# Field

### Related Doc: package algebra

#### trait Field extends CommutativeRing with RingWithDivision

Fields are commutative rings in which all non-zero elements have multiplicative inverses.

Linear Supertypes
Known Subclasses
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. Field
2. RingWithDivision
3. CommutativeRing
4. CommutativePseudoRing
5. Ring
6. PseudoRing
7. AnyRef
8. Any
1. Hide All
2. Show all
Visibility
1. Public
2. All

### Abstract Value Members

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

Division operation

Division operation

Definition Classes
RingWithDivision
2. #### abstract val dom: Sort

Domain of the ring

Domain of the ring

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

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

Ring multiplication

Ring multiplication

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

The one element of this ring

The one element of this ring

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

Definition Classes
PseudoRing
8. #### 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. #### final def getClass(): Class[_]

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

Definition Classes
AnyRef → Any

13. #### final def isInstanceOf[T0]: Boolean

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

Difference between two terms

Difference between two terms

Definition Classes
PseudoRing
15. #### def multiplicativeGroup: Group with Abelian

Non-zero elements now give rise to an Abelian group

16. #### def multiplicativeMonoid: Monoid with Abelian

Multiplication gives rise to an Abelian monoid

Multiplication gives rise to an Abelian monoid

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

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

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

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

N-ary sums

N-ary sums

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

N-ary sums

N-ary sums

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

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

`num * s`

`num * s`

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

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

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )