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Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

Let Delta_1, Delta_2, and Delta_3 be tetrahedra in projective three-space P^3. Then the tetrahedra are said to be desmically related if there exist constants alpha, beta, and ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...

Taking the ratio x/y of two numbers x and y, also written x÷y. Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called ...