Re: Re: Re: Simplifying and Rearranging

*To*: mathgroup at smc.vnet.net*Subject*: [mg95986] Re: [mg95983] Re: [mg95956] Re: Simplifying and Rearranging*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sat, 31 Jan 2009 06:43:05 -0500 (EST)*References*: <gls1u8$hjl$1@smc.vnet.net> <200901301047.FAA06653@smc.vnet.net>*Reply-to*: drmajorbob at longhorns.com

David Park accomplishes much of what he is suggesting, already, in his Presentations package. In example after example, he does quite a good job with step-by-step derivations by manipulating one expression to get the next. I think he's just looking for more ideas from the community and possibly help (even from WRI) in getting further. He's NOT suggesting anything that can't be done or isn't worth doing. Anyone who thinks otherwise should seriously delve into the Presentations package and see what I mean. Bobby On Sat, 31 Jan 2009 00:15:33 -0600, Daniel Lichtblau <danl at wolfram.com> wrote: > 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 > > > -- DrMajorBob at longhorns.com

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