Interface RegularRingElem<C extends RegularRingElem<C>>

Type Parameters:

C - regular ring element type

All Superinterfaces:

AbelianGroupElem<C>, Comparable<C>, Element<C>, GcdRingElem<C>, MonoidElem<C>, RingElem<C>, 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.

Method Summary

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 AbelianGroupElem

abs, isZERO, negate, signum, subtract, sum

Methods inherited from interface Element

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

Methods inherited from interface MonoidElem

divide, inverse, isONE, isUnit, leftDivide, leftRemainder, multiply, power, quotientRemainder, remainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface RingElem

egcd, gcd, leftGcd, rightGcd

Method Details

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.