Package edu.jas.structure
Interface RingElem<C extends RingElem<C>>
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- 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
,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.- Author:
- Heinz Kredel
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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
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Methods inherited from interface edu.jas.structure.Element
compareTo, copy, equals, factory, hashCode, toScript, toScriptFactory
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Methods inherited from interface edu.jas.structure.MonoidElem
divide, inverse, isONE, isUnit, leftDivide, leftRemainder, multiply, power, quotientRemainder, remainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Method Detail
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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).
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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).
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