mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called...

mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial...

sequence of monomials is finite. Although Gröbner basis theory does not depend on a particular choice of an admissible monomial ordering, three monomial orderings...

consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an...

depending on the evaluation of the basis functions at the data points). The monomial basis for the vector space of analytic functions is given by { x n ∣ n...

In abstract algebra, a monomial ideal is an ideal generated by monomials in a multivariate polynomial ring over a field. Let K {\displaystyle \mathbb...

{\displaystyle H} . To define the monomial representation, we first need to introduce the notion of monomial space. A monomial space is a triple ( V , X , (...

In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is...

monomial group is solvable. Every supersolvable group and every solvable A-group is a monomial group. Factor groups of monomial groups are monomial,...

In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field F {\displaystyle \mathbb {F} } is a linear combination...

is a monomial. It is the simplest kind of a sparse polynomial after the monomials. A binomial is a polynomial which is the sum of two monomials. A binomial...

polynomials that contain only one type of monomial, with only those copies required to obtain symmetry. Any monomial in X1, ..., Xn can be written as X1α1...

requires the choice of a monomial order, that is a total order, which is compatible with the monoid structure of the monomials. Here "compatible" means...

In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive...

In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following: Let A be a Noetherian local ring of Krull...

X_{n}).} Here the "lacunary part" Placunary is defined as the sum of all monomials in P which contain only a proper subset of the n variables X1, ..., Xn...

bi- with the Greek poly-. That is, it means a sum of many terms (many monomials). The word polynomial was first used in the 17th century. The x occurring...

variable occurs to a power of 2 {\displaystyle 2} or higher; that is, each monomial is a constant times a product of distinct variables. For example f ( x...

denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say a x n k , {\displaystyle a{\sqrt[{n}]{x}}^{k},} with...

parameter t and a partition λ. They are Schur functions when t is 0 and monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials...

elementary algebra, a trinomial is a polynomial consisting of three terms or monomials. 3 x + 5 y + 8 z {\displaystyle 3x+5y+8z} with x , y , z {\displaystyle...

Riemann surface.He also introduced and named the concept called Standard monomial theory. He was a recipient of the Padma Bhushan in 2009, the third highest...

point corresponding to x {\displaystyle x} . Computing the residue of a monomial ∮ C z k d z {\displaystyle \oint _{C}z^{k}\,dz} makes most residue computations...

In algebra, a toric ideal is an ideal generated by differences of two monomials. An affine or projective algebraic variety defined by a toric prime ideal...

polynomials, the standard basis thus consists of the monomials and is commonly called monomial basis. For matrices M m × n {\displaystyle {\mathcal {M}}_{m\times...

logarithm, though most commonly base 10 (common logs) are used. Given a monomial equation y = a x k , {\displaystyle y=ax^{k},} taking the logarithm of...

{\displaystyle \mathbb {N} ^{n}} each encoding the exponents within a monomial, consider the multivariate polynomial f ( x ) = ∑ k c k x a k {\displaystyle...

{\displaystyle g_{1},\dots ,g_{p}} are monomials. In the context of geometric programming (unlike standard mathematics), a monomial is a function from R + + n {\displaystyle...

variables X1, ..., Xn, written hk for k = 0, 1, 2, ..., is the sum of all monomials of total degree k in the variables. Formally, h k ( X 1 , X 2 , … , X...

rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.) Moment...