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Consider the following two polynomials in F17[x]
(a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials.
(b) Use the FFT algorithm, by hand, to multiply these two polynomials.
Remember that if a polynomial has degree 3 or less then it is irreducible if and only if it has at least one linear factor, that (x - a) is a linear factor of a polynomial f(x) if and only if f(a) = 0 and that for small elds it is easy to check by hand if a particular value is a root of a polynomial.
(a) Which of the following polynomials are reducible and irreducible in F5[x]? What is the factorization of the reducible ones?
(b) Does the following system have a unique solution of smallest degree:
It’s been a busy weekend for Larry. Five people in his neighborhood left on vacation Saturday morning and each of them left a pet for Larry to care for until they return. It’s a go
Consider the following linear programming problem: Min (12x 1 +18x 2 ) X 1 + 2x 2 ≤ 40 X 1 ≤ 50 X 1 + X 2 = 40 X
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Question Write a short note on the following: 1 The weekly salaries of a group of employees are given in the following table. Find the mean and standard deviation of the
Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
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Solve the recurrence relation T (K) = 2T (K-1), T (0) = 1 Ans: The following equation can be written in the subsequent form: t n - 2t n-1 = 0 Here now su
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Financial institutions often create synthetic instruments out of existing instruments. In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their
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