polynomial form

English

polynomial form (plural polynomial forms)

(algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)

Garret Birkhoff; Saunders Mac Lane (1953) A Survey of Modern Algebra, Revised edition, New York: Macmillan, published 1960, §3.1, page 58
Prime.mover; Barto (2012), “Definition:Polynomial (Abstract Algebra)/Formal Definition/Free Monoid”, in Definition:Polynomial (Abstract Algebra)‎, Proof Wiki, retrieved 2017-11-16

单词	polynomial form
释义	polynomial form English Noun polynomial form (plural polynomial forms) (algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.) References Garret Birkhoff; Saunders Mac Lane (1953) A Survey of Modern Algebra, Revised edition, New York: Macmillan, published 1960, §3.1, page 58 Prime.mover; Barto (2012), “Definition:Polynomial (Abstract Algebra)/Formal Definition/Free Monoid”, in Definition:Polynomial (Abstract Algebra)‎, Proof Wiki, retrieved 2017-11-16
随便看	eufòrics eufòries eufòriques eufónica eufónicas eufónico eufónicos eufórbio eufória eufórica eufóricamente eufóricas eufórico eufóricos eufórikus eufóriák eufônica eufônicas eufônico eufônicos eug euga eugadh eugaidh eugaidhean