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If A and B are commutative unit rings, and A is a subring of B, then A is called integrally closed in B if every element of B which is integral over A belongs to A; in other ...

A polynomial p(x)=sumc_ix^i is said to split over a field K if p(x)=aproduct_(i)(x-alpha_i) where a and alpha_i are in K. Then the polynomial is said to split into linear ...

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

A shuffling algorithm used in a class of random number generators.

A set of points which do not lie on any of a certain class of hyperplanes.

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...