Simple Algorithm for Judging Equivalence of Differential-Algebraic Equation Systems

Abstract

Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing whether equation groups containing multiple equations are equivalent. However, existing tools cannot judge the equivalence of two equation groups; thus, we develop an algorithm to judge such an equivalence using a computer algebra system. The proposed algorithm first eliminates variables appearing only in either equation group. It then checks the equivalence of the equations one by one. If each equation in one equation group is equivalent to an equation in the other, the equation groups are judged equivalent; otherwise, non-equivalent. We generated 50 pairs of equation groups for evaluation. The proposed method accurately judged the equivalence of all pairs. This method is expected to facilitate comprehension of a large amount of mathematical information in STEM documents. Furthermore, this is a necessary step for machines to understand equations, including process models.