Uses of Class
edu.jas.ufd.Quotient

Packages that use Quotient

Package	Description
edu.jas.application	Groebner base application package.
edu.jas.gbufd	Groebner bases using unique factorization package.
edu.jas.integrate	Elementary Integration package.
edu.jas.ufd	Unique factorization domain package.

Uses of Quotient in edu.jas.application

Methods in edu.jas.application that return types with arguments of type Quotient

Modifier and Type	Method	Description
IdealWithUniv<Quotient<C>>	Ideal.extension(GenPolynomialRing<C> efac)	Ideal extension.
IdealWithUniv<Quotient<C>>	Ideal.extension(QuotientRing<C> qfac)	Ideal extension.
IdealWithUniv<Quotient<C>>	Ideal.extension(java.lang.String... vars)	Ideal extension.
static <C extends GcdRingElem<C>> FactorAbstract<Quotient<C>>	FactorFactory.getImplementation(QuotientRing<C> fac)	Determine suitable implementation of factorization algorithms, case Quotient<C>.

Method parameters in edu.jas.application with type arguments of type Quotient

Modifier and Type	Method	Description
static <C extends GcdRingElem<C>> IdealWithUniv<C>	Ideal.contraction(IdealWithUniv<Quotient<C>> eid)	Ideal contraction.
IdealWithUniv<C>	Ideal.permContraction(IdealWithUniv<Quotient<C>> eideal)	Ideal contraction and permutation.

Uses of Quotient in edu.jas.gbufd

Methods in edu.jas.gbufd that return types with arguments of type Quotient

Modifier and Type	Method	Description
java.util.List<GenPolynomial<Quotient<C>>>	GroebnerBaseQuotient.GB(int modv, java.util.List<GenPolynomial<Quotient<C>>> F)	Groebner base using fraction free computation.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
java.util.List<GenPolynomial<Quotient<C>>>	GroebnerBaseQuotient.minimalGB(java.util.List<GenPolynomial<Quotient<C>>> Gp)	Minimal ordered Groebner basis.

Method parameters in edu.jas.gbufd with type arguments of type Quotient

Modifier and Type	Method	Description
java.util.List<GenPolynomial<Quotient<C>>>	GroebnerBaseQuotient.GB(int modv, java.util.List<GenPolynomial<Quotient<C>>> F)	Groebner base using fraction free computation.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>	GBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>	SGBFactory.getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)	Determine suitable implementation of GB algorithms, case Quotient coefficients.
java.util.List<GenPolynomial<Quotient<C>>>	GroebnerBaseQuotient.minimalGB(java.util.List<GenPolynomial<Quotient<C>>> Gp)	Minimal ordered Groebner basis.

Uses of Quotient in edu.jas.integrate

Fields in edu.jas.integrate declared as Quotient

Modifier and Type	Field	Description
Quotient<C>	QuotIntegral.quot	Original rational function with coefficients from C.

Fields in edu.jas.integrate with type parameters of type Quotient

Modifier and Type	Field	Description
java.util.List<Quotient<C>>	QuotIntegral.rational	Integral of the polynomial and rational part.

Methods in edu.jas.integrate that return Quotient

Modifier and Type	Method	Description
Quotient<C>	ElementaryIntegration.derivative(Quotient<C> r)	Deprecated. (forRemoval=true) use PolyUfdUtil.derivative()

Methods in edu.jas.integrate with parameters of type Quotient

Modifier and Type	Method	Description
Quotient<C>	ElementaryIntegration.derivative(Quotient<C> r)	Deprecated. (forRemoval=true) use PolyUfdUtil.derivative()
QuotIntegral<C>	ElementaryIntegration.integrate(Quotient<C> r)	Integration of a rational function.

Constructors in edu.jas.integrate with parameters of type Quotient

Constructor	Description
QuotIntegral(Quotient<C> r, GenPolynomial<C> p, java.util.List<GenPolynomial<C>> rat)	Constructor.
QuotIntegral(Quotient<C> r, GenPolynomial<C> p, java.util.List<GenPolynomial<C>> rat, java.util.List<LogIntegral<C>> log)	Constructor.

Uses of Quotient in edu.jas.ufd

Fields in edu.jas.ufd declared as Quotient

Modifier and Type	Field	Description
(package private) Quotient<C>	QuotientTaylorFunction.quo

Methods in edu.jas.ufd that return Quotient

Modifier and Type	Method	Description
Quotient<C>	Quotient.abs()	Quotient absolute value.
static <C extends GcdRingElem<C>> Quotient<C>	PolyUfdUtil.approximantOfPade(UnivPowerSeriesRing<C> upr, TaylorFunction<C> f, C a, int m, int n)	Pade approximant [m/n] of function f.
Quotient<C>	Quotient.copy()	Clone this.
Quotient<C>	QuotientRing.copy(Quotient<C> c)	Copy Quotient element c.
Quotient<C>	QuotientRing.create(GenPolynomial<C> n)	Create from numerator.
Quotient<C>	QuotientRing.create(GenPolynomial<C> n, GenPolynomial<C> d)	Create from numerator, denominator pair.
static <C extends GcdRingElem<C>> Quotient<C>	PolyUfdUtil.derivative(Quotient<C> r)	Derivation of a univariate rational function.
static <C extends GcdRingElem<C>> Quotient<C>	PolyUfdUtil.derivative(Quotient<C> Q, int r)	Polynomial quotient partial derivative variable r.
Quotient<C>	Quotient.divide(Quotient<C> S)	Quotient division.
Quotient<C>[]	Quotient.egcd(Quotient<C> b)	Extended greatest common divisor.
Quotient<C>	QuotientRing.fromInteger(long a)	Get a Quotient element from a long value.
Quotient<C>	QuotientRing.fromInteger(java.math.BigInteger a)	Get a Quotient element from a BigInteger value.
Quotient<C>	Quotient.gcd(Quotient<C> b)	Greatest common divisor.
Quotient<C>	QuotientRing.getONE()	Get the one element.
Quotient<C>	QuotientRing.getZERO()	Get the zero element.
Quotient<C>	Quotient.inverse()	Quotient inverse.
Quotient<C>	Quotient.monic()	Quotient monic.
Quotient<C>	Quotient.multiply(C b)	Quotient multiplication by coefficient.
Quotient<C>	Quotient.multiply(GenPolynomial<C> b)	Quotient multiplication by GenPolynomial.
Quotient<C>	Quotient.multiply(Quotient<C> S)	Quotient multiplication.
Quotient<C>	Quotient.negate()	Quotient negate.
Quotient<C>	QuotientRing.parse(java.io.Reader r)	Parse Quotient from Reader.
Quotient<C>	QuotientRing.parse(java.lang.String s)	Parse Quotient from String.
Quotient<C>[]	Quotient.quotientRemainder(Quotient<C> S)	Quotient and remainder by division of this by S.
Quotient<C>	QuotientRing.random(int n)	Quotient random.
Quotient<C>	QuotientRing.random(int k, int l, int d, float q)	Generate a random quotient polynomial.
Quotient<C>	QuotientRing.random(int n, java.util.Random rnd)	Quotient random.
Quotient<C>	Quotient.remainder(Quotient<C> S)	Quotient remainder.
Quotient<C>	Quotient.subtract(Quotient<C> S)	Quotient subtraction.
Quotient<C>	Quotient.sum(Quotient<C> S)	Quotient summation.

Methods in edu.jas.ufd that return types with arguments of type Quotient

Modifier and Type	Method	Description
java.util.List<GenPolynomial<Quotient<C>>>	FactorQuotient.baseFactorsSquarefree(GenPolynomial<Quotient<C>> P)	GenPolynomial base factorization of a squarefree polynomial.
GenPolynomial<Quotient<C>>	SquarefreeInfiniteFieldCharP.baseRootCharacteristic(GenPolynomial<Quotient<C>> P)	GenPolynomial char-th root univariate polynomial.
static <C extends GcdRingElem<C>> GenExteriorPolynomial<Quotient<C>>	PolyUfdUtil.exteriorDerivativeQuot(GenExteriorPolynomial<Quotient<C>> P)	GenExteriorPolynomial over polynomial quotient exterior derivative.
static <C extends GcdRingElem<C>> java.util.SortedMap<Quotient<C>,java.lang.Long>	PolyUfdUtil.factors(Quotient<C> A)	Factors of Quotient rational function.
java.util.List<GenPolynomial<Quotient<C>>>	FactorQuotient.factorsSquarefree(GenPolynomial<Quotient<C>> P)	GenPolynomial factorization of a squarefree polynomial.
java.util.List<Quotient<C>>	QuotientRing.generators()	Get a list of the generating elements.
static <C extends GcdRingElem<C>> FactorAbstract<Quotient<C>>	FactorFactory.getImplementation(QuotientRing<C> fac)	Determine suitable implementation of factorization algorithms, case Quotient<C>.
static <C extends GcdRingElem<C>> SquarefreeAbstract<Quotient<C>>	SquarefreeFactory.getImplementation(QuotientRing<C> fac)	Determine suitable implementation of squarefree factorization algorithms, case Quotient<C>.
static <C extends GcdRingElem<C>> GenPolynomial<Quotient<C>>	PolyUfdUtil.quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, GenPolynomial<GenPolynomial<C>> A)	Rational function from integral polynomial coefficients.
static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Quotient<C>>>	PolyUfdUtil.quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, java.util.Collection<GenPolynomial<GenPolynomial<C>>> L)	Rational function from integral polynomial coefficients.
GenPolynomial<GenPolynomial<Quotient<C>>>	SquarefreeInfiniteFieldCharP.recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<Quotient<C>>> P)	GenPolynomial char-th root univariate polynomial with polynomial coefficients.
GenPolynomial<Quotient<C>>	SquarefreeInfiniteFieldCharP.rootCharacteristic(GenPolynomial<Quotient<C>> P)	GenPolynomial char-th root main variable.
java.util.SortedMap<Quotient<C>,java.lang.Long>	SquarefreeInfiniteFieldCharP.rootCharacteristic(Quotient<C> P)	Characteristics root of a Quotient.
java.util.SortedMap<Quotient<C>,java.lang.Long>	SquarefreeInfiniteFieldCharP.squarefreeFactors(Quotient<C> P)	Squarefree factors of a Quotient.

Methods in edu.jas.ufd with parameters of type Quotient

Modifier and Type	Method	Description
int	Quotient.compareTo(Quotient<C> b)	Quotient comparison.
Quotient<C>	QuotientRing.copy(Quotient<C> c)	Copy Quotient element c.
static <C extends GcdRingElem<C>> Quotient<C>	PolyUfdUtil.derivative(Quotient<C> r)	Derivation of a univariate rational function.
static <C extends GcdRingElem<C>> Quotient<C>	PolyUfdUtil.derivative(Quotient<C> Q, int r)	Polynomial quotient partial derivative variable r.
Quotient<C>	Quotient.divide(Quotient<C> S)	Quotient division.
Quotient<C>[]	Quotient.egcd(Quotient<C> b)	Extended greatest common divisor.
static <C extends GcdRingElem<C>> C	PolyUfdUtil.evaluateAll(RingFactory<C> cfac, Quotient<C> A, java.util.List<C> a)	Evaluate all variables.
static <C extends GcdRingElem<C>> C	PolyUfdUtil.evaluateMain(RingFactory<C> cfac, Quotient<C> A, C a)	Evaluate at main variable.
static <C extends GcdRingElem<C>> java.util.SortedMap<Quotient<C>,java.lang.Long>	PolyUfdUtil.factors(Quotient<C> A)	Factors of Quotient rational function.
Quotient<C>	Quotient.gcd(Quotient<C> b)	Greatest common divisor.
static <C extends GcdRingElem<C>> boolean	PolyUfdUtil.isFactorization(Quotient<C> P, java.util.SortedMap<Quotient<C>,java.lang.Long> F)	Quotient is (squarefree) factorization.
Quotient<C>	Quotient.multiply(Quotient<C> S)	Quotient multiplication.
Quotient<C>[]	Quotient.quotientRemainder(Quotient<C> S)	Quotient and remainder by division of this by S.
Quotient<C>	Quotient.remainder(Quotient<C> S)	Quotient remainder.
java.util.SortedMap<Quotient<C>,java.lang.Long>	SquarefreeInfiniteFieldCharP.rootCharacteristic(Quotient<C> P)	Characteristics root of a Quotient.
java.util.SortedMap<Quotient<C>,java.lang.Long>	SquarefreeInfiniteFieldCharP.squarefreeFactors(Quotient<C> P)	Squarefree factors of a Quotient.
Quotient<C>	Quotient.subtract(Quotient<C> S)	Quotient subtraction.
Quotient<C>	Quotient.sum(Quotient<C> S)	Quotient summation.

Method parameters in edu.jas.ufd with type arguments of type Quotient

Modifier and Type	Method	Description
java.util.List<GenPolynomial<Quotient<C>>>	FactorQuotient.baseFactorsSquarefree(GenPolynomial<Quotient<C>> P)	GenPolynomial base factorization of a squarefree polynomial.
GenPolynomial<Quotient<C>>	SquarefreeInfiniteFieldCharP.baseRootCharacteristic(GenPolynomial<Quotient<C>> P)	GenPolynomial char-th root univariate polynomial.
static <C extends GcdRingElem<C>> GenExteriorPolynomial<Quotient<C>>	PolyUfdUtil.exteriorDerivativeQuot(GenExteriorPolynomial<Quotient<C>> P)	GenExteriorPolynomial over polynomial quotient exterior derivative.
java.util.List<GenPolynomial<Quotient<C>>>	FactorQuotient.factorsSquarefree(GenPolynomial<Quotient<C>> P)	GenPolynomial factorization of a squarefree polynomial.
static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUfdUtil.integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, GenPolynomial<Quotient<C>> A)	Integral polynomial from rational function coefficients.
static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<GenPolynomial<C>>>	PolyUfdUtil.integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, java.util.Collection<GenPolynomial<Quotient<C>>> L)	Integral polynomial from rational function coefficients.
static <C extends GcdRingElem<C>> boolean	PolyUfdUtil.isFactorization(Quotient<C> P, java.util.SortedMap<Quotient<C>,java.lang.Long> F)	Quotient is (squarefree) factorization.
static <C extends GcdRingElem<C>> GenPolynomial<Quotient<C>>	PolyUfdUtil.quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, GenPolynomial<GenPolynomial<C>> A)	Rational function from integral polynomial coefficients.
static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Quotient<C>>>	PolyUfdUtil.quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, java.util.Collection<GenPolynomial<GenPolynomial<C>>> L)	Rational function from integral polynomial coefficients.
GenPolynomial<GenPolynomial<Quotient<C>>>	SquarefreeInfiniteFieldCharP.recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<Quotient<C>>> P)	GenPolynomial char-th root univariate polynomial with polynomial coefficients.
GenPolynomial<Quotient<C>>	SquarefreeInfiniteFieldCharP.rootCharacteristic(GenPolynomial<Quotient<C>> P)	GenPolynomial char-th root main variable.

Constructors in edu.jas.ufd with parameters of type Quotient

Constructor	Description
QuotientTaylorFunction(Quotient<C> q)
QuotientTaylorFunction(Quotient<C> q, long f)

Constructor parameters in edu.jas.ufd with type arguments of type Quotient

Constructor	Description
SquarefreeInfiniteFieldCharP(RingFactory<Quotient<C>> fac)	Constructor.