Описать класс "полином" - Для чего нужен конструктор по умолчанию?

#include <iostream>
#include "conio.h"
#include <algorithm>
#include "math.h"
class Polynom {
int n;
double *koef;
public:
Polynom(); //конструкторы
Polynom(int k);
Polynom(int k,double *mas);
Polynom(const Polynom&ob); //конструктор копирования
~Polynom(){delete[]koef;}
void GiveMemory(int k);
void SetPolynom(int k,double *mas);
void SetDegree(int k){n=k;}; //установить степень
void CalculateValue(double x); //вычислить значение
int GetDegree(){return n;}; //получить степень
double GetOneCoefficient(int i){return(koef[i]);};
Polynom operator+(Polynom ob); //перегрузка операторов
Polynom operator*(Polynom ob);
double& operator[](int i){return(koef[i]);}//перегрузка []
Polynom& operator= (const Polynom p) {
if(&p==this) return *this;
if(koef) delete [] koef;
n=p.n;
koef=new double [p.n+1];
for(int i=0;i<=p.n;i++)
koef[i]=p.koef[i];
return *this;
}
friend std::ostream& operator<<(std::ostream& mystream,Polynom &ob);
friend std::istream& operator>>(std::istream& mystream,Polynom &ob);
int min(int n,int m)
{return (n<m)? n:m; }
int max(int n,int m)
{return (n>m)? n:m; }
};
//*********** Polynom() **********************************
Polynom::Polynom()
{
n=rand();
koef=new double[n+1];
if(!koef){std::cout<<"Error";getch();return;}
for(int i=n;i>=0;i--)
koef[i]=rand()-5;
}
//************* Polynom(int k) *******************************
Polynom::Polynom(int k)
{ n=k;
koef=new double[n+1];
if(!koef){std::cout<<"Error";getch();return;}
for(int i=n;i>=0;i--)
koef[i]=rand()-5;
}
//****************** Polynom(int k,double mas[]) ******************
Polynom::Polynom(int k,double mas[])
{n=k;
koef=new double[n+1];
if(!koef){std::cout<<"Error";getch();return;}
for(int i=n;i>=0;i--)
koef[i]=mas[i];
}
//*************** Polynom(const Polynom&ob) *********************
Polynom::Polynom(const Polynom&ob)
{n=ob.n;
koef=new double[n+1];
if(!koef){std::cout<<"Error";getch();return;}
for(int i=0;i<=n;i++)
koef[i]=ob.koef[i];
}
//**************** void GiveMemory(int k) **********************
void Polynom::GiveMemory(int k)
{
if(koef) delete [] koef;
koef=new double[k+1];
if(!koef){std::cout<<"Error";getch();return;}
}
//******************** SetPolynom **************************
void Polynom::SetPolynom(int k,double *mas)
{ n=k;
if(koef) delete [] koef;
koef = new double [n+1];
for(int i=n;i>=0;i--)
koef[i]=mas[i];
}
//*************** CalculateValue *****************************
void Polynom::CalculateValue(double x=1.0)
{ double s;
int i;
for(s=koef[0],i=1;i<=n;i++)
s=s+koef[i]*pow(x,i);
std::cout<<"f("<<x<<")="; std::cout<<s<<std::endl;
}
//**************** Polynom operator+(Polynom ob) ***************
Polynom Polynom::operator+(Polynom ob)
{ int i;
Polynom rab;
rab.GiveMemory(max(n,ob.GetDegree() ));
for(i=0;i<=min(n,ob.GetDegree());i++)
rab.koef[i]=koef[i]+ob.GetOneCoefficient(i);
if(n<ob.GetDegree())
{
for(i=min(n,ob.GetDegree())+1;i<=ob .GetDegree();i++)
rab.koef[i]=ob.GetOneCoefficient(i);
rab.n=ob.GetDegree();
}
else
{
for(i=min(n,ob.GetDegree())+1;i<=n; i++) rab.koef[i]=koef[i];
rab.n=n;
}
return rab;
}
//*************** Polynom operator*(Polynom ob) ***************
Polynom Polynom::operator*(Polynom ob)
{
int i,j,k;
double s;
Polynom rab;
rab.GiveMemory(n+ob.GetDegree());
for(i=0;i<=n+ob.GetDegree();i++)
{ s=0;
for(j=0;j<=n;j++)
for(k=0;k<=ob.GetDegree();k++)
if(j+k==i)s=s+koef[j]*ob.GetOneCoefficient(k);
rab.koef[i]=s;
}
rab.n=n+ob.GetDegree();
return rab;
}
//********** ostream& operator<<(ostream& mystream,Polynom &ob) ******
std::ostream& operator<<(std::ostream& mystream,Polynom &ob)
{ char c=' '; //пропустим “+” перед первым коэффициентом
for(int i=ob.n;i>=0;i--)
{ double ai=ob.koef[i];
if(ai==0) continue;
else {if(ai>0) mystream<<c; mystream<<ai;}
if(i==0) continue; else mystream<<"x";
if(i==1) continue; else mystream<<"^"<<i;
if(ai!=0)c='+';
}
if(c==' ')mystream<<0;
mystream<<std::endl;
return mystream;
}
//********* istream& operator>>(istream& mystream,Polynom &ob) *
std::istream& operator>>(std::istream& mystream,Polynom &ob)
{
int i;
std::cout<<"Enter Degree:"; mystream>>ob.n; std::cout<<std::endl;
for(i=ob.n;i>=0;i--)
{
std::cout<<"Enter koeff "<<i<<":"; mystream>>ob.koef[i];
}
return mystream;
}
 
//******************** MAIN ****************************
using namespace std;
int main(int argc, char* argv[])
{ 
    const int m=3;
Polynom f,g,masp[m],*p1,s;
int n=5,i;
double K[6]={1.0,3.2,0.0,4.1,0.0,1.1};
p1=new Polynom(n,K);
cout<<*p1;
p1->CalculateValue(2.0);
cin>>f;
cout<<" f(x)= "; cout<<f;
cout<<" g(x)= "; cout<<g;
s=f+g;
cout<<"f(x)+g(x) = "; cout<<s;
s=f*g;
cout<<" f(x)*g(x) = "; cout<<s;
s=masp[0]; cout<<masp[0];
for(i=1;i<m;i++)
{ s=s+masp[i]; cout<<masp[i];}
cout<<"Summa: "; cout<< s;
delete p1;
return 0;
}