Thanks, the second answer is enlightened for me, but I hope some simple picture(maybe at the some p-adic numbers) to show what it looks like. In fact, I read the Escassut's book Ultrametric Banach algebras to learn more algebraic Banach algebras, but do not expert such big terminology. Maybe I can remember some basic claim, but I am not sure how much it will be used.

A good background for my question, thank you all the same.

It is also a possible definition, I think it is equivalence to the definition here, defining the complex convex hull first, then it is complex convex iff its hull is itself.

Maybe my question is not very exact,MY interesting is not at the computer algebra,I just want to know the method to find or prove the generic initial ideal.If my example is something complicated to work by hand,you can change other easy case.Miller's book use the comprehensive Grobner basis,does it important?

I am just a beginner,does any example to show it?