivariatePolynomial[E]]

    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef
  35. implicit def ringMethods[E](ring: Frac[E]): Rationals[E]

    Delegate Frac methods for rings.Rationals

    Delegate Frac methods for rings.Rationals

    Definition Classes
    Predef
  36. implicit def ringMethods[Poly <: IPolynomial[Poly], E](ring: IPolynomialRing[Poly, E]): poly.IPolynomialRing[Poly]

    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef
  37. object AlgebraicNumberField extends Serializable
  38. object Conversions

    Since

    2.3

  39. object GF
  40. object GaloisField extends Serializable
  41. object GaloisField64 extends Serializable
  42. object Ideal extends Serializable
  43. object IdealZp64
  44. object Monomial
    Definition Classes
    Predef
  45. object MonomialZp64
    Definition Classes
    Predef
  46. object MultipleFieldExtension extends Serializable
  47. object MultivariateRing extends Serializable
  48. object MultivariateRingZp64 extends Serializable
  49. object PolynomialRing
  50. object Rational
    Definition Classes
    Predef
  51. object RingSupport
  52. object SimpleFieldExtension extends Serializable
  53. object UnivariatePolynomial
    Definition Classes
    Predef
  54. object UnivariatePolynomialZp64
    Definition Classes
    Predef
  55. object UnivariateRingZp64 extends Serializable
  56. object syntax extends LowPrioritySyntax
  57. object util

    Since

    2.1

Inherited from Predef

Inherited from AnyRef

Inherited from Any

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