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Re: Deleting Integrate[] transformation rule

• To: mathgroup at smc.vnet.net
• Subject: [mg87629] Re: Deleting Integrate[] transformation rule
• From: Szabolcs <szhorvat at gmail.com>
• Date: Tue, 15 Apr 2008 05:45:07 -0400 (EDT)
• References: <ftq5ab$it$1@smc.vnet.net> <ftscv1$b81$1@smc.vnet.net>

On Apr 14, 11:44 am, UHAP023 at alpha1.rhbnc.ac.uk wrote:
>
> My apologies. I typed the above in a rush, hence the syntax errors --
> including I notice an extraneous ']' in the derivative expression.
> However you did not address the question.  It must be possible to
> Unprotect Integrate[] and modify it to remove the transformation rule that
> it uses to pattern match and convert integrand expressions of the form
> 1/Sqrt[1-m*Sin[phi]^2] to resultant integral expressions of the form
> EllipticF[phi,m] -- thus preventing EllipticF[] appearing in any result
> produced by Integrate[].  It is unclear to me from the Mathematica 4.0 docs
> I have how to do this.  The Hold* family of functions, HoldComplete in
> particular look relevant??  Can anybody confirm/refute and supply a worked
> example of this procedure?
>

Hi Tom,

It is not possible to access the source code of Integrate (some parts
of it are not even written in the Mathematica language, but
implemented at a lower level).  Even if we had access to the source
code, I imagine that modifying it would not be a trivial task.
(Unlike derivation, symbolic integration cannot generally be done by
simply applying a set of transformation rules recursively.)

You will find some notes about the implementation of Integrate here:

http://reference.wolfram.com/mathematica/note/SomeNotesOnInternalImplementation.html