Title: A Computer Algebra-Based Expert System for Diagnosis of Anorexia Authors: Cristina Perez-Carretero (1) Luis M. Laita (1) Eugenio Roanes-Lozano (2) Luis Lazaro (3) Jesus Gonzalez-Cajal (3,4) (1) Dept. Artificial Intelligence, Univ. Politecnica Madrid (2) Dept. Algebra, Univ. Complutense Madrid (3) C.U. Cardenal Cisneros (4) Hospital de la Princesa Abstract: This paper deals with the construction of a Logic and Computer Algebra-based expert system devoted to diagnosis of anorexia. Predisposition, triggering and maintenance factors, together with symptoms of the illness, behave as logical antecedents of production rules. These production rules lead, through the partial measure of the intensity of the factors and symptoms, to a final diagnosis. The inference engine works with polynomial expressions which are the translation of the production rules. The inference processes are translated to ideal membership problems.