Package 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, BigQuaternionInteger, BigRational, Complex, ComplexAlgebraicNumber, GenMatrix, GenPolynomial, GenSolvablePolynomial, GenWordPolynomial, Local, Local, LocalSolvablePolynomial, ModInt, 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	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.
default C	leftDivide(C a)	Left division.
default C	leftRemainder(C a)	Left remainder.
C	multiply(C S)	Multiply this with S.
default C	power(long n)	Power of this to the n-th.
default C[]	quotientRemainder(C S)	Quotient and remainder by division of this by S.
C	remainder(C S)	Remainder after division of this by S.
default C	rightDivide(C a)	Right division.
default C	rightRemainder(C a)	Right remainder.
default C[]	twosidedDivide(C a)	Two-sided division.
default C	twosidedRemainder(C a)	Two-sided remainder.

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.

quotientRemainder

default C[] quotientRemainder(C S)

Quotient and remainder by division of this by S.

Parameters:

S -

Returns:

[this/S, this - (this/S)*S].

rightDivide

default C rightDivide(C a)

Right division. Returns commutative divide if not overwritten.

Parameters:

a - element.

Returns:

right, with a * right = this

leftDivide

default C leftDivide(C a)

Left division. Returns commutative divide if not overwritten.

Parameters:

a - element.

Returns:

left, with left * a = this

rightRemainder

default C rightRemainder(C a)

Right remainder. Returns commutative remainder if not overwritten.

Parameters:

a - element.

Returns:

r = this - a * (1/right), where a * right = this.

leftRemainder

default C leftRemainder(C a)

Left remainder. Returns commutative remainder if not overwritten.

Parameters:

a - element.

Returns:

r = this - (1/left) * a, where left * a = this.

twosidedDivide

default C[] twosidedDivide(C a)

Two-sided division. Returns commutative divide if not overwritten.

Parameters:

a - element.

Returns:

[left,right], with left * a * right = this

twosidedRemainder

default C twosidedRemainder(C a)

Two-sided remainder. Returns commutative remainder if not overwritten.

Parameters:

a - element.

Returns:

r = this - (a/left) * a * (a/right), where left * a * right = this.

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.

power

default C power(long n)

Power of this to the n-th.

Parameters:

n - integer exponent.

Returns:

a**n, with a**0 = 1 and a**{-n} = {1/a}**n. Java 8 only