monomial ordering

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• Monomial order — In mathematics, a monomial order is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the following two properties: If u < v and w is any other monomial, then uw<vw. In other words, the ordering… …   Wikipedia

• Monomial — In mathematics, in the context of polynomials, the word monomial can have one of two different meanings: The first is a product of powers of variables, or formally any value obtained by finitely many multiplications of a variable. If only a… …   Wikipedia

• Gröbner basis — In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating subset of an ideal I in a polynomial ring R. One can view it as a multivariate, non linear… …   Wikipedia

• Multivariate division algorithm — In mathematics, polynomials in more than one variable do not form a Euclidean domain, so it is not possible to construct a true division algorithm; but an approximate multivariate division algorithm can be constructed. Given a polynomial g,… …   Wikipedia

• Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… …   Wikipedia

• Poincaré–Birkhoff–Witt theorem — In the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (Poincaré (1900), G. D. Birkhoff (1937), Witt (1937); frequently contracted to PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie… …   Wikipedia

• Buchberger's algorithm — In computational algebraic geometry and computational commutative algebra, Buchberger s algorithm is a method of transforming a given set of generators for a polynomial ideal into a Gröbner basis with respect to some monomial order. It was… …   Wikipedia

• List of order theory topics — Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providing a framework for saying when one thing is less than or precedes another. An alphabetical list of many… …   Wikipedia

• Formal power series — In mathematics, formal power series are devices that make it possible to employ much of the analytical machinery of power series in settings that do not have natural notions of convergence. They are also useful, especially in combinatorics, for… …   Wikipedia

• List of order topics — This is a list of order topics, by Wikipedia page.An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value, optimization (mathematics), domain theory.Basic… …   Wikipedia

• Scalar field theory — In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a scalar , in contrast to a vector or tensor field. The quanta of the… …   Wikipedia