Re: Some bugs in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg59637] Re: Some bugs in Mathematica
- From: "Alex" <akhmel at hotmail.com>
- Date: Mon, 15 Aug 2005 06:50:29 -0400 (EDT)
- References: <ddk8nf$1ck$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Bill Rowe wrote:
>
> In essence, for the same reason a human misses a particular simplification, >i.e., Mathematica simply hasn't been told about that particular simplification.
>
> Simplfy and FullSiimplfy have a finite set of transforms to apply to achieve >simplification. If none of these result in a simplification, the result is >returned in its original form. This is not one bit different than a human who >tries to simplify an expression by every means he knows and stops when none of >his attempts work.
This is exactly my point. People who made Mathematica did some very
sloppy job, when integral clearly expressible in terms of elementary
functions is given in a super over-complicated form. It is a sloppy job
and it should be corrected.
> Do you really want Mathematica to try every possible gouping of variables in >a complex expression that might result in a simpler expression?
YES. And even more than that, this is how algorithm of integration
should look: Mathematica should have a huge computerized table of
integrals and its first step should be in comparison with the table and
if the integral is found in the table, the result should be printed and
that's the end of it. Step 2: if the integral is not found in the
table, then typical substitution should be tried to reduce the integral
to the one available in the table and those should definitely include
such substitutions such as inversion, trigonometric or hyperbolic
function substitution, etc. Only when these 2 steps fail, any internal
algorithm of integration should be used.
>For arbitrary expressions, I suspect an attempt to do this would cause the >execution time of FullSimplify to increase exponentially with complexity and >it would be trivial to come up with examples that would lead to unacceptable >execution times on even the fastest hardware.
>
You are wrong. The system should look at the integrand and by its
appearance to decide whether is computable in terms of elementary
functions. If yes, the methods are well developed and results can be
achieved in no time.
> Mathematica is simply a very useful tool. Like any tool, it has limitations >and isn't perfect. Used intelligently, Mathematica produces useful results in >reasonable time. Used blindly, you get pretty much what you deserve.
It has been my experience that whenever something totally inadequate is
pointed out, the response is "we are not perfect". There is difference
between being not perfect and totally inadequate. We are talking about
elementary integral here.
Ok, please help me to use Mathematica intelligently. I have an
expression:
y= Integrate[1/(r*Sqrt[r^2-a^2]*Sqrt[r^2-b^2]),{r,a,x}]
I need to express explicitly x as a function of y. I know how to do it
with my result through ArcTanh. I do not know how to do it through
Appel function. Now, please show me how to use Mathematica
intelligently and get the desired result.
Alex
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