Karatsubas algorithm, Mathematics

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

Posted Date: 2/26/2013 1:00:37 AM | Location : United States







Related Discussions:- Karatsubas algorithm, Assignment Help, Ask Question on Karatsubas algorithm, Get Answer, Expert's Help, Karatsubas algorithm Discussions

Write discussion on Karatsubas algorithm
Your posts are moderated
Related Questions
Value Of The Game The game value refers to the average pay off per play of the game over an extended period of time


The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin

solve a trader purchases coffee at the rate of Rs. 350 per kg and mixes it with chicory bought at the rate of Rs.750 per kg in the ratio 5:2.If he sells the mixture at the rate of

The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th

introduction to decimals

Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first draw

Rolle's Theorem  Assume f(x) is a function which satisfies all of the following. 1. f(x) is continuous in the closed interval [a,b]. 2. f(x) is differentiable in the ope

E1) What is the difference between the two models listed above? Which is more difficult for children to understand? E2) List some activities and word problems that you would exp

PROOF OF VARIOUS LIMIT PROPERTIES In this section we are going to prove several of the fundamental facts and properties about limits which we saw previously. Before proceeding