Package edu.jas.ps

Class UnivPowerSeriesRing<C extends RingElem<C>>

    • Field Detail

      • random

        protected static final java.util.Random random
        A default random sequence generator.
      • DEFAULT_TRUNCATE

        public static final int DEFAULT_TRUNCATE
        Default truncate.
        See Also:
        Constant Field Values
      • truncate

        int truncate
        Truncate.
      • DEFAULT_NAME

        public static final java.lang.String DEFAULT_NAME
        Default variable name.
        See Also:
        Constant Field Values
      • var

        java.lang.String var
        Variable name.
    • Constructor Detail

      • UnivPowerSeriesRing

        private UnivPowerSeriesRing()
        No argument constructor.
      • UnivPowerSeriesRing

        public UnivPowerSeriesRing​(RingFactory<C> coFac)
        Constructor.
        Parameters:
        coFac - coefficient ring factory.
      • UnivPowerSeriesRing

        public UnivPowerSeriesRing​(RingFactory<C> coFac,
                                   int truncate)
        Constructor.
        Parameters:
        coFac - coefficient ring factory.
        truncate - index of truncation.
      • UnivPowerSeriesRing

        public UnivPowerSeriesRing​(RingFactory<C> coFac,
                                   java.lang.String name)
        Constructor.
        Parameters:
        coFac - coefficient ring factory.
        name - of the variable.
      • UnivPowerSeriesRing

        public UnivPowerSeriesRing​(GenPolynomialRing<C> pfac)
        Constructor.
        Parameters:
        pfac - polynomial ring factory.
      • UnivPowerSeriesRing

        public UnivPowerSeriesRing​(RingFactory<C> cofac,
                                   int truncate,
                                   java.lang.String name)
        Constructor.
        Parameters:
        cofac - coefficient ring factory.
        truncate - index of truncation.
        name - of the variable.
    • Method Detail

      • fixPoint

        public UnivPowerSeries<C> fixPoint​(UnivPowerSeriesMap<C> map)
        Fixed point construction.
        Parameters:
        map - a mapping of power series.
        Returns:
        fix point wrt map.
      • toString

        public java.lang.String toString()
        To String.
        Overrides:
        toString in class java.lang.Object
        Returns:
        string representation of this.
      • toScript

        public java.lang.String toScript()
        Get a scripting compatible string representation.
        Specified by:
        toScript in interface ElemFactory<C extends RingElem<C>>
        Returns:
        script compatible representation for this ElemFactory.
        See Also:
        ElemFactory.toScript()
      • equals

        public boolean equals​(java.lang.Object B)
        Comparison with any other object.
        Overrides:
        equals in class java.lang.Object
        See Also:
        Object.equals(java.lang.Object)
      • hashCode

        public int hashCode()
        Hash code for this .
        Overrides:
        hashCode in class java.lang.Object
        See Also:
        Object.hashCode()
      • getEXP

        public UnivPowerSeries<C> getEXP()
        Get the power series of the exponential function.
        Returns:
        exp(x) as UnivPowerSeries.
      • getSIN

        public UnivPowerSeries<C> getSIN()
        Get the power series of the sinus function.
        Returns:
        sin(x) as UnivPowerSeries.
      • getCOS

        public UnivPowerSeries<C> getCOS()
        Get the power series of the cosine function.
        Returns:
        cos(x) as UnivPowerSeries.
      • getTAN

        public UnivPowerSeries<C> getTAN()
        Get the power series of the tangens function.
        Returns:
        tan(x) as UnivPowerSeries.
      • solveODE

        public UnivPowerSeries<C> solveODE​(UnivPowerSeries<C> f,
                                           C c)
        Solve an ordinary differential equation. y' = f(y) with y(0) = c.
        Parameters:
        f - a UnivPowerSeries.
        c - integration constant.
        Returns:
        f.integrate(c).
      • isCommutative

        public boolean isCommutative()
        Is commutative.
        Specified by:
        isCommutative in interface MonoidFactory<C extends RingElem<C>>
        Returns:
        true, if this ring is commutative, else false.
      • isAssociative

        public boolean isAssociative()
        Query if this ring is associative.
        Specified by:
        isAssociative in interface MonoidFactory<C extends RingElem<C>>
        Returns:
        true if this ring is associative, else false.
      • isField

        public boolean isField()
        Query if this ring is a field.
        Specified by:
        isField in interface RingFactory<C extends RingElem<C>>
        Returns:
        false.
      • characteristic

        public java.math.BigInteger characteristic()
        Characteristic of this ring.
        Specified by:
        characteristic in interface RingFactory<C extends RingElem<C>>
        Returns:
        characteristic of this ring.
      • fromInteger

        public UnivPowerSeries<C> fromInteger​(long a)
        Get a (constant) UnivPowerSeries<C> from a long value.
        Specified by:
        fromInteger in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        a - long.
        Returns:
        a UnivPowerSeries<C>.
      • fromInteger

        public UnivPowerSeries<C> fromInteger​(java.math.BigInteger a)
        Get a (constant) UnivPowerSeries<C> from a java.math.BigInteger.
        Specified by:
        fromInteger in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        a - BigInteger.
        Returns:
        a UnivPowerSeries<C>.
      • polyRing

        public GenPolynomialRing<C> polyRing()
        Get the corresponding GenPolynomialRing<C>.
        Returns:
        GenPolynomialRing<C>.
      • fromPolynomial

        public UnivPowerSeries<C> fromPolynomial​(GenPolynomial<C> a)
        Get a UnivPowerSeries<C> from a GenPolynomial<C>.
        Parameters:
        a - GenPolynomial<C>.
        Returns:
        a UnivPowerSeries<C>.
      • fromVector

        public UnivPowerSeries<C> fromVector​(GenVector<C> a)
        Get a UnivPowerSeries<C> from a GenVector<C>.
        Parameters:
        a - GenVector<C>.
        Returns:
        a UnivPowerSeries<C>.
      • random

        public UnivPowerSeries<C> random()
        Generate a random power series with k = 5, d = 0.7.
        Returns:
        a random power series.
      • random

        public UnivPowerSeries<C> random​(int k)
        Generate a random power series with d = 0.7.
        Specified by:
        random in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        k - bitsize of random coefficients.
        Returns:
        a random power series.
      • random

        public UnivPowerSeries<C> random​(int k,
                                         java.util.Random rnd)
        Generate a random power series with d = 0.7.
        Specified by:
        random in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        k - bit-size of random coefficients.
        rnd - is a source for random bits.
        Returns:
        a random power series.
      • random

        public UnivPowerSeries<C> random​(int k,
                                         float d)
        Generate a random power series.
        Parameters:
        k - bit-size of random coefficients.
        d - density of non-zero coefficients.
        Returns:
        a random power series.
      • random

        public UnivPowerSeries<C> random​(int k,
                                         float d,
                                         java.util.Random rnd)
        Generate a random power series.
        Parameters:
        k - bit-size of random coefficients.
        d - density of non-zero coefficients.
        rnd - is a source for random bits.
        Returns:
        a random power series.
      • generate

        public UnivPowerSeries<C> generate​(java.util.function.IntFunction<C> gener)
        Generate a power series via lambda expression.
        Parameters:
        gener - lambda expression.
        Returns:
        a generated power series.
      • parse

        public UnivPowerSeries<C> parse​(java.lang.String s)
        Parse a power series. Note: not implemented.
        Specified by:
        parse in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        s - String.
        Returns:
        power series from s.
      • parse

        public UnivPowerSeries<C> parse​(java.io.Reader r)
        Parse a power series. Note: not implemented.
        Specified by:
        parse in interface ElemFactory<C extends RingElem<C>>
        Parameters:
        r - Reader.
        Returns:
        next power series from r.
      • seriesOfTaylor

        public UnivPowerSeries<C> seriesOfTaylor​(TaylorFunction<C> f,
                                                 C a)
        Taylor power series.
        Parameters:
        f - function.
        a - expansion point.
        Returns:
        Taylor series of f.