NoncomRingElem

Type Parameters:

C - ring element type

All Superinterfaces:

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

All Known Implementing Classes:

WordResidue
```
public interface NoncomRingElem<C extends NoncomRingElem<C>>
extends RingElem<C>
```
Non-commutative ring element interface. Defines right divide and right remainder.

Author:

Heinz Kredel

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`C`	`rightDivide(C a)`	Right division.
`C`	`rightRemainder(C a)`	Right remainder.
`C[]`	`twosidedDivide(C a)`	Two-sided division.
`C`	`twosidedRemainder(C a)`	Two-sided remainder.

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

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

- Method Detail
  - rightDivide
```
C rightDivide(C a)
```
    Right division.
    
    Specified by:
    
    rightDivide in interface MonoidElem<C extends NoncomRingElem<C>>
    
    Parameters:
    
    a - element.
    
    Returns:
    
    right, with a * right = this
  - rightRemainder
```
C rightRemainder(C a)
```
    Right remainder.
    
    Specified by:
    
    rightRemainder in interface MonoidElem<C extends NoncomRingElem<C>>
    
    Parameters:
    
    a - element.
    
    Returns:
    
    r = this - a * (a/right), where a * right = this.
  - twosidedDivide
```
C[] twosidedDivide(C a)
```
    Two-sided division.
    
    Specified by:
    
    twosidedDivide in interface MonoidElem<C extends NoncomRingElem<C>>
    
    Parameters:
    
    a - element.
    
    Returns:
    
    [left,right], with left * a * right = this
  - twosidedRemainder
```
C twosidedRemainder(C a)
```
    Two-sided remainder.
    
    Specified by:
    
    twosidedRemainder in interface MonoidElem<C extends NoncomRingElem<C>>
    
    Parameters:
    
    a - element.
    
    Returns:
    
    r = this - (a/left) * a * (a/right), where left * a * right = this.