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

Patrice has worked a certain how many hours has she worked, Patrice has wor...

Patrice has worked a certain amount of hours so far this week. Tomorrow she will work four more hours to finish out the week along with a total of 10 hours. How many hours has she

Find out the volume of the solid -y = (x -1) ( x - 3)2, Find out the volume...

Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r

ALGEBRA, FIND PRODUCT (-41)*(102)

FIND PRODUCT (-41)*(102)

Linear programming, Consider the following linear programming problem: M...

Consider the following linear programming problem: Min (12x 1 +18x 2 )             X 1 + 2x 2 ≤ 40             X 1 ≤ 50             X 1 + X 2 = 40             X

Determine that the series is convergent or divergent, Determine or find out...

Determine or find out if the subsequent series is convergent or divergent.  If it converges find out its value. Solution To find out if the series is convergent we fir

Metric and costamary, can you please help me with this topic that im on in ...

can you please help me with this topic that im on in classand I just don''t get it and can u help me with dividing fractions adding mutply subtract add

Solving equations by completing the square method, I need help for Solving ...

I need help for Solving Equations by Completing the Square Method, can anybody help me out for this?

If pth term of ap is q and qth term is p. p.t its nth term, If the p th te...

If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans:    APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p

John and charlie have a whole of 80 dollars he has x dollar, John and Charl...

John and Charlie have a whole of 80 dollars. John has x dollars. How much money does Charlie have? This problem translates to the expression 42 + (11 - 9) ÷ 2. Using order of o

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