Horner's Algorithm

#This program will take a polynomial written in standard form and 

#determine the coefficients of the Taylor series expansion of the polynomial 

#evaluated at some center, c. 

#Variable Initialization

#Retrieve polynomial degree from user

n = int(input("Poly. Degree:"))

#Initialize list to store coefficient values and polynomial terms

coeff = [0 for x in range(n+1)]

poly = [0 for x in range(n+1)]

Tay_coeff = [0 for x in range(n+1)]

Tay_poly = [0 for x in range(n+1)]

print("Please enter poly. coefficients:")

#Populate coefficient array with user input

correct = False

while correct == False:

    for i in range(0,n+1):

        coeff[i] = input("Degree {0} coeff: ".format(i))

        coeff[i] = float(coeff[i])

        #Poly list created to store polynomial terms

        poly[i]= str(coeff[i]) + "x^{0}".format(i)

        if i < n:

            poly[i] += " +"

    print("Entered Polynomial: ", *poly)

    correct = bool(input("Is this the polynomial you owuld like to expand?"))

#Request point for Taylor Series Expansion

c = float(input("c = "))

#Begin implementation of complete Horner's Algorithm.

Tay_coeff = coeff

print("**")

print(Tay_coeff)

print(coeff)

for k in range(0,n):

    for j in range(n-1,k-1,-1):

        Tay_coeff[j]=Tay_coeff[j] + (c * Tay_coeff[j+1])

for i in range(0,n+1):

        Tay_poly[i]= str(Tay_coeff[i]) + "(x-{0})^{1}".format(c,i)

        if i < n:

            Tay_poly[i] += " +"     

print(*Tay_poly)