Class

cc.redberry.rings.scaladsl

GaloisField

Related Doc: package scaladsl

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final case class GaloisField[E](theRing: FiniteField[UnivariatePolynomial[E]], variable: String, ringOption: Option[UnivariateRing[E]] = None) extends IUnivariateRing[UnivariatePolynomial[E], E] with Product with Serializable

Galois field with arbitrary prime base

theRing

the rings.poly.FiniteField

variable

the variable of univariate polynomials representing this Galois field

Linear Supertypes
Serializable, Serializable, Product, Equals, IUnivariateRing[UnivariatePolynomial[E], E], IPolynomialRing[UnivariatePolynomial[E], E], Ring[UnivariatePolynomial[E]], RingSupport[UnivariatePolynomial[E]], ElementParser[UnivariatePolynomial[E]], ToStringSupport[UnivariatePolynomial[E]], AnyRef, Any
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Inherited
  1. GaloisField
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. IUnivariateRing
  7. IPolynomialRing
  8. Ring
  9. RingSupport
  10. ElementParser
  11. ToStringSupport
  12. AnyRef
  13. Any
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new GaloisField(theRing: FiniteField[UnivariatePolynomial[E]], variable: String, ringOption: Option[UnivariateRing[E]] = None)

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    theRing

    the rings.poly.FiniteField

    variable

    the variable of univariate polynomials representing this Galois field

Type Members

  1. final type CoefficientType = E

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    Type of coefficients

    Type of coefficients

    Definition Classes
    IPolynomialRing

  2. final type ElementType = UnivariatePolynomial[E]

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    Element type

    Element type

    Definition Classes
    Ring

  3. final type PolyType = UnivariatePolynomial[E]

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    Type of polynomials

    Type of polynomials

    Definition Classes
    IPolynomialRing

Value Members

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

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    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any

  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  4. def _show(obj: Any): String

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    To string

    To string

    Definition Classes
    IPolynomialRing → Ring

  5. def addConstant(poly: UnivariatePolynomial[E], el: E): UnivariatePolynomial[E]

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    Add coefficient ring element

    Add coefficient ring element

    Definition Classes
    GaloisField → IPolynomialRing

  6. final def apply(a: E, b: E, c: E, d: E, e: E): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    IPolynomialRing

  7. final def apply(a: E, b: E, c: E, d: E): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    IPolynomialRing

  8. final def apply(a: E, b: E, c: E): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    IPolynomialRing

  9. final def apply(a: E, b: E): (UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    IPolynomialRing

  10. final def apply(value: E): UnivariatePolynomial[E]

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    Definition Classes
    IPolynomialRing

  11. final def apply(a: String, b: String, c: String, d: String, e: String): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    Ring

  12. final def apply(a: String, b: String, c: String, d: String): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    Ring

  13. final def apply(a: String, b: String, c: String): (UnivariatePolynomial[E], UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    Ring

  14. final def apply(a: String, b: String): (UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Definition Classes
    Ring

  15. final def apply(e: ElementType): UnivariatePolynomial[E]

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    Definition Classes
    Ring

  16. final def apply(int: IntZ): UnivariatePolynomial[E]

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    Definition Classes
    Ring

  17. final def apply(int: BigInt): UnivariatePolynomial[E]

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    Definition Classes
    Ring

  18. final def apply(int: Int): UnivariatePolynomial[E]

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    Definition Classes
    Ring

  19. final def apply(string: String): UnivariatePolynomial[E]

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    Parse

    Parse

    Definition Classes
    Ring

  20. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  21. def at(poly: UnivariatePolynomial[E], index: Int): E

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    i-th coefficient

    i-th coefficient

    Definition Classes
    IUnivariateRing

  22. def cc(poly: UnivariatePolynomial[E]): E

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    Constant coefficient

    Constant coefficient

    Definition Classes
    GaloisField → IPolynomialRing

  23. val cfRing: Ring[E]

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    The coefficient ring

    The coefficient ring

    Definition Classes
    GaloisField → IPolynomialRing

  24. def cfValue(i: Int): E

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    Value of integer in coefficient ring

    Value of integer in coefficient ring

    Definition Classes
    GaloisField → IPolynomialRing

  25. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  26. def create(coefficients: E*): UnivariatePolynomial[E]

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    Create univariate polynomial from the array of coefficients

    Create univariate polynomial from the array of coefficients

    Definition Classes
    GaloisField → IUnivariateRing

  27. final def divRem(a: UnivariatePolynomial[E], b: UnivariatePolynomial[E]): (UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Shortcut for /% operation

    Shortcut for /% operation

    Attributes
    protected[cc.redberry.rings.scaladsl]
    Definition Classes
    IPolynomialRing

  28. def divideAndRemainder(poly: UnivariatePolynomial[E], el: E): (UnivariatePolynomial[E], UnivariatePolynomial[E])

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    Divide by coefficient ring element

    Divide by coefficient ring element

    Definition Classes
    GaloisField → IPolynomialRing

  29. def divideConstant(poly: UnivariatePolynomial[E], el: E): UnivariatePolynomial[E]

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    Divide by coefficient ring element

    Divide by coefficient ring element

    Definition Classes
    GaloisField → IPolynomialRing

  30. final def element(e: Any): UnivariatePolynomial[E]

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    Casts e to element of this

    Casts e to element of this

    Definition Classes
    Ring

  31. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef

  32. def eval(poly: UnivariatePolynomial[E], point: E): E

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    Evaluate poly at a given point

    Evaluate poly at a given point

    Definition Classes
    GaloisField → IUnivariateRing

  33. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  34. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any

  35. def getConstant(value: E): UnivariatePolynomial[E]

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    Constant polynomial with specified value

    Constant polynomial with specified value

    Definition Classes
    GaloisField → IPolynomialRing

  36. final def index(variable: String): Int

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    Index of variable with specified string representation

    Index of variable with specified string representation

    Definition Classes
    IPolynomialRing

  37. def isElement(e: Any): Boolean

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    Reflection: determines whether is element of this

    Reflection: determines whether is element of this

    Definition Classes
    IPolynomialRing → Ring

  38. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  39. def lc(poly: UnivariatePolynomial[E]): E

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    Leading coefficient

    Leading coefficient

    Definition Classes
    GaloisField → IPolynomialRing

  40. def multiplyConstant(poly: UnivariatePolynomial[E], el: E): UnivariatePolynomial[E]

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    Multiply by coefficient ring element

    Multiply by coefficient ring element

    Definition Classes
    GaloisField → IPolynomialRing

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

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    Definition Classes
    AnyRef

  42. final def notify(): Unit

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    Definition Classes
    AnyRef

  43. final def notifyAll(): Unit

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    Definition Classes
    AnyRef

  44. def parse(string: String): UnivariatePolynomial[E]

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    Parse polynomial

    Parse polynomial

    Definition Classes
    GaloisField → IPolynomialRing → Ring → ElementParser

  45. def ringEv(ev: UnivariatePolynomial[E]): Ring[UnivariatePolynomial[E]]

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    Definition Classes
    Ring → RingSupport

  46. def show(obj: WithVariables): String

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    String representation of polynomial from this ring

    String representation of polynomial from this ring

    Definition Classes
    GaloisField → IPolynomialRing

  47. final def show(list: Traversable[_]): String

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    String representation of a seq of polynomials

    String representation of a seq of polynomials

    Definition Classes
    IPolynomialRing

  48. final def show(arg: Any): String

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    Pretty toString

    Pretty toString

    Definition Classes
    Ring

  49. def subtractConstant(poly: UnivariatePolynomial[E], el: E): UnivariatePolynomial[E]

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    Subtract coefficient ring element

    Subtract coefficient ring element

    Definition Classes
    GaloisField → IPolynomialRing

  50. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef

  51. val theRing: FiniteField[UnivariatePolynomial[E]]

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    the rings.poly.FiniteField

    the rings.poly.FiniteField

    Definition Classes
    GaloisField → IUnivariateRing → IPolynomialRing → Ring

  52. final def toString(element: UnivariatePolynomial[E]): String

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    <invalid inheritdoc annotation>

    <invalid inheritdoc annotation>

    Definition Classes
    Ring → ToStringSupport

  53. val toString: String

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    String representation of this ring

    String representation of this ring

    Definition Classes
    GaloisField → IPolynomialRing → Ring → AnyRef → Any

  54. final def variable(variable: String): Int

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    Index of variable with specified string representation

    Index of variable with specified string representation

    Definition Classes
    IPolynomialRing

  55. val variable: String

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    the variable of univariate polynomials representing this Galois field

    the variable of univariate polynomials representing this Galois field

    Definition Classes
    GaloisField → IUnivariateRing

  56. val variables: Array[String]

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    polynomial variables

    polynomial variables

    Definition Classes
    IPolynomialRing

  57. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  58. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  59. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  60. final lazy val x: UnivariatePolynomial[E]

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    The first variable

    The first variable

    Definition Classes
    IPolynomialRing

  61. final lazy val y: UnivariatePolynomial[E]

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    The second variable

    The second variable

    Definition Classes
    IPolynomialRing

  62. final lazy val z: UnivariatePolynomial[E]

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    The third variable

    The third variable

    Definition Classes
    IPolynomialRing

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from IUnivariateRing[UnivariatePolynomial[E], E]

Inherited from IPolynomialRing[UnivariatePolynomial[E], E]

Inherited from Ring[UnivariatePolynomial[E]]

Inherited from RingSupport[UnivariatePolynomial[E]]

Inherited from ElementParser[UnivariatePolynomial[E]]

Inherited from ToStringSupport[UnivariatePolynomial[E]]

Inherited from AnyRef

Inherited from Any

Ungrouped