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...

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...

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...

In abstract algebra, a monomial ideal is an ideal generated by monomials in a multivariate polynomial ring over a field. A toric ideal is an ideal generated...

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,...

{\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 , (...

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...

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

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...

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...

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...

polynomial in which no variable occurs to a power of 2 or higher; that is, each monomial is a constant times a product of distinct variables. For example f(x,y...

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...

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...

in J (usual sum of vectors). In particular, the product of two monomials is a monomial whose exponent vector is the sum of the exponent vectors of the...

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...

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...

suspected that Co0 was transitive on Λ2, and indeed he found a new matrix, not monomial and not an integer matrix. Let η be the 4-by-4 matrix 1 2 ( 1 − 1 − 1 −...

is the non-negative monomial matrices: a non-negative matrix has non-negative inverse if and only if it is a (non-negative) monomial matrix. Note that thus...

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...

multivariate polynomials with respect to a monomial order, see Gröbner basis § Leading term, coefficient and monomial. In linear algebra, a system of linear...

extends to monomials; thus, sin 3x = sin(3x) and even sin ⁠1/2⁠xy = sin(xy/2), but sin x + y = sin(x) + y, because x + y is not a monomial. However, this...

each of which consists of a coefficient from R multiplied by a monomial, where each monomial is a product of finitely many finite powers of indeterminates...

Infinite sum of monomials...

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...

one dimensional representation is called a monomial representation, because it can be represented as monomial matrices. Some groups have the property that...