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An ideal is a subset I of elements in a ring R that forms an additive group and has the property that, whenever x belongs to R and y belongs to I, then xy and yx belong to I. ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

The Berlekamp-van Lint-Seidel graph is the Hamiltonian strongly regular graph on 243 vertices with parameters (243,22,1,2). It is also distance-regular with intersection ...

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

The free module of rank n over a nonzero unit ring R, usually denoted R^n, is the set of all sequences {a_1,a_2,...,a_n} that can be formed by picking n (not necessarily ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...