polynomials

Here's my implementation of a addition of two polynomials using a linked List. For example if I want to add 3x^2+5^x+3 and 4x^3+5x+2 first I check if there are similar exponents in the two polynomials and if so I add their coefficients and I append the exponents to a string. After adding similar exponents then using the string I add the remaining parts in both polynomials to the final result. public class Node2{ int coef; int exp; Node2 next; Node2(int c,int e,Node2 n){ coef=c; exp=e; next=n; } Node2(int c,int e){ coef=c; exp=e; } } public class LinkedPoly{ static String exponent=""; Node2

Someone asked me this interesting question and I think it worthwhile posting it here, as there has not been any relevant thread on Stack Overflow. Suppose I have polynomial coefficients in a length- n vector pc , where a polynomial of degree n - 1 for variable x can be expressed in its raw form: pc[1] + pc[2] * x + pc[3] * x ^ 2 + ... + pc[n] * x ^ (n - 1) R core function polyroot can find all roots of this polynomial in complex domain. But often we are also interested in extrema, as for a univariate function, local minima and maxima turn up alternately, breaking the function into monotonic

I tried to find out how to calculate the error detection capabilities of arbitrary CRC polynomials. I know that there are various error detection capabilities that may (or may not) apply to an arbitrary polynomial: Detection of a single bit error: All CRCs can do this since this only requires a CRC width >= 1. Detection of burst errors: All CRCs can detect burst errors up to a size that equals their width. Detection of odd numbers of bit errors: CRC with polynomials with an even number of terms (which means an even number of 1-bits in the full binary polynomial) can do this. Detection of