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Formally, a rational map: between two varieties is an equivalence class of pairs (,) in which is a morphism of varieties from a non-empty open set to , and two such pairs (,) and (′ ′, ′) are considered equivalent if and ′ ′ coincide on the intersection ′ (this is, in particular, vacuously true if the intersection is empty, but since is assumed irreducible, this is impossible).
Also simply application or app. Computer software designed to perform a group of coordinated functions, tasks, or activities for the benefit of the user. Common examples of applications include word processors, spreadsheets, accounting applications, web browsers, media players, aeronautical flight simulators, console games, and photo editors. This contrasts with system software, which is ...
Object–relational mapping (ORM, O/RM, and O/R mapping tool) in computer science is a programming technique for converting data between a relational database and the memory (usually the heap) of an object-oriented programming language.
As described in the example above, there are two main types of reductions used in computational complexity, the many-one reduction and the Turing reduction.Many-one reductions map instances of one problem to instances of another; Turing reductions compute the solution to one problem, assuming the other problem is easy to solve.
A birational map from X to Y is a rational map f : X ⇢ Y such that there is a rational map Y ⇢ X inverse to f.A birational map induces an isomorphism from a nonempty open subset of X to a nonempty open subset of Y, and vice versa: an isomorphism between nonempty open subsets of X, Y by definition gives a birational map f : X ⇢ Y.
Rational relations that are partial functions, i.e. that relate every input string from Σ* to at most one Γ*, are called rational functions. Finite-state transducers are often used for phonological and morphological analysis in natural language processing research and applications.
Other mapping problems arise when: One scheme has one element that needs to be split up with different parts of it placed in multiple other elements in the second scheme ("one-to-many" mapping) One scheme allows an element to be repeated more than once while another only allows that element to appear once with multiple terms in it
Computer mapping may refer to any mapping procedure done with the aid of computers: in computer graphics. 3D projection; texture mapping, normal mapping, tone mapping, ... etc. in geography geographic information system. Web mapping; Generic Mapping Tools; any of various methods in bioinformatics that have to do with gene mapping