# NPTEL Computational Number Theory and Algebra Assignment 8 Answer

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NPTEL Computational Number Theory and Algebra Assignment 8 Answer – Here All The Questions and Answers Provided to Help All The Students and NPTEL Candidate as a Reference Purpose, It is Mandetory to Submit Your Weekly Assignment By Your Own Understand Level.

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## NPTEL Computational Number Theory and Algebra Assignment

ABOUT THE COURSE :
Algebra plays an important role in both finding algorithms, and understanding the limitations of computation. This course will focus on some of the fundamental algebraic concepts that arise in computation, and the algebraic algorithms that have applications in real life. The course will cover the problems of fast integer (or polynomial) multiplication (or factoring), fast matrix multiplication, primality testing, computing discrete logarithm, error-correcting codes, lattice- based cryptography, etc. The course intends to introduce both basic concepts and practical applications.

INTENDED AUDIENCE  : Computer Science & Engineering, Mathematics, Electronics, Physics, & similar disciplines.
PREREQUISITES  : Preferable (but not necessary)– Theory of Computation, Algorithms, Algebra
INDUSTRIES  SUPPORT     : Cryptography, Coding theory, Computer Algebra, Symbolic Computing Software, Cyber Security, Learning Software

Next Week Assignment Answers

This course can have Associate in Nursing unproctored programming communication conjointly excluding the Proctored communication, please check announcement section for date and time. The programming communication can have a weightage of twenty fifth towards the ultimate score.

Final score = Assignment score + Unproctored programming exam score + Proctored Exam score
• Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
• ( All assignments in a particular week will be counted towards final scoring – quizzes and programming assignments).
• Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam – out of 100
• Proctored Exam score =50% of the proctored certification exam score out of 100
YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF ASSIGNMENT SCORE >=10/25 AND
UNPROCTORED PROGRAMMING EXAM SCORE >=10/25 AND PROCTORED EXAM SCORE >= 20/50.
If any one of the 3 criteria is not met, you will not be eligible for the certificate even if the Final score >= 40/100.

## BELOW YOU CAN GET YOUR NPTEL Computational Number Theory and Algebra Assignment 8 Answer 2022? :

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1 point
What is the exact maximum number of monomials, a polynomial of degree d in n variables, can have?

Ans  – A
1 point

Let f be any degree d, n-variate polynomial over an infinite field FF. What is the maximum number of roots of f in FnFn and what is the maximum number of irreducible factors of f in F[x1,x2,,xn]F[x1,x2,…,xn], respectively?

Ans  – B
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1 point

Let the density of roots of a polynomial over a set T of tuples be defined as the number of roots in the set T divided by the size of set T. Let a be the density of roots of f=x2y2f=x2−y2 over the set T={0,1,2}×{0,1,2}T={0,1,2}×{0,1,2}. Let b be the upper bound on density of roots obtained from Polynomial Identity Lemma covered in class (the probability). What are the values of a,b respectively?

Ans  – C
1 point

Which of the following is true for f(x,y):=x2+xy+1f(x,y):=x2+xy+1 with coefficients in the finite field FpFp?

1. ff is almost-monic in xx.

2. ff is almost-monic in yy.

Ans  – B
1 point

Let f(x):=x2+6f(x):=x2+6 be a univariate polynomial in Z[x]Z[x]. For what value of prime pp, Hensel’s lifting is applicable to fmodpfmodp?

Ans  – C
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1 point
Which of the following is true?

1. Hilbert’s irreducibility theorem relates factoring a general multivariate polynomial to factoring a low-variate polynomial.

2. Kaltofen’s blackbox multivariate factoring algorithm runs in deterministic polynomial time.

Ans  – D
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