Rational

java.lang.Object
- birds.Rational

public class Rational
extends java.lang.Object

Constructor Summary

Constructors
Constructor and Description
`Rational(double[] _num, double _den)` Class constructor: Set numerator and denominator of a rational function
`Rational(double[] _num, double[] _den)` Class constructor: Set numerator and denominator of a rational function
`Rational(double _num, double _den)` Class constructor: Set numerator and denominator of a rational function
`Rational(double _num, double[] _den)` Class constructor: Set numerator and denominator of a rational function

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.lang.String`	`axes_intersection_points()` Calculate Axes intersection points
`Rational`	`der()` Calculate the derivative of a rational function
`static Rational`	`difference(Rational R1, Rational R2)` Calculate the difference of two rational functions
`java.lang.String`	`domain()` Calculate the domain of a rational function
`java.lang.String`	`features()` See the features of this Rational function
`double[]`	`getDen()` Get denominator
`double[]`	`getNum()` Get numerator
`double[]`	`getOutOfDomain()` Get out of domain points
`java.lang.String`	`horizontal_asymptotes()` Determine horizontal asymptotes
`java.lang.String`	`integral()` Calculate the integral of a Rational function
`double`	`integral(double a, double b)` Calculate the integral of a Rational function (Simpson's rule)
`double[]`	`integration_constants()` Calculate constants of different partial fractions
`java.lang.String`	`min_max()` Find min, max points of this Rational function
`Rational`	`monic_denominator()` Make denominator as monic polynomial
`java.lang.String`	`oblique_asymptotes()` Determine oblique asymptotes
`void`	`plot(double a, double b)` Rational function plot (matplotlib)
`static Rational`	`product(Rational R1, Rational R2)` Calculate the product of two rational functions
`java.lang.String`	`ps()` Calculate the positivity set of a rational function
`static Rational`	`reciprocal(Rational R1)` Calculate reciprocal of a rational function
`double[]`	`roots_multiset()` Calculate the set of roots of a rational function (the merged vector of numerator roots and denominator roots)
`double[]`	`roots()` Calculate the set of roots of a rational function
`void`	`setOutOfDomain(double[] out_of_domain)` Set out of domain points
`static double[]`	`simplify_den(double[] num, double[] den, boolean monic_den)` Simplify a rational function: this method returns the simplified numerator
`static double[]`	`simplify_num(double[] num, double[] den, boolean monic_den)` Simplify a rational function: this method returns the simplified numerator
`Rational`	`simplify(boolean monic_den)` Simplify a rational function
`static Rational`	`sum(Rational R1, Rational R2)` Calculate the sum of two rational functions
`java.lang.String`	`toPlot()` Write matplotlib code to plot a rational function
`java.lang.String`	`toString()` toString() method of rational function: It makes one-line String to explain the function
`java.lang.String`	`toString(boolean dec)` toString() method of a rational function
`double`	`value(double x)` Rational function value in x
`java.lang.String`	`vertical_asymptotes()` Determine vertical asymptotes

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - Rational
```
public Rational(double[] _num,
                double[] _den)
```
    Class constructor: Set numerator and denominator of a rational function
    
    Parameters:
    
    _num - polynomial components array, e.g. x^2-4 : {1,0,-4}
    
    _den - polynomial components array, e.g. x-4 : {1,-4}
  - Rational
```
public Rational(double _num,
                double[] _den)
```
    Class constructor: Set numerator and denominator of a rational function
    
    Parameters:
    
    _num - real number
    
    _den - polynomial components array, e.g. x-4 : {1,-4}
  - Rational
```
public Rational(double[] _num,
                double _den)
```
    Class constructor: Set numerator and denominator of a rational function
    
    Parameters:
    
    _num - polynomial components array, e.g. x^2-4 : {1,0,-4}
    
    _den - real number
  - Rational
```
public Rational(double _num,
                double _den)
```
    Class constructor: Set numerator and denominator of a rational function
    
    Parameters:
    
    _num - real number
    
    _den - real number
- Method Detail
  - integral
```
public double integral(double a,
                       double b)
                throws KingfisherExc
```
    Calculate the integral of a Rational function (Simpson's rule)
    
    Parameters:
    
    a - lower bound of interval e.g [4,10] you must insert 4
    
    b - upper bound of interval e.g [4,10] you must insert 10
    
    Returns:
    
    value of definite integral
    
    Throws:
    
    KingfisherExc
  - integral
```
public java.lang.String integral()
```
    Calculate the integral of a Rational function
    
    Returns:
    
    value of indefinite integral
  - simplify
```
public Rational simplify(boolean monic_den)
```
    Simplify a rational function
    
    Parameters:
    
    monic_den - If this boolean value is true, the method makes denominator a monic polynomial
    
    Returns:
    
    simplified function
  - simplify_num
```
public static double[] simplify_num(double[] num,
                                    double[] den,
                                    boolean monic_den)
```
    Simplify a rational function: this method returns the simplified numerator
    
    Parameters:
    
    num - Numerator of Rational function to simplify
    
    den - Denominator of Rational function to simplify
    
    monic_den - If this boolean value is true, the method makes denominator a monic polynomial
    
    Returns:
    
    simplified function
  - simplify_den
```
public static double[] simplify_den(double[] num,
                                    double[] den,
                                    boolean monic_den)
```
    Simplify a rational function: this method returns the simplified numerator
    
    Parameters:
    
    num - Numerator of Rational function to simplify
    
    den - Denominator of Rational function to simplify
    
    monic_den - If this boolean value is true, the method makes denominator a monic polynomial
    
    Returns:
    
    simplified function
  - der
```
public Rational der()
```
    Calculate the derivative of a rational function
    
    Returns:
    
    derivative
  - axes_intersection_points
```
public java.lang.String axes_intersection_points()
```
    Calculate Axes intersection points
    
    Returns:
    
    string to show intersection points
  - value
```
public double value(double x)
             throws KingfisherExc
```
    Rational function value in x
    
    Parameters:
    
    x - real number
    
    Returns:
    
    value
    
    Throws:
    
    KingfisherExc
  - domain
```
public java.lang.String domain()
```
    Calculate the domain of a rational function
    
    Returns:
    
    String to explain the domain
  - roots
```
public double[] roots()
```
    Calculate the set of roots of a rational function
    
    Returns:
    
    set of roots
  - roots_multiset
```
public double[] roots_multiset()
```
    Calculate the set of roots of a rational function (the merged vector of numerator roots and denominator roots)
    
    Returns:
    
    multiset of roots
  - sum
```
public static Rational sum(Rational R1,
                           Rational R2)
```
    Calculate the sum of two rational functions
    
    Parameters:
    
    R1 - first function
    
    R2 - second function
    
    Returns:
    
    sum
  - difference
```
public static Rational difference(Rational R1,
                                  Rational R2)
```
    Calculate the difference of two rational functions
    
    Parameters:
    
    R1 - first function
    
    R2 - second function
    
    Returns:
    
    difference
  - product
```
public static Rational product(Rational R1,
                               Rational R2)
```
    Calculate the product of two rational functions
    
    Parameters:
    
    R1 - first function
    
    R2 - second function
    
    Returns:
    
    product
  - reciprocal
```
public static Rational reciprocal(Rational R1)
```
    Calculate reciprocal of a rational function
    
    Parameters:
    
    R1 - rational function
    
    Returns:
    
    reciprocal
  - ps
```
public java.lang.String ps()
                    throws KingfisherExc
```
    Calculate the positivity set of a rational function
    
    Returns:
    
    String to explain the positivity set
    
    Throws:
    
    KingfisherExc
  - toPlot
```
public java.lang.String toPlot()
```
    Write matplotlib code to plot a rational function
    
    Returns:
    
    code
  - plot
```
public void plot(double a,
                 double b)
```
    Rational function plot (matplotlib)
    
    Parameters:
    
    a - lower bound of interval e.g [4,10] you must insert 4
    
    b - upper bound of interval e.g [4,10] you must insert 10
  - toString
```
public java.lang.String toString(boolean dec)
                          throws KingfisherExc
```
    toString() method of a rational function
    
    Parameters:
    
    dec - If this boolean value is true, the method writes the function such as a ratio of two decomposed polynomials
    
    Returns:
    
    String to explain the function
    
    Throws:
    
    KingfisherExc
  - monic_denominator
```
public Rational monic_denominator()
```
    Make denominator as monic polynomial
    
    Returns:
    
    the modified rational function
  - horizontal_asymptotes
```
public java.lang.String horizontal_asymptotes()
```
    Determine horizontal asymptotes
    
    Returns:
    
    horizontal asymptotes
  - vertical_asymptotes
```
public java.lang.String vertical_asymptotes()
```
    Determine vertical asymptotes
    
    Returns:
    
    vertical asymptotes
  - oblique_asymptotes
```
public java.lang.String oblique_asymptotes()
```
    Determine oblique asymptotes
    
    Returns:
    
    oblique asymptotes
  - integration_constants
```
public double[] integration_constants()
                               throws KingfisherExc
```
    Calculate constants of different partial fractions
    
    Returns:
    
    real vector with the constants of different partial fractions
    
    Throws:
    
    KingfisherExc
  - min_max
```
public java.lang.String min_max()
```
    Find min, max points of this Rational function
    
    Returns:
    
    Description of different stationary points
  - toString
```
public java.lang.String toString()
```
    toString() method of rational function: It makes one-line String to explain the function
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    String to explain the function
  - getNum
```
public double[] getNum()
```
    Get numerator
    
    Returns:
    
    numerator
  - getDen
```
public double[] getDen()
```
    Get denominator
    
    Returns:
    
    denominator
  - getOutOfDomain
```
public double[] getOutOfDomain()
```
    Get out of domain points
    
    Returns:
    
    out of domain points
  - features
```
public java.lang.String features()
```
    See the features of this Rational function
  - setOutOfDomain
```
public void setOutOfDomain(double[] out_of_domain)
```
    Set out of domain points
    
    Parameters:
    
    out_of_domain -

Class Rational

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Rational

Rational

Rational

Rational

Method Detail

integral

integral

simplify

simplify_num

simplify_den

der

axes_intersection_points

value

domain

roots

roots_multiset

sum

difference

product

reciprocal

ps

toPlot

plot

toString

monic_denominator

horizontal_asymptotes

vertical_asymptotes

oblique_asymptotes

integration_constants

min_max

toString

getNum

getDen

getOutOfDomain

features

setOutOfDomain