Description
Write a Python program to implement the New User Registration:
i. Prompt the user, who is doing registration, for entering a username and check its validity.
ii. A valid username must be a string of length 8-12 and consists of:
– at least 3 and at most 8 letters (a-z, A-Z)
– at least 2 and at most 6 digits (0-9)
– at most 1 underscore (_)
iii. Prompt the user for entering a password and check its validity.
iv. A valid password must be a string of length 10-16 and consist of:
– at least one lowercase letter (a-z)
– at least one uppercase letter (A-Z)
– at least one digit (0-9)
– at least one special character (@, #, %, &, $)
v. If the username or password is not valid, inform the user of the specific requirements it does not fulfill (e.g., “A valid password must contain 10-16 characters”, “A valid username must consist of at most 6 digits (0-9)”).
vi. Prompt again and again until a valid username and a valid password are entered.
![(1) Write a function which takes a list of the coefficients of a polynomial P(x) = a0 + a1x + a2x^2 + ... + anx^n of arbitrary degree n, and a value of x0, and returns P(x0). You can use the function given in lectures, ensuring you understand how it works. (2) Use the function to evaluate (a) P1(x) = 4x^4 + 3x^2 + 2 at x = 2. (b) P2(x) = 241x^4 at x = 2. Are these answers exact? Explain why or why not. (Use a print statement to show the evaluation of your function, and answer the question in a comment.) (3) The power series for the sine function sin(x) is given by sin(x) = Σ (1)^n * (2n+1)! * x^(2n+1) = x - x^3/3! + x^5/5! - x^7/7! + ..., for all x. Use the first four terms in this series in the Horner evaluation function at a suitable value of x to give an approximation of sin(π/4). (4) (a) Use your Horner's method function to evaluate the polynomial (x-1)^3 at the point x = 1.000001. (b) Is this answer correct? (c) Briefly explain why or why not. (5) In week 3 we wrote a function to convert from binary to decimal. This can be adapted to other bases; here we will explore octal (base 8). The efficiency of the function we wrote can be improved using the same principle as Horner's method. Write such a function (horner_octal_to_dec) using the ideas of Horner's method which takes a list whose entries are integers between 0 and 7, where the list represents a base-8 number, and returns the corresponding decimal integer (so the input [2,5,1] returns the integer 169).](https://gotit-pro.com/wp-content/uploads/2023/10/627bbfd5-a1bb-4d60-954c-b70c3537706b.jpg)
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