Resultant Definition

Resultant Sentence Examples

• There is no difficulty in expressing the resultant by the method of symmetric functions.

• It is the resultant of k polynomials each of degree m-I, and thus contains the coefficients of each form to the degree (m-I)'-1; hence the total degrees in the coefficients of the k forms is, by addition, k (m - 1) k - 1; it may further be shown that the weight of each term of the resultant is constant and equal to m(m-I) - (Salmon, l.c. p. loo).

• This can be seen at once because the factor in question being once repeated in both differentials, the resultant of the latter must vanish.

• In particular, when the product denotes an invariant we may transform each of the symbols a, b,...to x in succession, and take the sum of the resultant products; we thus obtain a covariant which is called the first evectant of the original invariant.

• Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.