Frequency estimation, especially with sampling rates below the Nyquist rate, has abundant applications in engineering. Recently, Chinese remainder theorem(CRT)-based frequency reconstruction from undersampled complex-value waveforms becomes one of the frontier focuses in the fields of signal processing, electromagnetism and optics etc. In this paper, we present several CRT-based algorithms for determining multiple frequencies via symmetric polynomials. The computational complexity of these algorithms is in the polynomial class (P).