On Wed, Oct 24, 2018 at 5:05 PM Waldek Hebisch <[email protected]> wrote: > > If you could find solution _in the fraction field_ then > the method would be fine. However, in general finding > rational solutions to polynomial system of equations is > uncomputable.
Can you suggest a reference? I could not find this result (well known?) after a quick search. > Groebner bases decide if there are solutions in > algebraic closure, but you may have algebraic > solutions without rational solutions. If you say that > you can find out if there is rational solution > (= factorization) you should better justify this and > explain what special properties of system you use. > Yes, that would be nice. Unfortunately SystemSolvePackage in FriCAS does not make any explicit claim about completeness. But it does refer to the method of triangular systems. The only special property that I can think of is that the equations in the system are at most quadratic. I do not know if that is sufficient. Another thing is that we are only interested in finding at least one explicit solution (if it exists). We do not need to know all solutions. > Classical factorization methods (in commutative case) > avoid uncomputability by recombining algebraic factors. > If you do not want recombination you should say how > you avoid uncomputability. > I agree. > To be clear: your code apparently makes some > assumptions. Both theory (uncomputablity in general > case) an practice suggest that those assumptions may > fail unless we can prove them. OK. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
