monomials's Usage Examples:

series is a compact way to express the number of monomials of a given degree: the number of monomials of degree d {\displaystyle d} in n {\displaystyle.

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.

is a total order, which is compatible with the monoid structure of the monomials.

simplest kind of polynomial after the monomials.

A binomial is a polynomial which is the sum of two monomials.

order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication.

rows and columns are indexed by monomials.

The entries of the matrix depend on the product of the indexing monomials only (cf.

elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.

Monomials are uniquely defined by their exponent vectors so computers can represent monomials efficiently as exponent vectors.

Furthermore, the number of perfect matchings is equal to the number of monomials in the polynomial det(A), and is also equal to the permanent of A {\displaystyle.

generated by monomials in a multivariate polynomial ring over a field.

A toric ideal is an ideal generated by differences of monomials (provided the.

theorem then asserts that these monomials form a basis for U(L) as a vector space.

It is easy to see that these monomials span U(L); the content of the.

algebraic group by giving an explicit basis of elements called standard monomials.

(an orthonormal basis), but not necessarily as an infinite sum of the monomials xn.

For polynomials, the standard basis thus consists of the monomials and is commonly called monomial basis.

ring R, together with a given basis similar to the basis of standard monomials of the coordinate ring of a Grassmannian.

over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators.

also called the homogeneity operator, because its eigenfunctions are the monomials in z: θ ( z k ) = k z k , k = 0 , 1 , 2 , … {\displaystyle \theta (z^{k})=kz^{k}.

posynomials and g 1 , … , g p {\displaystyle g_{1},\dots ,g_{p}} are monomials.

largest sum of exponents (for a multivariate polynomial) in any of its monomials; the multiplicative order, that is, the number of times the polynomial.