The knowledge-based system GRAPE and its application to Landau theory analysis for magnetic space groups

A knowldge-based project, the GRAPE system(Group Representation and Application in Physics Environment), is described in this paper. The GRAPE system is designed to provide physicists with a group theoretical environment to help them solve problems in group theory and representation. The user can communicate with GRAPE in plain English. At the present stage, it contains the knowledge of crystallography point groups, space groups as well as magnetic space groups both in group structure and group representations. The GRAPE system consists of five modules besides the knowledge base and the data base: a natural language interface, a computation module, a tutprial module, a bibliography module, and a program library. Group theoretical analysis for the Landau theory of continuous phase transitions has been the first application of the GRAPE system. The calculation for determining directions of phase transition at the Γ point for 230 space groups, 230 grey space groups and 674 black and white magnetic space groups has been performed.