# RingWithOrder

### Related Doc: package algebra

#### trait RingWithOrder extends PseudoRing

Rings that also possess an ordering relation

Linear Supertypes
PseudoRing, AnyRef, Any
Known Subclasses
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. RingWithOrder
2. PseudoRing
3. AnyRef
4. Any
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Visibility
1. Public
2. All

### Abstract Value Members

1. #### abstract val dom: Sort

Domain of the ring

Domain of the ring

Definition Classes
PseudoRing
2. #### abstract 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
PseudoRing
3. #### abstract def leq(s: ITerm, t: ITerm): IFormula

Less-than-or-equal operator

4. #### abstract def lt(s: ITerm, t: ITerm): IFormula

Less-than operator

5. #### abstract def minus(s: ITerm): ITerm

Definition Classes
PseudoRing
6. #### abstract def mul(s: ITerm, t: ITerm): ITerm

Ring multiplication

Ring multiplication

Definition Classes
PseudoRing
7. #### abstract def one: ITerm

The one element of this ring

The one element of this ring

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

Definition Classes
PseudoRing
9. #### abstract def zero: ITerm

The zero element of this ring

The zero element of this ring

Definition Classes
PseudoRing

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

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

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

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

Greater-than-or-equal operator

11. #### final def getClass(): Class[_]

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

Greater-than operator

13. #### def hashCode(): Int

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

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

Difference between two terms

Difference between two terms

Definition Classes
PseudoRing
16. #### final def ne(arg0: AnyRef): Boolean

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

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

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

N-ary sums

N-ary sums

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

N-ary sums

N-ary sums

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

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

`num * s`

`num * s`

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

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

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )