Python and Math

[Rustom Mody]

On Monday, May 19, 2014 3:45:22 PM UTC+5:30, Fabien wrote:
> Hi everyone,

> I am new on this forum (I come from IDL and am starting to learn python)

> This thread perfectly illustrates why Python is so scary to newcomers: 
> one question, three answers: yes, no, maybe.

> Python-fans sure would argue "freedom of choice" is the most important, 
> but "being able to find the right tool for me in less than three days" 
> surely is important too. The paradox of choice ;-)

Point taken.

So let me try to give pointwise answers to the OP's questions

Expanding and factoring equations of all degrees: 
http://docs.sympy.org/dev/modules/polys/wester.html

Numpy for gaussian elimination: https://gist.github.com/tkralphs/7554375
illustrates some of numpy's array-level features.

One thing about numpy that bugs me is that the docs never say how much
is taken straight from APL.  So here is the APL (which I dont claim to understand):

http://dfns.dyalog.com/n_gauss_jordan.htm

Here is an online APL you can run straight from the browser:
http://baruchel.hd.free.fr/apps/apl/


The more general question:

On Sunday, May 18, 2014 9:10:46 PM UTC+5:30, Grant Edwards wrote:
> On 2014-05-18, Bill Cunningham  wrote:
> >     Does Python have good mathematical capabilities?

> No.

> It has very good numerical computation capabilities, but it does not
> really do "math" (at least not what a mathemetician would consider
> "math").

vs Robert's

> Many mathematicians would disagree.
> 
>    http://sagemath.org/

Traditionally mathematicians do two kinds of things - calculating and proving.
Normal mathematicians dont make too much of a distinction between the two.
The more extremists in the one camp look down - as usual - on the other thus:

The provers call the calculators as "Just applied not pure mathematicians"
The calculators say of the provers: "They are not mathematicians but logicians"
(or philosophers)" [Chris had a funny quote on this a few weeks ago]

After computers, a new area emerged - explorers - which straddles proving and calculating.

In short, Grant is speaking from the prover angle whereas Robert is speaking from the
calculator angle.

There is one more point here:

Does language-X (in this case python) have a theoretically sound (ie mathematical) foundation?

Mathematicians coming to CS never bother with this whereas computer scientists, especially
theoretical CSists, at some point or other invariably come to this.

Since its not clear whether this question is being asked, I'm not saying anything more on
it.