Path: utzoo!attcan!uunet!lll-winken!decwrl!ucbvax!TERRA.OSCS.MONTANA.EDU!iphwk
From: iphwk@TERRA.OSCS.MONTANA.EDU (Bill Kinnersley)
Newsgroups: comp.sys.next
Subject: Re: Problem13
Message-ID: <9002141656.AA14667@terra.oscs.montana.edu>
Date: 14 Feb 90 16:56:50 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Lines: 29

Mathematica 1.2 on a NeXT, 94.6 seconds.

We NeXT users must still contend with the bug in Together[],
which cannot treat fractional powers correctly.

To prevent Together[] from seeing the Sqrt's, I reworded the problem.
I defined functions r and p in terms of their derivatives,
Togethered the result, then at last replaced r and p with the Sqrts.

Can someone who (unlike me) knows what they are doing,
say if there is a more efficient way to handle this?

Timing[
D1[f_] := D[D[D[D[f,x],x] + D[D[f,y],y] + D[D[f,z],z],x],x];
D2[f_] := n^2 * (D[D[f,x],x] + D[D[f,y],y]);
exp = Sin[n*r[x,y,z]*z/p[y,z]]/r[x,y,z];
Derivative[1,0,0][r][x_,y_,z_] := x/r[x,y,z];
Derivative[0,1,0][r][x_,y_,z_] := y/r[x,y,z];
Derivative[0,0,1][r][x_,y_,z_] := z/r[x,y,z];
Derivative[1,0][p][x_,y_] := x/p[x,y];
Derivative[0,1][p][x_,y_] := y/p[x,y];
Simplify[Together[D1[exp]+D2[exp]]/.
 {r[x,y,z]->Sqrt[x^2+y^2+z^2],p[y,z]->Sqrt[y^2+z^2]}]]

-- 
--Bill Kinnersley
  Physics Department   Montana State University    Bozeman, MT 59717
  INTERNET: iphwk@terra.oscs.montana.edu      BITNET: IPHWK@MTSUNIX1
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