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Re: Re: Deleting Integrate[] transformation rule

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87651] Re: [mg87609] Re: Deleting Integrate[] transformation rule
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 15 Apr 2008 05:49:18 -0400 (EDT)
  • References: <ftq5ab$it$1@smc.vnet.net> <ftscv1$b81$1@smc.vnet.net> <200804140944.FAA08180@smc.vnet.net>

It seems that not everything that "must be possible"  is always  
possible. In fact, in this case, it is definitely not possible. You  
cannot in "remove" any transformations used by Integrate. The best you  
can do is to try to post-process answers returned by Integrate using  
FunctionExpand or FullSimplify with chosen complexity functions, but  
doing this will not transform EllipticF[phi,m] into anything else. You  
can of course wrap Hold or HoldForm over EllipticF[phi,m] but that  
will simply prevent any integration from being carried out. Of course  
if that is what you wanted then, indeed, it is definitely possible.

Andrzej Kozlowski


On 14 Apr 2008, at 18:44, UHAP023 at alpha1.rhbnc.ac.uk wrote:
> Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> : UHAP023 at alpha1.rhbnc.ac.uk wrote:
>
> : > When integrating Mathematica knows the result of  
> D[EllipticF[phi,m, phi]] =
> :  
> ====================================================================!!
> : Syntax error: a square bracket is missing.
>
> : > 1/Sqrt[1-m*Sin[phi]^2]] and will produce expressions containing
> : > EllipticF[] in its result when it encounters such a pattern.  I  
> want
> : > to prevent this -- that is Unprotect Integrate[] and make it  
> forget
> : > this rule so that EllipticF[] will not appear in the result.
>
> : No need to do that: just use the correct syntax as in,
>
> : In[1]:= D[EllipticF[phi, m], phi]
>
> : Out[1]=
>
> :            1
> : ---------------------
> :                     2
> : Sqrt[1 - m Sin[phi] ]
>
> 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?
>
> Thanks
> Tom.
>
> : Regards,
> : -- Jean-Marc
>
> Ps. the email address in the header is just a spam trap.
>
> -- 
> Tom Crane, Dept. Physics, Royal Holloway, University of London,  
> Egham Hill,
> Egham, Surrey, TW20 0EX, England.
> Email:  T.Crane at rhul dot ac dot uk
> Fax:    +44 (0) 1784 472794
>



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