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

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  4. trait CfSyntax extends AnyRef

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  5. type DegreeVector = poly.multivar.DegreeVector

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

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    Ring of rationals

  7. final case class GaloisField[E](theRing: FiniteField[UnivariatePolynomial[E]], variable: String, ringOption: Option[UnivariateRing[E]] = None) extends AUnivariateRing[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

  8. final case class GaloisField64(theRing: FiniteField[UnivariatePolynomialZp64], variable: String) extends AUnivariateRingZp64 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

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

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    Ring of multivariate polynomials

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

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  11. 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

  12. type IUnivariatePolynomial[P <: poly.univar.IUnivariatePolynomial[P]] = poly.univar.IUnivariatePolynomial[P]

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

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    Ring of univariate polynomials

  14. 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

  15. type IntZ = BigInteger

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  16. class IntegerOps[E] extends AnyRef

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  17. trait IntegerSyntax extends AnyRef

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

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  19. type MonomialZp64 = poly.multivar.MonomialZp64

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

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  21. trait MultivariateCfSyntax extends AnyRef

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

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

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  24. type MultivariatePolynomialZp64 = poly.multivar.MultivariatePolynomialZp64

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  25. 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

  26. 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

  27. trait MultivariateSyntax extends AnyRef

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

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  29. type Ordering = Comparator[DegreeVector]

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

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  31. trait PolynomialCfSyntax extends AnyRef

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

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

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  34. trait PolynomialSetSyntax extends AnyRef

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

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  36. final case class QuotientRing[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](baseRing: IMultivariateRing[Term, Poly, E], ideal: Ideal[Term, Poly, E]) extends IMultivariateRing[Term, Poly, E] with Product with Serializable

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    Ideal in multivariate polynomial ring

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

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  38. final class RichArrayTuple[Poly] extends AnyRef

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    Definition Classes
    Predef

  39. sealed class Ring[E] extends ToStringSupport[E] with ElementParser[E] with RingSupport[E] with Serializable

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    Simple wrapper around Ring used to unify IPolynomialRing and Ring

  40. class RingOps[E] extends AnyRef

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  41. trait RingSupport[E] extends AnyRef

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  42. trait RingSyntax extends AnyRef

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

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  44. trait UnivariateCfSyntax extends AnyRef

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

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

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  47. type UnivariatePolynomialZp64 = poly.univar.UnivariatePolynomialZp64

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  48. final case class UnivariateQuotientRing[Poly <: IUnivariatePolynomial[Poly], E](baseRing: IUnivariateRing[Poly, E], modulus: Poly) extends IUnivariateRing[Poly, E] with Product with Serializable

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    Univariate quotient ring

  49. 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

  50. 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

  51. trait UnivariateSyntax extends AnyRef

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Value Members

  1. object Conversions

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    Since

    2.3

  2. object GF

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  3. object Ideal extends Serializable

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  4. object IdealZp64

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  5. object Monomial

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    Definition Classes
    Predef

  6. object MonomialZp64

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    Definition Classes
    Predef

  7. object MultivariateRing extends Serializable

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  8. object MultivariateRingZp64 extends Serializable

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  9. object PolynomialRing

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

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    Field of rationals (Q)

    Field of rationals (Q)

    Definition Classes
    Predef

  11. object Rational

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    Definition Classes
    Predef

  12. object RingSupport

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  13. object UnivariatePolynomial

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    Definition Classes
    Predef

  14. object UnivariatePolynomialZp64

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    Definition Classes
    Predef

  15. object UnivariateRingZp64 extends Serializable

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  16. val Z: Ring[BigInteger]

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    Ring of integers (Z)

    Ring of integers (Z)

    Definition Classes
    Predef

  17. 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

  18. 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

  19. 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

  20. 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

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

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    Definition Classes
    Predef

  22. implicit def asBigInteger(v: Long): BigInteger

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    Definition Classes
    Predef

  23. implicit def asBigInteger(v: Int): BigInteger

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    Definition Classes
    Predef

  24. implicit def asBigInteger(v: BigInteger): BigInteger

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    Definition Classes
    Predef

  25. implicit def asBigInteger(v: BigInt): BigInteger

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    Definition Classes
    Predef

  26. 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

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

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    Definition Classes
    Predef

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

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    Implicitly convert IntegersZp64 to Ring

    Implicitly convert IntegersZp64 to Ring

    Definition Classes
    Predef

  29. 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

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

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    Definition Classes
    Predef

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

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    Definition Classes
    Predef

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

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    Definition Classes
    Predef

  33. 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

  34. 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

  35. 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

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

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    Delegate FiniteField methods fo GaloisField64

    Delegate FiniteField methods fo GaloisField64

    Definition Classes
    Predef

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. object syntax extends LowPrioritySyntax

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  43. object util

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    Since

    2.1

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