Karatsubas algorithm, Mathematics

Assignment Help:

Consider the following two polynomials in F17[x]

214_Karatsubas algorithm.png

 

(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?

1616_Karatsubas algorithm1.png

(b) Does the following system have a unique solution of smallest degree:

1739_Karatsubas algorithm2.png


Related Discussions:- Karatsubas algorithm

Matrices, how to find inverse of matrix

how to find inverse of matrix

Which of the subsequent numbers is equivalent to 12.087, Which of the subse...

Which of the subsequent numbers is equivalent to 12.087? Zeros can be added to the end (right) of the decimal portion of a number without changing the value of the number; 12.

Proof by Condratiction, "Prove by contradiction that no root of the equatio...

"Prove by contradiction that no root of the equation x^18 -2x^13 + x^5 -3x^3 + x - 2 = 0 is an integer divisible by 3" Any help would be very much appreciated!

Linear algebra, solve for k such that the system 4x+ky=6 kx+y=-3

solve for k such that the system 4x+ky=6 kx+y=-3

Linear programming, how i do project in linear programming in agriculture

how i do project in linear programming in agriculture

Determine if the following sequences converge or diverge, Determine if the ...

Determine if the following sequences converge or diverge.  If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c

Least common denominator using primes, Least Common Denominator Using Prime...

Least Common Denominator Using Primes: A prime number is a whole number (integer) whose only factors are itself and one. So the first prime numbers are given as follows: 1,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd