polynomial form

English

Noun

polynomial form (plural polynomial forms)

1. (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 with Saunders Mac Lane (1953) A Survey of Modern Algebra, Revised edition, New York: Macmillan, published 1960, §3.1, page 58
• Prime.mover with Barto (2012) “Definition:Polynomial (Abstract Algebra)/Formal Definition/Free Monoid”, in Definition:Polynomial (Abstract Algebra)‎^[1], Proof Wiki, retrieved 2017-11-16