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a teacher at university in china who is not a mathematician.:)
18h

comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
Intuitively,there may be some gap in the argument. 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
Anyway,it is interesting to link the question to halting problem in such a way, but I think it is very subtle to link them. 
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revised 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
correctspelling 
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suggested  suggested edit on Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function? 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
An answer has to be there is no such algorithm. But if the series is transcendental, we can find it is, otherwise we may have no algorithm by which to find that it is algebraic 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
Very sorry, a similar question had been asked by me in May 11, I have completely forgotten the post of May 11 which appears in right column of the above post. And I have just thought about the question in another light, that is poles, branch points and natural boundary. but let's not close or delete the post, since we are expecting positive cases and have not gotten a complete list of positive cases 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
@NAME_IN_CAPS,yes,and when I read one of the articles,I have found that I know some result of the paper. Thank you very much. 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
@NAME_IN_CAPS,thank you very much,I have just search for the two authors' article,the titles seem to focus on my questions. 
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revised 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
added 75 characters in body 
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comment 
Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function?
@FelipeVoloch,yes.So we have to put some restriction on $a_i$,let me make some modification of the question. 
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asked  Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function? 
Sep 26 
comment 
Questions about transformation or integral transformation
@RobertBryant,yes,if so, it is very strong and tough questions. 
Sep 26 
comment 
Questions about transformation or integral transformation
@RobertBryant a famous mathematician has told me that it is Jacobian Conjecture ,but I think those questions are much weaker than Jacobian Conjecture 
Sep 24 
comment 
Questions about transformation or integral transformation
@RobertBryant,thank you very much,your comments are very helpful 
Sep 24 
awarded  Autobiographer 
Sep 24 
comment 
Questions about transformation or integral transformation
@RobertBryant,thank you for your comment.Yes,extending the simple case to complex one and one variable to $n$ variable is an approach.Since I am not a mathematician,I guess maybe someone can give a general complete answer.But to tell the truth,those question is not motivated by Jacobian Conjecture,nor do I have any intention to solve Jacobian Conjecture(in fact I am not so ambitious to try the Jacobian Conjecture),although it maybe is related to the Conjecture 
Sep 24 
comment 
Questions about transformation or integral transformation
@NoahS,yes,it is related,but some people think it is not clearly expressed,so it has been closed.Now I rephrase them and having asked mathematicians around me without any complete answer and constructive suggestion,I have to post it here. 
Sep 24 
asked  Questions about transformation or integral transformation 
Sep 15 
revised 
Solve a PDE related to free boundary problem
fixed grammar 
Sep 15 
suggested  suggested edit on Solve a PDE related to free boundary problem 