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A simple root of a Lie algebra is a positive root that is not the sum of two positive roots.

A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). More generally, if GCD(g,n)=1 (g and n are relatively ...

A spigot algorithm is an algorithm which generates digits of a quantity one at a time without using or requiring previously computed digits. Amazingly, spigot algorithms are ...

The algorithm for the construction of a Gröbner basis from an arbitrary ideal basis. Buchberger's algorithm relies on the concepts of S-polynomial and polynomial reduction ...

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

An elegant algorithm for constructing an Eulerian cycle (Skiena 1990, p. 193).

An algorithm for computing the eigenvalues and eigenvectors for large symmetric sparse matrices.

The square root inequality states that 2sqrt(n+1)-2sqrt(n)<1/(sqrt(n))<2sqrt(n)-2sqrt(n-1) for n>=1.

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

A lozenge (or rhombus) algorithm is a class of transformation that can be used to attempt to produce series convergence improvement (Hamming 1986, p. 207). The best-known ...