I am trying to write up a paper with some results form Mathematica (11.2) among other things. I need to know what algorithm does it use when I solve a system of polynomial equations which is underdetermined (infinitely many solutions). In particular, sometimes Mathematica also find real solutions that are embedded into the complex positive-dimensional components. I couldn't find a mentioned of the specific algorithm that Mathematica is using. I believe this code is written by @DanielLichtblau ? I know this question: What algorithms does NSolve use? But this does not mention the specific algorithm for underdetermined polynomial systems and in particular for finding real solutions embedded in complex curves (though Mathematica certainly find these!).