ntuplas

Ntuplas, singular ntupla, refer to n-element ordered tuples used in mathematics and computer science as a generalization of ordinary two- or three-element tuples. An ntupla is an ordered sequence (a1, a2, ..., an) where each element ai comes from a corresponding set Ai. The collection of all such ntuplas is the Cartesian product A1 × A2 × ... × An.

Key properties include that the order of elements matters, elements can repeat, and the length of an ntupla is fixed to n. This makes ntuplas a natural way to represent structured data where each position has a designated type or domain. In many contexts, ntuplas are treated as algebraic objects or data records, with equality defined componentwise: two ntuplas are equal if and only if all corresponding components are equal.

Applications of ntuplas span several fields. In databases, a relation of arity n is modeled as a subset of the Cartesian product A1 × A2 × ... × An, where each ntupla corresponds to a row and each position corresponds to a field. In programming languages, ntuplas serve as fixed-length data structures or as the argument lists to functions, and in mathematics they describe elements of product sets and coordinate representations in vector spaces when the domains are numeric.

Notation commonly uses parentheses, as in (a1, a2, ..., an), and, when all ai belong to numeric domains, ntuplas may be viewed as vectors in a space like Rn. While related to the concept of a tuple, ntuplas emphasize the fixed length and the positional role of each component.