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Re: Total Derivative and Output Display Question

• To: mathgroup at smc.vnet.net
• Subject: [mg65127] Re: Total Derivative and Output Display Question
• From: "Matt" <anonmous69 at netscape.net>
• Date: Wed, 15 Mar 2006 06:28:55 -0500 (EST)
• References: <duubsl$h0s$1@smc.vnet.net><dv69pb$ocs$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Daniel,
  Thanks for your response.  First off, let me clarify that I am not
knocking Mathematica, rather, whenever I find it difficult or
impossible to do something in Mathematica, I usually assume it is due
to my ignorance of the system, which is what I meant when I said that
my approach was burdensome and convoluted.
  Now, onto the question at hand.  The way in which you mapped the
Mathematica output to the traditional output with

Derivative[0, 1][z][x[r[t], s[t]], y[r[t], s[t]]]   to be dz/dy
Derivative[1][s][t]*Derivative[0, 1][y][r[t], s[t]] to be dy/ds ds/dt
Derivative[1][r][t]*Derivative[1, 0][y][r[t], s[t]] to be dy/dr dr/dt
Derivative[1][s][t]*Derivative[0, 1][x][r[t], s[t]] to be dx/ds ds/dt
Derivative[1][r][t]*Derivative[1, 0][x][r[t], s[t]] to be dx/dr dr/dt
Derivative[1, 0][z][x[r[t], s[t]], y[r[t], s[t]]]   to be dz/dx

is more or less exactly how I set up my replacement rules.  But even
after doing that, I still didn't get the output required, because
Mathematica rearranged the order of the derivatives, making the output
non-sensical (which, I admit, could be due to my applying the rules
incorrectly).  I know that I could go through some elaborate
machinations using HoldForm and finding the various parts I want to
rearrange (I think), but again, that seems to be a horrible solution to
a problem that should be so simple.  Mathematica is used for many
things, but actually doing mathematics is, I believe its raison d'etre.
 Granted, from what I read in the documentation, Mathematica's solution
is very general and elegant, it is, nonetheless gibberish to any
mathematician not familiar with the peculiarities of Mathematica
syntax.  I am just surprised that there isn't a simple and elegant way
to get output that would be readable by a person not familiar with
Mathematica.  For instance, a person trying to do their Calculus
homework would have spent much more time trying to contort
Mathematica's output into a form readable by the teacher, than they
would have by just working it out on paper and turning it in.

Matt