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


11h
comment What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers $\sqrt{A}$ and the integer $A$
@AndresCaicedo,Yes,there is a simple inequality.And possibly,some theorems cited from literatures may be unified?
11h
comment What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers $\sqrt{A}$ and the integer $A$
@AndresCaicedo,thank you,I am reading the blog and there are useful theorems
11h
comment What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers $\sqrt{A}$ and the integer $A$
@KConrad,no,but if there is a simple rule,that is a surprise to me.But I don't think there is such a rule.Maybe there is a simple inequality .
12h
asked What is the relation between the length of period of simple continued fraction expansion of quadratic algebraic numbers $\sqrt{A}$ and the integer $A$
1d
comment How to define the input of computable function or Turing machine over real numbers
Thank you a lot
2d
comment Given a formal power series ,decide whether there exists a polynomial the series satisfies and if it exists,how to write it down?
It has not solve the problem about algebraicity of power series over field with characteristics zero
Aug
24
comment Are there any patterns in simple continued fraction expansions of algebraic real numbers?
I think the formula for $2^{\frac{1}{3}}$ is interesting
Aug
24
comment Is any particular algebraic number known to have unbounded continued fraction coefficients?
Here annals.math.princeton.edu/2007/165-2/p04 is an article on Annals about computational complexity of irrational algebraic numbers and of some transcendental.
Aug
24
comment Is any particular algebraic number known to have unbounded continued fraction coefficients?
Here annals.math.princeton.edu/2007/165-2/p04 is an article on Annals about computational complexity of irrational algebraic numbers and of some transcendental numbers.
Aug
23
comment What is the probability that a randomly chosen number from set of c.e.number is period(number)?
The period numbers are in the class of computable irrational numbers with lower computational complexity.It is very interesting to know that most transcendental numbers in number theory are in this class,which is in the lower level in the hierarchy of computable numbers
Aug
23
comment What is the probability that a randomly chosen number from set of c.e.number is period(number)?
@ DenisHirschfeld,I am wondering if there has been or possibly will be any result about constructing irrational algebraic numbers with degree exceeding 2 by constructive mathematics.I intend to think that the coefficients continued fraction expansions of irrational algebraic numbers with degree exceeding 2 are all unbounded.I had just read Stuart's paper on a related generalization of this question.He(Prof.Kurtz)has proven that the related generalization of this question is undecidable,but he original question is still open.
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
@AndrejBauer,I see,and thank you again for your valuable comments.You know,I get a lot of knowledge from your comment and I still care how to solve my intended question . And I have just begin to browse part of pdf which you just tell me ,thank you very much for your help
Aug
13
comment Linkage between homotopy equivalence and identification of algorithms
Thank you very much.It is much more helpful than down vote by someone else
Aug
13
asked Linkage between homotopy equivalence and identification of algorithms
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
And by Complexity and Real Computation by Blum, Cucker, Shub, and Smale,we know the computational complexity of reals is independent of Turing Machine,it can be given a hierarchy by descriptive complexity that is something relevant to finit-model theory.But the hierarchy by descriptive complexity is coarser-grained.Maybe it can separate $NP$ and $P$,I am not sure if it can separate finer-grained complexity like $\sqrt{2}$ and $2^{\frac{1}{3}}$
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
[Cont] the existence of representation with the least computational complexity is puzzling,since we have to put restriction like length on the representation .Hence we have to take account of Kolmogorov complexity of the representation .But I am not sure combination of computational complexity and Kolmogorov complexity will give a definition that is fit into our intuition.
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
[Cont]and is there any total or partial ordering between these different representation of the same real by ordering of computational complexities of the computably isomorphic functions?If so,we can choose the least complex one as suitable representation to compare the computational complexity of reals,otherwise the comparison is meaningless.but by intuition,we know it meaningful.I am not sure if it exist,and if it is easy to get the ordering
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
@AndrejBauer,you say "We now know that an acceptable representation of the reals is one by rapid Cauchy sequences of rationals. (An important theorem states that any two representations of reals which are acceptable are actually computably isomorphic.)".Now,here we have to neglect the computational complexity of the actually computably isomorphic map or function.If we take account for the complexity of the isomorphic function,we can give hierarchy of computable reals.[cont]
Aug
13
comment How to define the input of computable function or Turing machine over real numbers
@AndrejBauer,thank you.I have just browsed your answer to that post.The main point is :Turing Machine can not implement the axioms for what we call reals,so to ask for a suitable representation of reals is impossible?
Aug
13
accepted How to define the input of computable function or Turing machine over real numbers