“…Existing algorithms for computing rational first integrals and Darboux polynomials of bounded degree. There is a vast literature regarding the computation of rational or elementary first integrals (see for example [FG10, MM97, Chè11, PS83, SGR90, Sin92, LZ10, DDdMS01, Poi91]) and Darboux polynomials (see for example [CMS09,CMS06,CGG05,Wei95,Dar78]). Note that, among these articles, very few restrict to the specific question of rational first integrals.…”