Question

The code should be written with python.

Question 1: Computing Polynomials [35 marks A polynomial is a mathematical expression that can be built using constants and variables by means of addition, multiplication and exponentiation to a non-negative integer power. While there can be complex polynomials with multiple variable, in this exercise we limit out scope to polynomials with a single variable. The variable of a polynomial can be substituted by any values and the mapping that is associated with the result of substitution is a function called a polynomial function. A polynomial function P(x) in a single variable x takes the following general form: P(x) = anx" + an-1x-1 + ... + a2x2 + ax + ao where ao, a, ..., an are the constants and x is the variable. The degree of a polynomial is the largest degree of any one term with non-zero coefficient. Example: Q(x) = 2x3 + x2 - 9x + 3 Q is a third-degree polynomial function. We can substitute the variable x with an arbitrary value to compute the value of Q for the arbitrary value. For example, Q(2) = 2 * 23 + 22 – 9+ 2 + 3 = 5

Answer 1

Please find the required python3 script that can handle both list and tuples (respective examples are given for both):

Note: Please mind the text indentation in function and for loop blocks!! An image of the same is being provided for help!

#=====================================================

def calc_poly(const_seq,var_poly):

   const_seq = list(const_seq); # To list conversion

   poly_val = 0; # Initializing summation variable

   for i in range(len(const_seq)):

      poly_val=poly_val + const_seq[i]*(var_poly**i); # Performing polynomial sum

   poly_val = round(poly_val,2); # Rounding upto 2 fractional digits

   return poly_val;

#========= Driver Program =========

const_seq = [3,-9,1,2]; # List version

var_poly = 2.3478;

print('Polynomial Value by list =',calc_poly(const_seq,var_poly));

const_seq = (3,-9,1,2); # Tuple version

var_poly = 2.3478;

print('Polynomial Value by tuple =',calc_poly(const_seq,var_poly));

#==================================================

Code image with proper indentation:

def calc poly(const_seq, var_poly): const_seq = list(const seq); # To list conversion poly_val = 0; # Initializing summation variable for i in range(len(const_seq)): poly_val=polyval + const_seq[i]*(var_poly**i); # Performing polynomial sum poly val = round(poly_val,2); # Rounding upto 2 fractional digits return poly_val; #========= Driver Program ======= const_seq = (3,-9,1,2]; # List version var_poly = 2.3478; print('Polynomial Value by list =',calc_poly(const_seq, var_poly)); const_seq = (3,-9,1,2); # Tuple version var_poly = 2.3478; print("Polynomial Value by tuple =',calc_poly(const_seq, var_poly));

Output:

Polynomial Value by list = 13.26 Polynomial Value by tuple = 13.26

Hope this helps!

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Answer 2

(a) What is the mathematical expression of the polynomial model if there is a single input variable X and one output variable Y?