|
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. 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 the definition of a polynomial). ==One indeterminate== The polynomial ring of the univariate polynomial over a field is a -vector space, which has : as an (infinite) basis. More generally, if is a ring, is a free module, which has the same basis. The polynomials of degree at most form also a vector space (or a free module in the case of a ring of coefficients), which has : as a basis The canonical form of a polynomial is its expression on this basis: : or, using the shorter sigma notation: : The monomial basis in naturally totally ordered, either by increasing degrees : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「monomial basis」の詳細全文を読む スポンサード リンク
|