# IntegerRing

### Related Doc: package algebra

#### object IntegerRing extends EuclidianRing with OrderedRing with CommutativeRing

The built-in ring of integers

Linear Supertypes
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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

Definition Classes
AnyRef → Any
2. #### final def ##(): Int

Definition Classes
AnyRef → Any
3. #### final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
4. #### def additiveGroup: Group with Abelian with SymbolicTimes

Addition gives rise to an Abelian group

Addition gives rise to an Abelian group

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

Definition Classes
Any
6. #### def clone(): AnyRef

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

Euclidian division

Euclidian division

Definition Classes
IntegerRingEuclidianRingRingWithDivision
8. #### val dom: Integer.type

Domain of the ring

Domain of the ring

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

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

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

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

Greater-than-or-equal operator

Greater-than-or-equal operator

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

Definition Classes
AnyRef → Any
14. #### def gt(s: ITerm, t: ITerm): IFormula

Greater-than operator

Greater-than operator

Definition Classes
RingWithOrder
15. #### def hashCode(): Int

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

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

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

Less-than-or-equal operator

Less-than-or-equal operator

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

Less-than operator

Less-than operator

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

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

Difference between two terms

Difference between two terms

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

Euclidian remainder

Euclidian remainder

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

Ring multiplication

Ring multiplication

Definition Classes
IntegerRingPseudoRing
24. #### def multiplicativeMonoid: Monoid with Abelian

Multiplication gives rise to an Abelian monoid

Multiplication gives rise to an Abelian monoid

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

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

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

Definition Classes
AnyRef
28. #### val one: ITerm

The one element of this ring

The one element of this ring

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

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

N-ary sums

N-ary sums

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

N-ary sums

N-ary sums

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

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

`num * s`

`num * s`

Definition Classes
PseudoRing
34. #### def toString(): String

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

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

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

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

The zero element of this ring

The zero element of this ring

Definition Classes
IntegerRingPseudoRing