关键词: 数学表达式, LaTeX, 公式解析, 公式索引, 公式基线层次, Treap

Abstract: Focused on the topic that the ordinary full-text searching technology could not realize mathematical expression retrieval resulted from the complex two-dimensional structure characteristics of formulae, a method of LaTeX formulae analyzing and indexing was proposed. On the basis of the fully consideration of formulae' characteristics and the structure of LaTeX language, a parsing algorithm was designed for analyzing LaTeX expressions and extracting their retrieval features. Taking it as a foundation, a hierarchical index model was designed which employed the information of operands and operators extracted from mathematical expressions through the parsing algorithm. The index model has two layers, Treap data structure layer and inverted index layer, which laid the foundation of the retrieval and matching to formulae. The experiment was carried out under the mode of browser/server through taking 6234 formulae from mathematical textbooks as data set. The parsing algorithm gets 124960 expression nodes from resource formulae of which the highest baseline level is 11. The average time consumed of the index system is 33.8317 seconds. The experimental results show the proposed parsing algorithm and the index method are helpful for realizing mathematical expression retrieval with high efficiency and correctness.

Key words: mathematical expression, LaTeX, formula analysis, formula index, formula baseline, Treap