RegularRingElem

Type Parameters:

C - regular ring element type

All Superinterfaces:

AbelianGroupElem<C>, java.lang.Comparable<C>, Element<C>, GcdRingElem<C>, MonoidElem<C>, RingElem<C>, java.io.Serializable

All Known Implementing Classes:

Product
```
public interface RegularRingElem<C extends RegularRingElem<C>>
extends GcdRingElem<C>
```
Regular ring element interface. Defines idempotent operations and idempotent tests.

Author:

Heinz Kredel

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`C`	`fillIdempotent(C S)`	Regular ring element fill with idempotent.
`C`	`fillOne()`	Regular ring element fill with one.
`C`	`idemComplement()`	Regular ring element idempotent complement.
`C`	`idempotent()`	Idempotent.
`C`	`idempotentAnd(C S)`	Regular ring element idempotent and.
`C`	`idempotentOr(C S)`	Regular ring element idempotent or.
`boolean`	`isFull()`	Is regular ring element full.
`boolean`	`isIdempotent()`	Is idempotent.

Methods inherited from interface edu.jas.structure.AbelianGroupElem
abs, isZERO, negate, signum, subtract, sum

Methods inherited from interface edu.jas.structure.Element
compareTo, copy, equals, factory, hashCode, toScript, toScriptFactory

Methods inherited from interface edu.jas.structure.MonoidElem
divide, inverse, isONE, isUnit, leftDivide, leftRemainder, multiply, power, quotientRemainder, remainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface edu.jas.structure.RingElem
egcd, gcd, leftGcd, rightGcd

- Method Detail
  - isFull
```
boolean isFull()
```
    Is regular ring element full.
    
    Returns:
    
    If every component is non zero, then true is returned, else false.
  - isIdempotent
```
boolean isIdempotent()
```
    Is idempotent.
    
    Returns:
    
    If this is a idempotent element then true is returned, else false.
  - idempotent
```
C idempotent()
```
    Idempotent.
    
    Returns:
    
    S with this*S = this.
  - idemComplement
```
C idemComplement()
```
    Regular ring element idempotent complement.
    
    Returns:
    
    1-this.idempotent().
  - idempotentAnd
```
C idempotentAnd(C S)
```
    Regular ring element idempotent and.
    
    Parameters:
    
    S - Product.
    
    Returns:
    
    this.idempotent() and S.idempotent().
  - idempotentOr
```
C idempotentOr(C S)
```
    Regular ring element idempotent or.
    
    Parameters:
    
    S - Product.
    
    Returns:
    
    this.idempotent() or S.idempotent().
  - fillIdempotent
```
C fillIdempotent(C S)
```
    Regular ring element fill with idempotent.
    
    Parameters:
    
    S - Product.
    
    Returns:
    
    fill this with S.idempotent().
  - fillOne
```
C fillOne()
```
    Regular ring element fill with one.
    
    Returns:
    
    fill this with one.