package scaladsl
- Since
1.0
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Type Members
- type AMonomial[E <: poly.multivar.AMonomial[E]] = poly.multivar.AMonomial[E]
- type AMultivariatePolynomial[T <: poly.multivar.AMonomial[T], P <: poly.multivar.AMultivariatePolynomial[T, P]] = poly.multivar.AMultivariatePolynomial[T, P]
-
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
- class CfOps [E, Poly <: IPolynomial[Poly]] extends AnyRef
- trait CfSyntax extends AnyRef
- type Coder[E] = io.Coder[E, _, _]
- type DegreeVector = poly.multivar.DegreeVector
-
final
case class
Frac
[E](ring: Ring[E]) extends Ring[Rational[E]] with Product with Serializable
Ring of rationals
-
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
-
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
-
sealed abstract
class
IMultivariateRing
[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E] extends IPolynomialRing[Poly, E]
Ring of multivariate polynomials
- type IPolynomial[P <: poly.IPolynomial[P]] = poly.IPolynomial[P]
-
abstract
class
IPolynomialRing
[Poly <: IPolynomial[Poly], E] extends Ring[Poly]
Base class for polynomial rings
Base class for polynomial rings
- E
coefficient type
- type IUnivariatePolynomial[P <: poly.univar.IUnivariatePolynomial[P]] = poly.univar.IUnivariatePolynomial[P]
-
sealed abstract
class
IUnivariateRing
[Poly <: IUnivariatePolynomial[Poly], E] extends IPolynomialRing[Poly, E]
Ring of univariate polynomials
-
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
- type IntZ = BigInteger
- class IntegerOps [E] extends AnyRef
- trait IntegerSyntax extends AnyRef
- type Monomial[E] = poly.multivar.Monomial[E]
- type MonomialZp64 = poly.multivar.MonomialZp64
- 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
- class MultivariateCfOps [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E] extends AnyRef
- trait MultivariateCfSyntax extends AnyRef
- class MultivariateOps [Poly <: AMultivariatePolynomial[_, Poly]] extends AnyRef
- type MultivariatePolynomial[E] = poly.multivar.MultivariatePolynomial[E]
- type MultivariatePolynomialZp64 = poly.multivar.MultivariatePolynomialZp64
-
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
-
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
- trait MultivariateSyntax extends AnyRef
- class MultivariateTermOps [Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly]] extends AnyRef
- type Ordering = Comparator[DegreeVector]
- class PolynomialCfOps [Poly <: IPolynomial[Poly], E] extends AnyRef
- trait PolynomialCfSyntax extends AnyRef
- type PolynomialFactorDecomposition[P <: IPolynomial[P]] = poly.PolynomialFactorDecomposition[P]
- class PolynomialSetOps [Poly <: IPolynomial[Poly]] extends AnyRef
- trait PolynomialSetSyntax extends AnyRef
- type PrecomputedInverse[Poly <: IUnivariatePolynomial[Poly]] = InverseModMonomial[Poly]
-
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
- type Rational[E] = rings.Rational[E]
-
final
class
RichArrayTuple[Poly] extends AnyRef
- Definition Classes
- Predef
-
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
- class RingOps [E] extends AnyRef
- trait RingSupport [E] extends AnyRef
- trait RingSyntax extends AnyRef
- sealed trait SimpleFieldExtension [E <: IUnivariatePolynomial[E], C] extends IPolynomialRing[E, C]
- class UnivariateCfOps [Poly <: IUnivariatePolynomial[Poly], E] extends AnyRef
- trait UnivariateCfSyntax extends AnyRef
- class UnivariateOps [Poly <: IUnivariatePolynomial[Poly]] extends AnyRef
- type UnivariatePolynomial[E] = poly.univar.UnivariatePolynomial[E]
- type UnivariatePolynomialZp64 = poly.univar.UnivariatePolynomialZp64
-
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
-
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
- trait UnivariateSyntax extends AnyRef
Value Members
-
def
GaussianIntegers(imaginaryUnit: String = "i"): AlgebraicNumberField[IntZ]
Ring of Gaussian integers (integer complex numbers).
Ring of Gaussian integers (integer complex numbers).
- Definition Classes
- Predef
-
lazy val
GaussianIntegers: AlgebraicNumberField[IntZ]
Ring of Gaussian integers (integer complex numbers).
Ring of Gaussian integers (integer complex numbers).
- Definition Classes
- Predef
-
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
-
def
GaussianRationals(imaginaryUnit: String): AlgebraicNumberField[Rational[IntZ]]
Field of Gaussian rationals (rational complex numbers).
Field of Gaussian rationals (rational complex numbers).
- Definition Classes
- Predef
-
lazy val
GaussianRationals: AlgebraicNumberField[Rational[IntZ]]
Field of Gaussian rationals (rational complex numbers).
Field of Gaussian rationals (rational complex numbers).
- Definition Classes
- Predef
-
val
Q: Ring[rings.Rational[BigInteger]]
Field of rationals (Q)
Field of rationals (Q)
- Definition Classes
- Predef
-
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
-
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
-
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
-
val
Z: Ring[BigInteger]
Ring of integers (Z)
Ring of integers (Z)
- Definition Classes
- Predef
-
def
Zp(modulus: BigInt): Ring[BigInteger]
Field of integers modulo
modulus
Field of integers modulo
modulus
- modulus
the modulus
- Definition Classes
- Predef
-
def
Zp(modulus: BigInteger): Ring[BigInteger]
Field of integers modulo
modulus
Field of integers modulo
modulus
- modulus
the modulus
- Definition Classes
- Predef
-
def
Zp(modulus: Long): Ring[BigInteger]
Field of integers modulo
modulus
Field of integers modulo
modulus
- modulus
the modulus
- Definition Classes
- Predef
-
def
Zp64(modulus: Long): IntegersZp64
Field of integers modulo
modulus
Field of integers modulo
modulus
- modulus
the modulus
- Definition Classes
- Predef
-
implicit
def
arrayToTuple[Poly](arr: Array[Poly]): RichArrayTuple[Poly]
- Definition Classes
- Predef
-
implicit
def
asBigInteger(v: Long): IntZ
- Definition Classes
- Predef
-
implicit
def
asBigInteger(v: Int): IntZ
- Definition Classes
- Predef
-
implicit
def
asBigInteger(v: BigInteger): IntZ
- Definition Classes
- Predef
-
implicit
def
asBigInteger(v: BigInt): IntZ
- Definition Classes
- Predef
-
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
-
implicit
def
asRandomGenerator(rnd: Random): RandomGenerator
- Definition Classes
- Predef
-
implicit
def
asRing(ring: IntegersZp64): Ring[Long]
Implicitly convert IntegersZp64 to Ring
Implicitly convert IntegersZp64 to Ring
- Definition Classes
- Predef
-
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
-
implicit
def
asRingElement[E](v: Long)(implicit ring: Ring[E]): E
- Definition Classes
- Predef
-
implicit
def
asRingElement[E](v: Int)(implicit ring: Ring[E]): E
- Definition Classes
- Predef
-
implicit
def
factors2Seq[E](factors: FactorDecomposition[E]): Seq[(E, Int)]
- Definition Classes
- Predef
- implicit def idealMethods[Term <: AMonomial[Term], Poly <: AMultivariatePolynomial[Term, Poly], E](ideal: Ideal[Term, Poly, E]): poly.multivar.Ideal[Term, Poly]
-
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
-
implicit
def
ringMethods[E](ring: GaloisField[E]): FiniteField[UnivariatePolynomial[E]]
Delegate FiniteField methods fo GaloisField64
Delegate FiniteField methods fo GaloisField64
- Definition Classes
- Predef
-
implicit
def
ringMethods(ring: GaloisField64): FiniteField[UnivariatePolynomialZp64]
Delegate FiniteField methods fo GaloisField64
Delegate FiniteField methods fo GaloisField64
- Definition Classes
- Predef
-
implicit
def
ringMethods(ring: MultivariateRingZp64): poly.MultivariateRing[MultivariatePolynomialZp64]
Delegate IPolynomialRing methods for IPolynomialRing
Delegate IPolynomialRing methods for IPolynomialRing
- Definition Classes
- Predef
-
implicit
def
ringMethods[E](ring: MultivariateRing[E]): poly.MultivariateRing[MultivariatePolynomial[E]]
Delegate IPolynomialRing methods for IPolynomialRing
Delegate IPolynomialRing methods for IPolynomialRing
- Definition Classes
- Predef
-
implicit
def
ringMethods(ring: UnivariateRingZp64): poly.UnivariateRing[UnivariatePolynomialZp64]
Delegate IPolynomialRing methods for IPolynomialRing
Delegate IPolynomialRing methods for IPolynomialRing
- Definition Classes
- Predef
-
implicit
def
ringMethods[E](ring: UnivariateRing[E]): poly.UnivariateRing[UnivariatePolynomial[E]]
Delegate IPolynomialRing methods for IPolynomialRing
Delegate IPolynomialRing methods for IPolynomialRing
- Definition Classes
- Predef
-
implicit
def
ringMethods[E](ring: Frac[E]): Rationals[E]
Delegate Frac methods for rings.Rationals
Delegate Frac methods for rings.Rationals
- Definition Classes
- Predef
-
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
- object AlgebraicNumberField extends Serializable
-
object
Conversions
- Since
2.3
- object GF
- object GaloisField extends Serializable
- object GaloisField64 extends Serializable
- object Ideal extends Serializable
- object IdealZp64
-
object
Monomial
- Definition Classes
- Predef
-
object
MonomialZp64
- Definition Classes
- Predef
- object MultipleFieldExtension extends Serializable
- object MultivariateRing extends Serializable
- object MultivariateRingZp64 extends Serializable
- object PolynomialRing
-
object
Rational
- Definition Classes
- Predef
- object RingSupport
- object SimpleFieldExtension extends Serializable
-
object
UnivariatePolynomial
- Definition Classes
- Predef
-
object
UnivariatePolynomialZp64
- Definition Classes
- Predef
- object UnivariateRingZp64 extends Serializable
- object syntax extends LowPrioritySyntax
-
object
util
- Since
2.1