iphwk@TERRA.OSCS.MONTANA.EDU (Bill Kinnersley) (02/15/90)
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
226 Transfer complete.iphwk@TERRA.OSCS.MONTANA.EDU (Bill Kinnersley) (02/15/90)
Sorry, that should have gone to sci.math.symbolic. But it does point out the problems we have in getting software updates. The released version Mathematica 1.2 has a serious bug, as noted. Users on other machines are supported by Wolfram Research, and they received a maintenance upgrade correcting the bug. When questioned, they say "Talk to NeXT about it." NeXT says, "Mumble, RSN." Not clear to me how (or even if) this will ever be fixed before the next version of the OS. -- --Bill Kinnersley Physics Department Montana State University Bozeman, MT 59717 INTERNET: iphwk@terra.oscs.montana.edu BITNET: IPHWK@MTSUNIX1 226 Transfer complete.