The fundamental problem of graph isomorphism is to check if two graphs are isomorphic. This problem has attracted recent interest and there are very efficient programs for solving that problem. For other combinatorial structures, there are ways for reducing the problem to a graph. The graph isomorphism programs provide another feature and it is the canonical form of a graph which is of great interest for enumeration problems. Positive definite quadratic forms are widely used in geometry of numbers and the relevant notion of equivalence is arithmetic equivalence. In this talk we build a canonical form for positive definite quadratic forms and we shortly consider extensions to other settings.