Monomial basis

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In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials. In fact, a polynomial may be uniquely written as a linear combination of monomials.

Univariate polynomials expressed on the monomial basis can be evaluated efficiently using Horner's method.


The monomial basis for the vector space of polynomials with degree n is the polynomial sequence of monomials

The monomial form of a polynomial is a linear combination of monomials

alternatively the shorter sigma notation can be used


A polynomial can always be converted into monomial form by calculating its Taylor expansion around 0.


A polynomial in

See also