Package | Description |
---|---|
cc.redberry.rings | |
cc.redberry.rings.poly | |
cc.redberry.rings.poly.multivar | |
cc.redberry.rings.poly.univar |
Modifier and Type | Field and Description |
---|---|
static UnivariateRing<UnivariatePolynomial<Rational<BigInteger>>> |
Rings.UnivariateRingQ
Ring of univariate polynomials over rationals (Q[x])
|
Modifier and Type | Method and Description |
---|---|
Rational<E> |
Rational.abs()
Returns the absolute value of this
Rational . |
Rational<E> |
Rational.add(E val)
Add
other to this |
Rational<E> |
Rational.add(long other)
Add
other to this |
Rational<E> |
Rational.add(Rational<E> other)
Add
other to this |
Rational<E> |
Rationals.add(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.copy(Rational<E> element) |
Rational<E>[] |
Rationals.createArray(int length) |
Rational<E>[][] |
Rationals.createArray2d(int length) |
Rational<E>[][] |
Rationals.createArray2d(int m,
int n) |
Rational<E> |
Rational.divide(E other)
Divide this by
other |
Rational<E> |
Rational.divide(long l)
Divide this by
other |
Rational<E> |
Rational.divide(Rational other)
Divide this by
other |
Rational<E>[] |
Rationals.divideAndRemainder(Rational<E> dividend,
Rational<E> divider) |
Rational<E> |
Rationals.gcd(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.getNegativeOne() |
Rational<E> |
Rationals.getOne() |
Rational<E> |
Rationals.getZero() |
<O> Rational<O> |
Rational.map(Ring<O> ring,
Function<E,O> function)
Maps rational to a new ring
|
Rational<E> |
Rational.multiply(E other)
Multiply this by
other |
Rational<E> |
Rational.multiply(long other)
Multiply this by
other |
Rational<E> |
Rational.multiply(Rational<E> other)
Multiply this by
other |
Rational<E> |
Rationals.multiply(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rational.negate()
Negates this
|
Rational<E> |
Rationals.negate(Rational<E> element) |
Rational<E>[] |
Rational.normal()
Reduces this rational to normal form by doing division with remainder, that is if
numerator = div *
denominator + rem then the array (div, rem/denominator) will be returned. |
static <E> Rational<E> |
Rational.one(Ring<E> ring)
Constructs one
|
Rational<E> |
Rationals.parse(ElementParser<E> parser,
String string) |
Rational<E> |
Rationals.parse(String string) |
Rational<E> |
Rational.pow(BigInteger exponent)
Raise this in a power
exponent |
Rational<E> |
Rational.pow(int exponent)
Raise this in a power
exponent |
Rational<E> |
Rational.pow(long exponent)
Raise this in a power
exponent |
Rational<E> |
Rationals.randomElement(org.apache.commons.math3.random.RandomGenerator rnd) |
Rational<E> |
Rationals.randomNonTrivialElement(org.apache.commons.math3.random.RandomGenerator rnd) |
Rational<E> |
Rational.reciprocal()
Return the multiplicative inverse of this rational.
|
Rational<E> |
Rationals.reciprocal(Rational<E> element) |
Rational<E> |
Rational.subtract(E other)
Subtracts
other from this |
Rational<E> |
Rational.subtract(long l)
Subtracts
other from this |
Rational<E> |
Rational.subtract(Rational<E> other)
Subtracts
other from this |
Rational<E> |
Rationals.subtract(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.valueOf(long val) |
Rational<E> |
Rationals.valueOf(Rational<E> val) |
Rational<E> |
Rationals.valueOfBigInteger(BigInteger val) |
static <E> Rational<E> |
Rational.zero(Ring<E> ring)
Constructs zero
|
Modifier and Type | Method and Description |
---|---|
Iterator<Rational<E>> |
Rationals.iterator() |
static MultivariateRing<MultivariatePolynomial<Rational<BigInteger>>> |
Rings.MultivariateRingQ(int nVariables)
Ring of multivariate polynomials over rationals (Q[x1, x2, ...])
|
Modifier and Type | Method and Description |
---|---|
Rational<E> |
Rational.add(Rational<E> other)
Add
other to this |
Rational<E> |
Rationals.add(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.add(Rational<E> a,
Rational<E> b) |
int |
Rationals.compare(Rational<E> o1,
Rational<E> o2) |
int |
Rationals.compare(Rational<E> o1,
Rational<E> o2) |
int |
Rational.compareTo(Rational<E> object) |
Rational<E> |
Rationals.copy(Rational<E> element) |
Rational<E> |
Rational.divide(Rational other)
Divide this by
other |
Rational<E>[] |
Rationals.divideAndRemainder(Rational<E> dividend,
Rational<E> divider) |
Rational<E>[] |
Rationals.divideAndRemainder(Rational<E> dividend,
Rational<E> divider) |
Rational<E> |
Rationals.gcd(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.gcd(Rational<E> a,
Rational<E> b) |
boolean |
Rationals.isOne(Rational element) |
boolean |
Rationals.isUnit(Rational element) |
boolean |
Rationals.isZero(Rational element) |
Rational<E> |
Rational.multiply(Rational<E> other)
Multiply this by
other |
Rational<E> |
Rationals.multiply(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.multiply(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.negate(Rational<E> element) |
Rational<E> |
Rationals.reciprocal(Rational<E> element) |
int |
Rationals.signum(Rational<E> element) |
Rational<E> |
Rational.subtract(Rational<E> other)
Subtracts
other from this |
Rational<E> |
Rationals.subtract(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.subtract(Rational<E> a,
Rational<E> b) |
Rational<E> |
Rationals.valueOf(Rational<E> val) |
Modifier and Type | Method and Description |
---|---|
static <E> MultivariatePolynomial<Rational<E>> |
Util.asOverRationals(Ring<Rational<E>> field,
MultivariatePolynomial<E> poly) |
static <E> UnivariatePolynomial<Rational<E>> |
Util.asOverRationals(Ring<Rational<E>> field,
UnivariatePolynomial<E> poly) |
static <E> MultivariatePolynomial<Rational<E>> |
Util.divideOverRationals(Ring<Rational<E>> field,
MultivariatePolynomial<E> poly,
E denominator) |
static <E> UnivariatePolynomial<Rational<E>> |
Util.divideOverRationals(Ring<Rational<E>> field,
UnivariatePolynomial<E> poly,
E denominator) |
Modifier and Type | Method and Description |
---|---|
static <E> MultivariatePolynomial<Rational<E>> |
Util.asOverRationals(Ring<Rational<E>> field,
MultivariatePolynomial<E> poly) |
static <E> UnivariatePolynomial<Rational<E>> |
Util.asOverRationals(Ring<Rational<E>> field,
UnivariatePolynomial<E> poly) |
static <E> MultivariatePolynomial<Rational<E>> |
Util.divideOverRationals(Ring<Rational<E>> field,
MultivariatePolynomial<E> poly,
E denominator) |
static <E> UnivariatePolynomial<Rational<E>> |
Util.divideOverRationals(Ring<Rational<E>> field,
UnivariatePolynomial<E> poly,
E denominator) |
static <E> Util.Tuple2<MultivariatePolynomial<E>,E> |
Util.toCommonDenominator(MultivariatePolynomial<Rational<E>> poly)
Brings polynomial with rational coefficients to common denominator
|
static <E> Util.Tuple2<UnivariatePolynomial<E>,E> |
Util.toCommonDenominator(UnivariatePolynomial<Rational<E>> poly)
Brings polynomial with rational coefficients to common denominator
|
Modifier and Type | Field and Description |
---|---|
UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBasis.HilbertSeries.initialNumerator
Initial numerator (numerator and denominator may have nontrivial GCD)
|
UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBasis.HilbertSeries.numerator
Reduced numerator (GCD is cancelled)
|
Modifier and Type | Method and Description |
---|---|
static <E> PolynomialFactorDecomposition<MultivariatePolynomial<Rational<E>>> |
MultivariateFactorization.FactorInQ(MultivariatePolynomial<Rational<E>> polynomial)
Factors multivariate polynomial over Q
|
static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasis.GroebnerBasisInQ(List<MultivariatePolynomial<Rational<BigInteger>>> generators,
Comparator<DegreeVector> monomialOrder,
GroebnerBasis.HilbertSeries hilbertSeries,
boolean tryModular)
Computes Groebner basis (minimized and reduced) of a given ideal over Q represented by a list of generators.
|
Modifier and Type | Method and Description |
---|---|
static <E> PolynomialFactorDecomposition<UnivariatePolynomial<Rational<E>>> |
UnivariateFactorization.FactorInQ(UnivariatePolynomial<Rational<E>> poly)
Factors polynomial over Q
|
Modifier and Type | Method and Description |
---|---|
static <E> PolynomialFactorDecomposition<UnivariatePolynomial<Rational<E>>> |
UnivariateFactorization.FactorInQ(UnivariatePolynomial<Rational<E>> poly)
Factors polynomial over Q
|
static UnivariatePolynomial<Rational<BigInteger>>[] |
UnivariateGCD.ModularExtendedGCD(UnivariatePolynomial<Rational<BigInteger>> a,
UnivariatePolynomial<Rational<BigInteger>> b)
Modular GCD algorithm for polynomials over Z.
|
static UnivariatePolynomial<Rational<BigInteger>>[] |
UnivariateGCD.ModularExtendedGCD(UnivariatePolynomial<Rational<BigInteger>> a,
UnivariatePolynomial<Rational<BigInteger>> b)
Modular GCD algorithm for polynomials over Z.
|
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