摘要

For any trigonometric polynomial phi(theta), we give a constructive algorithm by Sylvester elimination which produces matrices C-1, C-2, C-3 such that det(C-1 + R(phi(theta))C-2 + T(phi(theta))C-3) = 0. For a typical trigonometric polynomial, we assert that C-1 is positive definite, and thus the typical polynomial curve admits a determinantal representation.