Search Results for ""

Let F be a finite field with q elements, and let F_s be a field containing F such that [F_s:F]=s. Let chi be a nontrivial multiplicative character of F and chi^'=chi ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

The Eisenstein integers, sometimes also called the Eisenstein-Jacobi integers (Finch 2003, p. 601), are numbers of the form a+bomega, where a and b are normal integers, ...

The doublestruck capital letter Q, Q, denotes the field of rationals. It derives from the German word Quotient, which can be translated as "ratio." The symbol Q first ...

The name for the set of integers modulo m, denoted Z/mZ. If m is a prime p, then the modulus is a finite field F_p=Z/pZ.