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In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
In rhetoric, a scheme is a type of figure of speech that relies on the structure of the sentence, unlike the trope, which plays with the meanings of words. [ 1 ] A single phrase may involve both a trope and a scheme, e.g., may use both alliteration and allegory .
A rhyme scheme is the pattern of rhymes at the end of each line of a poem or song. It is usually referred to by using letters to indicate which lines rhyme; lines designated with the same letter all rhyme with each other. An example of the ABAB rhyming scheme, from "To Anthea, who may Command him Anything", by Robert Herrick:
An example of a singular (non-smooth) scheme over a field k is the closed subscheme x 2 = 0 in the affine line A 1 over k. An example of a singular (non-smooth) variety over k is the cuspidal cubic curve x 2 = y 3 in the affine plane A 2, which is smooth outside the origin (x,y) = (0,0).
Fix a scheme S, called a base scheme. Then a morphism : is called a scheme over S or an S-scheme; the idea of the terminology is that it is a scheme X together with a map to the base scheme S. For example, a vector bundle E → S over a scheme S is an S-scheme.
Any reduced scheme X has a unique normalization: a normal scheme Y with an integral birational morphism Y → X. (For X a variety over a field, the morphism Y → X is finite, which is stronger than "integral". [2]) The normalization of a scheme of dimension 1 is regular, and the normalization of a scheme of dimension 2 has only isolated ...
Both Proc.new and lambda in this example are ways to create a closure, but semantics of the closures thus created are different with respect to the return statement. In Scheme, definition and scope of the return control statement is explicit (and only arbitrarily named 'return' for the sake of the example). The following is a direct translation ...
For example, the phrase, "John, my best friend" uses the scheme known as apposition. Tropes (from Greek trepein, 'to turn') change the general meaning of words. An example of a trope is irony, which is the use of words to convey the opposite of their usual meaning ("For Brutus is an honorable man; / So are they all, all honorable men").