signsector
Signsector is a term used in some mathematical discussions to describe a region of a domain where a specified collection of real-valued functions attains a fixed sign pattern. It generalizes the idea of a one-dimensional sign chart to higher dimensions by partitioning input space according to the signs of several functions rather than a single function.
Formal definition: Let P = {p1, ..., pm} be real-valued functions defined on a domain D ⊆ R^n. For
Properties: If the functions p_i are polynomials, each S_σ is a semialgebraic set. The sectors form a
Examples: With p1(x,y) = x and p2(x,y) = y^2 − 1 on D = R^2, the signsectors correspond to regions
Applications and relation: The concept supports sign-condition approaches in real algebraic geometry, constraint solving, and piecewise-defined