Search Results for ""

A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

The Tschirnhausen cubic is a plane curve given by the polar equation r=asec^3(1/3theta). (1) Letting theta=3tan^(-1)t gives the parametric equations x = a(1-3t^2) (2) y = ...

The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...

A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), ...

A pivotal isogonal cubic is a self-isogonal cubic that possesses a pivot point, i.e., in which points P lying on the conic and their isogonal conjugates are collinear with a ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...

A cubic number is a figurate number of the form n^3 with n a positive integer. The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578). The protagonist Christopher ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...