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A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

The l^2-norm (also written "l^2-norm") |x| is a vector norm defined for a complex vector x=[x_1; x_2; |; x_n] (1) by |x|=sqrt(sum_(k=1)^n|x_k|^2), (2) where |x_k| on the ...

An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

The prescription that a trigonometry identity can be converted to an analogous identity for hyperbolic functions by expanding, exchanging trigonometric functions with their ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

An integer N which is a product of distinct primes and which satisfies 1/N+sum_(p|N)1/p=1 (Butske et al. 1999). The first few are 2, 6, 42, 1806, 47058, ... (OEIS A054377). ...

The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can ...