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A divergenceless vector

**field**, also called a solenoidal**field**, is a vector**field**for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...When working over a collection of fields, the base

**field**is the intersection of the fields in the collection, i.e., the**field**contained in all other fields.Let V be a vector space over a

**field**K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient**field**.The extension

**field**K of a**field**F is called a splitting**field**for the polynomial f(x) in F[x] if f(x) factors completely into linear factors in K[x] and f(x) does not factor ...A

**field**automorphism of a**field**F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...An imaginary quadratic

**field**is a quadratic**field**Q(sqrt(D)) with D<0. Special cases are summarized in the following table. D**field**members -1 Gaussian integer -3 Eisenstein ...Given an ordinary differential equation y^'=f(x,y), the slope

**field**for that differential equation is the vector**field**that takes a point (x,y) to a unit vector with slope ...A divergenceless

**field**can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...An algebraic integer of the form a+bsqrt(D) where D is squarefree forms a quadratic

**field**and is denoted Q(sqrt(D)). If D>0, the**field**is called a real quadratic**field**, and ...A finite extension K=Q(z)(w) of the

**field**Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ......