Interface RingElem<C extends RingElem<C>>

Type Parameters:

C - ring element type

All Superinterfaces:

AbelianGroupElem<C>, Comparable<C>, Element<C>, MonoidElem<C>, 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, GenExteriorPolynomial, 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.

Method Summary

Modifier and Type	Method	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 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

Method Details

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).