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A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...

If theta is a given irrational number, then the sequence of numbers {ntheta}, where {x}=x-|_x_|, is dense in the unit interval. Explicitly, given any alpha, 0<=alpha<=1, and ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

If R is a ring (commutative with 1), the height of a prime ideal p is defined as the supremum of all n so that there is a chain p_0 subset ...p_(n-1) subset p_n=p where all ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

A generalization of the Wilcoxon rank sum test.

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

A theorem which plays a fundamental role in computer science because it is one of the main tools for showing that certain orderings on trees are well-founded. These orderings ...

The Kuen surface is a special case of Enneper's negative curvature surfaces which can be given parametrically by x = (2(cosu+usinu)sinv)/(1+u^2sin^2v) (1) = ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...