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

Explain adding negative fraction, Explain Adding Negative Fraction? To...

Explain Adding Negative Fraction? To add negative fractions: 1. Find a common denominator. 2. Change the fractions to their equivalents, so that they have common denominators

HELP, A local pizza shop sells large pies for $7 each. If the cost of the o...

A local pizza shop sells large pies for $7 each. If the cost of the order is proportional to the number of pizzas would they charge a delivery charge per pizza or per order ?

Bcubi bui, hellow my name is isa soo what is your name?? i love the name ex...

hellow my name is isa soo what is your name?? i love the name experts mind so what is 8000+98800+600+935=what i do not know so can you tell me thank you oh thir is another one wha

Bottleneck for each product, A company makes 2 products, Product A and Prod...

A company makes 2 products, Product A and Product B. The product characteristics are shown in the following table. Product A B

Mechanical vibrations, While we first looked at mechanical vibrations we lo...

While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.

A card is drawn from a well shuffled deck of cards, A card is drawn from a ...

A card is drawn from a well shuffled deck of cards (i) What are the odds in favour of getting spade? (Ans: 1:3, 3:1, 3:10, 1:25) (ii)  What are the odds against getting a spa

Find relation between x and y while lies on straight line, Find the relatio...

Find the relation between x and y when the point (x,y) lies on the straight line joining the points (2,-3) and (1,4) [ Hint: Use area of triangle is 0] Ans :   Hint: If the poi

Determine multiplications required to obtain the determinant, Don't count t...

Don't count the number of divisions. Do not use asymptotic notation, instead provide exact answers. (i) What is the maximum number of multiplications required to solve a system

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