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#ifndef POLYNOMIAL$\_$H

#define POLYNOMIAL$\_$H

#include

#include

#include

#include "term.h$"$

class Polynomial $\{$

public:

$/**$

$*$ Create a bad$/$invalid polynomial of degree $-1.$

$*$ Arithmetic operations are not permitted on this bad value

$*$ and may cause a program to crash. Nonetheless, this value

$*$ is useful as a way of signalling invalid results. $*/$

Polynomial$()$;

$/**$

$*$ Create a polynomial representing a linear or constant formula ax $+$ b$.$

$*/$

Polynomial $($int b$,$ int a $=0)$;

$/**$

$*$ Create a polynomial containing a collections of terms.

$*$ @param terms a set of terms

$*/$

Polynomial $($std::initializer$\_$list terms$)$;

$/**$

$*$ Create a polynomial with the given coefficients.

$*$ E$.$g$.,$

$*$ double c$[]=\{1,2,3\}$;

$*$ Polynomial p $(3,$ c$)$;

$*$ creates a polynomial p representing: $1+2*$x $+3*$x$^2$

$*$

$*$ @param nCoeff number of coefficients in the input array

$*$ @param coeff the coefficients of the new polynomial, starting

$*$ with power $0.$

$*/$

Polynomial $($int nCoeff, int coeff$[])$;

$/**$

$*$ Get the coefficient of the term with the indicated power.

$*$ @param power the power of a term

$*$ @return the corresponding coefficient, or zero if power $<0$ or if

$*$ power $>$ getDegree$()$

$*/$

int getCoeff$($int power$)$ const;

$/**$

$*$ The degree of a polynomial is the largest exponent of x with a

$*$ non$-$zero coefficient. E$.$g$.,$

$*$ x$^3+2$x $+1$ has degree $3$

$*42$ has degree $0(42==42*$ x$^0)$

$*0$ is a special case and is regarded as degree $-1$

$*$

$*$ @return the degree of this polynomial

$*/$

int getDegree$()$ const;

$/**$

$*$ Add a polynomial to this one, returning their sum.

$*$

$*$ @param p another polynomial

$*$ @return the sum of the two polynomials

$*/$

Polynomial operator$+($const Polynomial& p$)$ const;

$/**$

$*$ Multiply this polynomial by a scalar.

$*$ @param scale the value by which to multiply each term in this polynomial

$*$ @return the polynomial resulting from this multiplication

$*/$

Polynomial operator$*($int scale$)$ const;

$/**$

$*$ Multiply this polynomial by a Term.

$*$ @param Term the value by which to multiply each term in this polynomial

$*$ @return the polynomial resulting from this multiplication

$*/$

Polynomial operator$*($Term term$)$ const;

$/**$

$*$ Multiply this polynomial by a scalar, altering this polynomial.

$*$ @param scale the value by which to multiply each term in this polynomial

$*/$

void operator$*=($int scale$)$;

$/**$

$*$ Divide one polynomial by another, if possible.

$*$

$*$ @param p the demoninator, the polynomial being divided into this one

$*$ @return the polynomial resulting from this division or the bad

$*$ value Polynomial$()$ if p cannot be divided into this polynomial

$*$ to get a quotient polynomial with integer coefficients and no remainder.

$*/$

Polynomial operator$/($const Polynomial& p$)$ const;

$/**$

$*$ Compare this polynomial for equality against another.

$*$

$*$ @param p another polynomial

$*$ @return true iff the polynomials have the same degree and their corresponding

$*$ coefficients are equal.

$*/$

bool operator$==($const Polynomial& p$)$ const;

private:

$/**$

$*$ @brief The degree of the polynomial.

$*$

$*$ This is the largest power of x having a non$-$zero coefficient, or

$*$ zero if the polynomial has all zero coefficients.$)$ Note that

$*$ adding polynomials together or scaling polynomials $($multiplying by

$*$ a constant$)$ could reduce the degree of the result.

$*$

$*/$

int degree;

ddd$/**$

$*$ List of terms, in ascending order of power.

$*$ Terms with zero coefficients are dropped.

$*$ An empty list of degree $0$ is the polynomial: $0.$

$*/$

std::list terms;

$//$ For example, the polynomial x$^2+2$x $-1$ would have:

$//$ degree: $2$

$//$ terms: $\{$Term$(-1,0),$ Term$(2,1),$ Term$(1,2)\}$

$//$

$//$ The polynomial $4$x$^2-12$ would have:

$//$ degree: $2$

$//$ terms: $\{$Term$(-12,0),$ Term$(4,2)\}$

$//$

$//$ The polynomial $42$ would have:

$//$ degree: $0$

$//$ terms: $\{$Term$(42,0)\}$

$//$

$//$ The polynomial $0$ would have:

$//$ degree: $0$

$//$ terms: $\{\}$

$//$

$//$ A special "bad" value used to signal an unsuccessful operations is

$//$ degree: $-1$

$//$ terms: $\{\}$

$**$

$*$ A utility function to scan the current polynomial, putting it into

$*$ "normal form". In this case, the normal form will drop all terms with

$*$ zero coefficients, adjusting the degree as necessary.

$*$

$*$ Polynomials should be kept in normal form at all times outside of the

$*$ actual member function bodies of this class.

$*/$

void normalize$()$;

$//$ A "friend" declaration means that the following function or class will

$//$ have access to this class's private data members, just as if it were a

$//$ member function of this class.

friend std::ostream& operator$<<($std::ostream&$,$ const Polynomial&$)$;

$/**$

$*$ Note: a member function of the Polynomial class must have a polynomial

$*$as the first argument $($e$.$g$.,$ poly.operator$*($x$)<==>$ poly$*$x$).$ These

$*$function simply allows for the multiplication to be written with the polynomial on the right.

$*$@param the value to multiply the polynomial by

$*$@param p a polynomial

$*$@return the product of scale and p

$*/$

inline

Polynomial operator$*($int by$,$ const Polynomial& p$)$

$\{$return p $*$ by;$\}$

inline

bool operator!$=($const Polynomial& p$,$ const Polynomial& q$)$

$\{$

return $!($p$==$q$)$;

$\}$

#endif