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automatic evaluations, was Re: An open letter

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16585] automatic evaluations, was Re: An open letter
  • From: Martin Kraus <mkraus at theorie3.physik.uni-erlangen.de>
  • Date: Wed, 17 Mar 1999 23:54:59 -0500
  • Organization: Regionales Rechenzentrum Erlangen, Germany
  • References: <7cleqb$9oh@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jack Goldberg wrote:
> 
> Hi Group,
> 

> I am fairly confident that this type of problem can be solved by
> a judicious combination of "holds"  and "releaseholds" and "evaluates".

And HoldForms and all the stuff related (I remember Unevaluated and 
Literal, but never was able to apply these things in a sensible way).

> The fact remains that it is something of a challange.  It shouldn't
> be. I say this because at least one other CAS has an easy means for
> accomplishing this goal.
> 
> What say yo'all?
> 
> Jack
> 

My solution is to use undefined symbols. For example in order to
show the product rule, DO NOT define u[x] and v[x] and then 
evaluate

dproduct := D[u[x] * v[x], x]

It gives you the "unevaluated" result. Then you can define f and g
and asking for dresult will give you the evaluated result. 
(The same works for your example of integration by parts.)

Applying general formulas by defining previously undefined symbols
looks rather natural to me. 

However, what you are asking for is more a kind of tracing an
evaluation I guess. But which steps of the evaluation should be
reported? Only user defined? Why?

Greetings

Martin Kraus


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