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## Re: Guessing "exact" values

Andrzej Kozlowski May 18, 2007 3:47 AM
Posted in group: comp.soft-sys.math.mathematica
 Mathematica can "recognize" algebraic numbers, by using the function RootApproximant (or the function Recognize in the Legacy NumberTherory package):ToRadicals[RootApproximant[N[Sqrt[2] + Sqrt[3], 30]]]Sqrt[5 + 2*Sqrt[6]]This may not look so impressive  until you check:FullSimplify[Sqrt[2] + Sqrt[3] - Sqrt[5 + 2*Sqrt[6]]]0Anyway, doing this for algebraic numbers has a solid mathematical basis: the so called LLL Lattice Reduction) algorithm. I don=92t know, =however, of any mathematical basis for "recognizing" transcendentals, =except by means of  stored values or some other "ad hoc" approach (essentially "sophisticated guessing")Andrzej KozlowskiOn 17 May 2007, at 18:59, Murray Eisenberg wrote:> As I remember, at IMS'06 (Avignon) Stephen Wolfram (via remote link-=> up)> played with a function to do just that.  Did I remember correctly?>> If so, I cannot recall the name of the function, so I don't know > whether> the function made it into 6.0.  The closest thing I can find is> RootApproximant, but that doesn't seem to "recognize" an expression> involving a transcendental number.>> Szabolcs wrote:>> "Another computer algebra system" has a function, identify(), which>> attempts to guess the exact expression that evaluates to a particular>> numerical value.>>>> Example:>>>> In[1]:= N[3Pi+3/2,10]>>>> Out[1]= 10.92477796>>>>> identify(10.92477796);>>                                    3>>                                    - + 3 Pi>>                                    2>>>> Is there a package with similar functionality for Mathematica?>>>> Szabolcs>>>> --> Murray Eisenberg                     mur...@math.umass.edu> Mathematics & Statistics Dept.> Lederle Graduate Research Tower      phone 413 549-1020 (H)> University of Massachusetts                413 545-2859 (W)> 710 North Pleasant Street            fax   413 545-1801> Amherst, MA 01003-9305>