cc.redberry.rings.poly

Class PolynomialMethods

java.lang.Object

cc.redberry.rings.poly.PolynomialMethods

public final class PolynomialMethods
extends Object

High-level methods for polynomials.

Since:

1.0

Method Summary

Modifier and Type	Method and Description
static <Poly extends IPolynomial<Poly>> boolean	coprimeQ(Iterable<Poly> polynomials) Returns whether specified polynomials are coprime.
static <Poly extends IPolynomial<Poly>> boolean	coprimeQ(Poly... polynomials) Returns whether specified polynomials are coprime.
static <Poly extends IPolynomial<Poly>> Poly[]	divideAndRemainder(Poly a, Poly b) Returns quotient and remainder of a and b.
static <Poly extends IPolynomial<Poly>> Poly	divideExact(Poly a, Poly b) Returns the quotient of a and b or throws ArithmeticException if exact division is not possible
static <Poly extends IPolynomial<Poly>> Poly	divideOrNull(Poly a, Poly b) Returns the quotient of a and b or throws ArithmeticException if exact division is not possible
static <Poly extends IPolynomial<Poly>> PolynomialFactorDecomposition<Poly>	Factor(Poly poly) Factor polynomial.
static <Poly extends IPolynomial<Poly>> PolynomialFactorDecomposition<Poly>	FactorSquareFree(Poly poly) Square-free factorization of polynomial.
static <Poly extends IPolynomial<Poly>> boolean	irreducibleQ(Poly poly) Returns whether specified polynomial is irreducible
static <T extends IUnivariatePolynomial<T>> T[]	PolynomialExtendedGCD(T a, T b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <Poly extends IPolynomial<Poly>> Poly	PolynomialGCD(Iterable<Poly> array) Compute GCD of collection of polynomials.
static <Poly extends IPolynomial<Poly>> Poly	PolynomialGCD(Poly... array) Compute GCD of array of polynomials.
static <Poly extends IPolynomial<Poly>> Poly	PolynomialGCD(Poly a, Poly b) Compute GCD of two polynomials.
static <T extends IPolynomial<T>> T	polyPow(T base, BigInteger exponent) Returns base in a power of non-negative exponent
static <T extends IPolynomial<T>> T	polyPow(T base, BigInteger exponent, boolean copy) Returns base in a power of non-negative exponent.
static <T extends IPolynomial<T>> T	polyPow(T base, int exponent, boolean copy, gnu.trove.map.hash.TIntObjectHashMap<T> cache) Returns base in a power of non-negative exponent
static <T extends IPolynomial<T>> T	polyPow(T base, long exponent) Returns base in a power of non-negative exponent
static <T extends IPolynomial<T>> T	polyPow(T base, long exponent, boolean copy) Returns base in a power of non-negative exponent
static <Poly extends IPolynomial<Poly>> Poly	remainder(Poly a, Poly b) Returns quotient and remainder of a and b.

Methods inherited from class java.lang.Object

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

Method Detail

Factor

public static <Poly extends IPolynomial<Poly>> PolynomialFactorDecomposition<Poly> Factor(Poly poly)

Factor polynomial.

Parameters:

poly - the polynomial

Returns:

irreducible factor decomposition

FactorSquareFree

public static <Poly extends IPolynomial<Poly>> PolynomialFactorDecomposition<Poly> FactorSquareFree(Poly poly)

Square-free factorization of polynomial.

Parameters:

poly - the polynomial

Returns:

irreducible square-free factor decomposition

PolynomialGCD

public static <Poly extends IPolynomial<Poly>> Poly PolynomialGCD(Poly a,
                                                                  Poly b)

Compute GCD of two polynomials.

Parameters:

a - the polynomial

b - the polynomial

Returns:

the GCD

PolynomialGCD

public static <Poly extends IPolynomial<Poly>> Poly PolynomialGCD(Poly... array)

Compute GCD of array of polynomials.

Parameters:

array - the polynomials

Returns:

the GCD

PolynomialGCD

public static <Poly extends IPolynomial<Poly>> Poly PolynomialGCD(Iterable<Poly> array)

Compute GCD of collection of polynomials.

Parameters:

array - the polynomials

Returns:

the GCD

PolynomialExtendedGCD

public static <T extends IUnivariatePolynomial<T>> T[] PolynomialExtendedGCD(T a,
                                                                             T b)

Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b). Half-GCD algorithm is used.

Parameters:

a - the univariate polynomial

b - the univariate polynomial

Returns:

array of [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b) (gcd is monic)

See Also:

UnivariateGCD.PolynomialExtendedGCD(IUnivariatePolynomial, IUnivariatePolynomial)

divideAndRemainder

public static <Poly extends IPolynomial<Poly>> Poly[] divideAndRemainder(Poly a,
                                                                         Poly b)

Returns quotient and remainder of a and b.

Parameters:

a - the dividend

b - the divider

Returns:

{quotient, remainder}

remainder

public static <Poly extends IPolynomial<Poly>> Poly remainder(Poly a,
                                                              Poly b)

Returns quotient and remainder of a and b.

Parameters:

a - the dividend

b - the divider

Returns:

{quotient, remainder}

divideOrNull

public static <Poly extends IPolynomial<Poly>> Poly divideOrNull(Poly a,
                                                                 Poly b)

Returns the quotient of a and b or throws ArithmeticException if exact division is not possible

Parameters:

a - the dividend

b - the divider

Returns:

quotient

Throws:

ArithmeticException - if exact division is not possible

divideExact

public static <Poly extends IPolynomial<Poly>> Poly divideExact(Poly a,
                                                                Poly b)

Returns the quotient of a and b or throws ArithmeticException if exact division is not possible

Parameters:

a - the dividend

b - the divider

Returns:

quotient

Throws:

ArithmeticException - if exact division is not possible

coprimeQ

public static <Poly extends IPolynomial<Poly>> boolean coprimeQ(Poly... polynomials)

Returns whether specified polynomials are coprime.

Parameters:

polynomials - the polynomials

Returns:

whether specified polynomials are coprime

coprimeQ

public static <Poly extends IPolynomial<Poly>> boolean coprimeQ(Iterable<Poly> polynomials)

Returns whether specified polynomials are coprime.

Parameters:

polynomials - the polynomials

Returns:

whether specified polynomials are coprime

irreducibleQ

public static <Poly extends IPolynomial<Poly>> boolean irreducibleQ(Poly poly)

Returns whether specified polynomial is irreducible

polyPow

public static <T extends IPolynomial<T>> T polyPow(T base,
                                                   BigInteger exponent,
                                                   boolean copy)

Returns base in a power of non-negative exponent.

Parameters:

base - the base

exponent - the non-negative exponent

copy - whether to clone base; if not the data of base will be lost

Returns:

base in a power of e

polyPow

public static <T extends IPolynomial<T>> T polyPow(T base,
                                                   long exponent)

Returns base in a power of non-negative exponent

Parameters:

base - the base

exponent - the non-negative exponent

Returns:

base in a power of e

polyPow

public static <T extends IPolynomial<T>> T polyPow(T base,
                                                   BigInteger exponent)

Returns base in a power of non-negative exponent

Parameters:

base - the base

exponent - the non-negative exponent

Returns:

base in a power of e

polyPow

public static <T extends IPolynomial<T>> T polyPow(T base,
                                                   long exponent,
                                                   boolean copy)

Returns base in a power of non-negative exponent

Parameters:

base - the base

exponent - the non-negative exponent

copy - whether to clone base; if not the data of base will be lost

Returns:

base in a power of e

polyPow

public static <T extends IPolynomial<T>> T polyPow(T base,
                                                   int exponent,
                                                   boolean copy,
                                                   gnu.trove.map.hash.TIntObjectHashMap<T> cache)

Returns base in a power of non-negative exponent

Parameters:

base - the base

exponent - the non-negative exponent

copy - whether to clone base; if not the data of base will be lost

cache - cache to store all intermediate powers

Returns:

base in a power of e