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

the comic book, a) The first comic book is of shakitman was sold in 1938. ...

a) The first comic book is of shakitman was sold in 1938. In 2010, the estimated price for this comic book in good condition was about $500,000. This represented a return of 25 per

Prove that a tree with n vertices has n - 1 edges, Prove that A tree with n...

Prove that A tree with n vertices has (n - 1) edges.    Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should

common divisors greater than one, Let R be the relation on Z + defined by...

Let R be the relation on Z + defined by aRb iff gcd(a; b) = 1 (that is, a and b have no common divisors greater than one). Explain whether R is reflexive, irreflexive, symmetri

Tests for relative minimum, Tests for relative minimum For a relative ...

Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx)  = f´(x) = 0 ii.The second derivative, which i

Reflection , How do you reflect about the origin

How do you reflect about the origin

What is a system of equations?, What is a System of Equations? And its Solu...

What is a System of Equations? And its Solution? Here is an example of a system of equations (also called a simultaneous system of equations) x 2 + y = 3

Proof of sum-difference of two functions, Proof of Sum/Difference of Two Fu...

Proof of Sum/Difference of Two Functions : (f(x) + g(x))′  = f ′(x) +  g ′(x)  It is easy adequate to prove by using the definition of the derivative.  We will start wi

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