x2pq

x2pq is a notational convention used in mathematical and computational contexts to describe a map that takes a single input x and produces a two-component output, typically written as (p, q). The name reflects the idea of deriving two quantities from one source, with p and q representing two associated components.

Formally, x2pq denotes a function F that assigns to x a pair F(x) = (p, q), where p = f(x) and q = g(x) for some chosen functions f and g. Depending on the setting, x may be a real number, a vector, or an element of a more general space, and f and g may be linear or nonlinear. If f and g are defined on a common domain and their images are compatible, F maps x into a two-dimensional space or a two-component object relevant to the problem.

Examples illustrate common usages. For a real input x, one might define F(x) = (x^2, sin x), so p = x^2 and q = sin x. For a vector x in R^n, F(x) could be (a^T x, b^T x) for fixed vectors a and b, producing two scalar projections p and q. In data processing, x2pq can be used to generate a compact two-feature representation from a single input, facilitating tasks such as feature engineering or coordinate splitting.

Notes and variations. x2pq is not a standardized mathematical object with a universal definition; interpretations depend on the chosen f and g and the problem domain. As such, the term appears primarily in informal descriptions, notes, or project-specific documentation rather than in canonical references. See also coordinate projection, feature pairing, and pairing functions.