def solve(self,U,V,method):

if(method=="newton"):

return (self.Newton(U,V))

else:

return (self.Lagrange(U,V))

def pattern(self,cofficient):

l=len(cofficient);

temp=[];

for i in range(l-1):

temp.append(str(cofficient[l-(i+1)])+'x^'+str(l-(i+1))+str('+'))

temp.append(str(cofficient[0])+'x^'+str(0));

str1=''.join(temp)

return(str1)

def Lagrange(self,U,V):

n=len(U)

w=(-1*U[0],1)

for i in range(1,n):

w=P.polymul(w,(-1*U[i],1))

result=array([0.0 for i in range(len(w)-1)])

derivative=P.polyder(w)

for i in range(n):

result+=(P.polydiv(w,(-1*U[i],1))[0]*V[i])/P.polyval(U[i],derivative)

temp=list(result);

cofficient=temp

l=len(cofficient);

temp=[];

for i in range(l-1):

temp.append(str(cofficient[l-(i+1)])+'x^'+str(l-(i+1))+str('+'))

temp.append(str(cofficient[0])+'x^'+str(0));

str1=''.join(temp)

return(str1)

def plot(self,U,V,ctr):

X1=arange(min(U)-2,max(U)+2,0.1)

x=[1]

for i in range(len(U)):

x=P.polymul(x,[-1*U[i],1])

plt.axis([-10,10,min(V)-1,max(V)+1])

b=[0]

for i in range(len(U)):

a=P.polydiv(x,[-1*U[i],1])

b=P.polyadd(P.polymul((P.polydiv(a[0],P.polyval(U[i],a[0])))[0],[V[i]]),b)

Y=P.polyval(X1,P.polymul((P.polydiv(a[0],P.polyval(U[i],a[0])))[0],[V[i]]))

plt.plot(X1,Y,'y')

plt.plot(U,V,'ro')

X1=arange(-5,5,0.1)

Y=P.polyval(X1,b)

plt.plot(X1,Y,'b',label='Required Polynomial')

plt.plot((-8,8),(0,0),'k')

plt.grid(b=True, which='both', color='0.65',linestyle='-')

Y=list(Y)

plt.plot((0,0),(-max(Y)-5,max(Y)+5),'k')

plt.xlabel('x-axis')

plt.ylabel('y-axis')

plt.legend(loc=1)

filename = "this_plot"+str(ctr)+".png"

path = "C:\\Users\HP\Anaconda3\static"

fullpath = os.path.join(path, filename)