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Generic point. In algebraic geometry, a generic point P of an algebraic variety X is a point in a general position, at which all generic properties are true, a generic property being a property which is true for almost every point. In classical algebraic geometry, a generic point of an affine or projective algebraic variety of dimension d is a ...
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic curve cryptography (ECC). The literature presents this operation as scalar multiplication, as written in Hessian form of an elliptic curve. A widespread name for this operation is also ...
An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve.There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields such as number theory, and more recently in cryptography and Digital Signature Authentication (See elliptic curve cryptography and elliptic curve DSA).
Tacit programming, also called point-free style, is a programming paradigm in which function definitions do not identify the arguments (or "points") on which they operate. Instead the definitions merely compose other functions, among which are combinators that manipulate the arguments. Tacit programming is of theoretical interest, because the ...
In mathematics, pointless topology, also called point-free topology (or pointfree topology) and locale theory, is an approach to topology that avoids mentioning points, and in which the lattices of open sets are the primitive notions. [1] In this approach it becomes possible to construct topologically interesting spaces from purely algebraic data.
The Kelvin water dropper, invented by Scottish scientist William Thomson (Lord Kelvin) in 1867, [1] is a type of electrostatic generator. Kelvin referred to the device as his water-dropping condenser. The apparatus is variously called the Kelvin hydroelectric generator, the Kelvin electrostatic generator, or Lord Kelvin's thunderstorm.
The projected points, in red, are the Chebyshev nodes. In numerical analysis, Chebyshev nodes are a set of specific real algebraic numbers, used as nodes for polynomial interpolation. They are the projection of equispaced points on the unit circle onto the real interval the diameter of the circle. The Chebyshev nodes of the first kind, also ...
γ is a topological generator of Γ; L n is the p-Hilbert class field of F n. H n is the Galois group Gal(L n /F n), isomorphic to the subgroup of elements of the ideal class group of F n whose order is a power of p. H ∞ is the inverse limit of the Galois groups H n. V is the vector space H ∞ ⊗ Z p Q p. ω is the Teichmüller character. V ...