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Consider a polynomial p(x) defined as p(x) = II (qx + 1) = (x + 1)(2x + 1)(3x + 1)... (Nx + 1), where N is a strictly positive integer. Write a function named 'polynomial_with_roots()', which takes 2 input arguments: • a strictly positive integer 'N', . a positive integer 'm' such that 0 ≤ m ≤N, and returns the power series coefficient am, as an integer, where p(x) = ax. Hint: You will need to be careful and e.g. make use of integer arithmetic throughout (even avoiding use of NumPy integer arrays -- use lists instead!) in order to avoid problems with numerical roundoff and overflow which will otherwise be encountered for larger 'N'. For example: Test print (polynomial_with_roots (40, 40)) print (polynomial_with_roots (2, 0)) 1 print (polynomial_with_roots (2, 1)) 3 print (polynomial_with_roots(2, 2)) 2 Result 815915283247897734345611269596115894272000000000 2-def 1def polynomial_with_roots(N, m): # Add code here

Consider a polynomial p(x) defined as p(x) = II (qx + 1) = (x + 1)(2x + 1)(3x + 1)... (Nx + 1), where N is a strictly positive integer. Write a function named 'polynomial_with_roots()', which takes 2 input arguments: • a strictly positive integer 'N', . a positive integer 'm' such that 0 ≤ m ≤N, and returns the power series coefficient am, as an integer, where p(x) = ax. Hint: You will need to be careful and e.g. make use of integer arithmetic throughout (even avoiding use of NumPy integer arrays -- use lists instead!) in order to avoid problems with numerical roundoff and overflow which will otherwise be encountered for larger 'N'. For example: Test print (polynomial_with_roots (40, 40)) print (polynomial_with_roots (2, 0)) 1 print (polynomial_with_roots (2, 1)) 3 print (polynomial_with_roots(2, 2)) 2 Result 815915283247897734345611269596115894272000000000 2-def 1def polynomial_with_roots(N, m): # Add code here

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Please program this question in correct format with necessary code comments and docstring. Then use the examples test below to check if your code works. By the way, it will be helpful if you can leave some explanations.

Consider a polynomial p(x) defined as p(x) = [₁ (qx + 1) = (x + 1)(2x + 1)(3x + 1) ... (Nx + 1), where N is a strictly positive integer. Write a function named 'polynomial_with_roots()', which takes 2 input arguments: • a strictly positive integer `N`, • a positive integer `m` such that 0 ≤ m ≤ N, and returns the power series coefficient am, as an integer, where N p(x) = Σπo aqx. q=0 Hint: You will need to be careful and e.g. make use of integer arithmetic throughout (even avoiding use of NumPy integer arrays -- use lists instead!) in order to avoid problems with numerical roundoff and overflow which will otherwise be encountered for larger 'N'. For example: Test Result 815915283247897734345611269596115894272000000000 print (polynomial_with_roots (40, 40)) print (polynomial_with_roots (2, 0)) 1 print (polynomial_with_roots (2, 1)) 3 print (polynomial_with_roots (2, 2)) 2 1 def polynomial_with_roots(N, m): 2 # Add code here
Transcribed Image Text:Consider a polynomial p(x) defined as p(x) = [₁ (qx + 1) = (x + 1)(2x + 1)(3x + 1) ... (Nx + 1), where N is a strictly positive integer. Write a function named 'polynomial_with_roots()', which takes 2 input arguments: • a strictly positive integer `N`, • a positive integer `m` such that 0 ≤ m ≤ N, and returns the power series coefficient am, as an integer, where N p(x) = Σπo aqx. q=0 Hint: You will need to be careful and e.g. make use of integer arithmetic throughout (even avoiding use of NumPy integer arrays -- use lists instead!) in order to avoid problems with numerical roundoff and overflow which will otherwise be encountered for larger 'N'. For example: Test Result 815915283247897734345611269596115894272000000000 print (polynomial_with_roots (40, 40)) print (polynomial_with_roots (2, 0)) 1 print (polynomial_with_roots (2, 1)) 3 print (polynomial_with_roots (2, 2)) 2 1 def polynomial_with_roots(N, m): 2 # Add code here
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