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

Determine the length of the field, A rectangular field is to be fenced in c...

A rectangular field is to be fenced in completely. The width is given as 22 yd and the total area is 990 yd 2 . Determine the length of the field? a. 31 yd b. 45 yd c. 968

Find a relationship chart and closeness ranks, 1.A manufacturing facility c...

1.A manufacturing facility consists of five departments, 1, 2, 3, 4 and 5. It produces four components having the manufacturing product routings and production volumes indicated in

Mean roots, Find all the eighth roots of (19 + 7 i)

Find all the eighth roots of (19 + 7 i)

Word problem, A jet flew at an average speed of 480mph from Point X to Poin...

A jet flew at an average speed of 480mph from Point X to Point Y. Because of head winds, the jet averaged only 440mph on the return trip, and the return trip took 25 minutes longer

Multiplying fractions involving negative numbers, Q. Multiplying Fractions ...

Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe

Shortcuts of fraction and squareroot, I am student of M.com and also doing...

I am student of M.com and also doing practice to crack bank or other competitive exam..please tell me shortcuts

Properties of t distribution, Properties of t distribution 1. The t di...

Properties of t distribution 1. The t distribution ranges from - ∞ to ∞ first as does the general distribution 2. The t distribution as the standard general distribution is

Second order differential equations, In the earlier section we looked at fi...

In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti

What is the minimum number of students, Question 1: What is the minimum...

Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who

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