Object

ap.algebra

IntegerRing

Related Doc: package algebra

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object IntegerRing extends EuclidianRing with OrderedRing with CommutativeRing

The built-in ring of integers

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Inherited
  1. IntegerRing
  2. OrderedRing
  3. RingWithOrder
  4. EuclidianRing
  5. RingWithDivision
  6. CommutativeRing
  7. CommutativePseudoRing
  8. Ring
  9. PseudoRing
  10. AnyRef
  11. Any
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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 additiveGroup: Group with Abelian

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    Addition gives rise to an Abelian group

    Addition gives rise to an Abelian group

    Definition Classes
    PseudoRing
  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  6. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  7. def div(s: ITerm, t: ITerm): ITerm

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    Euclidian division

    Euclidian division

    Definition Classes
    IntegerRingEuclidianRingRingWithDivision
  8. val dom: Integer.type

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    Domain of the ring

    Domain of the ring

    Definition Classes
    IntegerRingPseudoRing
  9. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  10. def equals(arg0: Any): Boolean

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    Definition Classes
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  11. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  12. def geq(s: ITerm, t: ITerm): IFormula

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    Greater-than-or-equal operator

    Greater-than-or-equal operator

    Definition Classes
    RingWithOrder
  13. final def getClass(): Class[_]

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    Definition Classes
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  14. def gt(s: ITerm, t: ITerm): IFormula

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    Greater-than operator

    Greater-than operator

    Definition Classes
    RingWithOrder
  15. def hashCode(): Int

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    Definition Classes
    AnyRef → Any
  16. def int2ring(s: ITerm): ITerm

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    Conversion of an integer term to a ring term

    Conversion of an integer term to a ring term

    Definition Classes
    IntegerRingPseudoRing
  17. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  18. def leq(s: ITerm, t: ITerm): IFormula

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    Less-than-or-equal operator

    Less-than-or-equal operator

    Definition Classes
    IntegerRingRingWithOrder
  19. def lt(s: ITerm, t: ITerm): IFormula

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    Less-than operator

    Less-than operator

    Definition Classes
    IntegerRingRingWithOrder
  20. def minus(s: ITerm): ITerm

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    Additive inverses

    Additive inverses

    Definition Classes
    IntegerRingPseudoRing
  21. def minus(s: ITerm, t: ITerm): ITerm

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    Difference between two terms

    Difference between two terms

    Definition Classes
    PseudoRing
  22. def mod(s: ITerm, t: ITerm): ITerm

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    Euclidian remainder

    Euclidian remainder

    Definition Classes
    IntegerRingEuclidianRing
  23. def mul(s: ITerm, t: ITerm): ITerm

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    Ring multiplication

    Ring multiplication

    Definition Classes
    IntegerRingPseudoRing
  24. def multiplicativeMonoid: Monoid with Abelian

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    Multiplication gives rise to an Abelian monoid

    Multiplication gives rise to an Abelian monoid

    Definition Classes
    CommutativeRingRing
  25. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  26. final def notify(): Unit

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    Definition Classes
    AnyRef
  27. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  28. val one: ITerm

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    The one element of this ring

    The one element of this ring

    Definition Classes
    IntegerRingPseudoRing
  29. def plus(s: ITerm, t: ITerm): ITerm

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    Ring addition

    Ring addition

    Definition Classes
    IntegerRingPseudoRing
  30. def product(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  31. def summation(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

    Definition Classes
    PseudoRing
  32. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  33. def times(num: IdealInt, s: ITerm): ITerm

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    num * s

    num * s

    Definition Classes
    PseudoRing
  34. def toString(): String

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    Definition Classes
    PseudoRing → AnyRef → Any
  35. final def wait(): Unit

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    Definition Classes
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    Annotations
    @throws( ... )
  36. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
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    Annotations
    @throws( ... )
  37. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  38. val zero: ITerm

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    The zero element of this ring

    The zero element of this ring

    Definition Classes
    IntegerRingPseudoRing

Inherited from OrderedRing

Inherited from RingWithOrder

Inherited from EuclidianRing

Inherited from RingWithDivision

Inherited from CommutativeRing

Inherited from CommutativePseudoRing

Inherited from Ring

Inherited from PseudoRing

Inherited from AnyRef

Inherited from Any

Ungrouped