This project is meant to be yet another practice for library creation.
You should create a class HunPolynomial. It should be submitted in two files: HunPolynomial.h and HunPolynomial.cpp. This class represents polynomials with integer coefficients and a single variable x and positive integer exponents. The examples of such polynomials are
5*x^3 – 12*x – 1
– 34*x^2 + x
Pay attention to how we print polynomials above:
we separate + and – signs with spaces unless polynomial starts with the – sign. If polynomial starts with the – sign, that sign doesn't have leading space. Polynomial cannot start with the + sign.
"power of" is denoted by ^ symbol.
multiplication is denoted by * and is never omitted.
multiplication symbol * doesn't have spaces to the left or to the right.
variable name is always lower-case x.
terms with the coefficient of 0 aren't printed
terms with a coefficient of 1 or -1 are printed without the coefficient unless it's a constant term (the rightmost term with no variable).
+ and – never follow each other.
You must use this format when printing polynomials.
We will represent polynomials using vectors of int. Each element of the vector corresponds to a polynomial coefficient. The element with index 0 corresponds to the most significant term. Coefficient with the value 0 are stored in vector (even though they are not printed). For example,
5*x^3 – 12*x – 1 => std::vector<int>{5, 0, -12, -1}
– 34*x^2 + x => std::vector<int>{-34, 0, 1, 0}
You must implement a decent program structure and decent programming style.
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Class HunPolymonial has the following public methods:
Default constructor that constructs an empty polynomial
Parametrized constructor that takes a vector of integers and initializes polynomial according to the polynomial representation rules above.
Method Set that takes a vector of integers that represents a polynomial and sets polynomial to that value.
Operator +. It uses standard polynomial addition rules.
Operator –. It uses standard polynomial subtraction rules.
Operator *. It uses standard polynomial multiplication rules.
Operator << that allows printing. Printing should happen according to the printing rules discussed above. Attention, operator<< won't be a class member. Writing such operator is discussed in our textbook in C++ Interlude 6, section 2 (page 441). In general, C++ Interlude 6 (page 435) discusses overloading operators for your class.
Operator () that takes a float x0 and returns a float value of polynomial in point x0 . Ignore a possibility of overflows.
