Trait

ap.algebra

EuclidianRing

Related Doc: package algebra

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trait EuclidianRing extends CommutativeRing with RingWithDivision

Euclidian rings extend rings with operations for division and remainder, with the Euclidian definition: plus(mul(div(s, t), t), mod(s, t)) === s, with f(mod(s, t)) in [0, abs(t)) for some appropriate embedding into real numbers.

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Inherited
  1. EuclidianRing
  2. RingWithDivision
  3. CommutativeRing
  4. CommutativePseudoRing
  5. Ring
  6. PseudoRing
  7. AnyRef
  8. Any
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Abstract Value Members

  1. abstract def div(s: ITerm, t: ITerm): ITerm

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    Euclidian division

    Euclidian division

    Definition Classes
    EuclidianRingRingWithDivision
  2. abstract val dom: Sort

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    Domain of the ring

    Domain of the ring

    Definition Classes
    PseudoRing
  3. abstract 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
    PseudoRing
  4. abstract def minus(s: ITerm): ITerm

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    Additive inverses

    Additive inverses

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

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    Euclidian remainder

  6. abstract def mul(s: ITerm, t: ITerm): ITerm

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    Ring multiplication

    Ring multiplication

    Definition Classes
    PseudoRing
  7. abstract def one: ITerm

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    The one element of this ring

    The one element of this ring

    Definition Classes
    PseudoRing
  8. abstract def plus(s: ITerm, t: ITerm): ITerm

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    Ring addition

    Ring addition

    Definition Classes
    PseudoRing
  9. abstract def zero: ITerm

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    The zero element of this ring

    The zero element of this ring

    Definition Classes
    PseudoRing

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

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

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    Definition Classes
    AnyRef → Any
  9. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  10. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  11. def hashCode(): Int

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    Definition Classes
    AnyRef → Any
  12. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  13. def minus(s: ITerm, t: ITerm): ITerm

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    Difference between two terms

    Difference between two terms

    Definition Classes
    PseudoRing
  14. 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
  15. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  18. def product(terms: ITerm*): ITerm

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    N-ary sums

    N-ary sums

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

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    N-ary sums

    N-ary sums

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

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

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    num * s

    num * s

    Definition Classes
    PseudoRing
  22. def toString(): String

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

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

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from RingWithDivision

Inherited from CommutativeRing

Inherited from CommutativePseudoRing

Inherited from Ring

Inherited from PseudoRing

Inherited from AnyRef

Inherited from Any

Ungrouped