Sorry I did not comment to this sooner I hope this clarifyes my question.
I thought this question were complitely forgotten. Many thank's for answering to this one. I am not exactly an expert in alg.geom but it is one of the ''tools''
that I use.
And let me say here: You guys have done wonderful job with Singular. I own you more than you can imagine. Otherwise I would have to had settle with Macaulay 2 or CoCoa
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I am just asking that if I=<f_1,...f_n>\in C[x1,...,xn] and V(I) is irreducible in Zariski topology
then if you change the the ring variables (x1,...xn) to reals (assuming that the multiplyers of monomials of generators f_i are real)
then I=<f_1,...,f_n>\in R[x1,...xn] and V(I) is also irreducible in Zariski topology.
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So basically I am asking if a variety V(I)\in C^n can not be presented as a nontrivial union of two varieties is it true that
then V(I) \in R^n can not be presented as a nontrivial union of two subvarieties (when you change the ring variables to reals).
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Probably this is a very trivial question, but I have lot's of other things on my mind right now. If the question is still unclear just let me know I try to answer you asap.