Package cc.redberry.rings.poly.univar

Class UnivariatePolynomialArithmetic

java.lang.Object

cc.redberry.rings.poly.univar.UnivariatePolynomialArithmetic

public final class UnivariatePolynomialArithmetic
extends Object

Helper methods for univariate polynomial arithmetic.

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static <T extends IUnivariatePolynomial<T>> T	createMonomialMod(long exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Creates x^exponent mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	createMonomialMod(BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Creates x^exponent mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polyAddMod(T m1, T m2, T polyModulus, boolean copy)	Returns the remainder of the sum (m1 + m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polyAddMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns the remainder of the sum (m1 + m2) and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	polyMod(T dividend, T polyModulus, boolean copy)	Returns the remainder of dividend and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polyMod(T dividend, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns the remainder of dividend and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	polyMultiplyMod(T m1, T m2, T polyModulus, boolean copy)	Returns the remainder of the product (m1 * m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polyMultiplyMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns the remainder of the product (m1 * m2) and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	polyNegateMod(T m1, T polyModulus, boolean copy)	Returns the remainder of the negated poly -m1 and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polyNegateMod(T m1, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns the remainder of the negated poly -m1 and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	polyPow(T base, long exponent, boolean copy)	Returns base in a power of non-negative exponent
static <T extends IUnivariatePolynomial<T>> T	polyPowMod(T base, long exponent, T polyModulus, boolean copy)	Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	polyPowMod(T base, long exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	polyPowMod(T base, BigInteger exponent, T polyModulus, boolean copy)	Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	polyPowMod(T base, BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	polySubtractMod(T m1, T m2, T polyModulus, boolean copy)	Returns the remainder of the difference (m1 - m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	polySubtractMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)	Returns the remainder of the difference (m1 - m2) and polyModulus using fast algorithm for pre-conditioned modulus.

Methods inherited from class java.lang.Object

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

Method Details

polyMod

public static <T extends IUnivariatePolynomial<T>>
T polyMod(T dividend,
T polyModulus,
boolean copy)

Returns the remainder of dividend and polyModulus.

Parameters:

dividend - the polynomial

polyModulus - the modulus

copy - whether to clone dividend; if not, the result will be placed directly to dividend and the original dividend data will be lost

Returns:

dividend % polyModulus

polyMod

public static <T extends IUnivariatePolynomial<T>>
T polyMod(T dividend,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns the remainder of dividend and polyModulus using fast algorithm for pre-conditioned modulus.

Parameters:

dividend - the polynomial

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

copy - whether to clone dividend; if not, the result will be placed directly to dividend and the original dividend data will be lost

Returns:

dividend % polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyMultiplyMod

public static <T extends IUnivariatePolynomial<T>>
T polyMultiplyMod(T m1,
T m2,
T polyModulus,
boolean copy)

Returns the remainder of the product (m1 * m2) and polyModulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 * m2) % polyModulus

polyMultiplyMod

public static <T extends IUnivariatePolynomial<T>>
T polyMultiplyMod(T m1,
T m2,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns the remainder of the product (m1 * m2) and polyModulus using fast algorithm for pre-conditioned modulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 * m2) % polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyAddMod

public static <T extends IUnivariatePolynomial<T>>
T polyAddMod(T m1,
T m2,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns the remainder of the sum (m1 + m2) and polyModulus using fast algorithm for pre-conditioned modulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 + m2) % polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyAddMod

public static <T extends IUnivariatePolynomial<T>>
T polyAddMod(T m1,
T m2,
T polyModulus,
boolean copy)

Returns the remainder of the sum (m1 + m2) and polyModulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 + m2) % polyModulus

polySubtractMod

public static <T extends IUnivariatePolynomial<T>>
T polySubtractMod(T m1,
T m2,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns the remainder of the difference (m1 - m2) and polyModulus using fast algorithm for pre-conditioned modulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 - m2) % polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polySubtractMod

public static <T extends IUnivariatePolynomial<T>>
T polySubtractMod(T m1,
T m2,
T polyModulus,
boolean copy)

Returns the remainder of the difference (m1 - m2) and polyModulus.

Parameters:

m1 - the first multiplier

m2 - the second multiplier

polyModulus - the modulus

copy - whether to clone m1; if not, the result will be placed directly to the data structure of the first multiplier m1 and the original data of m1 will be lost

Returns:

(m1 - m2) % polyModulus

polyNegateMod

public static <T extends IUnivariatePolynomial<T>>
T polyNegateMod(T m1,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns the remainder of the negated poly -m1 and polyModulus using fast algorithm for pre-conditioned modulus.

Parameters:

m1 - the polynomial

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

copy - whether to clone m1; if not, the result will be placed directly to the data structure of m1 and the original data of m1 will be lost

Returns:

(-m1) % polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyNegateMod

public static <T extends IUnivariatePolynomial<T>>
T polyNegateMod(T m1,
T polyModulus,
boolean copy)

Returns the remainder of the negated poly -m1 and polyModulus.

Parameters:

m1 - the polynomial

polyModulus - the modulus

copy - whether to clone m1; if not, the result will be placed directly to the data structure of m1 and the original data of m1 will be lost

Returns:

(-m1) % polyModulus

polyPow

public static <T extends IUnivariatePolynomial<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

polyPowMod

public static <T extends IUnivariatePolynomial<T>>
T polyPowMod(T base,
long exponent,
T polyModulus,
boolean copy)

Returns base in a power of non-negative exponent modulo polyModulus

Parameters:

base - the base

exponent - the non-negative exponent

polyModulus - the modulus

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

Returns:

base in a power of e modulo polyModulus

polyPowMod

public static <T extends IUnivariatePolynomial<T>>
T polyPowMod(T base,
long exponent,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns base in a power of non-negative exponent modulo polyModulus

Parameters:

base - the base

exponent - the non-negative exponent

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

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

Returns:

base in a power of e modulo polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyPowMod

public static <T extends IUnivariatePolynomial<T>>
T polyPowMod(T base,
BigInteger exponent,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod,
boolean copy)

Returns base in a power of non-negative exponent modulo polyModulus

Parameters:

base - the base

exponent - the non-negative exponent

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

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

Returns:

base in a power of e modulo polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyPowMod

public static <T extends IUnivariatePolynomial<T>>
T polyPowMod(T base,
BigInteger exponent,
T polyModulus,
boolean copy)

Returns base in a power of non-negative exponent modulo polyModulus

Parameters:

base - the base

exponent - the non-negative exponent

polyModulus - the modulus

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

Returns:

base in a power of e modulo polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

createMonomialMod

public static <T extends IUnivariatePolynomial<T>>
T createMonomialMod(long exponent,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod)

Creates x^exponent mod polyModulus.

Parameters:

exponent - the monomial exponent

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

Returns:

x^exponent mod polyModulus

createMonomialMod

public static <T extends IUnivariatePolynomial<T>>
T createMonomialMod(BigInteger exponent,
T polyModulus,
UnivariateDivision.InverseModMonomial<T> invMod)

Creates x^exponent mod polyModulus.

Parameters:

exponent - the monomial exponent

polyModulus - the modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

Returns:

x^exponent mod polyModulus