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
alternatively the shorter sigma notation can be used
A polynomial can always be converted into monomial form by calculating its Taylor expansion around 0.