Package cc.redberry.rings.poly

Class Util

java.lang.Object

cc.redberry.rings.poly.Util

public final class Util
extends Object

Since:

1.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Util.Tuple2<A,B>

Method Summary

Modifier and Type	Method	Description
static <E> MultivariatePolynomial<Rational<E>>	asOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly)
static <E> UnivariatePolynomial<Rational<E>>	asOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly)
static boolean	canConvertToZp64(IPolynomial poly)	Test whether poly is over Zp with modulus less then 2^63
static <E> E	commonDenominator(MultivariatePolynomial<Rational<E>> poly)	Returns a common denominator of given poly
static <E> E	commonDenominator(UnivariatePolynomial<Rational<E>> poly)	Returns a common denominator of given poly
static <E> MultivariatePolynomial<Rational<E>>	divideOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly, E denominator)
static <E> UnivariatePolynomial<Rational<E>>	divideOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly, E denominator)
static void	ensureOverField(IPolynomial... polys)
static void	ensureOverFiniteField(IPolynomial... polys)
static void	ensureOverZ(IPolynomial... polys)
static <T extends IPolynomial<T>> boolean	isOverMultipleFieldExtension(T poly)	Whether coefficient domain is F(alpha1, alpha2, ...)
static <T extends IPolynomial<T>> boolean	isOverQ(T poly)	Whether coefficient domain is Q
static <T extends IPolynomial<T>> boolean	isOverRationals(T poly)	Whether coefficient domain is rationals
static <T extends IPolynomial<T>> boolean	isOverRingOfIntegersOfSimpleNumberField(T poly)	Whether coefficient domain is Q(alpha)
static <T extends IPolynomial<T>> boolean	isOverSimpleFieldExtension(T poly)	Whether coefficient domain is F(alpha)
static <T extends IPolynomial<T>> boolean	isOverSimpleNumberField(T poly)	Whether coefficient domain is Q(alpha)
static <T extends IPolynomial<T>> boolean	isOverZ(T poly)	Whether coefficient domain is Z
static <E> Util.Tuple2<MultivariatePolynomial<E>,E>	toCommonDenominator(MultivariatePolynomial<Rational<E>> poly)	Brings polynomial with rational coefficients to common denominator
static <E> Util.Tuple2<UnivariatePolynomial<E>,E>	toCommonDenominator(UnivariatePolynomial<Rational<E>> poly)	Brings polynomial with rational coefficients to common denominator

Methods inherited from class java.lang.Object

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

Method Detail

ensureOverFiniteField

public static void ensureOverFiniteField(IPolynomial... polys)

ensureOverField

public static void ensureOverField(IPolynomial... polys)

ensureOverZ

public static void ensureOverZ(IPolynomial... polys)

canConvertToZp64

public static boolean canConvertToZp64(IPolynomial poly)

Test whether poly is over Zp with modulus less then 2^63

isOverRationals

public static <T extends IPolynomial<T>> boolean isOverRationals(T poly)

Whether coefficient domain is rationals

isOverSimpleFieldExtension

public static <T extends IPolynomial<T>> boolean isOverSimpleFieldExtension(T poly)

Whether coefficient domain is F(alpha)

isOverMultipleFieldExtension

public static <T extends IPolynomial<T>> boolean isOverMultipleFieldExtension(T poly)

Whether coefficient domain is F(alpha1, alpha2, ...)

isOverSimpleNumberField

public static <T extends IPolynomial<T>> boolean isOverSimpleNumberField(T poly)

Whether coefficient domain is Q(alpha)

isOverRingOfIntegersOfSimpleNumberField

public static <T extends IPolynomial<T>> boolean isOverRingOfIntegersOfSimpleNumberField(T poly)

Whether coefficient domain is Q(alpha)

isOverQ

public static <T extends IPolynomial<T>> boolean isOverQ(T poly)

Whether coefficient domain is Q

isOverZ

public static <T extends IPolynomial<T>> boolean isOverZ(T poly)

Whether coefficient domain is Z

toCommonDenominator

public static <E> Util.Tuple2<UnivariatePolynomial<E>,E> toCommonDenominator(UnivariatePolynomial<Rational<E>> poly)

Brings polynomial with rational coefficients to common denominator

Parameters:

poly - the polynomial

Returns:

(reduced poly, common denominator)

commonDenominator

public static <E> E commonDenominator(UnivariatePolynomial<Rational<E>> poly)

Returns a common denominator of given poly

commonDenominator

public static <E> E commonDenominator(MultivariatePolynomial<Rational<E>> poly)

Returns a common denominator of given poly

toCommonDenominator

public static <E> Util.Tuple2<MultivariatePolynomial<E>,E> toCommonDenominator(MultivariatePolynomial<Rational<E>> poly)

Brings polynomial with rational coefficients to common denominator

Parameters:

poly - the polynomial

Returns:

(reduced poly, common denominator)

asOverRationals

public static <E> UnivariatePolynomial<Rational<E>> asOverRationals(Ring<Rational<E>> field,
                                                                    UnivariatePolynomial<E> poly)

asOverRationals

public static <E> MultivariatePolynomial<Rational<E>> asOverRationals(Ring<Rational<E>> field,
                                                                      MultivariatePolynomial<E> poly)

divideOverRationals

public static <E> UnivariatePolynomial<Rational<E>> divideOverRationals(Ring<Rational<E>> field,
                                                                        UnivariatePolynomial<E> poly,
                                                                        E denominator)

divideOverRationals

public static <E> MultivariatePolynomial<Rational<E>> divideOverRationals(Ring<Rational<E>> field,
                                                                          MultivariatePolynomial<E> poly,
                                                                          E denominator)