2009/7/1 William Stein <wst...@gmail.com>:
> Perhaps I'm missing the point, but I'm taking this as a message to
> focus in Sage more on the algebraic/symbolic side of mathematics
> (e.g., Magma, Maple, Mathematica) rather than the numerical side, at
> least for the time being.    I don't have a problem with that
> personally, since that is what I do best, and where most of my
> personal interests are.

I'm joining this conversation late, so I am glad to see the
conclusions reached so far (not to give up on numerics!).

If I may highlight a distinction (maybe obvious to some) between SAGE
and NumPy-based experiments:

Sage provides a "language" for eloquently expressing
algebraic/symbolical problems.  On the other hand, NumPy is mainly a
library (that provides a data structure with accompanying operations).

This means that users of that library expect to run their code
unmodified on any Python platform where it is available (Sage
included).  Whether this expectation is reasonable or not is up for
debate, but I certainly found it surprising that I had to modify my
code in order to compute things in Sage.

On a more practical level, it frightens me that Maxima spawns so
easily without my even knowing, simply by refering to a certain
variable or by using the wrong "exp".  That's the kind of thing that
kills numerics performance!

I'm not convinced that commercial packages have crossed this barrier
successfully either.  I've seen talks where people switch between
Maple and MATLAB to do different tasks, which tells me that this is a
more general problem that is far from solved.

Stéfan

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