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Say we have two transcendental numbers, u and v. And u presumably can be obtained as a result of applying a rational function $Q$ with integer coefficients to v. Is it possible to find such rational function?

In other words we need to find two polynomials $P_1$ and $P_2$ with integer coefficients such that

$u=\frac{P_1(v)}{P_2(v)}$

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    You would want to include the restriction that $P_1$ and $P_2$ have no common factors.2011-04-30
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    Yes, of course. I meant the simplest form of that function.2011-04-30
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    If we find at leat one pair of polynomials we can cancel the common factors out of course so the task is ti find at least one such pair or the function Q directly.2011-04-30
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    It looks as if even the case of $P_2=1$ is hard...2011-04-30
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    How are you given $u$ and $v$?2011-04-30
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    Well I meant can there be such function of u and v that gives the polynomial's coefficients irrespective of the method of how u and v are given.2011-04-30

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