calculator
Class RatPoly

java.lang.Object
  calculator.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

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

RatPoly()

RatPoly(int c, int e)

RatPoly(RatTerm rt)

Method Summary

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) Division operation (truncating).
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

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)

Effects:

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

Requires:

rt.getExpt() >= 0

RatPoly

public RatPoly(int c,
               int e)

Effects:

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

Requires:

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'

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.

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.

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.

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)

Division operation (truncating).

Returns:

a RatPoly, q, such that q = "this / p"; if p = 0 or this.isNaN() or p.isNaN(), returns some q such that q.isNaN()

Division of polynomials is defined as follows: Given two polynomials u and v, with v != "0", we can divide u by v to obtain a quotient polynomial q and a remainder polynomial r satisfying the condition u = "q * v + r", where the degree of r is strictly less than the degree of v, the degree of q is no greater than the degree of u, and r and q have no negative exponents.

For the purposes of this class, the operation "u / v" returns q as defined above.

The following are examples of div's behavior: "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").

Note that this truncating behavior is similar to the behavior of integer division on computers.

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.

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.

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.

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.

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 "(+|-)" refer to either a plus or minus sign, as needed. 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.

Valid example outputs include "x^17-3/2*x^2+1", "-x+1", "-1/2", and "0".

valueOf

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

Builds a new RatPoly, given a descriptive String.

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

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.