Re: ******** Video: FOSS Superiority Versus Commercial Software **********

On 11/29/24 8:58 AM, Farley Flud wrote:

On Thu, 28 Nov 2024 19:30:59 -0600, Physfitfreak wrote:
 

>
I have a feeling it was a matter of default interval. Wolfram, by
default, may have used  6 times shorter intervals in computing the dots,
giving 6 times more dots to find.
>

 I did not use default values.
 The Mathematica code specifies "PlotPoints --> 50" which means to initially
use 50 sample points in each direction (x,y,z).  However, the algorithm
may change this in a recursive manner.
 With MathMod, I specified "Grid": ["500"] which I believe means 500 points
in each direction, but the MathMod documentation is not ideal (this is
expected of a single author FOSS project).
 Also, the plotting algorithms may differ and they probably do.
 Mathematica does not publish its algorithms and I would have to read the
MathMod source code to discover its algorithm.
    

ٰIf you think the difference in speed was due to substantially different algorithms then I'd still give it a probability that Wolfram's intentionally did not use the symmetries which are known beforehand, to cut down the computation time, and MathMod did. The latter may have just solved a two-dimensional curve then revolved it around vertical axis to form the image.
I think so because a 6 times computation time difference is just too high. So I don't throw Wolfram's away just like that.