Package cc.redberry.rings.poly.multivar
Class GroebnerBases.HilbertSeries
- java.lang.Object
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- cc.redberry.rings.poly.multivar.GroebnerBases.HilbertSeries
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- Enclosing class:
- GroebnerBases
public static final class GroebnerBases.HilbertSeries extends Object
Hilbert-Poincare series HPS(t) = P(t) / (1 - t)^m
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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)
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Method Summary
Modifier and Type Method Description int
degree()
The degree of idealint
dimension()
The dimension of idealboolean
equals(Object o)
int
hashCode()
UnivariatePolynomial<Rational<BigInteger>>
hilbertPolynomial()
Hilbert polynomialUnivariatePolynomial<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)^mUnivariatePolynomial<Rational<BigInteger>>
remainderNumerator()
Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^mString
toString()
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Field Detail
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initialNumerator
public final UnivariatePolynomial<Rational<BigInteger>> initialNumerator
Initial numerator (numerator and denominator may have nontrivial GCD)
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initialDenominatorExponent
public final int initialDenominatorExponent
Initial denominator exponent (numerator and denominator may have nontrivial GCD)
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numerator
public final UnivariatePolynomial<Rational<BigInteger>> numerator
Reduced numerator (GCD is cancelled)
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denominatorExponent
public final int denominatorExponent
Denominator exponent of reduced HPS(t) (that is ideal Krull dimension)
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Method Detail
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dimension
public int dimension()
The dimension of ideal
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degree
public int degree()
The degree of ideal
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integralPart
public UnivariatePolynomial<Rational<BigInteger>> integralPart()
Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m
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remainderNumerator
public UnivariatePolynomial<Rational<BigInteger>> remainderNumerator()
Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m
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hilbertPolynomialZ
public UnivariatePolynomial<Rational<BigInteger>> hilbertPolynomialZ()
Integral Hilbert polynomial (i.e. Hilbert polynomial multiplied by (dimension - 1)!)
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hilbertPolynomial
public UnivariatePolynomial<Rational<BigInteger>> hilbertPolynomial()
Hilbert polynomial
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