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 average bit rate - huffman codebook, 1. Consider a source wi...

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

Determine the fraction of the time, Ipswich has two ambulances. Ambulance 1...

Ipswich has two ambulances. Ambulance 1 is based at the local college and ambulance 2 is based downtown. If a request for an ambulance comes from the local college, the college-bas

Find the largest clique, Generate G(1000,1/2) and find the largest clique ...

Generate G(1000,1/2) and find the largest clique you can.  A clique is a complete sub graph, that is, a set of vertices each pair of which is connected by an edge.

What is the least number of students needed in a class, What is the least n...

What is the least number of students needed in a class to be sure that at least 6 will receive similar grade if there are five probable grades A, B,C, D and F?  Ans: Let us re

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

What is the evaluation of angle, In a periscope, a pair of mirrors is mount...

In a periscope, a pair of mirrors is mounted parallel to each other as given. The path of light becomes a transversal. If ∠2 evaluate 50°, what is the evaluation of ∠3? a. 50°

Trignometric Equations, Equation for the given intervaks in the intervaks, ...

Equation for the given intervaks in the intervaks, giving ypout answer correct to 0.1 1.sin x = 0.8 0 2. cos x =-0.3 -180 3.4cos theta- cos theta=2 0 4. 10tan theta+3=0 0

Evaluate algebraic word problems, Evaluate algebraic word problems: A ...

Evaluate algebraic word problems: A utility has three nuclear facilities which supply a total of 600 megawatts (Mw) of electricity to a particular area.  The largest facility

Relation and functions, Prove that if f and g are functions, then f interse...

Prove that if f and g are functions, then f intersect g is a function by showing f intersect g = glA A={x:g(x)=f(x)}

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