Functional Classification Study For Mathematical Formulas Retrieval

Mathematical formulae retrieval is the research focus in the information field. A mathematical formula has complex structural information and semantic information, and a formula can express a variety of meanings of mathematics, one mathematical meaning can have a variety of forms. In addition, users have different requirements for mathematical formulae retrieval function when they use mathematical formulae retrieval with different scenes, however the existing mathematical formulae retrieval system have a certain gap for user requirement analysis.First of all, the paper has carried on the analysis for the characteristics of mathematical formula systematically, gives the definition of mathematical formula, introduce the formula on the features of structural and semantic aspects. On this basis, study the substructure and nested structure of formula deeply, proposing the variable abstraction and the formula generalization based on the items generalization, two methods to obtain and describe the nested structure of formula well. Based on this, advances the structure depth used to describe the structural nested complexity of formula. This paper puts forward the structure similar degree for describing the degree of structural similarity between different formulae, which provides a way for sort the results of structural similar formula also.Secondly, the paper study semantic characteristics, equivalent formula and relative calculation formula, and gives the definition, enumerates the common equivalent form and common relative calculation formula.Finally, the paper surveys and analyzes the user scenarios, combining the characteristics of formula, puts forward the eight functional requirements for mathematical formulae retrieval: Full Match, Partial Match, Semantic Match, Structural Match, Equivalent Match, Relative Calculation Match, Graph Match, and Combination Match. The connotations and denotations of the eight kinds of requirements are defined in this paper. Furthermore, we compare and analyze the current studies on mathematical formulae retrieval according to eight types of functional requirements. We finally give some suggestions on the potential technical improvements on mathematical formulae retrieval.The function of Mathematical formulas retrieval provide convenient to the users’ needs to retrieve, it also brings opportunities for information retrieval technology development and social progress, Combining the mathematical formulas retrieval and mathematical calculations organically, is a new research direction in this field.