English Dictionary

polynomial form

名詞

(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.)

日本語の意味

代数学において、不定元（または複数の不定元）のべき乗の線形結合、またはその積の形をとる表現。ここで、各項の係数は整域や体に属する。

Before applying the theorem, rewrite the expression in polynomial form to make coefficient comparison straightforward.

定理を適用する前に、その式を不定元の冪の線形結合として書き直すと、係数の比較が簡単になります。

意味（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.)

polynomial forms （ plural ）