## Class 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 Detail

• #### 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 Detail

• #### 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`