edu.jas.structure

Interface NoncomRingElem<C extends NoncomRingElem<C>>

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

Modifier and Type	Method and 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.RingElem

egcd, gcd, leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.AbelianGroupElem

abs, isZERO, negate, signum, subtract, sum

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.Element

compareTo, copy, equals, factory, hashCode, toScript, toScriptFactory

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.