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A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.

The magnitude (length) of a vector x=(x_1,x_2,...,x_n) is given by |x|=sqrt(x_1^2+x_2^2+...+x_n^2).

If the first nonzero component of the vector difference A-B is >0, then A≻B. If the first nonzero component of A-B is <0, then A≺B.

Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

The index set for the collection of submodules in a graded module.

A set M of all polynomials in s variables, x_1, ..., x_s such that if P, P_1, and P_2 are members, then so are P_1+P_2 and QP, where Q is any polynomial in x_1, ..., x_s.

A basis of a modular system M is any set of polynomials B_1, B_2, ... of M such that every polynomial of M is expressible in the form R_1B_1+R_2B_2+..., where R_1, R_2, ... ...

The ring R[x] of polynomials in a variable x.