Engineers and scientists wishing to perform harmonic analysis of waveforms may need to use discrete methods in preference to analytical methods partly because of the volume of algebra in analytical methods. Powerful computer algebra (in this study MAPLE) now offers a new mathematical environment which permits the investigation of analytical methods in harmonic analysis. MAPLE procedures are developed to investigate the harmonic structure of single‐phase and three‐phase waveforms of thyristor and triac circuits. The paper achieves three purposes: first it illustrates the use of a new mathematical tool available to the scientist and engineer; second it adds to a sparse, but growing, knowledge of the operation of computer algebra procedures; finally, it reveals the fine structure of the harmonic behaviour of these circuits.