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Monomial order. In 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 ring, satisfying the property of respecting multiplication, i.e., If and is any other monomial, then . Monomial orderings are most commonly used with Gröbner bases ...
Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that. and either R = 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R ...
Multilinear polynomial. In algebra, a multilinear polynomial[1] is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily simultaneously. It is a 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.
The divided power envelope is a fundamental tool in the theory of PD differential operators and crystalline cohomology, where it is used to overcome technical difficulties which arise in positive characteristic. The divided power functor is used in the construction of co-Schur functors.
A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, is a monomial. The constant is a monomial, being equal to the empty product and to for any variable . If only a single variable is considered, this ...
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Monomial basis. In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that 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 immediate consequence of ...
Download Desktop Gold. AOL Desktop Gold is included at no additional cost with your membership. 2. Under 'All Products' scroll to 'AOL Desktop Gold'. If you have an AOL Desktop Gold trial or subscription. Using the link in the Official AOL signup confirmation email you received. 1.