The emphasis lies on 'trying' Concerning image processing and control 
theory matlab is prefered by most with good reason (for reference: I come 
from these areas)
Since numpy/scipy/matplotlib is on board with Sage, it can easily challenge 
Mathematica in these areas, since the scipy packages can compare quite good 
with
Matlab. And I dare say that sage can easily outsmart the symbolic toolbox 
of Matlab.

On another note: Sage comes with Cython (and of course other possibilities) 
which is much smarter than MEX from matlab concerning low level programming 
for fast code.
And I remember well that a colleague of mine switched very fast to 
Numpy/Cython, because he got sick of MEX files.
A comparison between MEX and Cython would also be a good point.

I suppose some direct use cases where Sage is directly compared to the 
other 4Ms and shows why it is better suited, would be important to such a 
comparison.
Some of the formentioned things above are some reasons why at least I 
prefer Sage over Matlab and Mathematica. 
Maybe it would be a good Idea to collect some more concrete examples?

A short list of other strong points besides the one from above


   1.  The price: Of course
   2. Open
   3. Covers broad functionality
   4. Expandable: It is easy to build Sage packages and expand it's 
   functionality.
   5. The Notebook: It is easy to use, and has very nice typesetting 
   (compared to Mathematica it is far better I think; this could also be in a 
   comparison)
   6. Python: One could always argue about the language itself, but in 
   contrast to the others Sage uses a general purpose language. So it easy to 
   combine Sage with other programs (Ever build standalone Programs with the 
   others?)
   7. Most important Python packages for Math ready to go
   8. A nice community
   9. The price!
   10. ...

Has someone more examples why he/she uses Sage instead of one of the 4Ms? 

Maybe a survey along the users would be also good Idea? This could extend 
the list,
and maybe would at least be a start.


On Monday, December 1, 2014 6:27:56 AM UTC+1, Dr. David Kirkby (Kirkby 
Microwave Ltd) wrote:
>
> On 27 Nov 2014 20:51, "maldun" <dom...@gmx.net <javascript:>> wrote:
>
> > I personally a comparison of sage with the other Systems is quite hard, 
> since all of the other 4Ms concentrate more or less
> > on particular fields of mathematic (e.g. Matlab focus on numerics, 
> Mathematica more on Calculus etc.)
> > Sage is far from perfect but tries to cover all fields at once.
>
> Although I have never tested it myself,  several sources say Mathematica 
> is the best program for symbolic maths.  
>
> But to me at least Mathematica covers a very wide area of mathematics. 
> Inage processing,  control theory,  number theory, numerics, financial etc. 
> I think it tries to cover pretty much everything.  
>
> I believe any attempt to compare the packages would be very difficult and 
> I doubt it is possible to remove personal bias. 
>
> It is totally objective to say Sage is free, whereas neither Mathematica 
> or MATLAB are. But just about other comparison else is going to be 
> subjective. 
>
> Dave.
>

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