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A generator, in category theory, is an object that can be used to distinguish morphisms; In topology, a collection of sets that generate the topology is called a subbase; Generating set of a topological algebra: S is a generating set of a topological algebra A if the smallest closed subalgebra of A containing S is A
A general theorem of Matiyasevich says that if a set is defined by a system of Diophantine equations, it can also be defined by a system of Diophantine equations in only 9 variables. [8] Hence, there is a prime-generating polynomial inequality as above with only 10 variables. However, its degree is large (in the order of 10 45). On the other ...
The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals (that is, with rational coefficients). Galois theory was introduced by Évariste Galois to specify criteria for deciding if an algebraic equation may be solved in terms of ...
This Lie algebra is finite-dimensional and it has the same dimension as the manifold G. The Lie algebra of G determines G up to "local isomorphism", where two Lie groups are called locally isomorphic if they look the same near the identity element. Problems about Lie groups are often solved by first solving the corresponding problem for the Lie ...
Lie point symmetry is a concept in advanced mathematics.Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations [1] [2] [3] (ODEs).
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.