Package

cc.redberry.rings

scaladsl

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package scaladsl

Since

1.0

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Type Members

  1. type AMonomial[E <: poly.multivar.AMonomial[E]] = poly.multivar.AMonomial[E]

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  2. type AMultivariatePolynomial[T <: poly.multivar.AMonomial[T], P <: poly.multivar.AMultivariatePolynomial[T, P]] = poly.multivar.AMultivariatePolynomial[T, P]

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  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

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    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

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  5. trait CfSyntax extends AnyRef

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  6. type Coder[E] = io.Coder[E, _, _]

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  7. type DegreeVector = poly.multivar.DegreeVector

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  8. final case class Frac[E](ring: Ring[E]) extends Ring[Rational[E]] with Product with Serializable

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    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

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    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

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    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]

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    Ring of multivariate polynomials

  12. type IPolynomial[P <: poly.IPolynomial[P]] = poly.IPolynomial[P]

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  13. abstract class IPolynomialRing[Poly <: IPolynomial[Poly], E] extends Ring[Poly]

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    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]

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  15. sealed abstract class IUnivariateRing[Poly <: IUnivariatePolynomial[Poly], E] extends IPolynomialRing[Poly, E]

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    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

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    Ideal in multivariate polynomial ring

  17. type IntZ = BigInteger

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  18. class IntegerOps[E] extends AnyRef

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  19. trait IntegerSyntax extends AnyRef

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  20. type Monomial[E] = poly.multivar.Monomial[E]

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  21. type MonomialZp64 = poly.multivar.MonomialZp64

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  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

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  23. class MultivariateCfOps[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E] extends AnyRef

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  24. trait MultivariateCfSyntax extends AnyRef

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  25. class MultivariateOps[Poly <: AMultivariatePolynomial[_, Poly]] extends AnyRef

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  26. type MultivariatePolynomial[E] = poly.multivar.MultivariatePolynomial[E]

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  27. type MultivariatePolynomialZp64 = poly.multivar.MultivariatePolynomialZp64

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  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

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    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

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    Zp[variables] with specified modulus

    Zp[variables] with specified modulus

    coefficientDomain

    coefficient ring

  30. trait MultivariateSyntax extends AnyRef

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  31. class MultivariateTermOps[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly]] extends AnyRef

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  32. type Ordering = Comparator[DegreeVector]

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  33. class PolynomialCfOps[Poly <: IPolynomial[Poly], E] extends AnyRef

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  34. trait PolynomialCfSyntax extends AnyRef

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  35. type PolynomialFactorDecomposition[P <: IPolynomial[P]] = poly.PolynomialFactorDecomposition[P]

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  36. class PolynomialSetOps[Poly <: IPolynomial[Poly]] extends AnyRef

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  37. trait PolynomialSetSyntax extends AnyRef

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  38. type PrecomputedInverse[Poly <: IUnivariatePolynomial[Poly]] = InverseModMonomial[Poly]

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  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

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    Multivariate quotient ring

  40. type Rational[E] = rings.Rational[E]

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  41. final class RichArrayTuple[Poly] extends AnyRef

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    Definition Classes
    Predef

  42. sealed class Ring[E] extends Stringifiable[E] with IParser[E] with RingSupport[E] with Serializable

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    Simple wrapper around Ring used to unify IPolynomialRing and Ring

  43. class RingOps[E] extends AnyRef

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  44. trait RingSupport[E] extends AnyRef

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  45. trait RingSyntax extends AnyRef

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  46. sealed trait SimpleFieldExtension[E <: IUnivariatePolynomial[E], C] extends IPolynomialRing[E, C]

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  47. class UnivariateCfOps[Poly <: IUnivariatePolynomial[Poly], E] extends AnyRef

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  48. trait UnivariateCfSyntax extends AnyRef

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  49. class UnivariateOps[Poly <: IUnivariatePolynomial[Poly]] extends AnyRef

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  50. type UnivariatePolynomial[E] = poly.univar.UnivariatePolynomial[E]

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  51. type UnivariatePolynomialZp64 = poly.univar.UnivariatePolynomialZp64

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  52. final case class UnivariateRing[E](cfRing: Ring[E], variable: String) extends AUnivariateRing[E] with Product with Serializable

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    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

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    Ring of Zp[x] polynomials

    Ring of Zp[x] polynomials

    cfRingZp64

    coefficient ring

    variable

    variable

  54. trait UnivariateSyntax extends AnyRef

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Value Members

  1. object AlgebraicNumberField extends Serializable

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  2. object Conversions

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    Since

    2.3

  3. object GF

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  4. object GaloisField extends Serializable

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  5. object GaloisField64 extends Serializable

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

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    Ring of Gaussian integers (integer complex numbers).

    Ring of Gaussian integers (integer complex numbers).

    Definition Classes
    Predef

  7. lazy val GaussianIntegers: AlgebraicNumberField[IntZ]

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    Ring of Gaussian integers (integer complex numbers).

    Ring of Gaussian integers (integer complex numbers).

    Definition Classes
    Predef

  8. def GaussianNumbers[E](ring: Ring[E], imaginaryUnit: String = "i"): AlgebraicNumberField[E]

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    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

  9. def GaussianRationals(imaginaryUnit: String): AlgebraicNumberField[Rational[IntZ]]

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    Field of Gaussian rationals (rational complex numbers).

    Field of Gaussian rationals (rational complex numbers).

    Definition Classes
    Predef

  10. lazy val GaussianRationals: AlgebraicNumberField[Rational[IntZ]]

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    Field of Gaussian rationals (rational complex numbers).

    Field of Gaussian rationals (rational complex numbers).

    Definition Classes
    Predef

  11. object Ideal extends Serializable

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  12. object IdealZp64

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  13. object Monomial

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    Definition Classes
    Predef

  14. object MonomialZp64

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    Definition Classes
    Predef

  15. object MultipleFieldExtension extends Serializable

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  16. object MultivariateRing extends Serializable

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  17. object MultivariateRingZp64 extends Serializable

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  18. object PolynomialRing

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  19. val Q: Ring[rings.Rational[BigInteger]]

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    Field of rationals (Q)

    Field of rationals (Q)

    Definition Classes
    Predef

  20. object Rational

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    Definition Classes
    Predef

  21. object RingSupport

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  22. object SimpleFieldExtension extends Serializable

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  23. def SplittingField[E](poly: UnivariatePolynomial[E], variables: Array[String]): MultipleFieldExtension[Monomial[E], MultivariatePolynomial[E], UnivariatePolynomial[E], E]

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    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef

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

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    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef

  25. def SplittingFieldZp64(poly: UnivariatePolynomialZp64, variables: Array[String]): MultipleFieldExtension[MonomialZp64, MultivariatePolynomialZp64, UnivariatePolynomialZp64, Long]

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    Splitting field of a given polynomial.

    Splitting field of a given polynomial.

    Definition Classes
    Predef

  26. object UnivariatePolynomial

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    Definition Classes
    Predef

  27. object UnivariatePolynomialZp64

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    Definition Classes
    Predef

  28. object UnivariateRingZp64 extends Serializable

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  29. val Z: Ring[BigInteger]

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    Ring of integers (Z)

    Ring of integers (Z)

    Definition Classes
    Predef

  30. def Zp(modulus: BigInt): Ring[BigInteger]

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    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef

  31. def Zp(modulus: BigInteger): Ring[BigInteger]

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    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef

  32. def Zp(modulus: Long): Ring[BigInteger]

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    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef

  33. def Zp64(modulus: Long): IntegersZp64

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    Field of integers modulo modulus

    Field of integers modulo modulus

    modulus

    the modulus

    Definition Classes
    Predef

  34. implicit def arrayToTuple[Poly](arr: Array[Poly]): RichArrayTuple[Poly]

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    Definition Classes
    Predef

  35. implicit def asBigInteger(v: Long): IntZ

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    Definition Classes
    Predef

  36. implicit def asBigInteger(v: Int): IntZ

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    Definition Classes
    Predef

  37. implicit def asBigInteger(v: BigInteger): IntZ

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    Definition Classes
    Predef

  38. implicit def asBigInteger(v: BigInt): IntZ

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    Definition Classes
    Predef

  39. implicit def asIdeal[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ideal: poly.multivar.Ideal[Term, Poly]): Ideal[Term, Poly, E]

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    Implicitly convert rings.poly.multivar.Ideal to Ideal

    Implicitly convert rings.poly.multivar.Ideal to Ideal

    Definition Classes
    Predef

  40. implicit def asRandomGenerator(rnd: Random): RandomGenerator

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    Definition Classes
    Predef

  41. implicit def asRing(ring: IntegersZp64): Ring[Long]

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    Implicitly convert IntegersZp64 to Ring

    Implicitly convert IntegersZp64 to Ring

    Definition Classes
    Predef

  42. implicit def asRing[E](ring: rings.Ring[E]): Ring[E]

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    Implicitly convert rings.Ring to Ring

    Implicitly convert rings.Ring to Ring

    Definition Classes
    Predef

  43. implicit def asRingElement[E](v: Long)(implicit ring: Ring[E]): E

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    Definition Classes
    Predef

  44. implicit def asRingElement[E](v: Int)(implicit ring: Ring[E]): E

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    Definition Classes
    Predef

  45. implicit def factors2Seq[E](factors: FactorDecomposition[E]): Seq[(E, Int)]

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    Definition Classes
    Predef

  46. implicit def idealMethods[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ideal: Ideal[Term, Poly, E]): poly.multivar.Ideal[Term, Poly]

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    Delegate Ideal methods for Ideal

    Delegate Ideal methods for Ideal

    Definition Classes
    Predef

  47. implicit def ringMethods[E](ring: Ring[E]): rings.Ring[E]

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    Delegate rings.Ring methods for Ring

    Delegate rings.Ring methods for Ring

    Definition Classes
    Predef

  48. implicit def ringMethods[E](ring: GaloisField[E]): FiniteField[UnivariatePolynomial[E]]

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    Delegate FiniteField methods fo GaloisField64

    Delegate FiniteField methods fo GaloisField64

    Definition Classes
    Predef

  49. implicit def ringMethods(ring: GaloisField64): FiniteField[UnivariatePolynomialZp64]

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    Delegate FiniteField methods fo GaloisField64

    Delegate FiniteField methods fo GaloisField64

    Definition Classes
    Predef

  50. implicit def ringMethods(ring: MultivariateRingZp64): poly.MultivariateRing[MultivariatePolynomialZp64]

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    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef

  51. implicit def ringMethods[E](ring: MultivariateRing[E]): poly.MultivariateRing[MultivariatePolynomial[E]]

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    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef

  52. implicit def ringMethods(ring: UnivariateRingZp64): poly.UnivariateRing[UnivariatePolynomialZp64]

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    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef

  53. implicit def ringMethods[E](ring: UnivariateRing[E]): poly.UnivariateRing[UnivariatePolynomial[E]]

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    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef

  54. implicit def ringMethods[Poly <: IPolynomial[Poly], E](ring: IPolynomialRing[Poly, E]): poly.IPolynomialRing[Poly]

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    Delegate IPolynomialRing methods for IPolynomialRing

    Delegate IPolynomialRing methods for IPolynomialRing

    Definition Classes
    Predef

  55. object syntax extends LowPrioritySyntax

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  56. object util

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    Since

    2.1

Inherited from Predef

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