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• From: mathgroup-adm at christensen.cybernetics.net
• Date: Wed, 26 Oct 1994 01:04:09 -0500
• Apparently-to: <wri-mathgroup at wri.com>
• Apparently-to: <ianc at wri.com>

```--------------
From:	MX%"Jack.Goldberg at math.lsa.umich.edu"    21-OCT-1994 05:21
In a recent note to sci.math.symbolic, Richard Chen at Yale (I believe
this is correct) asked how to simplify the output of
Integrate[sec[x],{x,0,ArcCos[s]}]
<snip>
ArcTrig[Trig[x]] = x,  where Trig is any of Cos, Sin, Tan etc.
There is no single command that does this but I think there
ought to be.  I'll go one step further.  Let  f  be a function with an
inverse, InverseFunction[f].  Now  f[InverseFunction[f][x]] =  x  but
this simplification does not occur in the other order
InverseFunction[f][f[x]]
<snip>

I think this is deliberate on the part of Mma and not necessarily bad.  You can
get  into trouble simplifying things because the inverse of a function is not
necessarily a function itself because they may not be single valued.  The trig
functions are good examples.  The Sin is single valued but the Arcsin is not.
The user may not want the principle value given by an ordinary calculator.
Depending on the problem, the user may be the best one to choose the value of
the inverse among many possible ones.

Chip

```

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