Consider a polynomial p(x) defined as p(x) = ₁ (qx + 1) = (x + 1)(2x + 1)(3x + 1) ... (Nx + 1), q=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,

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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how to solve this problem in python

Consider a polynomial p(x) defined as
p(x) = ₁ (qx + 1) = (x + 1)(2x + 1)(3x + 1) ... (Nx + 1),
µ₁ q=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) = 2 go aqxa.
Σ 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
print (polynomial_with_roots
print (polynomial_with_roots (2, 0))
print (polynomial_with_roots (2, 1))
print (polynomial_with_roots (2, 2))
Result
(40, 40)) 815915283247897734345611269596115894272€
1
3
2
Transcribed Image Text:Consider a polynomial p(x) defined as p(x) = ₁ (qx + 1) = (x + 1)(2x + 1)(3x + 1) ... (Nx + 1), µ₁ q=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) = 2 go aqxa. Σ 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 print (polynomial_with_roots print (polynomial_with_roots (2, 0)) print (polynomial_with_roots (2, 1)) print (polynomial_with_roots (2, 2)) Result (40, 40)) 815915283247897734345611269596115894272€ 1 3 2
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