edu.jas.structure

Interface RingElem<C extends RingElem<C>>

Type Parameters:

C - ring element type

All Superinterfaces:

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

All Known Subinterfaces:

AlgebraElem<A,C>, FieldElem<C>, GcdRingElem<C>, NoncomRingElem<C>, Polynomial<C>, RegularRingElem<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, WordResidue

public interface RingElem<C extends RingElem<C>>
extends AbelianGroupElem<C>, MonoidElem<C>

Ring element interface. Combines additive and multiplicative methods. Adds also gcd because of polynomials.

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method and Description
C[]	egcd(C b) Extended greatest common divisor.
C	gcd(C b) Greatest common divisor.
default C	leftGcd(C b) Left greatest common divisor.
default C	rightGcd(C b) Right greatest common divisor.

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, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface edu.jas.structure.Element

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

Method Detail

gcd

C gcd(C b)

Greatest common divisor.

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

C[] egcd(C b)

Extended greatest common divisor.

Parameters:

b - other element.

Returns:

[ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).

leftGcd

default C leftGcd(C b)

Left greatest common divisor. Returns commutative greatest common divisor if not overwritten.

Parameters:

b - other element.

Returns:

leftGcd(this,b).

rightGcd

default C rightGcd(C b)

Right greatest common divisor. Returns commutative greatest common divisor if not overwritten.

Parameters:

b - other element.

Returns:

rightGcd(this,b).