Wang worked on algorithmic elimination theory, geometric reasoning and knowledge management, and applications of symbolic computation to qualitative analysis of differential equations. In 1993 he proposed an elimination method for triangular decomposition of polynomial systems,[6] which has been referred to as Wang's method and compared with other three methods.[7] Later on he introduced the concepts of regular systems and simple systems[8] and devised algorithms for regular and simple triangular decompositions.[9][10] He also developed a package, called Epsilon,[11] which implements his methods.[12][13]
Wang popularized the use of methods and tools of computer algebra for symbolic analysis of stability and bifurcation of differential and biological systems. He constructed a class of cubic differential systems with six small-amplitude limit cycles[14] and rediscovered the incompleteness of Kukles' center conditions of 1944,[15] which stimulated the study of Kukles' system in hundred papers.[16] Since 2004 he has been involved in research projects on geometric knowledge management and discovery. With co-workers he developed an algorithmic approach for automated discovery of geometric theorems from images of diagrams.[17]
Wang served as General Chair of ISSAC 2007 and is founding Editor-in-Chief and Managing Editor of Mathematics in Computer Science[18] and Executive Associate Editor-in-Chief of SCIENCE CHINA Information Sciences.[19]
^Jin, Xiaofan; Wang, Dongming (1990). "On the conditions of Kukles for the existence of a centre". Bulletin of the London Mathematical Society. 22 (1): 1–4. doi:10.1112/blms/22.1.1.
^Christopher, C. J.; Lloyd, N. G. (1990). "On the paper of Jin and Wang concerning the conditions for a centre in certain cubic systems". Bulletin of the London Mathematical Society. 22 (1): 5–12. doi:10.1112/blms/22.1.5.
^Chen, Xiaoyu; Song, Dan; Wang, Dongming (2015). "Automated generation of geometric theorems from images of diagrams". Annals of Mathematics and Artificial Intelligence. 74 (3–4): 333–358. arXiv:1406.1638. doi:10.1007/s10472-014-9433-7.