The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.

; Incidence list: The edges are represented by an array containing pairs ( tuples if directed ) of vertices ( that the edge connects ) and possibly weight and other data.

x, y, u and v denote here tuples of variables rather than single variables ; e. g. really stands for where are some distinct variables.

There are various complex data objects such as array, list, indices, tuples, etc.

The μ-recursive functions ( or partial μ-recursive functions ) are partial functions that take finite tuples of natural numbers and return a single natural number.

This is because one can arrange all possible tuples of values of the unknowns in a sequence and then, for a given value of the parameter ( s ), test these tuples, one after another, to see whether they are solutions of the corresponding equation.

Braces "" are almost never used for tuples, as they are the standard notation for sets.

In computer science, tuples are directly implemented as product types in most functional programming languages.

The distinction between tuples in the relational model and those in set theory is only superficial ; the above example can be interpreted as a 2-tuple if an arbitrary total order is imposed on the attributes ( e. g. ) and then the elements are distinguished by this ordering rather than by the attributes themselves.

In this case, tuples are typically triplets ( 3-tuples ).

Conditional tests are most commonly used to perform selections and joins on individual tuples.

The Cartesian product is defined differently from the one in set theory in the sense that tuples are considered to be ' shallow ' for the purposes of the operation.

To see the connection with the classical picture, note that for any set S of polynomials ( over an algebraically closed field ), it follows from Hilbert's Nullstellensatz that the points of V ( S ) ( in the old sense ) are exactly the tuples ( a < sub > 1 </ sub >, ..., a < sub > n </ sub >) such that ( x < sub > 1 </ sub >-a < sub > 1 </ sub >, ..., x < sub > n </ sub >-a < sub > n </ sub >) contains S ; moreover, these are maximal ideals and by the " weak " Nullstellensatz, an ideal of any affine coordinate ring is maximal if and only if it is of this form.

Two common classes of algebraic type are product types, i. e. tuples and records, and sum types, also called tagged unions or variant types.

Since a relation contains no duplicate tuples, the set of all its attributes is a superkey if NULL values are not used.

However, Dickson's lemma concerns only tuples of natural numbers, and over the natural numbers there are only finitely many minimal pairs.

The set of tuples that are greater than or equal to some particular tuple forms a positive orthant with its apex at the given tuple.

Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences ( though mathematics does speak of ordered sets, and these can be seen to include the musical kind in some sense, they are far more involved ).

Therefore, if u and v are non-zero elements of U, there is an element of R that induces an endomorphism of U transforming u to v. The natural question now is whether this can be generalized to arbitrary ( finite ) tuples of elements.

More precisely, find necessary and sufficient conditions on the tuple ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >) and ( y < sub > 1 </ sub >, ..., y < sub > n </ sub >) separately, so that there is an element of R with the property that x < sub > i </ sub >· r = y < sub > i </ sub > for all i. If D is the set of all R-module endomorphisms of U, then Schur's lemma asserts that D is a division ring, and the Jacobson density theorem answers the question on tuples in the affirmative, provided that the x's are linearly independent over D.

In computer science, records ( also called tuples, structs, or compound data ) are among the simplest data structures.

These relations consist of a heading and a set of zero or more tuples in arbitrary order.

* Extension ( predicate logic ), the set of tuples of values that satisfy the predicate

: A relation is a tuple with, the header, and, the body, a set of tuples that all have the domain.

* Relation ( database ), a set of tuples in a relational database

In the relational model, a relation is a ( possibly empty ) finite set of tuples all having the same finite set of attributes.

You must be careful to avoid a mismatch that may arise between the two languages because negation, applied to a formula of the calculus, constructs a formula that may be true on an infinite set of possible tuples, while the difference operator of relational algebra always returns a finite result.

A relation is a set of tuples.

The set of all tuples over D is denoted as T < sub > D </ sub >.

The result of the query is the set of tuples X < sub > i </ sub > to X < sub > n </ sub > which makes the DRC formula true.

The tuples ( A, B, t ) where A is an invertible complex n by n matrix, B is any complex n by n matrix, and t is any complex number from an open set in complex space of dimension 2n < sup > 2 </ sup > + 1.

For functional programming, it provides several constructs and a set of immutable types: tuples, records, discriminated unions and lists.

# the relation does not have two distinct tuples ( i. e. rows or records in common database language ) with the same values for these attributes ( which means that the set of attributes is a superkey )

* In every infinite set of-tuples of natural numbers, there exist two tuples and such that, for every,.

The tuples in correspond one-for-one with the monomials over a set of variables.

The row is then interpreted as a relvar composed of a set of tuples, with each tuple consisting of the two items: the name of the relevant column and the value this row provides for that column.

Note that this implementation assumes the join attributes are unique, i. e., there is no need to output multiple tuples for a given value of the key.

GLib provides advanced data structures, such as memory chunks, doubly and singly linked lists, hash tables, dynamic strings and string utilities, such as a lexical scanner, string chunks ( groups of strings ), dynamic arrays, balanced binary trees, N-ary trees, quarks ( a two-way association of a string and a unique integer identifier ), keyed data lists, relations and tuples.

It tells us that in every instance of a certain relational schema the tuples can be identified by their values for certain attributes.

In database theory, the relational model uses a tuple definition similar to tuples as functions, but each tuple element is identified by a distinct name, called an attribute, instead of a number ; this leads to a more user-friendly and practical notation, A tuple in the relational model is formally defined as a finite function that maps attributes to values.

A relational database consists of sets of tuples with the same attributes.

A superkey is defined in the relational model of database organization as a set of attributes of a relation variable for which it holds that in all relations assigned to that variable, there are no two distinct tuples ( rows ) that have the same values for the attributes in this set.