One of the most important differences between Sage and Mathematica, is that 
no one of the developers has such a big ego than Stephen Wolfram. It even 
got it's own music theme: https://mollyrocket.com/11235

And we all know that Python will never decipher the universe like the 
Wolfram language will *cough**cough*

Back to Topic:

I like that idea very much. But I think instead of simply comparing Sage 
with one of the other 4M's
we should focus on emphasizing that Sage covers a lot of the functionality 
for no cost.

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.

This is what I love about this project: With the complete power of all 
Python libraries, one can do calculus, algebra and numerics
equally strong in one box, without transfering forth and back between 
commercial codes, which try to be incompatible as possible.
This can be quite frustrating if you work on topics where Calculus, 
Symbolics and Numerics heavily mix (e.g. Continuum mechanics;
>From the symbolic expression to the variational formulation, to the finite 
element matrix)

On Tuesday, November 18, 2014 10:35:21 PM UTC+1, William wrote:
>
> See this interesting document: 
>
>    
> http://www.maplesoft.com/products/maple/compare/HowMapleComparestoMathematica.pdf
>  
>
> It would be valuable to our users (and potential users) if we had a 
> similar document which explains and *argues* for why we believe our 
> approach to mathematical software is better than the ones taken by 
> Mathematica, Magma, Maple, and Matlab. 
>
> Some samples from their document: "About 95% of Maple's functionality 
> is written in the  Maple programming language, and every Maple user 
> can freely inspect the source code for any of these predefined Maple 
> library routines. [...] In Mathematica, the source code for all the 
> predefined library routines written in the Mathematica  programming 
> language is hidden from the user." (*) 
>
> When arguing for Maple's language over the Mathematica language, they 
> say "Functional programs are often opaque; most people,  even 
> experienced programmers, find functional-style  programs to be 
> significantly harder to write, read, and  debug." 
>
> (*) We had a specific situation a few years ago where an academic 
> wrote a package in maple, and a student at UW wanted to write a 
> similar open source package in Python.  We specifically asked 
> Maplesoft if the student could look at the source code of Maple, which 
> is "open" in the sense they list above, then be inspired by it in 
> writing his own Python code.   They came back and clearly said "no 
> way; absolutely not!" 
>
>
> -- 
> William Stein 
> Professor of Mathematics 
> University of Washington 
> http://wstein.org 
>

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