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Re: Re: Simplifying and Rearranging Expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg95983] Re: [mg95956] Re: Simplifying and Rearranging Expressions
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 31 Jan 2009 01:15:33 -0500 (EST)
• References: <gls1u8$hjl$1@smc.vnet.net> <200901301047.FAA06653@smc.vnet.net>

AES wrote:
> In article <gls1u8$hjl$1 at smc.vnet.net>,
>  "David Park" <djmpark at comcast.net> wrote:
> [...]
>> Various routines such as Together, Apart, Factor, TrigReduce, TrigFactor,
>> TrigExpand, TrigToExp, GroebnerBasis etc., can be useful in getting a
>> specific form. MapAt is very useful for doing surgery on specific parts of
>> an expression. Mathematica often gets two factors that have extra minus
>> signs. You can correct that by mapping Minus onto the two factors. For
>> integrals in the wrong form you could cheat by trying to find the constant
>> by which they differ by subtracting and simplifying, and then use that in
>> the derivation.
> 
> Let's say it like it is:  It's not just "difficult" for ordinary users 
> to use and control many of these advanced tools:  It's basically 
> **impossible** for the average user to learn what some of these tools 
> do, because they're so complex and the results can depend so critically 
> on what you put into them; all you end up doing is thrashing around 
> endlessly, trying to get them to produce the results you want.

It may well be difficult to use these in order to produce results that 
satisfy certain constraints. But the functions named above are mostly 
well defined in terms of what they do. This is in contrast to, say, 
Simplify, which has operational semantics that are generally well known, 
but is impossible to pin down in terms of expected result.


> The more powerful they get, the less they're worth trying to learn.  
> [...]
> If your goal is to have Mathematica notebooks serve simultaneously as 
> "exposition documents" and "calculation performing documents", might 
> this be a lot easier than endless fighting with option-laden and 
> temporally unstable Mathematica expressions like "Together, Apart, 
> Factor, TrigReduce, TrigFactor, TrigExpand, TrigToExp, GroebnerBasis" 
> and all their even more arcane extensions?

Again, these all have well defined semantics and produce results that 
conform to vertain criteria. They are most definitely helpful to have 
around, if you do work that requires any sort of canonical forms of 
results. And there are other situations in which they can be useful or 
even essential. This may not be true of your work, but if it involves 
phases that do symbolic computation of any consequence, I would not be 
surprised if you are missing out on some very useful tools.


Daniel Lichtblau
Wolfram Research

• References:
  • Re: Simplifying and Rearranging Expressions
    • From: AES <siegman@stanford.edu>