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A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

Neville's algorithm is an interpolation algorithm which proceeds by first fitting a polynomial of degree 0 through the point (x_k,y_k) for k=1, ..., n, i.e., P_k(x)=y_k. A ...

The identities between the symmetric polynomials Pi_k(x_1,...,x_n) and the sums of kth powers of their variables S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k. (1) The identities are ...

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

There are a number of attractive polyhedron compounds consisting of nine octahedra. The compound illustrated above can be constructed as the dual of cube 9-compound. The ...