Package cc.redberry.rings.poly.multivar

Class MultivariateDivision

java.lang.Object

cc.redberry.rings.poly.multivar.MultivariateDivision

public final class MultivariateDivision
extends Object

Division with remainder of multivariate polynomials (multivariate reduction).

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	divideAndRemainder(Poly dividend, Poly divider)	Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	divideAndRemainder(Poly dividend, Poly... dividers)	Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	divideExact(Poly dividend, Poly divider)	Divides dividend by divider or throws exception if exact division is not possible
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	divideOrNull(Poly dividend, Poly divider)	Divides dividend by divider or returns null if exact division is not possible
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	dividesQ(Poly dividend, Poly divider)	Tests whether divisor is a divisor of poly
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	nontrivialQuotientQ(Poly dividend, Poly divider)	Tests whether there is nontrivial quotient dividend / divider
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	pseudoRemainder(Poly dividend, Collection<Poly> dividers)	Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	pseudoRemainder(Poly dividend, Poly divider)	Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	pseudoRemainder(Poly dividend, Poly... dividers)	Performs multivariate pseudo division with remainder and returns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	remainder(Poly dividend, Collection<Poly> dividers)	Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	remainder(Poly dividend, Poly divider)	Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	remainder(Poly dividend, Poly... dividers)	Performs multivariate division with remainder and returns the remainder.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

divideAndRemainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[] divideAndRemainder(Poly dividend,
                                                                                                                                   Poly... dividers)

Performs multivariate division with remainder. The resulting array of quotients and remainder (last element of the returned array) satisfies dividend = quotient_1 * divider_1 + quotient_2 * divider_2 + ... + remainder .

Parameters:

dividend - the dividend

dividers - the dividers

Returns:

array of quotients and remainder in the last position

remainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly remainder(Poly dividend,
                                                                                                                        Poly... dividers)

Performs multivariate division with remainder and returns the remainder.

Parameters:

dividend - the dividend

dividers - the dividers

Returns:

the remainder

pseudoRemainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly pseudoRemainder(Poly dividend,
                                                                                                                              Poly... dividers)

Performs multivariate pseudo division with remainder and returns the remainder.

Parameters:

dividend - the dividend

dividers - the dividers

Returns:

the "pseudo" remainder

divideAndRemainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[] divideAndRemainder(Poly dividend,
                                                                                                                                   Poly divider)

Performs multivariate division with remainder.

Parameters:

dividend - the dividend

divider - the divider

Returns:

array of quotient and remainder

remainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly remainder(Poly dividend,
                                                                                                                        Collection<Poly> dividers)

Performs multivariate division with remainder and rerurns the remainder.

Parameters:

dividend - the dividend

dividers - the dividers

Returns:

array of quotients and remainder at the last position

remainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly remainder(Poly dividend,
                                                                                                                        Poly divider)

Performs multivariate division with remainder and rerurns the remainder.

Parameters:

dividend - the dividend

divider - the divider

Returns:

array of quotients and remainder at the last position

pseudoRemainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly pseudoRemainder(Poly dividend,
                                                                                                                              Collection<Poly> dividers)

Performs multivariate division with remainder and rerurns the remainder.

Parameters:

dividend - the dividend

dividers - the dividers

Returns:

array of quotients and remainder at the last position

pseudoRemainder

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly pseudoRemainder(Poly dividend,
                                                                                                                              Poly divider)

Performs multivariate division with remainder and rerurns the remainder.

Parameters:

dividend - the dividend

divider - the divider

Returns:

array of quotients and remainder at the last position

divideExact

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly divideExact(Poly dividend,
                                                                                                                          Poly divider)

Divides dividend by divider or throws exception if exact division is not possible

Parameters:

dividend - the dividend

divider - the divider

Returns:

dividend / divider

Throws:

ArithmeticException - if exact division is not possible

divideOrNull

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly divideOrNull(Poly dividend,
                                                                                                                           Poly divider)

Divides dividend by divider or returns null if exact division is not possible

Parameters:

dividend - the dividend

divider - the divider

Returns:

dividend / divider or null if exact division is not possible

dividesQ

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean dividesQ(Poly dividend,
                                                                                                                          Poly divider)

Tests whether divisor is a divisor of poly

Parameters:

dividend - the polynomial

divider - the divisor to check

Returns:

whether divisor is a divisor of poly

nontrivialQuotientQ

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean nontrivialQuotientQ(Poly dividend,
                                                                                                                                     Poly divider)

Tests whether there is nontrivial quotient dividend / divider

Parameters:

dividend - the dividend

divider - the divider

Returns:

whether divisor is a divisor of poly