polynomial division多項式除算?---remainder剰余

Main article: Euclidean division of polynomials< https://en.wikipedia.org/wiki/Euclidean_division_of_polynomials >
Euclidean division of polynomials is very similar to Euclidean division of integers and leads to polynomial remainders. Its existence is based on the following theorem: Given two univariate polynomials a(x) and b(x) (where b(x) is a non-zero polynomial ) defined over a field (in particular, the reals or complex numbers), there exist two polynomials q(x) (the quotient) and r(x) (the remainder ) which satisfy:
a(x) = b(x)q(x) + r(x)
where
deg(r(x)) < deg(b(x)),
where "deg(...) " denotes the degree of the polynomial (the degree of the constant polynomial whose value is always 0 can be defined to be negative, so that this degree condition will always be valid when this is the remainder ). Moreover, q(x) and r(x) are uniquely determined by these relations.
This differs from the Euclidean division of integers in that, for the integers, the degree condition is replaced by the bounds on the remainder r (non-negative and less than the divisor, which insures that r is unique. ) The similarity between Euclidean division for integers and that for polynomials motivates the search for the most general algebraic setting in which Euclidean division is valid. The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed.
Polynomial division leads to a result known as the polynomial remainder theorem: If a polynomial f(x) is divided by x − k, the remainder is the constant r = f(k).
< https://en.wikipedia.org/wiki/Remainder >
{prime number relationship素数の関係may beカナ？？・？・ }

c.f, ,
remainder残り、残り物、残余、余り、剰余、残留者、遺跡、遺物、継承権
left over使い残しの, 残存？
domains領域？？
https://ja.wikipedia.org/wiki/%E5%89%B0%E4%BD%99
/wiki/剰余

(relevant, )
https://shinichiwanko2000.livedoor.blog/archives/29615017.html
2025年11月03日 example(IEEE 754 floating-point support )--/wiki/C99 ←　in programming languages-remainder
{building block, fundamental thing基本的なんthusだけど?!・expansi[vityly ]bilityly?? 発展性はinfinity無限see ifカナ??・！・、・, , }