edu.jas.structure

Interface MonoidElem<C extends MonoidElem<C>>

Type Parameters:

C - element type

All Superinterfaces:

java.lang.Comparable<C>, Element<C>, java.io.Serializable

All Known Subinterfaces:

AlgebraElem<A,C>, FieldElem<C>, GcdRingElem<C>, NoncomRingElem<C>, Polynomial<C>, RegularRingElem<C>, RingElem<C>, StarRingElem<C>

All Known Implementing Classes:

AlgebraicNumber, BigComplex, BigDecimal, BigDecimalComplex, BigInteger, BigOctonion, BigQuaternion, BigRational, Complex, ComplexAlgebraicNumber, GenMatrix, GenPolynomial, GenSolvablePolynomial, GenWordPolynomial, Local, Local, LocalSolvablePolynomial, ModInteger, ModLong, MultiVarPowerSeries, Product, QLRSolvablePolynomial, Quotient, Quotient, QuotSolvablePolynomial, RealAlgebraicNumber, RealAlgebraicNumber, RecSolvablePolynomial, RecSolvableWordPolynomial, Residue, Residue, ResidueSolvablePolynomial, ResidueSolvableWordPolynomial, SolvableLocal, SolvableLocalResidue, SolvableQuotient, SolvableResidue, UnivPowerSeries, Word, WordResidue

public interface MonoidElem<C extends MonoidElem<C>>
extends Element<C>

Monoid element interface. Defines the multiplicative methods.

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method and Description
C	divide(C S) Divide this by S.
C	inverse() Inverse of this.
boolean	isONE() Test if this is one.
boolean	isUnit() Test if this is a unit.
C	multiply(C S) Multiply this with S.
C	remainder(C S) Remainder after division of this by S.

Methods inherited from interface edu.jas.structure.Element

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

Method Detail

isONE

boolean isONE()

Test if this is one.

Returns:

true if this is 1, else false.

isUnit

boolean isUnit()

Test if this is a unit. I.e. there exists x with this.multiply(x).isONE() == true.

Returns:

true if this is a unit, else false.

multiply

C multiply(C S)

Multiply this with S.

Parameters:

S -

Returns:

this * S.

divide

C divide(C S)

Divide this by S.

Parameters:

S -

Returns:

this / S.

remainder

C remainder(C S)

Remainder after division of this by S.

Parameters:

S -

Returns:

this - (this / S) * S.

inverse

C inverse()

Inverse of this. Some implementing classes will throw NotInvertibleException if the element is not invertible.

Returns:

x with this * x = 1, if it exists.