# Re: "frac2" button

```I hate to do this, but there is a wonderful library for the HP (only
about 1.5 kb) that does what this guy is looking for.  It's called QPI.
It can't give the result you want all the time (since it only handles a
finite number of representations and is limited by the input as well as
some other things) but it converts numbers to fractions, multiples of
pi, exponential form, logarithmic form, or square roots.  Here are some
examples:

.6123724356 -> 1/2*sqrt(3/2)
.3737373737 -> 37/99
4.71238898  -> 3/2*pi
12.18249396 -> e^(5/2)
.2876820724 -> ln(4/3)

I just thought I should mention this since the discussion seemed to be
drifting along the lines of feasibility.  So I thought you should know.

-David-

Blakely wrote:
>
> I hear roumers of ppl working on a symbolic manipulation for the ti-86!
> does anyone have any further info on how or where i can get this
> invofmatin?
>
> Tavis Segura <tsegura@rice.edu> wrote in article
> <34CD5CB0.1C4C@rice.edu>...
> > First of all, the TI-92 does symbolic math, but once you approximate
> > your numbers, you are not much better off than you are on the '85.  The
> > "exact()" command is not foolproof: do divination there.  Take a look.
> > The function
> >
> > approx(sqrt(2)/2)
> >
> > will return .70710678118655 for an answer.  In that case,
> >
> > exact(.70710678118655)
> >
> > would return sqrt(2)/2, wouldn't it?  Not a chance.  All it gives you is
> > a large fraction:
> >
> > 14142135623731
> > --------------
> > 20000000000000
> >
> > Adjusting the tolerance (a second parameter to adjust for roundoff
> > errors) does not do any better:
> >
> > exact(.70710678118655,1*10^-13)
> >
> >  =   2744210
> >      -------
> >      3880899
> >
> > In short, The TI-92 cannot do this "frac2" stuff.  It is a truly amazing
> > machine, but don't expect too many miracles.  (Sigh) I guess you have to
> > figure out the numbers yourself (like multiplying by sqrt(2) in this
> > example to get approximately 1.) or using better judgement about what
> > you want your calculator to approximate.
> >
> > Tavis
> >
> > Chopps wrote:
> > >
> > > then how do you explain how the ti-92 does it?  I want some kind of
> > > symbolic manipulation, that i hear ppl are working on!!!
> > >
> > > RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU> wrote in article
> > > <01ISU8F74CAUCIRDY1@ritvax.isc.rit.edu>...
> > >
> > >
> > > > As soon as you can input a decimal that is _exactly_ equal to half
> > > > the square root of 3, then you can start thinking about how to create
>
> > > > a "frac2" button that will report this.  But that will be a very long
> > > > time!
> > > >
> > > > The best you can possibly do is make a _guess_ or a _bet_ that the
> > > > decimal value in your hands was really meant to be an approximation
> > > > of some particular easily-described irrational value.  If you have
> > > > some 12- or 13-place representation stored in memory W, for example,
> > > > you might try using Frac on W^2 and decide whether you like what you
> > > > see.  Another plausible effort might be to divide W by pi (and try
> > > > Frac again, maybe).  Of course, what you have might just be a
> > > > representation of 2 minus the square root of 3, or the
> > > > cube root of 5 plus the cube root of 7, or pi^2, or some weirder
> > > > number that you will never guess the secret of.  Calculators are
> > > > wonderful, but they have no supernatural powers of divination (as far
> > > > as I know, anyway).  :-)}
> > > >
> >

```

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