Embedded software in critical systems rise a need for software analysis, especially for guaranteeing safety properties. In the late seventies, Cousot & Cousot introduced a general framework, called abstract interpretation, dedicated to the conception of particular analyses: static analyses. Among the program properties of interest, discovering algebraic relationships between variables allows for proving the lack of run-time errors. While the inference of linear relationships is e fficiently solved, computing polynomial equalities as invariants is still a challenge, a fortiori is the inequality counterpart. After a brief overview of existing techniques for invariant inference, this report investigates the viability of a constraint-based method dedicated to the inference of polynomial inequalities as program invariants.