Christian Bueno
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 Jul 16 awarded Supporter Mar 11 comment Is the algebraic closure of the rational functions over R a subset of the set of partial functions from R to C? Thanks Pierre for pointing out that big hole about $P(R,C)$ not having a clear ring structure. I will think about that and see if that can be resolved in a nice way. As for your comment about $\sqrt{x}$, I would say there is no problem since I would define the domain to be $R$ and the codomain to be $C$ so that $\sqrt{−a}=\sqrt{a}i$ for $a>0$. Mar 9 revised Is the algebraic closure of the rational functions over R a subset of the set of partial functions from R to C? In the last post I made the question more well-defined and in this one added a mention of what kind of answer I am looking for. Mar 9 awarded Editor Mar 9 comment Is the algebraic closure of the rational functions over R a subset of the set of partial functions from R to C? Sorry for the ambiguity, I have made what I meant much more precise now. This kinda of problem seems like that kind that has a clear answer and a method of construction as well. Mar 9 revised Is the algebraic closure of the rational functions over R a subset of the set of partial functions from R to C? added 999 characters in body; edited title Mar 9 asked Is the algebraic closure of the rational functions over R a subset of the set of partial functions from R to C? Feb 16 comment Looking for methods to solve multivariate non-traditional polynomial sequence recurrence relations Sounds like the approach is inherently one of algebraic geometry. Are there any standard ways of computing what the roots for polynomials in these fields would be? I would expect we would need a generalized notion of a radicals. And if an expression for the solutions don't always exist, would it be out of the question to look for an approximation to the roots which live in the closure of $Frac(Z[s,t,p])$ by using elements of the closure of $Frac(R[s,t,p])$? Feb 13 awarded Student Feb 13 asked Looking for methods to solve multivariate non-traditional polynomial sequence recurrence relations