# Group

### Related Doc: package algebra

#### trait Group extends Monoid

Groups are monoids that additionally have inverses

Linear Supertypes
Monoid, Semigroup, AnyRef, Any
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### Abstract Value Members

1. #### abstract val dom: Sort

Domain of the semigroup

Domain of the semigroup

Definition Classes
Semigroup
2. #### abstract def identity: ITerm

The neutral element of this monoid

The neutral element of this monoid

Definition Classes
Monoid
3. #### abstract def inverse(s: ITerm): ITerm

Inverse elements

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

Binary operation of the semigroup

Binary operation of the semigroup

Definition Classes
Semigroup

### 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. #### final def asInstanceOf[T0]: T0

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

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
6. #### final def eq(arg0: AnyRef): Boolean

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

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

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

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

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

Definition Classes
Any
12. #### final def ne(arg0: AnyRef): Boolean

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

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

Definition Classes
AnyRef
15. #### final def synchronized[T0](arg0: ⇒ T0): T0

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

`num * s`

`num * s`

Definition Classes
GroupMonoidSemigroup
17. #### def toString(): String

Definition Classes
Semigroup → AnyRef → Any
18. #### final def wait(): Unit

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )