Re: Simplifying and Rearranging Expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg96050] Re: Simplifying and Rearranging Expressions
- From: John Doty <jpd at whispertel.LoseTheH.net>
- Date: Tue, 3 Feb 2009 06:32:19 -0500 (EST)
- References: <email@example.com> <firstname.lastname@example.org> <email@example.com>
David Bailey wrote:
> John Doty wrote:
>> David Park wrote:
>>> Nevertheless, even simple rearrangement can be difficult. I sometimes think
>>> of it as doing surgery on expressions. I believe it is generally desirable
>>> to use Mathematica to rearrange an expression and not retype the expression.
>>> Retyping is too error prone.
>> In most cases, any description of how to rearrange an expression to a
>> specific form in a CAS will be more complex than a retyped expression. I
>> believe this is a theorem.
>> Therefore, in most cases, the easiest way will be to retype. It's not
>> error prone if you check it, e.g.:
>> Simplify[ retyped == original ]
> Testing successive transformations in this way is useful, but not all
> transformations are exact. Particularly in physics, it is common to take
> a Taylor expansion of part of an expression,
Plot[ approx - exact ] or FindMaximum, or whatever it is you do to
check an approximation. Mathematica is an extremely good tool for
finding and evaluating approximations (it's one of my most common
applications). But you can't do that blindly with any tool.
Besides, Mathematica can do things like Taylor expansions, and you can
check that your approximate form is the same as Mathematica's.
> or maybe even change
> notation is some subtle way.
Usually, I find that a human-comprehensible transformation can be easily
expressed in Mathematica in one direction or the other.
But you haven't addressed my point. What you are asking for is, of
mathematical necessity, the hard way to do the job except in special
cases (e.g. Together). Wolfram seems to like special cases, so if you
can rigorously define one or two, I'm sure they can be added. But
avoiding the need for "surgery" in general is not a practical goal.
John Doty, Noqsi Aerospace, Ltd.
The axiomatic method of mathematics is one of the great achievements of
our culture. However, it is only a method. Whereas the facts of
mathematics once discovered will never change, the method by which these
facts are verified has changed many times in the past, and it would be
foolhardy to expect that changes will not occur again at some future
date. - Gian-Carlo Rota
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