Uses of Class
cc.redberry.rings.bigint.BigInteger

Packages that use BigInteger

Package	Description
cc.redberry.rings
cc.redberry.rings.bigint	Provides classes for performing arbitrary-precision integer arithmetic (BigInteger) and arbitrary-precision decimal arithmetic (BigDecimal).
cc.redberry.rings.poly
cc.redberry.rings.poly.multivar
cc.redberry.rings.poly.univar
cc.redberry.rings.primes
cc.redberry.rings.util

Uses of BigInteger in cc.redberry.rings

Fields in cc.redberry.rings declared as BigInteger

Modifier and Type	Field	Description
BigInteger	IntegersZp.modulus	The modulus.

Fields in cc.redberry.rings with type parameters of type BigInteger

Modifier and Type	Field	Description
static AlgebraicNumberField<UnivariatePolynomial<BigInteger>>	Rings.GaussianIntegers	Ring of Gaussian integers (integer complex numbers).
static AlgebraicNumberField<UnivariatePolynomial<Rational<BigInteger>>>	Rings.GaussianRationals	Field of Gaussian rationals (rational complex numbers).
static Rationals<BigInteger>	Rings.Q	Field of rationals (Q)
static UnivariateRing<UnivariatePolynomial<Rational<BigInteger>>>	Rings.UnivariateRingQ	Ring of univariate polynomials over rationals (Q[x])
static UnivariateRing<UnivariatePolynomial<BigInteger>>	Rings.UnivariateRingZ	Ring of univariate polynomials over integers (Z[x])

Methods in cc.redberry.rings that return BigInteger

Modifier and Type	Method	Description
BigInteger	Integers.abs(BigInteger el)
BigInteger	Integers.add(BigInteger a, BigInteger b)
BigInteger	IntegersZp.add(BigInteger a, BigInteger b)
BigInteger	Integers.binomial(long n, long k)	Gives a binomial coefficient C(n, k)
BigInteger	ImageRing.cardinality()
BigInteger	Integers.cardinality()
BigInteger	IntegersZp.cardinality()
BigInteger	Rationals.cardinality()
BigInteger	Ring.cardinality()	Returns the number of elements in this ring (cardinality) or null if ring is infinite
BigInteger	ImageRing.characteristic()
BigInteger	Integers.characteristic()
BigInteger	IntegersZp.characteristic()
BigInteger	Rationals.characteristic()
BigInteger	Ring.characteristic()	Returns characteristic of this ring
static BigInteger	ChineseRemainders.ChineseRemainders(BigInteger[] primes, BigInteger[] remainders)	Runs Chinese Remainders algorithm
static BigInteger	ChineseRemainders.ChineseRemainders(BigInteger prime1, BigInteger prime2, BigInteger remainder1, BigInteger remainder2)	Runs Chinese Remainders algorithm
BigInteger	IntegersZp.divide(BigInteger a, BigInteger b)
BigInteger[]	Integers.divideAndRemainder(BigInteger a, BigInteger b)
BigInteger[]	IntegersZp.divideAndRemainder(BigInteger a, BigInteger b)
BigInteger	Integers.gcd(BigInteger a, BigInteger b)
BigInteger	Integers.getNegativeOne()
BigInteger	IntegersZp.modulus(BigInteger val)	Returns val mod this.modulus
BigInteger	Integers.multiply(BigInteger a, BigInteger b)
BigInteger	IntegersZp.multiply(BigInteger a, BigInteger b)
BigInteger	Integers.negate(BigInteger element)
BigInteger	IntegersZp.negate(BigInteger element)
BigInteger	ARing.perfectPowerBase()
BigInteger	ImageRing.perfectPowerBase()
BigInteger	Rationals.perfectPowerBase()
BigInteger	Ring.perfectPowerBase()	Returns base so that cardinality == base^exponent or null if cardinality is not finite
BigInteger	ARing.perfectPowerExponent()
BigInteger	ImageRing.perfectPowerExponent()
BigInteger	Rationals.perfectPowerExponent()
BigInteger	Ring.perfectPowerExponent()	Returns exponent so that cardinality == base^exponent or null if cardinality is not finite
BigInteger	Integers.pow(BigInteger base, int exponent)
BigInteger	Integers.pow(BigInteger base, long exponent)
BigInteger	Integers.pow(BigInteger base, BigInteger exponent)
BigInteger	IntegersZp.randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
BigInteger	Integers.reciprocal(BigInteger element)
BigInteger	IntegersZp.reciprocal(BigInteger element)
static BigInteger[]	RationalReconstruction.reconstruct(BigInteger n, BigInteger modulus, BigInteger numeratorBound, BigInteger denominatorBound)	Performs a rational number reconstruction.
static BigInteger[]	RationalReconstruction.reconstructFarey(BigInteger n, BigInteger modulus)	Performs a rational number reconstruction via Farey images, that is reconstructuction with bound B = sqrt(N/2 - 1/2)
static BigInteger[]	RationalReconstruction.reconstructFareyErrorTolerant(BigInteger n, BigInteger modulus)	Performs a error tolerant rational number reconstruction as described in Algorithm 5 of Janko Boehm, Wolfram Decker, Claus Fieker, Gerhard Pfister, "The use of Bad Primes in Rational Reconstruction", https://arxiv.org/abs/1207.1651v2
BigInteger	Integers.remainder(BigInteger a, BigInteger b)
BigInteger	IntegersZp.remainder(BigInteger a, BigInteger b)
BigInteger	Integers.subtract(BigInteger a, BigInteger b)
BigInteger	IntegersZp.subtract(BigInteger a, BigInteger b)
BigInteger	IntegersZp.symmetricForm(BigInteger value)	Converts value to a symmetric representation of Zp
BigInteger	Integers.valueOf(long val)
BigInteger	Integers.valueOf(BigInteger val)
BigInteger	IntegersZp.valueOf(long val)
BigInteger	IntegersZp.valueOf(BigInteger val)

Methods in cc.redberry.rings that return types with arguments of type BigInteger

Modifier and Type	Method	Description
FactorDecomposition<BigInteger>	Integers.factor(BigInteger element)
FactorDecomposition<BigInteger>	IntegersZp.factor(BigInteger element)
FactorDecomposition<BigInteger>	Integers.factorSquareFree(BigInteger element)
FactorDecomposition<BigInteger>	IntegersZp.factorSquareFree(BigInteger element)
static FiniteField<UnivariatePolynomial<BigInteger>>	Rings.GF(BigInteger prime, int exponent)	Galois field with the cardinality prime ^ exponent for arbitrary large prime
Iterator<BigInteger>	Integers.iterator()
Iterator<BigInteger>	IntegersZp.iterator()
static MultivariateRing<MultivariatePolynomial<Rational<BigInteger>>>	Rings.MultivariateRingQ(int nVariables)	Ring of multivariate polynomials over rationals (Q[x1, x2, ...])
static MultivariateRing<MultivariatePolynomial<BigInteger>>	Rings.MultivariateRingZ(int nVariables)	Ring of multivariate polynomials over integers (Z[x1, x2, ...])
static MultivariateRing<MultivariatePolynomial<BigInteger>>	Rings.MultivariateRingZp(int nVariables, BigInteger modulus)	Ring of multivariate polynomials over Zp integers (Zp[x1, x2, ...]) with arbitrary large modulus
static UnivariateRing<UnivariatePolynomial<BigInteger>>	Rings.UnivariateRingZp(BigInteger modulus)	Ring of univariate polynomials over Zp integers (Zp[x]) with arbitrary large modulus

Methods in cc.redberry.rings with parameters of type BigInteger

Modifier and Type	Method	Description
BigInteger	Integers.abs(BigInteger el)
BigInteger	Integers.add(BigInteger a, BigInteger b)
BigInteger	IntegersZp.add(BigInteger a, BigInteger b)
static BigInteger	ChineseRemainders.ChineseRemainders(BigInteger[] primes, BigInteger[] remainders)	Runs Chinese Remainders algorithm
static BigInteger	ChineseRemainders.ChineseRemainders(BigInteger prime1, BigInteger prime2, BigInteger remainder1, BigInteger remainder2)	Runs Chinese Remainders algorithm
BigInteger	IntegersZp.divide(BigInteger a, BigInteger b)
BigInteger[]	Integers.divideAndRemainder(BigInteger a, BigInteger b)
BigInteger[]	IntegersZp.divideAndRemainder(BigInteger a, BigInteger b)
FactorDecomposition<BigInteger>	Integers.factor(BigInteger element)
FactorDecomposition<BigInteger>	IntegersZp.factor(BigInteger element)
FactorDecomposition<BigInteger>	Integers.factorSquareFree(BigInteger element)
FactorDecomposition<BigInteger>	IntegersZp.factorSquareFree(BigInteger element)
BigInteger	Integers.gcd(BigInteger a, BigInteger b)
static FiniteField<UnivariatePolynomial<BigInteger>>	Rings.GF(BigInteger prime, int exponent)	Galois field with the cardinality prime ^ exponent for arbitrary large prime
boolean	Integers.isMinusOne(BigInteger bigInteger)
boolean	Integers.isUnit(BigInteger element)
boolean	IntegersZp.isUnit(BigInteger element)
BigInteger	IntegersZp.modulus(BigInteger val)	Returns val mod this.modulus
long	IntegersZp64.modulus(BigInteger val)	Returns val % this.modulus
BigInteger	Integers.multiply(BigInteger a, BigInteger b)
BigInteger	IntegersZp.multiply(BigInteger a, BigInteger b)
static MultivariateRing<MultivariatePolynomial<BigInteger>>	Rings.MultivariateRingZp(int nVariables, BigInteger modulus)	Ring of multivariate polynomials over Zp integers (Zp[x1, x2, ...]) with arbitrary large modulus
BigInteger	Integers.negate(BigInteger element)
BigInteger	IntegersZp.negate(BigInteger element)
I	ImageRing.pow(I base, BigInteger exponent)
BigInteger	Integers.pow(BigInteger base, int exponent)
BigInteger	Integers.pow(BigInteger base, long exponent)
BigInteger	Integers.pow(BigInteger base, BigInteger exponent)
Rational<E>	Rational.pow(BigInteger exponent)	Raise this in a power exponent
default E	Ring.pow(E base, BigInteger exponent)	Returns base in a power of exponent (non negative)
BigInteger	Integers.reciprocal(BigInteger element)
BigInteger	IntegersZp.reciprocal(BigInteger element)
static BigInteger[]	RationalReconstruction.reconstruct(BigInteger n, BigInteger modulus, BigInteger numeratorBound, BigInteger denominatorBound)	Performs a rational number reconstruction.
static BigInteger[]	RationalReconstruction.reconstructFarey(BigInteger n, BigInteger modulus)	Performs a rational number reconstruction via Farey images, that is reconstructuction with bound B = sqrt(N/2 - 1/2)
static BigInteger[]	RationalReconstruction.reconstructFareyErrorTolerant(BigInteger n, BigInteger modulus)	Performs a error tolerant rational number reconstruction as described in Algorithm 5 of Janko Boehm, Wolfram Decker, Claus Fieker, Gerhard Pfister, "The use of Bad Primes in Rational Reconstruction", https://arxiv.org/abs/1207.1651v2
BigInteger	Integers.remainder(BigInteger a, BigInteger b)
BigInteger	IntegersZp.remainder(BigInteger a, BigInteger b)
int	Integers.signum(BigInteger element)
BigInteger	Integers.subtract(BigInteger a, BigInteger b)
BigInteger	IntegersZp.subtract(BigInteger a, BigInteger b)
BigInteger	IntegersZp.symmetricForm(BigInteger value)	Converts value to a symmetric representation of Zp
static UnivariateRing<UnivariatePolynomial<BigInteger>>	Rings.UnivariateRingZp(BigInteger modulus)	Ring of univariate polynomials over Zp integers (Zp[x]) with arbitrary large modulus
BigInteger	Integers.valueOf(BigInteger val)
BigInteger	IntegersZp.valueOf(BigInteger val)
I	ImageRing.valueOfBigInteger(BigInteger val)
Rational<E>	Rationals.valueOfBigInteger(BigInteger val)
E	Ring.valueOfBigInteger(BigInteger val)	Returns ring element associated with specified integer
static IntegersZp	Rings.Zp(BigInteger modulus)	Ring of integers modulo modulus (arbitrary large modulus)

Constructors in cc.redberry.rings with parameters of type BigInteger

Constructor	Description
IntegersZp(BigInteger modulus)	Creates Zp ring for specified modulus.

Uses of BigInteger in cc.redberry.rings.bigint

Fields in cc.redberry.rings.bigint declared as BigInteger

Modifier and Type	Field	Description
static BigInteger	BigInteger.FIVE	The BigInteger constant five.
static BigInteger	BigInteger.FOUR	The BigInteger constant four.
static BigInteger	BigInteger.INT_MAX_VALUE	The BigInteger constant Int.MAX_VALUE.
static BigInteger	BigInteger.LONG_MAX_VALUE	The BigInteger constant Long.MAX_VALUE.
static BigInteger	BigInteger.NEGATIVE_ONE	The BigInteger constant -1.
static BigInteger	BigInteger.NEGATIVE_TWO	The BigInteger constant negative two.
static BigInteger	BigInteger.ONE	The BigInteger constant one.
static BigInteger	BigInteger.SEVEN	The BigInteger constant seven.
static BigInteger	BigInteger.SHORT_MAX_VALUE	The BigInteger constant Int.MAX_VALUE.
static BigInteger	BigInteger.SIX	The BigInteger constant six.
static BigInteger	BigInteger.TEN	The BigInteger constant ten.
static BigInteger	BigInteger.THREE	The BigInteger constant three.
static BigInteger	BigInteger.TWO	The BigInteger constant two.
static BigInteger	BigInteger.ZERO	The BigInteger constant zero.

Methods in cc.redberry.rings.bigint that return BigInteger

Modifier and Type	Method	Description
BigInteger	BigInteger.abs()	Returns a BigInteger whose value is the absolute value of this BigInteger.
static BigInteger	BigIntegerUtil.abs(BigInteger a)
BigInteger	BigInteger.add(BigInteger val)	Returns a BigInteger whose value is (this + val).
BigInteger	BigInteger.and(BigInteger val)	Returns a BigInteger whose value is (this & val).
BigInteger	BigInteger.andNot(BigInteger val)	Returns a BigInteger whose value is (this & ~val).
static BigInteger	BigIntegerUtil.binomial(int n, int k)	Binomial coefficient
BigInteger	BigInteger.clearBit(int n)	Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared.
BigInteger	BigInteger.decrement()
BigInteger	BigInteger.divide(BigInteger val)	Returns a BigInteger whose value is (this / val).
BigInteger	BigInteger.divide(BigInteger val, int numThreads)	Returns a BigInteger whose value is (this / val), using multiple threads if the numbers are sufficiently large.
BigInteger[]	BigInteger.divideAndRemainder(BigInteger val)	Returns an array of two BigIntegers containing (this / val) followed by (this % val).
BigInteger[]	BigInteger.divideAndRemainder(BigInteger val, int numThreads)	Returns an array of two BigIntegers containing (this / val) followed by (this % val). Uses a specified number of threads if the inputs are sufficiently large.
BigInteger[]	BigInteger.divideAndRemainderParallel(BigInteger val)	Returns an array of two BigIntegers containing (this / val) followed by (this % val). Uses multiple threads if the numbers are sufficiently large.
BigInteger	BigInteger.divideExact(BigInteger val)	Returns a BigInteger whose value is (this / val).
BigInteger	BigInteger.divideParallel(BigInteger val)	Returns a BigInteger whose value is (this / val), using multiple threads if the numbers are sufficiently large.
static BigInteger	BigIntegerUtil.factorial(int number)	Factorial of a number
BigInteger	BigInteger.flipBit(int n)	Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped.
BigInteger	BigInteger.gcd(BigInteger val)	Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val).
static BigInteger	BigIntegerUtil.gcd(BigInteger[] integers, int from, int to)	Returns the greatest common an array of longs
static BigInteger	BigIntegerUtil.gcd(BigInteger a, BigInteger b)
BigInteger	BigInteger.increment()
BigInteger	BigInteger.max(BigInteger val)	Returns the maximum of this BigInteger and val.
static BigInteger	BigIntegerUtil.max(BigInteger a, BigInteger b)
BigInteger	BigInteger.min(BigInteger val)	Returns the minimum of this BigInteger and val.
BigInteger	BigInteger.mod(long m)	Returns a BigInteger whose value is (this mod m).
BigInteger	BigInteger.mod(BigInteger m)	Returns a BigInteger whose value is (this mod m).
BigInteger	BigInteger.modInverse(BigInteger m)	Returns a BigInteger whose value is (this-1 mod m).
BigInteger	BigInteger.modPow(BigInteger exponent, BigInteger m)	Returns a BigInteger whose value is (thisexponent mod m).
BigInteger	BigInteger.multiply(BigInteger val)	Returns a BigInteger whose value is (this * val).
BigInteger	BigInteger.multiply(BigInteger val, int numThreads)	Multiplies this number by another using a specified number of threads if the inputs are sufficiently large.
BigInteger	BigInteger.multiplyParallel(BigInteger val)	Multiplies this number by another using multiple threads if the numbers are sufficiently large.
BigInteger	BigInteger.negate()	Returns a BigInteger whose value is (-this).
BigInteger	BigInteger.nextProbablePrime()	Returns the first integer greater than this BigInteger that is probably prime.
BigInteger	BigInteger.not()	Returns a BigInteger whose value is (~this).
BigInteger	BigInteger.or(BigInteger val)	Returns a BigInteger whose value is (this | val).
static BigInteger[]	BigIntegerUtil.perfectPowerDecomposition(BigInteger n)	Tests whether n is a perfect power n == a^b and returns {a, b} if so and null otherwise
BigInteger	BigInteger.pow(int exponent)	Returns a BigInteger whose value is (thisexponent).
static BigInteger	BigIntegerUtil.pow(long base, long exponent)	Returns base in a power of e (non negative)
static BigInteger	BigIntegerUtil.pow(BigInteger base, int exponent)	Returns base in a power of e (non negative)
static BigInteger	BigIntegerUtil.pow(BigInteger base, long exponent)	Returns base in a power of e (non negative)
static BigInteger	BigIntegerUtil.pow(BigInteger base, BigInteger exponent)	Returns base in a power of e (non negative)
static BigInteger	BigInteger.probablePrime(int bitLength, Random rnd)	Returns a positive BigInteger that is probably prime, with the specified bitLength.
BigInteger	BigInteger.remainder(BigInteger val)	Returns a BigInteger whose value is (this % val).
BigInteger	BigInteger.remainder(BigInteger val, int numThreads)	Returns a BigInteger whose value is (this % val) using a specified number of threads if the inputs are sufficiently large.
BigInteger	BigInteger.remainderParallel(BigInteger val)	Returns a BigInteger whose value is (this % val), using multiple threads if the inputs are sufficiently large.
BigInteger	BigInteger.setBit(int n)	Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set.
BigInteger	BigInteger.shiftLeft(int n)	Returns a BigInteger whose value is (this << n).
BigInteger	BigInteger.shiftRight(int n)	Returns a BigInteger whose value is (this >> n).
static BigInteger	BigIntegerUtil.sqrtCeil(BigInteger val)	Returns ceil square root of val
static BigInteger	BigIntegerUtil.sqrtFloor(BigInteger val)	Returns floor square root of val
BigInteger	BigInteger.subtract(BigInteger val)	Returns a BigInteger whose value is (this - val).
BigInteger	BigDecimal.toBigInteger()	Converts this BigDecimal to a BigInteger.
BigInteger	BigDecimal.toBigIntegerExact()	Converts this BigDecimal to a BigInteger, checking for lost information.
BigInteger	BigDecimal.unscaledValue()	Returns a BigInteger whose value is the unscaled value of this BigDecimal.
static BigInteger	BigInteger.valueOf(int val)	Returns a BigInteger whose value is equal to that of the specified long.
static BigInteger	BigInteger.valueOf(long val)	Returns a BigInteger whose value is equal to that of the specified long.
static BigInteger	BigInteger.valueOfSigned(long bits)	Converts signed long to BigInteger
static BigInteger	BigInteger.valueOfUnsigned(long bits)	Converts unsigned long to BigInteger
BigInteger	BigInteger.xor(BigInteger val)	Returns a BigInteger whose value is (this ^ val).

Methods in cc.redberry.rings.bigint with parameters of type BigInteger

Modifier and Type	Method	Description
static BigInteger	BigIntegerUtil.abs(BigInteger a)
BigInteger	BigInteger.add(BigInteger val)	Returns a BigInteger whose value is (this + val).
BigInteger	BigInteger.and(BigInteger val)	Returns a BigInteger whose value is (this & val).
BigInteger	BigInteger.andNot(BigInteger val)	Returns a BigInteger whose value is (this & ~val).
int	BigInteger.compareTo(BigInteger val)	Compares this BigInteger with the specified BigInteger.
BigInteger	BigInteger.divide(BigInteger val)	Returns a BigInteger whose value is (this / val).
BigInteger	BigInteger.divide(BigInteger val, int numThreads)	Returns a BigInteger whose value is (this / val), using multiple threads if the numbers are sufficiently large.
BigInteger[]	BigInteger.divideAndRemainder(BigInteger val)	Returns an array of two BigIntegers containing (this / val) followed by (this % val).
BigInteger[]	BigInteger.divideAndRemainder(BigInteger val, int numThreads)	Returns an array of two BigIntegers containing (this / val) followed by (this % val). Uses a specified number of threads if the inputs are sufficiently large.
BigInteger[]	BigInteger.divideAndRemainderParallel(BigInteger val)	Returns an array of two BigIntegers containing (this / val) followed by (this % val). Uses multiple threads if the numbers are sufficiently large.
BigInteger	BigInteger.divideExact(BigInteger val)	Returns a BigInteger whose value is (this / val).
BigInteger	BigInteger.divideParallel(BigInteger val)	Returns a BigInteger whose value is (this / val), using multiple threads if the numbers are sufficiently large.
BigInteger	BigInteger.gcd(BigInteger val)	Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val).
static BigInteger	BigIntegerUtil.gcd(BigInteger[] integers, int from, int to)	Returns the greatest common an array of longs
static BigInteger	BigIntegerUtil.gcd(BigInteger a, BigInteger b)
BigInteger	BigInteger.max(BigInteger val)	Returns the maximum of this BigInteger and val.
static BigInteger	BigIntegerUtil.max(BigInteger a, BigInteger b)
BigInteger	BigInteger.min(BigInteger val)	Returns the minimum of this BigInteger and val.
BigInteger	BigInteger.mod(BigInteger m)	Returns a BigInteger whose value is (this mod m).
BigInteger	BigInteger.modInverse(BigInteger m)	Returns a BigInteger whose value is (this-1 mod m).
BigInteger	BigInteger.modPow(BigInteger exponent, BigInteger m)	Returns a BigInteger whose value is (thisexponent mod m).
BigInteger	BigInteger.multiply(BigInteger val)	Returns a BigInteger whose value is (this * val).
BigInteger	BigInteger.multiply(BigInteger val, int numThreads)	Multiplies this number by another using a specified number of threads if the inputs are sufficiently large.
BigInteger	BigInteger.multiplyParallel(BigInteger val)	Multiplies this number by another using multiple threads if the numbers are sufficiently large.
BigInteger	BigInteger.or(BigInteger val)	Returns a BigInteger whose value is (this | val).
static BigInteger[]	BigIntegerUtil.perfectPowerDecomposition(BigInteger n)	Tests whether n is a perfect power n == a^b and returns {a, b} if so and null otherwise
static BigInteger	BigIntegerUtil.pow(BigInteger base, int exponent)	Returns base in a power of e (non negative)
static BigInteger	BigIntegerUtil.pow(BigInteger base, long exponent)	Returns base in a power of e (non negative)
static BigInteger	BigIntegerUtil.pow(BigInteger base, BigInteger exponent)	Returns base in a power of e (non negative)
BigInteger	BigInteger.remainder(BigInteger val)	Returns a BigInteger whose value is (this % val).
BigInteger	BigInteger.remainder(BigInteger val, int numThreads)	Returns a BigInteger whose value is (this % val) using a specified number of threads if the inputs are sufficiently large.
BigInteger	BigInteger.remainderParallel(BigInteger val)	Returns a BigInteger whose value is (this % val), using multiple threads if the inputs are sufficiently large.
static BigInteger	BigIntegerUtil.sqrtCeil(BigInteger val)	Returns ceil square root of val
static BigInteger	BigIntegerUtil.sqrtFloor(BigInteger val)	Returns floor square root of val
BigInteger	BigInteger.subtract(BigInteger val)	Returns a BigInteger whose value is (this - val).
BigInteger	BigInteger.xor(BigInteger val)	Returns a BigInteger whose value is (this ^ val).

Constructors in cc.redberry.rings.bigint with parameters of type BigInteger

Constructor	Description
BigDecimal(BigInteger val)	Translates a BigInteger into a BigDecimal.
BigDecimal(BigInteger unscaledVal, int scale)	Translates a BigInteger unscaled value and an int scale into a BigDecimal.
BigDecimal(BigInteger unscaledVal, int scale, MathContext mc)	Translates a BigInteger unscaled value and an int scale into a BigDecimal, with rounding according to the context settings.
BigDecimal(BigInteger val, MathContext mc)	Translates a BigInteger into a BigDecimal rounding according to the context settings.

Uses of BigInteger in cc.redberry.rings.poly

Fields in cc.redberry.rings.poly declared as BigInteger

Modifier and Type	Field	Description
static BigInteger	MachineArithmetic.b_MAX_SUPPORTED_MODULUS	Max supported modulus

Methods in cc.redberry.rings.poly that return BigInteger

Modifier and Type	Method	Description
BigInteger	QuotientRing.cardinality()
BigInteger	SimpleFieldExtension.cardinality()
BigInteger	QuotientRing.characteristic()
BigInteger	SimpleFieldExtension.characteristic()
BigInteger	IPolynomial.coefficientRingCardinality()	Returns cardinality of the coefficient ring of this poly
BigInteger	IPolynomial.coefficientRingCharacteristic()	Returns characteristic of the coefficient ring of this poly
BigInteger	IPolynomial.coefficientRingPerfectPowerBase()	Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
BigInteger	IPolynomial.coefficientRingPerfectPowerExponent()	Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

Methods in cc.redberry.rings.poly with parameters of type BigInteger

Modifier and Type	Method	Description
Poly	IPolynomial.multiplyByBigInteger(BigInteger factor)	Multiplies this by factor
static <T extends IPolynomial<T>> T	PolynomialMethods.polyPow(T base, BigInteger exponent)	Returns base in a power of non-negative exponent
static <T extends IPolynomial<T>> T	PolynomialMethods.polyPow(T base, BigInteger exponent, boolean copy)	Returns base in a power of non-negative exponent.
mPoly	MultipleFieldExtension.valueOfBigInteger(BigInteger val)
Poly	QuotientRing.valueOfBigInteger(BigInteger val)
E	SimpleFieldExtension.valueOfBigInteger(BigInteger val)

Uses of BigInteger in cc.redberry.rings.poly.multivar

Fields in cc.redberry.rings.poly.multivar with type parameters of type BigInteger

Modifier and Type	Field	Description
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.initialNumerator	Initial numerator (numerator and denominator may have nontrivial GCD)
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.numerator	Reduced numerator (GCD is cancelled)

Methods in cc.redberry.rings.poly.multivar that return BigInteger

Modifier and Type	Method	Description
BigInteger	MultivariatePolynomial.coefficientRingCardinality()
BigInteger	MultivariatePolynomialZp64.coefficientRingCardinality()
BigInteger	MultivariatePolynomial.coefficientRingCharacteristic()
BigInteger	MultivariatePolynomialZp64.coefficientRingCharacteristic()
BigInteger	MultivariatePolynomial.coefficientRingPerfectPowerBase()
BigInteger	MultivariatePolynomialZp64.coefficientRingPerfectPowerBase()
BigInteger	MultivariatePolynomial.coefficientRingPerfectPowerExponent()
BigInteger	MultivariatePolynomialZp64.coefficientRingPerfectPowerExponent()

Methods in cc.redberry.rings.poly.multivar that return types with arguments of type BigInteger

Modifier and Type	Method	Description
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZ(MultivariatePolynomial<BigInteger> poly, boolean copy)	Returns Z[X] polynomial formed from the coefficients of the poly.
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.asPolyZ()	Returns polynomial over Z formed from the coefficients of this
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly)	Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.asPolyZSymmetric()	Returns polynomial over Z formed from the coefficients of this represented in symmetric modular form ( -modulus/2 <= cfx <= modulus/2).
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.cyclic(int n)
static PolynomialFactorDecomposition<MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	MultivariateFactorization.FactorInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> polynomial)	Factors multivariate polynomial over simple number field via Trager's algorithm
static PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>	MultivariateFactorization.FactorInZ(MultivariatePolynomial<BigInteger> polynomial)	Factors multivariate polynomial over Z
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBases.GroebnerBasisInQ(List<MultivariatePolynomial<Rational<BigInteger>>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular)	Computes Groebner basis (minimized and reduced) of a given ideal over Q represented by a list of generators.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.GroebnerBasisInZ(List<MultivariatePolynomial<BigInteger>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular)	Computes Groebner basis (minimized and reduced) of a given ideal over Z represented by a list of generators.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.GroebnerBasisInZ(List<MultivariatePolynomial<BigInteger>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular)	Computes Groebner basis (minimized and reduced) of a given ideal over Z represented by a list of generators.
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.hilbertPolynomial()	Hilbert polynomial
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.hilbertPolynomialZ()	Integral Hilbert polynomial (i.e.
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.integralPart()	Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura(int i)
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura10()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura11()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura12()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura13()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura14()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura2()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura3()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura4()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura5()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura6()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura7()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura8()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura9()
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)	Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp)	Modular GCD algorithm for polynomials over Z.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateResultants.ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable)	Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateResultants.ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable)	Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)	Modular algorithm with Zippel sparse interpolation for resultant over Z
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string)	Deprecated. use #parse(string, ring, ordering, variables)
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, String... variables)	Parse multivariate Z[X] polynomial from string.
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, Comparator<DegreeVector> ordering)	Deprecated. use #parse(string, ring, ordering, variables)
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, Comparator<DegreeVector> ordering, String... variables)	Parse multivariate Z[X] polynomial from string.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateGCD.PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateGCD.PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, BigInteger bound, Comparator<DegreeVector> ordering, org.apache.commons.math3.random.RandomGenerator rnd)	Generates random Z[X] polynomial with coefficients bounded by bound
static MultivariatePolynomial<BigInteger>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd)	Generates random Z[X] polynomial
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.remainderNumerator()	Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)	Computes polynomial resultant of two polynomials over Z
Monomial<BigInteger>	MonomialZp64.toBigMonomial()
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.toBigPoly()	Returns polynomial over Z formed from the coefficients of this
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)	Sparse modular GCD algorithm for polynomials over Z.

Methods in cc.redberry.rings.poly.multivar with parameters of type BigInteger

Modifier and Type	Method	Description
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
Monomial<E>	IMonomialAlgebra.MonomialAlgebra.multiply(Monomial<E> a, BigInteger b)
MonomialZp64	IMonomialAlgebra.MonomialAlgebraZp64.multiply(MonomialZp64 a, BigInteger b)
Term	IMonomialAlgebra.multiply(Term a, BigInteger b)	Multiplies term by a number
MultivariatePolynomial<E>	MultivariatePolynomial.multiplyByBigInteger(BigInteger factor)
MultivariatePolynomialZp64	MultivariatePolynomialZp64.multiplyByBigInteger(BigInteger factor)
static MultivariatePolynomial<BigInteger>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, BigInteger bound, Comparator<DegreeVector> ordering, org.apache.commons.math3.random.RandomGenerator rnd)	Generates random Z[X] polynomial with coefficients bounded by bound

Method parameters in cc.redberry.rings.poly.multivar with type arguments of type BigInteger

Modifier and Type	Method	Description
static MultivariatePolynomialZp64	MultivariatePolynomial.asOverZp64(MultivariatePolynomial<BigInteger> poly)	Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomialZp64	MultivariatePolynomial.asOverZp64(MultivariatePolynomial<BigInteger> poly, IntegersZp64 ring)	Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZ(MultivariatePolynomial<BigInteger> poly, boolean copy)	Returns Z[X] polynomial formed from the coefficients of the poly.
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly)	Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
static PolynomialFactorDecomposition<MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	MultivariateFactorization.FactorInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> polynomial)	Factors multivariate polynomial over simple number field via Trager's algorithm
static PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>	MultivariateFactorization.FactorInZ(MultivariatePolynomial<BigInteger> polynomial)	Factors multivariate polynomial over Z
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBases.GroebnerBasisInQ(List<MultivariatePolynomial<Rational<BigInteger>>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular)	Computes Groebner basis (minimized and reduced) of a given ideal over Q represented by a list of generators.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.GroebnerBasisInZ(List<MultivariatePolynomial<BigInteger>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular)	Computes Groebner basis (minimized and reduced) of a given ideal over Z represented by a list of generators.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries)	Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse)	Modular Groebner basis algorithm.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)	Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp)	Modular GCD algorithm for polynomials over Z.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateResultants.ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable)	Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateResultants.ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable)	Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)	Modular algorithm with Zippel sparse interpolation for resultant over Z
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateGCD.PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateGCD.PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)	Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)	Computes polynomial resultant of two polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)	Sparse modular GCD algorithm for polynomials over Z.

Uses of BigInteger in cc.redberry.rings.poly.univar

Fields in cc.redberry.rings.poly.univar with type parameters of type BigInteger

Modifier and Type	Field	Description
UnivariatePolynomial<BigInteger>	HenselLifting.bQuadraticLift.base	Initial Z[x] poly

Methods in cc.redberry.rings.poly.univar that return BigInteger

Modifier and Type	Method	Description
BigInteger	UnivariatePolynomial.coefficientRingCardinality()
BigInteger	UnivariatePolynomialZ64.coefficientRingCardinality()
BigInteger	UnivariatePolynomialZp64.coefficientRingCardinality()
BigInteger	UnivariatePolynomial.coefficientRingCharacteristic()
BigInteger	UnivariatePolynomialZ64.coefficientRingCharacteristic()
BigInteger	UnivariatePolynomialZp64.coefficientRingCharacteristic()
BigInteger	UnivariatePolynomial.coefficientRingPerfectPowerBase()
BigInteger	UnivariatePolynomialZ64.coefficientRingPerfectPowerBase()
BigInteger	UnivariatePolynomialZp64.coefficientRingPerfectPowerBase()
BigInteger	UnivariatePolynomial.coefficientRingPerfectPowerExponent()
BigInteger	UnivariatePolynomialZ64.coefficientRingPerfectPowerExponent()
BigInteger	UnivariatePolynomialZp64.coefficientRingPerfectPowerExponent()
static BigInteger	UnivariatePolynomial.mignotteBound(UnivariatePolynomial<BigInteger> poly)	Returns Mignotte's bound (sqrt(n+1) * 2^n max |this|) of the poly
static BigInteger	UnivariateResultants.ModularResultant(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular algorithm for computing resultants over Z
static BigInteger	UnivariatePolynomial.norm1(UnivariatePolynomial<BigInteger> poly)	Returns L1 norm of the polynomial, i.e.
static BigInteger	UnivariatePolynomial.norm2(UnivariatePolynomial<BigInteger> poly)	Returns L2 norm of the polynomial, i.e.
static BigInteger	UnivariateResultants.polyPowNumFieldCfBound(BigInteger maxCf, BigInteger maxMinPolyCf, int minPolyDeg, int exponent)
static BigInteger[]	RandomUnivariatePolynomials.randomBigArray(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements bounded by bound (by absolute value).

Methods in cc.redberry.rings.poly.univar that return types with arguments of type BigInteger

Modifier and Type	Method	Description
UnivariatePolynomial<BigInteger>	HenselLifting.bLinearLift.aCoFactorMod()
UnivariatePolynomial<BigInteger>	HenselLifting.bLinearLift.aFactorMod()
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.asPolyZSymmetric(UnivariatePolynomial<BigInteger> poly)	Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
UnivariatePolynomial<BigInteger>	HenselLifting.bLinearLift.bCoFactorMod()
UnivariatePolynomial<BigInteger>	HenselLifting.bLinearLift.bFactorMod()
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.create(long... data)	Creates new univariate Z[x] polynomial
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.create(Ring<BigInteger> ring, long... data)	Creates univariate polynomial over specified ring (with integer elements) with the specified coefficients
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)	Factors polynomial in Q(alpha)[x] via Trager's algorithm
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)	Factors polynomial in Q(alpha)[x] via Trager's algorithm
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)	Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedResultantGCDInQ(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)	Modular extended GCD algorithm for polynomials over Q with the use of resultants.
static UnivariatePolynomial<BigInteger>[]	UnivariateGCD.ModularExtendedResultantGCDInZ(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular extended GCD algorithm for polynomials over Z with the use of resultants.
static UnivariatePolynomial<BigInteger>	UnivariateGCD.ModularGCD(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular GCD algorithm for polynomials over Z.
static UnivariatePolynomial<Rational<BigInteger>>	UnivariateResultants.ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Modular resultant in simple number field
static UnivariatePolynomial<BigInteger>	UnivariateResultants.ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Modular resultant in the ring of integers of number field
UnivariatePolynomial<BigInteger>	HenselLifting.bLinearLift.polyMod()
UnivariatePolynomial<BigInteger>	HenselLifting.bQuadraticLift.polyMod()
static UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	UnivariateGCD.PolynomialGCDInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Computes GCD via Langemyr & Mccallum modular algorithm over algebraic number field
static UnivariatePolynomial<UnivariatePolynomial<BigInteger>>	UnivariateGCD.PolynomialGCDInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Computes some GCD associate via Langemyr & Mccallum modular algorithm over algebraic integers
static UnivariatePolynomial<BigInteger>	IrreduciblePolynomials.randomIrreduciblePolynomialOverZ(int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible polynomial over Z
static UnivariatePolynomial<BigInteger>	RandomUnivariatePolynomials.randomMonicPoly(int degree, BigInteger modulus, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree.
static UnivariatePolynomial<BigInteger>	RandomUnivariatePolynomials.randomPoly(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree with elements bounded by bound (by absolute value).
UnivariatePolynomial<BigInteger>	UnivariatePolynomialZ64.toBigPoly()	Converts this to a polynomial over BigIntegers
UnivariatePolynomial<BigInteger>	UnivariatePolynomialZp64.toBigPoly()	Converts this to a polynomial over BigIntegers

Methods in cc.redberry.rings.poly.univar with parameters of type BigInteger

Modifier and Type	Method	Description
static HenselLifting.bLinearLift	HenselLifting.createLinearLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates linear Hensel lift.
static HenselLifting.lLinearLift	HenselLifting.createLinearLift(BigInteger modulus, UnivariatePolynomialZ64 poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates linear Hensel lift.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.createMonomialMod(BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Creates x^exponent mod polyModulus.
static HenselLifting.bQuadraticLift	HenselLifting.createQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomial<BigInteger> aFactor, UnivariatePolynomial<BigInteger> bFactor)	Creates quadratic Hensel lift.
static HenselLifting.bQuadraticLift	HenselLifting.createQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates quadratic Hensel lift.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
UnivariatePolynomial<E>	UnivariatePolynomial.multiplyByBigInteger(BigInteger factor)
UnivariatePolynomialZ64	UnivariatePolynomialZ64.multiplyByBigInteger(BigInteger factor)
UnivariatePolynomialZp64	UnivariatePolynomialZp64.multiplyByBigInteger(BigInteger factor)
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.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	UnivariatePolynomialArithmetic.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 BigInteger	UnivariateResultants.polyPowNumFieldCfBound(BigInteger maxCf, BigInteger maxMinPolyCf, int minPolyDeg, int exponent)
static BigInteger[]	RandomUnivariatePolynomials.randomBigArray(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements bounded by bound (by absolute value).
static UnivariatePolynomial<BigInteger>	RandomUnivariatePolynomials.randomMonicPoly(int degree, BigInteger modulus, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree.
static UnivariatePolynomial<BigInteger>	RandomUnivariatePolynomials.randomPoly(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree with elements bounded by bound (by absolute value).

Method parameters in cc.redberry.rings.poly.univar with type arguments of type BigInteger

Modifier and Type	Method	Description
static UnivariatePolynomialZ64	UnivariatePolynomial.asOverZ64(UnivariatePolynomial<BigInteger> poly)	Converts poly over BigIntegers to machine-sized polynomial in Z
static UnivariatePolynomialZp64	UnivariatePolynomial.asOverZp64(UnivariatePolynomial<BigInteger> poly)	Converts Zp[x] poly over BigIntegers to machine-sized polynomial in Zp
static UnivariatePolynomialZp64	UnivariatePolynomial.asOverZp64(UnivariatePolynomial<BigInteger> poly, IntegersZp64 ring)	Converts Zp[x] poly over BigIntegers to machine-sized polynomial in Zp
static UnivariatePolynomialZp64	UnivariatePolynomial.asOverZp64Q(UnivariatePolynomial<Rational<BigInteger>> poly, IntegersZp64 ring)	Converts Zp[x] poly over rationals to machine-sized polynomial in Zp
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.asPolyZSymmetric(UnivariatePolynomial<BigInteger> poly)	Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.create(Ring<BigInteger> ring, long... data)	Creates univariate polynomial over specified ring (with integer elements) with the specified coefficients
static HenselLifting.bLinearLift	HenselLifting.createLinearLift(long modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates linear Hensel lift.
static HenselLifting.bLinearLift	HenselLifting.createLinearLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates linear Hensel lift.
static HenselLifting.bQuadraticLift	HenselLifting.createQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomial<BigInteger> aFactor, UnivariatePolynomial<BigInteger> bFactor)	Creates quadratic Hensel lift.
static HenselLifting.bQuadraticLift	HenselLifting.createQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> poly, UnivariatePolynomialZp64 aFactor, UnivariatePolynomialZp64 bFactor)	Creates quadratic Hensel lift.
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)	Factors polynomial in Q(alpha)[x] via Trager's algorithm
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)	Factors polynomial in Q(alpha)[x] via Trager's algorithm
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static List<UnivariatePolynomial<BigInteger>>	HenselLifting.liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)	Lifts modular factorization until modulus will overcome desiredBound.
static BigInteger	UnivariatePolynomial.mignotteBound(UnivariatePolynomial<BigInteger> poly)	Returns Mignotte's bound (sqrt(n+1) * 2^n max |this|) of the poly
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)	Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedResultantGCDInQ(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)	Modular extended GCD algorithm for polynomials over Q with the use of resultants.
static UnivariatePolynomial<BigInteger>[]	UnivariateGCD.ModularExtendedResultantGCDInZ(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular extended GCD algorithm for polynomials over Z with the use of resultants.
static UnivariatePolynomial<BigInteger>	UnivariateGCD.ModularGCD(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular GCD algorithm for polynomials over Z.
static BigInteger	UnivariateResultants.ModularResultant(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)	Modular algorithm for computing resultants over Z
static UnivariatePolynomial<Rational<BigInteger>>	UnivariateResultants.ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Modular resultant in simple number field
static UnivariatePolynomial<BigInteger>	UnivariateResultants.ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Modular resultant in the ring of integers of number field
static BigInteger	UnivariatePolynomial.norm1(UnivariatePolynomial<BigInteger> poly)	Returns L1 norm of the polynomial, i.e.
static BigInteger	UnivariatePolynomial.norm2(UnivariatePolynomial<BigInteger> poly)	Returns L2 norm of the polynomial, i.e.
static double	UnivariatePolynomial.norm2Double(UnivariatePolynomial<BigInteger> poly)	Returns L2 norm of the poly, i.e.
static UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	UnivariateGCD.PolynomialGCDInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)	Computes GCD via Langemyr & Mccallum modular algorithm over algebraic number field
static UnivariatePolynomial<UnivariatePolynomial<BigInteger>>	UnivariateGCD.PolynomialGCDInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)	Computes some GCD associate via Langemyr & Mccallum modular algorithm over algebraic integers
static boolean	UnivariateGCD.updateCRT(ChineseRemainders.ChineseRemaindersMagic<BigInteger> magic, UnivariatePolynomial<BigInteger> accumulated, UnivariatePolynomialZp64 update)	Apply CRT to a poly
static boolean	UnivariateGCD.updateCRT(ChineseRemainders.ChineseRemaindersMagic<BigInteger> magic, UnivariatePolynomial<BigInteger> accumulated, UnivariatePolynomialZp64 update)	Apply CRT to a poly

Constructors in cc.redberry.rings.poly.univar with parameters of type BigInteger

Constructor	Description
bQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> base, UnivariatePolynomial<BigInteger> aFactor, UnivariatePolynomial<BigInteger> bFactor, UnivariatePolynomial<BigInteger> aCoFactor, UnivariatePolynomial<BigInteger> bCoFactor)

Constructor parameters in cc.redberry.rings.poly.univar with type arguments of type BigInteger

Constructor	Description
bQuadraticLift(BigInteger modulus, UnivariatePolynomial<BigInteger> base, UnivariatePolynomial<BigInteger> aFactor, UnivariatePolynomial<BigInteger> bFactor, UnivariatePolynomial<BigInteger> aCoFactor, UnivariatePolynomial<BigInteger> bCoFactor)

Uses of BigInteger in cc.redberry.rings.primes

Methods in cc.redberry.rings.primes that return BigInteger

Modifier and Type	Method	Description
static BigInteger	BigPrimes.fermat(BigInteger n, long upperBound)	Fermat's factoring algorithm works like trial division, but walks in the opposite direction.
BigInteger	SieveOfAtkin.getLimitAsBigInteger()
static BigInteger	BigPrimes.nextPrime(BigInteger n)	Return the smallest prime greater than or equal to n.
static BigInteger	BigPrimes.PollardP1(BigInteger n, long upperBound)	Pollards's p-1 algorithm.
static BigInteger	BigPrimes.PollardRho(BigInteger n, int attempts, org.apache.commons.math3.random.RandomGenerator rn)	Pollards's rho algorithm (random search version).
static BigInteger	BigPrimes.PollardRho(BigInteger n, long upperBound)	Pollards's rho algorithm.
static BigInteger	BigPrimes.QuadraticSieve(BigInteger n, int bound)

Methods in cc.redberry.rings.primes that return types with arguments of type BigInteger

Modifier and Type	Method	Description
static List<BigInteger>	BigPrimes.primeFactors(BigInteger num)	Prime factors decomposition.

Methods in cc.redberry.rings.primes with parameters of type BigInteger

Modifier and Type	Method	Description
static SieveOfAtkin	SieveOfAtkin.createSieve(BigInteger limit)
static BigInteger	BigPrimes.fermat(BigInteger n, long upperBound)	Fermat's factoring algorithm works like trial division, but walks in the opposite direction.
static boolean	BigPrimes.isPrime(BigInteger n)	Strong primality test.
static boolean	BigPrimes.LucasPrimalityTest(BigInteger n, int k, org.apache.commons.math3.random.RandomGenerator rnd)
static BigInteger	BigPrimes.nextPrime(BigInteger n)	Return the smallest prime greater than or equal to n.
static BigInteger	BigPrimes.PollardP1(BigInteger n, long upperBound)	Pollards's p-1 algorithm.
static BigInteger	BigPrimes.PollardRho(BigInteger n, int attempts, org.apache.commons.math3.random.RandomGenerator rn)	Pollards's rho algorithm (random search version).
static BigInteger	BigPrimes.PollardRho(BigInteger n, long upperBound)	Pollards's rho algorithm.
static List<BigInteger>	BigPrimes.primeFactors(BigInteger num)	Prime factors decomposition.
static BigInteger	BigPrimes.QuadraticSieve(BigInteger n, int bound)

Uses of BigInteger in cc.redberry.rings.util

Methods in cc.redberry.rings.util that return BigInteger

Modifier and Type	Method	Description
static BigInteger[]	ArraysUtil.getSortedDistinct(BigInteger[] values)	Sort array & return array with removed repetitive values.
static BigInteger[]	ArraysUtil.negate(BigInteger[] arr)
static BigInteger[]	RandomUtil.randomBigIntegerArray(int length, BigInteger min, BigInteger max, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements bounded by bound (by absolute value).
static BigInteger	RandomUtil.randomInt(BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Returns random integer in range [0, bound).

Methods in cc.redberry.rings.util with parameters of type BigInteger

Modifier and Type	Method	Description
static BigInteger[]	ArraysUtil.getSortedDistinct(BigInteger[] values)	Sort array & return array with removed repetitive values.
static BigInteger[]	ArraysUtil.negate(BigInteger[] arr)
static BigInteger[]	RandomUtil.randomBigIntegerArray(int length, BigInteger min, BigInteger max, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements bounded by bound (by absolute value).
static BigInteger	RandomUtil.randomInt(BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)	Returns random integer in range [0, bound).