Abstract. The problem of polynomial invariants generation for iterative loops with loop initial statement and nonsingular linear operator in the loop body is considered. The set of such invariants forms the ideal in polynomial ring in the loop variables. An algorithm to calculate basic invariants for a Jordanian cell linear operator and for the diagonalized linear operator with irreducible minimal characteristic polynomial are presented. The theorem about the structure of the basis of invariants ideal is proved: it consists of basic invariants of Jordanian cells and basis invariants of the diagonalized part for the linear operator under consideration.

Keywords: static analysis of programs, linear loop, loop invariant, invariant polynomial.