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

Find the sum of all natural no. between 101 and 304, Find the sum of all na...

Find the sum of all natural no. between 101 & 304 which are divisible by 3 or 5. Find their sum. Ans:    No let 101 and 304, which are divisible by 3. 102, 105..........

Repetition need not be boring-ways to aid learning maths, Repetition Need N...

Repetition Need Not Be Boring :  From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an

What is the probability of tossing a head, Q. What is the probability of to...

Q. What is the probability of tossing a head? List the sample space for tossing a coin once. What is the probability of tossing a head? Solution:  If you tossed a coin once

Graph for the sequence - sequences and series, Graph for the Sequence F...

Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu

Example of multiplication of complex numbers, Multiply following and write ...

Multiply following and write the answers in standard form.  (a) 7 i ( -5 + 2 i )  (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu

Compound and simple interest, Your grandparents gave you a gift of R2 000 o...

Your grandparents gave you a gift of R2 000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the R2 000 at 8% per

Linear programming, I want to send to you a file for my question.How. Could...

I want to send to you a file for my question.How. Could you please send my a link for that.

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