Uses of Class
cc.redberry.rings.bigint.BigInteger
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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 -
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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 infiniteBigInteger
ImageRing. characteristic()
BigInteger
Integers. characteristic()
BigInteger
IntegersZp. characteristic()
BigInteger
Rationals. characteristic()
BigInteger
Ring. characteristic()
Returns characteristic of this ringstatic BigInteger
ChineseRemainders. ChineseRemainders(BigInteger[] primes, BigInteger[] remainders)
Runs Chinese Remainders algorithmstatic BigInteger
ChineseRemainders. ChineseRemainders(BigInteger prime1, BigInteger prime2, BigInteger remainder1, BigInteger remainder2)
Runs Chinese Remainders algorithmBigInteger
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)
Returnsval 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()
Returnsbase
so thatcardinality == base^exponent
or null if cardinality is not finiteBigInteger
ARing. perfectPowerExponent()
BigInteger
ImageRing. perfectPowerExponent()
BigInteger
Rationals. perfectPowerExponent()
BigInteger
Ring. perfectPowerExponent()
Returnsexponent
so thatcardinality == base^exponent
or null if cardinality is not finiteBigInteger
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/1207.1651v2BigInteger
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)
Convertsvalue
to a symmetric representation of ZpBigInteger
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 cardinalityprime ^ exponent
for arbitrary largeprime
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 modulusstatic UnivariateRing<UnivariatePolynomial<BigInteger>>
Rings. UnivariateRingZp(BigInteger modulus)
Ring of univariate polynomials over Zp integers (Zp[x]) with arbitrary large modulusMethods 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 algorithmstatic BigInteger
ChineseRemainders. ChineseRemainders(BigInteger prime1, BigInteger prime2, BigInteger remainder1, BigInteger remainder2)
Runs Chinese Remainders algorithmBigInteger
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 cardinalityprime ^ exponent
for arbitrary largeprime
boolean
Integers. isMinusOne(BigInteger bigInteger)
boolean
Integers. isUnit(BigInteger element)
boolean
IntegersZp. isUnit(BigInteger element)
BigInteger
IntegersZp. modulus(BigInteger val)
Returnsval mod this.modulus
long
IntegersZp64. modulus(BigInteger val)
Returnsval % 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 modulusBigInteger
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 powerexponent
default E
Ring. pow(E base, BigInteger exponent)
Returnsbase
in a power ofexponent
(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/1207.1651v2BigInteger
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)
Convertsvalue
to a symmetric representation of Zpstatic UnivariateRing<UnivariatePolynomial<BigInteger>>
Rings. UnivariateRingZp(BigInteger modulus)
Ring of univariate polynomials over Zp integers (Zp[x]) with arbitrary large modulusBigInteger
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 integerstatic IntegersZp
Rings. Zp(BigInteger modulus)
Ring of integers modulomodulus
(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 coefficientBigInteger
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 numberBigInteger
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 ofabs(this)
andabs(val)
.static BigInteger
BigIntegerUtil. gcd(BigInteger[] integers, int from, int to)
Returns the greatest common an array of longsstatic BigInteger
BigIntegerUtil. gcd(BigInteger a, BigInteger b)
BigInteger
BigInteger. increment()
BigInteger
BigInteger. max(BigInteger val)
Returns the maximum of this BigInteger andval
.static BigInteger
BigIntegerUtil. max(BigInteger a, BigInteger b)
BigInteger
BigInteger. min(BigInteger val)
Returns the minimum of this BigInteger andval
.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
-1mod 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)
Multipliesthis
number by another using a specified number of threads if the inputs are sufficiently large.BigInteger
BigInteger. multiplyParallel(BigInteger val)
Multipliesthis
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 thisBigInteger
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 whethern
is a perfect powern == a^b
and returns{a, b}
if so andnull
otherwiseBigInteger
BigInteger. pow(int exponent)
Returns a BigInteger whose value is (thisexponent).static BigInteger
BigIntegerUtil. pow(long base, long exponent)
Returnsbase
in a power ofe
(non negative)static BigInteger
BigIntegerUtil. pow(BigInteger base, int exponent)
Returnsbase
in a power ofe
(non negative)static BigInteger
BigIntegerUtil. pow(BigInteger base, long exponent)
Returnsbase
in a power ofe
(non negative)static BigInteger
BigIntegerUtil. pow(BigInteger base, BigInteger exponent)
Returnsbase
in a power ofe
(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 ofval
static BigInteger
BigIntegerUtil. sqrtFloor(BigInteger val)
Returns floor square root ofval
BigInteger
BigInteger. subtract(BigInteger val)
Returns a BigInteger whose value is(this - val)
.BigInteger
BigDecimal. toBigInteger()
Converts thisBigDecimal
to aBigInteger
.BigInteger
BigDecimal. toBigIntegerExact()
Converts thisBigDecimal
to aBigInteger
, checking for lost information.BigInteger
BigDecimal. unscaledValue()
Returns aBigInteger
whose value is the unscaled value of thisBigDecimal
.static BigInteger
BigInteger. valueOf(int val)
Returns a BigInteger whose value is equal to that of the specifiedlong
.static BigInteger
BigInteger. valueOf(long val)
Returns a BigInteger whose value is equal to that of the specifiedlong
.static BigInteger
BigInteger. valueOfSigned(long bits)
Converts signed long to BigIntegerstatic BigInteger
BigInteger. valueOfUnsigned(long bits)
Converts unsigned long to BigIntegerBigInteger
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 ofabs(this)
andabs(val)
.static BigInteger
BigIntegerUtil. gcd(BigInteger[] integers, int from, int to)
Returns the greatest common an array of longsstatic BigInteger
BigIntegerUtil. gcd(BigInteger a, BigInteger b)
BigInteger
BigInteger. max(BigInteger val)
Returns the maximum of this BigInteger andval
.static BigInteger
BigIntegerUtil. max(BigInteger a, BigInteger b)
BigInteger
BigInteger. min(BigInteger val)
Returns the minimum of this BigInteger andval
.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
-1mod 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)
Multipliesthis
number by another using a specified number of threads if the inputs are sufficiently large.BigInteger
BigInteger. multiplyParallel(BigInteger val)
Multipliesthis
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 whethern
is a perfect powern == a^b
and returns{a, b}
if so andnull
otherwisestatic BigInteger
BigIntegerUtil. pow(BigInteger base, int exponent)
Returnsbase
in a power ofe
(non negative)static BigInteger
BigIntegerUtil. pow(BigInteger base, long exponent)
Returnsbase
in a power ofe
(non negative)static BigInteger
BigIntegerUtil. pow(BigInteger base, BigInteger exponent)
Returnsbase
in a power ofe
(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 ofval
static BigInteger
BigIntegerUtil. sqrtFloor(BigInteger val)
Returns floor square root ofval
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 aBigInteger
into aBigDecimal
.BigDecimal(BigInteger unscaledVal, int scale)
Translates aBigInteger
unscaled value and anint
scale into aBigDecimal
.BigDecimal(BigInteger unscaledVal, int scale, MathContext mc)
Translates aBigInteger
unscaled value and anint
scale into aBigDecimal
, with rounding according to the context settings.BigDecimal(BigInteger val, MathContext mc)
Translates aBigInteger
into aBigDecimal
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 modulusMethods 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 polyBigInteger
IPolynomial. coefficientRingCharacteristic()
Returns characteristic of the coefficient ring of this polyBigInteger
IPolynomial. coefficientRingPerfectPowerBase()
Returnsbase
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finiteBigInteger
IPolynomial. coefficientRingPerfectPowerExponent()
Returnsexponent
so thatcoefficientRingCardinality() == base^exponent
or null if cardinality is not finiteMethods in cc.redberry.rings.poly with parameters of type BigInteger Modifier and Type Method Description Poly
IPolynomial. multiplyByBigInteger(BigInteger factor)
Multiplies this byfactor
static <T extends IPolynomial<T>>
TPolynomialMethods. polyPow(T base, BigInteger exponent)
Returnsbase
in a power of non-negativeexponent
static <T extends IPolynomial<T>>
TPolynomialMethods. polyPow(T base, BigInteger exponent, boolean copy)
Returnsbase
in a power of non-negativeexponent
.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 thisstatic 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 algorithmstatic PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>
MultivariateFactorization. FactorInZ(MultivariatePolynomial<BigInteger> polynomial)
Factors multivariate polynomial over Zstatic 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 polynomialUnivariatePolynomial<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)^mstatic 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 reconstructionstatic 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 reconstructionstatic 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 fieldstatic 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 integersstatic MultivariatePolynomial<BigInteger>
MultivariateResultants. ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)
Modular algorithm with Zippel sparse interpolation for resultant over Zstatic 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 Zstatic MultivariatePolynomial<UnivariatePolynomial<BigInteger>>
MultivariateGCD. PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Calculates greatest common divisor of two multivariate polynomials over Zstatic MultivariatePolynomial<BigInteger>
MultivariateGCD. PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)
Calculates greatest common divisor of two multivariate polynomials over Zstatic 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 bybound
static MultivariatePolynomial<BigInteger>
RandomMultivariatePolynomials. randomPolynomial(int nVars, int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd)
Generates random Z[X] polynomialUnivariatePolynomial<Rational<BigInteger>>
GroebnerBases.HilbertSeries. remainderNumerator()
Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^mstatic MultivariatePolynomial<BigInteger>
MultivariateResultants. ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)
Computes polynomial resultant of two polynomials over ZMonomial<BigInteger>
MonomialZp64. toBigMonomial()
MultivariatePolynomial<BigInteger>
MultivariatePolynomialZp64. toBigPoly()
Returns polynomial over Z formed from the coefficients of thisstatic 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 reconstructionstatic 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 resultstatic 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 numberMultivariatePolynomial<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 bybound
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 integersstatic MultivariatePolynomialZp64
MultivariatePolynomial. asOverZp64(MultivariatePolynomial<BigInteger> poly, IntegersZp64 ring)
Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integersstatic 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 algorithmstatic PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>
MultivariateFactorization. FactorInZ(MultivariatePolynomial<BigInteger> polynomial)
Factors multivariate polynomial over Zstatic 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 reconstructionstatic 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 reconstructionstatic 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 fieldstatic 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 integersstatic MultivariatePolynomial<BigInteger>
MultivariateResultants. ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)
Modular algorithm with Zippel sparse interpolation for resultant over Zstatic 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 Zstatic MultivariatePolynomial<UnivariatePolynomial<BigInteger>>
MultivariateGCD. PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Calculates greatest common divisor of two multivariate polynomials over Zstatic MultivariatePolynomial<BigInteger>
MultivariateGCD. PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)
Calculates greatest common divisor of two multivariate polynomials over Zstatic MultivariatePolynomial<BigInteger>
MultivariateResultants. ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable)
Computes polynomial resultant of two polynomials over Zstatic 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 reconstructionstatic 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 resultstatic 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] polyMethods 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 polystatic BigInteger
UnivariateResultants. ModularResultant(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b)
Modular algorithm for computing resultants over Zstatic 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 lengthdegree + 1
with elements bounded bybound
(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] polynomialstatic UnivariatePolynomial<BigInteger>
UnivariatePolynomial. create(Ring<BigInteger> ring, long... data)
Creates univariate polynomial over specified ring (with integer elements) with the specified coefficientsstatic PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>
UnivariateFactorization. FactorInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)
Factors polynomial in Q(alpha)[x] via Trager's algorithmstatic PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>
UnivariateFactorization. FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)
Factors polynomial in Q(alpha)[x] via Trager's algorithmstatic List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static UnivariatePolynomial<Rational<BigInteger>>[]
UnivariateGCD. ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)
Computes[gcd(a,b), s, t]
such thats * 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 fieldstatic UnivariatePolynomial<BigInteger>
UnivariateResultants. ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Modular resultant in the ring of integers of number fieldUnivariatePolynomial<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 fieldstatic UnivariatePolynomial<UnivariatePolynomial<BigInteger>>
UnivariateGCD. PolynomialGCDInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Computes some GCD associate via Langemyr & Mccallum modular algorithm over algebraic integersstatic UnivariatePolynomial<BigInteger>
IrreduciblePolynomials. randomIrreduciblePolynomialOverZ(int degree, org.apache.commons.math3.random.RandomGenerator rnd)
Generated random irreducible polynomial over Zstatic UnivariatePolynomial<BigInteger>
RandomUnivariatePolynomials. randomMonicPoly(int degree, BigInteger modulus, org.apache.commons.math3.random.RandomGenerator rnd)
Creates random polynomial of specifieddegree
.static UnivariatePolynomial<BigInteger>
RandomUnivariatePolynomials. randomPoly(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)
Creates random polynomial of specifieddegree
with elements bounded bybound
(by absolute value).UnivariatePolynomial<BigInteger>
UnivariatePolynomialZ64. toBigPoly()
Converts this to a polynomial over BigIntegersUnivariatePolynomial<BigInteger>
UnivariatePolynomialZp64. toBigPoly()
Converts this to a polynomial over BigIntegersMethods 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>>
TUnivariatePolynomialArithmetic. createMonomialMod(BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)
Createsx^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 untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.UnivariatePolynomial<E>
UnivariatePolynomial. multiplyByBigInteger(BigInteger factor)
UnivariatePolynomialZ64
UnivariatePolynomialZ64. multiplyByBigInteger(BigInteger factor)
UnivariatePolynomialZp64
UnivariatePolynomialZp64. multiplyByBigInteger(BigInteger factor)
static <T extends IUnivariatePolynomial<T>>
TUnivariatePolynomialArithmetic. polyPowMod(T base, BigInteger exponent, T polyModulus, boolean copy)
Returnsbase
in a power of non-negativeexponent
modulopolyModulus
static <T extends IUnivariatePolynomial<T>>
TUnivariatePolynomialArithmetic. polyPowMod(T base, BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy)
Returnsbase
in a power of non-negativeexponent
modulopolyModulus
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 lengthdegree + 1
with elements bounded bybound
(by absolute value).static UnivariatePolynomial<BigInteger>
RandomUnivariatePolynomials. randomMonicPoly(int degree, BigInteger modulus, org.apache.commons.math3.random.RandomGenerator rnd)
Creates random polynomial of specifieddegree
.static UnivariatePolynomial<BigInteger>
RandomUnivariatePolynomials. randomPoly(int degree, BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)
Creates random polynomial of specifieddegree
with elements bounded bybound
(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 Zstatic UnivariatePolynomialZp64
UnivariatePolynomial. asOverZp64(UnivariatePolynomial<BigInteger> poly)
Converts Zp[x] poly over BigIntegers to machine-sized polynomial in Zpstatic UnivariatePolynomialZp64
UnivariatePolynomial. asOverZp64(UnivariatePolynomial<BigInteger> poly, IntegersZp64 ring)
Converts Zp[x] poly over BigIntegers to machine-sized polynomial in Zpstatic UnivariatePolynomialZp64
UnivariatePolynomial. asOverZp64Q(UnivariatePolynomial<Rational<BigInteger>> poly, IntegersZp64 ring)
Converts Zp[x] poly over rationals to machine-sized polynomial in Zpstatic 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 coefficientsstatic 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 algorithmstatic PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>
UnivariateFactorization. FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly)
Factors polynomial in Q(alpha)[x] via Trager's algorithmstatic List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorization(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomialZp64> modularFactors, boolean quadratic)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static List<UnivariatePolynomial<BigInteger>>
HenselLifting. liftFactorizationQuadratic(BigInteger modulus, BigInteger desiredBound, UnivariatePolynomial<BigInteger> poly, List<UnivariatePolynomial<BigInteger>> modularFactors)
Lifts modular factorization untilmodulus
will overcomedesiredBound
.static BigInteger
UnivariatePolynomial. mignotteBound(UnivariatePolynomial<BigInteger> poly)
Returns Mignotte's bound (sqrt(n+1) * 2^n max |this|) of the polystatic UnivariatePolynomial<Rational<BigInteger>>[]
UnivariateGCD. ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b)
Computes[gcd(a,b), s, t]
such thats * 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 Zstatic UnivariatePolynomial<Rational<BigInteger>>
UnivariateResultants. ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)
Modular resultant in simple number fieldstatic UnivariatePolynomial<BigInteger>
UnivariateResultants. ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Modular resultant in the ring of integers of number fieldstatic 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 fieldstatic UnivariatePolynomial<UnivariatePolynomial<BigInteger>>
UnivariateGCD. PolynomialGCDInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)
Computes some GCD associate via Langemyr & Mccallum modular algorithm over algebraic integersstatic boolean
UnivariateGCD. updateCRT(ChineseRemainders.ChineseRemaindersMagic<BigInteger> magic, UnivariatePolynomial<BigInteger> accumulated, UnivariatePolynomialZp64 update)
Apply CRT to a polystatic boolean
UnivariateGCD. updateCRT(ChineseRemainders.ChineseRemaindersMagic<BigInteger> magic, UnivariatePolynomial<BigInteger> accumulated, UnivariatePolynomialZp64 update)
Apply CRT to a polyConstructors 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)
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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)
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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 lengthdegree + 1
with elements bounded bybound
(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 lengthdegree + 1
with elements bounded bybound
(by absolute value).static BigInteger
RandomUtil. randomInt(BigInteger bound, org.apache.commons.math3.random.RandomGenerator rnd)
Returns random integer in range[0, bound)
.
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