Package cc.redberry.rings.poly.multivar

Class GroebnerBases.HilbertSeries

java.lang.Object

cc.redberry.rings.poly.multivar.GroebnerBases.HilbertSeries

Enclosing class:

GroebnerBases

public static final class GroebnerBases.HilbertSeries
extends Object

Hilbert-Poincare series HPS(t) = P(t) / (1 - t)^m

Field Summary

Fields

Modifier and Type	Field	Description
int	denominatorExponent	Denominator exponent of reduced HPS(t) (that is ideal Krull dimension)
int	initialDenominatorExponent	Initial denominator exponent (numerator and denominator may have nontrivial GCD)
UnivariatePolynomial<Rational<BigInteger>>	initialNumerator	Initial numerator (numerator and denominator may have nontrivial GCD)
UnivariatePolynomial<Rational<BigInteger>>	numerator	Reduced numerator (GCD is cancelled)

Method Summary

Modifier and Type	Method	Description
int	degree()	The degree of ideal
int	dimension()	The dimension of ideal
boolean	equals(Object o)
int	hashCode()
UnivariatePolynomial<Rational<BigInteger>>	hilbertPolynomial()	Hilbert polynomial
UnivariatePolynomial<Rational<BigInteger>>	hilbertPolynomialZ()	Integral Hilbert polynomial (i.e.
UnivariatePolynomial<Rational<BigInteger>>	integralPart()	Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m
UnivariatePolynomial<Rational<BigInteger>>	remainderNumerator()	Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

initialNumerator

public final UnivariatePolynomial<Rational<BigInteger>> initialNumerator

Initial numerator (numerator and denominator may have nontrivial GCD)

initialDenominatorExponent

public final int initialDenominatorExponent

Initial denominator exponent (numerator and denominator may have nontrivial GCD)

numerator

public final UnivariatePolynomial<Rational<BigInteger>> numerator

Reduced numerator (GCD is cancelled)

denominatorExponent

public final int denominatorExponent

Denominator exponent of reduced HPS(t) (that is ideal Krull dimension)

Method Details

dimension

public int dimension()

The dimension of ideal

degree

public int degree()

The degree of ideal

integralPart

public UnivariatePolynomial<Rational<BigInteger>> integralPart()

Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m

remainderNumerator

public UnivariatePolynomial<Rational<BigInteger>> remainderNumerator()

Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m

hilbertPolynomialZ

public UnivariatePolynomial<Rational<BigInteger>> hilbertPolynomialZ()

Integral Hilbert polynomial (i.e. Hilbert polynomial multiplied by (dimension - 1)!)

hilbertPolynomial

public UnivariatePolynomial<Rational<BigInteger>> hilbertPolynomial()

Hilbert polynomial

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

toString

public String toString()

Overrides:

toString in class Object