This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
4x^2 + 2xy - 3y^2is a
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterm
In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension. In symbols, let
Let k be an algebraically closed field. Let P(X-11,...,X-nn, T) be the characteristic polynomial of the generic matrix (X-ij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective surface over k and A an Azumaya algebra on X of degree n, using a method suggested by M. Artin, we construct finite smooth splittings for A of degree n over X whose Galois closures are smooth.
Accelerating the convergence of some hypergeometric series with Gosper's method leads, in a most elementary way, to some series discovered by Ramanujan, Bauer and Dougall. In particular, it is shown that one of them can be traced back to the well-known formula of Wallis.