Introduction to Integer and Polynomial Arithmetic Technical Seminar Paper Presentation:
The most real life problem involves the computation of both integers and also polynomials. And in this paper we discuss about the methods which are involved in making the faster calculation. And also the previous algorithms can be used with modern approach for performing the computations most efficiently.
The finite power series includes the non negative integer and also the uni-variate polynomial. And most of the algorithms involved in manipulation of integer and polynomial are similar. The similar types of algorithms are involved in case of computations regarding to multiplication, division, calculation of GCD, also finding modular arithmetic and also residues.
When we consider computation of GCD, i.e. when we consider two integers a and b , then GCD is given as, GCD(a,b)=ma+nb where m and n are integer values. The algorithm for finding the GCD of two numbers using the integers m and also n is given in the paper. This algorithm is given as the Extended Euclidean Algorithm.
In the real life, most of the computation involves calculations based on integers and also polynomial also includes the computation of reciprocal to calculation of GCD in a modern approach. Techniques like Chinese remaindering and also modular polynomial arithmetic techniques are used for performing calculations fastly, the interpolation of polynomial is used for calculating polynomial arithmetic.
We can conclude that mostly the real life problem involves the computation of both integers and also polynomials. And in this paper we discuss about the methods which are involved in making the faster calculation including the comparison of all computing methods.
Download Integer and Polynomial Arithmetic Technical Seminar Paper Presentation for IT Students.