hw2

Class RatPoly

java.lang.Object

hw2.RatPoly

public final class RatPoly
extends java.lang.Object

RatPoly represents an immutable single-variate polynomial expression. RatPolys are sums of RatTerms with non-negative exponents.

Examples of RatPolys include "0", "x-10", and "x^3-2*x^2+5/3*x+3", and "NaN".

Field Summary

Fields

Modifier and Type	Field and Description
static RatPoly	NaN A constant holding a Not-a-Number (NaN) value of type RatPoly
static RatPoly	ZERO A constant holding a zero value of type RatPoly

Constructor Summary

Constructors

Constructor and Description
RatPoly()
RatPoly(int c, int e)
RatPoly(RatTerm rt)

Method Summary

Modifier and Type	Method and Description
RatPoly	add(RatPoly p) Addition operation.
RatPoly	antiDifferentiate(RatNum integrationConstant) Returns the antiderivative of this RatPoly.
int	degree() Returns the degree of this RatPoly.
RatPoly	differentiate() Return the derivative of this RatPoly.
RatPoly	div(RatPoly p) Truncating division operation.
boolean	equals(java.lang.Object obj) Standard equality operation.
double	eval(double d) Returns the value of this RatPoly, evaluated at d.
RatTerm	getTerm(int deg) Gets the RatTerm associated with degree 'deg'
int	hashCode() Standard hashCode function.
double	integrate(double lowerBound, double upperBound) Returns the integral of this RatPoly, integrated from lowerBound to upperBound.
boolean	isNaN() Returns true if this RatPoly is not-a-number.
RatPoly	mul(RatPoly p) Multiplication operation.
RatPoly	negate() Return the additive inverse of this RatPoly.
RatPoly	sub(RatPoly p) Subtraction operation.
java.lang.String	toString() Returns a string representation of this RatPoly.
static RatPoly	valueOf(java.lang.String polyStr) Builds a new RatPoly, given a descriptive String.

Methods inherited from class java.lang.Object

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

Field Detail

NaN

public static final RatPoly NaN

A constant holding a Not-a-Number (NaN) value of type RatPoly

ZERO

public static final RatPoly ZERO

A constant holding a zero value of type RatPoly

Constructor Detail

RatPoly

public RatPoly()

Effects:

Constructs a new Poly, "0".

RatPoly

public RatPoly(RatTerm rt)

Parameters:

rt - the single term which the new RatPoly equals

Effects:

Constructs a new Poly equal to "rt". If rt.isZero(), constructs a "0" polynomial.

Requires:

{@code rt.getExpt() >= 0}

RatPoly

public RatPoly(int c,
               int e)

Parameters:

c - the constant in the term which the new RatPoly equals

e - the exponent in the term which the new RatPoly equals

Effects:

Constructs a new Poly equal to "c*x^e". If c is zero, constructs a "0" polynomial.

Requires:

{@code e >= 0}

Method Detail

degree

public int degree()

Returns the degree of this RatPoly.

Returns:

the largest exponent with a non-zero coefficient, or 0 if this is "0"

Requires:

!this.isNaN()

getTerm

public RatTerm getTerm(int deg)

Gets the RatTerm associated with degree 'deg'

Parameters:

deg - the degree for which to find the corresponding RatTerm

Returns:

the RatTerm of degree 'deg'. If there is no term of degree 'deg' in this poly, then returns the zero RatTerm.

Requires:

!this.isNaN()

isNaN

public boolean isNaN()

Returns true if this RatPoly is not-a-number.

Returns:

true if and only if this has some coefficient = "NaN"

negate

public RatPoly negate()

Return the additive inverse of this RatPoly.

Returns:

a RatPoly equal to "0 - this"; if this.isNaN(), returns some r such that r.isNaN()

add

public RatPoly add(RatPoly p)

Addition operation.

Parameters:

p - the other value to be added

Returns:

a RatPoly, r, such that r = "this + p"; if this.isNaN() or p.isNaN(), returns some r such that r.isNaN()

Requires:

p != null

sub

public RatPoly sub(RatPoly p)

Subtraction operation.

Parameters:

p - the value to be subtracted

Returns:

a RatPoly, r, such that r = "this - p"; if this.isNaN() or p.isNaN(), returns some r such that r.isNaN()

Requires:

p != null

mul

public RatPoly mul(RatPoly p)

Multiplication operation.

Parameters:

p - the other value to be multiplied

Returns:

a RatPoly, r, such that r = "this * p"; if this.isNaN() or p.isNaN(), returns some r such that r.isNaN()

Requires:

p != null

div

public RatPoly div(RatPoly p)

Truncating division operation.

Truncating division gives the number of whole times that the divisor is contained within the dividend. That is, truncating division disregards or discards the remainder. Over the integers, truncating division is sometimes called integer division; for example, 10/3=3, 15/2=7.

Here is a formal way to define truncating division: u/v = q, if there exists some r such that:

• u = q * v + r
  
• The degree of r is strictly less than the degree of v.
• The degree of q is no greater than the degree of u.
• r and q have no negative exponents.

q is called the "quotient" and is the result of truncating division. r is called the "remainder" and is discarded.

Here are examples of truncating division:

• "x^3-2*x+3" / "3*x^2" = "1/3*x" (with r = "-2*x+3")
• "x^2+2*x+15 / 2*x^3" = "0" (with r = "x^2+2*x+15")
• "x^3+x-1 / x+1 = x^2-x+2 (with r = "-3")

Parameters:

p - the divisor

Returns:

the resurt of truncating division, this / p. If p = 0 or this.isNaN() or p.isNaN(), returns some q such that q.isNaN().

Requires:

p != null

differentiate

public RatPoly differentiate()

Return the derivative of this RatPoly.

Returns:

a RatPoly, q, such that q = dy/dx, where this == y. In other words, q is the derivative of this. If this.isNaN(), then return some q such that q.isNaN().

The derivative of a polynomial is the sum of the derivative of each term.

antiDifferentiate

public RatPoly antiDifferentiate(RatNum integrationConstant)

Returns the antiderivative of this RatPoly.

Parameters:

integrationConstant - the constant of integration to use when computating the antiderivative

Returns:

a RatPoly, q, such that dq/dx = this and the constant of integration is "integrationConstant" In other words, q is the antiderivative of this. If this.isNaN() or integrationConstant.isNaN(), then return some q such that q.isNaN().

The antiderivative of a polynomial is the sum of the antiderivative of each term plus some constant.

Requires:

integrationConstant != null

integrate

public double integrate(double lowerBound,
                        double upperBound)

Returns the integral of this RatPoly, integrated from lowerBound to upperBound.

The Fundamental Theorem of Calculus states that the definite integral of f(x) with bounds a to b is F(b) - F(a) where dF/dx = f(x) NOTE: Remember that the lowerBound can be higher than the upperBound.

Parameters:

lowerBound - the lower bound of integration

upperBound - the upper bound of integration

Returns:

a double that is the definite integral of this with bounds of integration between lowerBound and upperBound. If this.isNaN(), or either lowerBound or upperBound is Double.NaN, return Double.NaN.

eval

public double eval(double d)

Returns the value of this RatPoly, evaluated at d.

Parameters:

d - the value at which to evaluate this polynomial

Returns:

the value of this polynomial when evaluated at 'd'. For example, "x+2" evaluated at 3 is 5, and "x^2-x" evaluated at 3 is 6. If (this.isNaN() == true), return Double.NaN.

toString

public java.lang.String toString()

Returns a string representation of this RatPoly. Valid example outputs include "x^17-3/2*x^2+1", "-x+1", "-1/2", and "0".

Overrides:

toString in class java.lang.Object

Returns:

a String representation of the expression represented by this, with the terms sorted in order of degree from highest to lowest.

There is no whitespace in the returned string.

If the polynomial is itself zero, the returned string will just be "0".

If this.isNaN(), then the returned string will be just "NaN".

The string for a non-zero, non-NaN poly is in the form "(-)T(+|-)T(+|-)...", where "(-)" refers to a possible minus sign, if needed, and "(+|-)" refers to either a plus or minus sign. For each term, T takes the form "C*x^E" or "C*x" where C > 0, UNLESS: (1) the exponent E is zero, in which case T takes the form "C", or (2) the coefficient C is one, in which case T takes the form "x^E" or "x". In cases were both (1) and (2) apply, (1) is used.

valueOf

public static RatPoly valueOf(java.lang.String polyStr)

Builds a new RatPoly, given a descriptive String.

Parameters:

polyStr - a string of the format described in the @spec.requires clause.

Returns:

a RatPoly p such that p.toString() = polyStr

Requires:

'polyStr' is an instance of a string with no spaces that expresses a poly in the form defined in the toString() method.

Valid inputs include "0", "x-10", and "x^3-2*x^2+5/3*x+3", and "NaN".

hashCode

public int hashCode()

Standard hashCode function.

Overrides:

hashCode in class java.lang.Object

Returns:

an int that all objects equal to this will also return

equals

public boolean equals(java.lang.Object obj)

Standard equality operation.

Overrides:

equals in class java.lang.Object

Parameters:

obj - the object to be compared for equality

Returns:

true if and only if 'obj' is an instance of a RatPoly and 'this' and 'obj' represent the same rational polynomial. Note that all NaN RatPolys are equal.