This project will require you to create a program that will take a mathematical expression in a single variable $($x$)$ and either

evaluate the expression for a given value of x$,$ or

calculate the derivative $($with respect to x$)$ of the expression

The purpose of this project is to demonstrate a working knowledge of

Class creation

Inheritance

Polymorphism

You will need the following sub$-$classes of AbstractTerm:

A ConstantTerm object will represent a term of the form

$\backslash$pm a

where a is of type int. The derivative of a constant term is always

$+0$

A LinearTerm object will represent a term of the form

$\backslash$pm ax

where a is of type int and x is the independent variable. The derivative of a linear term is a constant term of the form

$\backslash$pm a

A PolynomialTerm object will represent a term of the form

$\backslash$pm ax$^$b

where a is of type int, b is a positive int greater than one, and x is the independent variable. If b$>2,$ the derivative of the polynomial term is a polynomial term of the form

$\backslash$pm $($ab$)$x$^($b$-1)$

If b$=2,$ the derivative of the polynomial term is a linear term of the form

$\backslash$pm $2$ax

A TrigTerm object will represent a term of the form

$\backslash$pm a cos$($x$)$

or

$\backslash$pm a sin$($x$)$

where a is of type int and x is the independent variable. The derivative of the sine term is a trigonometric term of the form

$\backslash$pm a cos$($x$)$

The derivative of the cosine term is a sine term of the form

$$a sin$($x$)$

Note that the sign flips when taking the derivative of cos$().$ Evaluation of trigonometric functions should be done in degrees.

Each subclass of AbstractTerm will need to override the following pure virtual functions:

derivative$()-$ returns a new AbstractTerm that represents the derivative of the current term

evaluate$($double$)-$ returns the evaluation of the term with the double value substituted for x

toString$()-$ returns a string representation of the term $($see below for examples$)$

TrigType Enumeration

The TrigType enumeration should have two values used to distinguish between the trigonometric functions:

COSINE

SINE

Expression class

The Expression class will need to contain an array or vector of AbstractTerms. It will also need the following functions:

getDerivative$()-$ returns a new Expression object containing the derivative of each term of the original object. Zero$-$valued constant terms should not be included.

getEvaluation$($double$)-$ returns the sum of the evaluations of the individual terms.

toString$()-$ returns a string version of the expression. The polynomial terms should be displayed in descending exponential order, followed by linear, constant, sine$,$ and cosine

An overloaded $+=$ operator that will add an AbstractTerm to the expression

A destructor that will delete all of the terms in the expression

main$()$

The main$()$ function will not be tested. Use it for your own tests.

EXAMPLE

AbstractTerm$*$ t$1=$ new LinearTerm$(5)$;

AbstractTerm$*$ t$2=$ new PolynomialTerm$(-4,3)$;

AbstractTerm$*$ t$3=$ new TrigTerm$(-6,$ TrigType::COSINE$)$;

cout $$ t$1->$toString$()$ endl; $//+5$x

cout $$ t$1->$evaluate$(5)$ endl; $//25$

cout $$ t$2->$toString$()$ endl; $//-4$x$^3$

cout $$ t$2->$evaluate$(2)$ endl; $//-32$

cout $$ t$3->$toString$()$ endl; $//-6$cos$($x$)$

cout $$ t$3->$evaluate$(45)$ endl; $//-4\mathrm{.}24$

Expression$*$ e$1=$ new Expression$()$;

$(*$e$1)+=$ t$1$;

$(*$e$1)+=$ t$2$;

$(*$e$1)+=$ t$3$;

Expression$*$ e$2=$ e$1->$getDerivative$()$;

cout $$ e$1->$toString$()$ endl; $//-4$x$^3+5$x $-6$cos$($x$)$

cout $$ e$2->$toString$()$ endl; $//-12$x$^2+5+6$sin$($x$)$

cout $$ e$1->$getEvaluation$(0)$ endl; $//-6$

cout $$ e$2->$getEvaluation$(0)$ endl; $//5$

delete e$2$;

delete e$1$;