RingElem

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

All Methods Instance Methods Abstract Methods Default Methods
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 edu.jas.structure.AbelianGroupElem
abs, isZERO, negate, signum, subtract, sum

Methods inherited from interface edu.jas.structure.Element
compareTo, copy, equals, factory, hashCode, toScript, toScriptFactory

Methods inherited from interface edu.jas.structure.MonoidElem
divide, inverse, isONE, isUnit, leftDivide, leftRemainder, multiply, power, quotientRemainder, remainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

- 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).