polynomial division多項式除算?---remainder剰余
Main article : 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)) 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...
