Is there a function in Maple or Mathematica that takes a truncated decimal expansion, and will try to guess at the value in terms of radicals? Can I use the gfun package in Maple for this? Thanks for any help or comments.
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The old versions of Mathematica had
As a neat example, here's where I use
which matches the results of formula 15 in the MathWorld link, while
matches formula 35.
Apparently it can be done, though not quite in the way you ask. Get very high precision accuracy for some number $x,$ then make a vector (list) out of $1,x,x^2, x^3, \ldots, x^n$ for some not large $n.$ You may then ask for an integer relation among these $(n+1)$ numbers, which gives you the coefficients of a polynomial for which $x$ is a root. In case you chose $n$ too large, ask to factor the polynomial over the integers, to get the lowest degree polynomial for which $x$ is a root. From that information you may, with some creativity, calculate an expression for $x$ in terms of radicals. This final step will only give satisfactory results in very special circumstances.