Path: utzoo!attcan!uunet!snorkelwacker!ai-lab!rice-chex!bson
From: bson@rice-chex.ai.mit.edu (Jan Brittenson)
Newsgroups: comp.sys.handhelds
Subject: Re: calculators vs computers
Message-ID: <10888@life.ai.mit.edu>
Date: 21 Sep 90 13:35:57 GMT
References: <1049@helens.Stanford.EDU>
Sender: news@ai.mit.edu
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In article <1049@helens.Stanford.EDU> 
   zimmer@calvin.stanford.edu (Andrew Zimmerman) writes:

 > I purchased an HP48sx a couple of months ago to play around with.
 > Anyway, my question is, "How do people actually use this type of
 > calculator/computer?"

   I got my 48 for several reasons. The major is that differentiation
is such a menial and boring task, and that the calculator does
differentiation and a couple of COLCTs in no time. QUAD, the solver,
and matrices are most handy as well. I'm surprised the 48 can't cope
with symbolic integration as well, a fair-sized form table and
substitution can take you quite far, certainly it's not much more
difficult to code substitution or integratiion in parts than chain
rule differentiation. The nontrivial cases will always have to be done
by hand, anyway. 

   This leads me to a question I'd like to post. It might help answer
your question.

   I just wrote the following simple program to see how feasible it
would be to let the calculator handle L'Hopital's rule:


<< { '&A/&B' 'dX(&A)/dX(&B)' }
   vMATCH 
   << EVAL COLCT >> IFT
>>

(slightly modified from my test, but it should work fine)
'd' above refers to the delta character.

Now, what I'd like is:

	- A means of supplying the variable of differentiation ('X'
	  above) as an argument without having to resort to
	  constructing algebraics using strings. I.e. something similar
	  to 'd&S(&A)/d&S(&B)' (see above) where S is a local symbol
	  bound to a name.

	- A means of telling whether an expression is indeterminable.
	  What can be done, is replacing '&X/&Y' with '&X=&Y',
	  splitting it up with EQ->, separately evaluate the numerator
	  and denominator, and checking for 0/0, inf/inf, 0*inf, etc,
	  where 'inf' would indicate an infinite-result error. A
	  simple solution on HP's behalf would have been to let 0 0 /
	  return the algebraic '0/0', and 1 0 / the name 'n7' (or some
	  other predefined special number) to indicate an infinite
	  result. Only in Symbolic mode, and by EVAL, naturally.

   (To those not familiar with L'Hopital's rule, the differentiation
is to be repeated until the expression takes a determinable form,
which is the limit.)