This paper explores computational approaches for detecting parallelism in classical Chinese poetry, a rhetorical device where two verses mirror each other in syntax, meaning, tone, and rhythm. We experiment with five classification methods: (1) verb position matching, (2) integrated semantic, syntactic, and word-segmentation analysis, (3) difference-based character embeddings, (4) structured examples (inner/outer couplets), and (5) GPT-guided classification. We use a manually annotated dataset, containing 6,125 pentasyllabic couplets, to evaluate performance. The results indicate that parallelism detection poses a significant challenge even for powerful LLMs such as GPT-4o, with the highest F1 score below 0.72. Nevertheless, each method contributes valuable insights into the art of parallelism in Chinese poetry, suggesting a new understanding of parallelism as a verbal expression of principal components in a culturally defined vector space.