Uses of Interface
edu.jas.structure.MonoidElem

Packages that use MonoidElem

Package	Description
edu.jas.application	Groebner base application package.
edu.jas.arith	Basic arithmetic package.
edu.jas.fd	Factorization domain package for solvable polynomial rings.
edu.jas.poly	Generic coefficients polynomial package.
edu.jas.ps	Generic coefficients power series package.
edu.jas.root	Real and Complex Root Computation package.
edu.jas.structure	Basic structural interfaces.
edu.jas.ufd	Unique factorization domain package.
edu.jas.vector	Generic vector and matrix package.

Uses of MonoidElem in edu.jas.application

Classes in edu.jas.application that implement MonoidElem

Modifier and Type	Class	Description
class	Local<C extends GcdRingElem<C>>	Local ring element based on GenPolynomial with RingElem interface.
class	LocalSolvablePolynomial<C extends GcdRingElem<C>>	LocalSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on bi-variate real algebraic numbers.
class	Residue<C extends GcdRingElem<C>>	Residue ring element based on GenPolynomial with RingElem interface.
class	ResidueSolvablePolynomial<C extends GcdRingElem<C>>	ResidueSolvablePolynomial generic solvable polynomials with solvable residue coefficients implementing RingElem.
class	ResidueSolvableWordPolynomial<C extends GcdRingElem<C>>	ResidueSolvableWordPolynomial solvable polynomials with WordResidue coefficients implementing RingElem.
class	SolvableLocal<C extends GcdRingElem<C>>	SolvableLocal ring element based on pairs of GenSolvablePolynomial with GcdRingElem interface.
class	SolvableLocalResidue<C extends GcdRingElem<C>>	SolvableLocalResidue, that is a (left) rational function, based on pairs of GenSolvablePolynomial with GcdRingElem interface.
class	SolvableResidue<C extends GcdRingElem<C>>	SolvableResidue ring element based on GenSolvablePolynomial with GcdRingElem interface.
class	WordResidue<C extends GcdRingElem<C>>	WordResidue ring element based on GenWordPolynomial with GcdRingElem interface.

Uses of MonoidElem in edu.jas.arith

Classes in edu.jas.arith that implement MonoidElem

Modifier and Type	Class	Description
class	BigComplex	BigComplex class based on BigRational implementing the RingElem respectively the StarRingElem interface.
class	BigDecimal	BigDecimal class to make java.math.BigDecimal available with RingElem interface.
class	BigDecimalComplex	BigComplex class based on BigDecimal implementing the RingElem respectively the StarRingElem interface.
class	BigInteger	BigInteger class to make java.math.BigInteger available with RingElem respectively the GcdRingElem interface.
class	BigOctonion	BigOctonion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
class	BigQuaternion	BigQuaternion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
class	BigQuaternionInteger	Integer BigQuaternion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
class	BigRational	Immutable arbitrary-precision rational numbers.
class	ModInt	ModInt class with RingElem interface.
class	ModInteger	ModInteger class with GcdRingElem interface.
class	ModLong	ModLong class with RingElem interface.
class	Product<C extends RingElem<C>>	Direct product element based on RingElem.

Uses of MonoidElem in edu.jas.fd

Classes in edu.jas.fd that implement MonoidElem

Modifier and Type	Class	Description
class	QuotSolvablePolynomial<C extends GcdRingElem<C>>	QuotSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	SolvableQuotient<C extends GcdRingElem<C>>	SolvableQuotient, that is a (left) rational function, based on GenSolvablePolynomial with RingElem interface.

Uses of MonoidElem in edu.jas.poly

Subinterfaces of MonoidElem in edu.jas.poly

Modifier and Type	Interface	Description
interface	Polynomial<C extends RingElem<C>>	Polynomial interface.

Classes in edu.jas.poly that implement MonoidElem

Modifier and Type	Class	Description
class	AlgebraicNumber<C extends RingElem<C>>	Algebraic number class.
class	Complex<C extends RingElem<C>>	Generic Complex class implementing the RingElem interface.
class	GenExteriorPolynomial<C extends RingElem<C>>	GenExteriorPolynomial generic polynomials implementing RingElem.
class	GenPolynomial<C extends RingElem<C>>	GenPolynomial generic polynomials implementing RingElem.
class	GenSolvablePolynomial<C extends RingElem<C>>	GenSolvablePolynomial generic solvable polynomials implementing RingElem.
class	GenWordPolynomial<C extends RingElem<C>>	GenWordPolynomial generic polynomials implementing RingElem.
class	IndexList	IndexList implements index lists for exterior polynomials.
class	Local<C extends RingElem<C>>	Local element based on RingElem pairs.
class	QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>	QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	Quotient<C extends RingElem<C>>	Quotient element based on RingElem pairs.
class	RecSolvablePolynomial<C extends RingElem<C>>	RecSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	RecSolvableWordPolynomial<C extends RingElem<C>>	RecSolvableWordPolynomial generic recursive solvable polynomials implementing RingElem.
class	Residue<C extends RingElem<C>>	Residue element based on RingElem residue.
class	Word	Word implements strings of letters for polynomials.

Uses of MonoidElem in edu.jas.ps

Classes in edu.jas.ps that implement MonoidElem

Modifier and Type	Class	Description
class	MultiVarPowerSeries<C extends RingElem<C>>	Multivariate power series implementation.
class	UnivPowerSeries<C extends RingElem<C>>	Univariate power series implementation.

Uses of MonoidElem in edu.jas.root

Classes in edu.jas.root that implement MonoidElem

Modifier and Type	Class	Description
class	ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on AlgebraicNumber.
class	RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Real algebraic number class based on AlgebraicNumber.

Uses of MonoidElem in edu.jas.structure

Classes in edu.jas.structure with type parameters of type MonoidElem

Modifier and Type	Interface	Description
interface	MonoidElem<C extends MonoidElem<C>>	Monoid element interface.
interface	MonoidFactory<C extends MonoidElem<C>>	Monoid factory interface.

Subinterfaces of MonoidElem in edu.jas.structure

Modifier and Type	Interface	Description
interface	AlgebraElem<A extends AlgebraElem<A,C>,C extends RingElem<C>>	Algabra element interface.
interface	FieldElem<C extends FieldElem<C>>	Field element interface.
interface	GcdRingElem<C extends GcdRingElem<C>>	Gcd ring element interface.
interface	NoncomRingElem<C extends NoncomRingElem<C>>	Non-commutative ring element interface.
interface	RegularRingElem<C extends RegularRingElem<C>>	Regular ring element interface.
interface	RingElem<C extends RingElem<C>>	Ring element interface.
interface	StarRingElem<C extends StarRingElem<C>>	Star ring element interface.

Methods in edu.jas.structure with type parameters of type MonoidElem

Modifier and Type	Method	Description
static <C extends MonoidElem<C>> C	Power.modPower(MonoidFactory<C> fac, C a, long n, C m)	power of a to the n-th modulo m.
static <C extends MonoidElem<C>> C	Power.modPower(MonoidFactory<C> fac, C a, java.math.BigInteger n, C m)	power of a to the n-th modulo m.
static <C extends MonoidElem<C>> C	Power.multiply(MonoidFactory<C> fac, java.util.List<C> A)	Multiply elements in list.
static <C extends MonoidElem<C>> C	Power.power(MonoidFactory<C> fac, C a, long n)	power of a to the n-th.

Methods in edu.jas.structure that return MonoidElem

Modifier and Type	Method	Description
default C[]	MonoidElem.quotientRemainder(C S)	Quotient and remainder by division of this by S.
default C[]	MonoidElem.twosidedDivide(C a)	Two-sided division.

Uses of MonoidElem in edu.jas.ufd

Classes in edu.jas.ufd that implement MonoidElem

Modifier and Type	Class	Description
class	Quotient<C extends GcdRingElem<C>>	Quotient, that is a rational function, based on GenPolynomial with RingElem interface.

Uses of MonoidElem in edu.jas.vector

Classes in edu.jas.vector that implement MonoidElem

Modifier and Type	Class	Description
class	GenMatrix<C extends RingElem<C>>	GenMatrix implements a generic matrix algebra over RingElem entries.