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Python and Math

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  Python and Math "Bill Cunningham" <nospam@nspam.invalid> - 2014-05-17 23:13 -0400
    Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-17 20:26 -0700
      Re: Python and Math "Bill Cunningham" <nospam@nspam.invalid> - 2014-05-18 01:04 -0400
    Re: Python and Math Chris Angelico <rosuav@gmail.com> - 2014-05-18 13:33 +1000
    Re: Python and Math Gary Herron <gary.herron@islandtraining.com> - 2014-05-17 21:12 -0700
    Re: Python and Math Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-05-18 04:51 +0000
      Re: Python and Math "Bill Cunningham" <nospam@nspam.invalid> - 2014-05-18 01:33 -0400
      Re: Python and Math Roy Smith <roy@panix.com> - 2014-05-18 09:25 -0400
        Re: Python and Math Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-05-18 15:05 +0100
    Re: Python and Math Wolfgang Keller <feliphil@gmx.net> - 2014-05-18 15:59 +0200
    Re: Python and Math Grant Edwards <invalid@invalid.invalid> - 2014-05-18 15:40 +0000
      Re: Python and Math "Bill Cunningham" <nospam@nspam.invalid> - 2014-05-18 14:09 -0400
        Re: Python and Math Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-05-20 20:40 -0400
        Re: Python and Math Tony the Tiger <tony@tiger.invalid> - 2014-05-21 00:59 +0000
          Re: Python and Math Robert Kern <robert.kern@gmail.com> - 2014-05-21 10:32 +0100
        Re: Python and Math Robert Kern <robert.kern@gmail.com> - 2014-05-21 10:34 +0100
      Re: Python and Math Robert Kern <robert.kern@gmail.com> - 2014-05-18 19:42 +0100
        Re: Python and Math Fabien <fabien.maussion@gmail.com> - 2014-05-19 12:15 +0200
          Re: Python and Math Tim Golden <mail@timgolden.me.uk> - 2014-05-19 11:30 +0100
          Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-19 05:46 -0700
            Re: Python and Math Chris Angelico <rosuav@gmail.com> - 2014-05-19 23:09 +1000
              Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-19 06:15 -0700
                Re: Python and Math Chris Angelico <rosuav@gmail.com> - 2014-05-19 23:24 +1000
                Re: Python and Math Gene Heskett <gheskett@wdtv.com> - 2014-05-19 10:22 -0400
          Re: Python and Math wxjmfauth@gmail.com - 2014-05-19 07:56 -0700
            Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-19 09:09 -0700
              Re: Python and Math wxjmfauth@gmail.com - 2014-05-19 12:07 -0700
                Re: Python and Math Tim Golden <mail@timgolden.me.uk> - 2014-05-19 20:18 +0100
                  Re: Python and Math wxjmfauth@gmail.com - 2014-05-20 02:19 -0700
                    Re: Python and Math Tim Golden <mail@timgolden.me.uk> - 2014-05-20 11:13 +0100
                      Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-20 04:20 -0700
                        Re: Python and Math Tim Golden <mail@timgolden.me.uk> - 2014-05-20 12:55 +0100
                          Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-20 07:14 -0700
                        Re: Python and Math "Frank Millman" <frank@chagford.com> - 2014-05-20 14:51 +0200
                          Re: Python and Math chris.barker@noaa.gov - 2014-05-21 16:14 -0700
                            Re: Python and Math wxjmfauth@gmail.com - 2014-05-21 23:52 -0700
                            Re: Python and Math "Frank Millman" <frank@chagford.com> - 2014-05-22 11:04 +0200
                      Re: Python and Math wxjmfauth@gmail.com - 2014-05-20 06:42 -0700
                        Re: Python and Math Rustom Mody <rustompmody@gmail.com> - 2014-05-20 07:23 -0700
                Re: Python and Math Cameron Simpson <cs@zip.com.au> - 2014-05-20 09:03 +1000

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#71717 — Python and Math

    Does Python have good mathematical capabilities? I am interested in 
learning a second language for mathematical purposes. I am considering 
looking at python, perl, fortran, Adas out. It looked too complicated to 
learn. Perl looked easy and I haven't really looked into python.

Bill

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#71718

On Sunday, May 18, 2014 8:43:11 AM UTC+5:30, Bill Cunningham wrote:
> Does Python have good mathematical capabilities? I am interested in 
> 
> learning a second language for mathematical purposes. I am considering 
> 
> looking at python, perl, fortran, Adas out. It looked too complicated to 
> 
> learn. Perl looked easy and I haven't really looked into python.
> 

What does the word 'mathematical' connote for you?
On the whole the term is so wide that its hard to answer without some
more context.

For example there's numpy,scipy for numerical and scientific* computing, there's sage, ipython etc.


Today many people who want a general purpose programming language with
a mathematical flair, choose Haskell

For statistics R is quite unbeatable (I am told), which is not python
or any of the others you mention.

Then there are specialized theorem proving systems.

Another question you should answer is "Whats the first programming
language you know?"

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#71724

"Rustom Mody" <rustompmody@gmail.com> wrote in message 
news:09bbda59-9c37-44b0-acfc-0571d4fe8fcb@googlegroups.com...

> What does the word 'mathematical' connote for you?
> On the whole the term is so wide that its hard to answer without some
> more context.
>
> For example there's numpy,scipy for numerical and scientific* computing, 
> there's sage, ipython etc.
>
>
> Today many people who want a general purpose programming language with
> a mathematical flair, choose Haskell
>
> For statistics R is quite unbeatable (I am told), which is not python
> or any of the others you mention.
>
> Then there are specialized theorem proving systems.
>
> Another question you should answer is "Whats the first programming
> language you know?"

    Well linear algebra and gaussian elemination. Expanding and factoring 
equations of all degrees and identities. Not so much statistics. Some 
geometry. Euclidean and spatial.

Bill

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#71720

On Sun, May 18, 2014 at 1:13 PM, Bill Cunningham <nospam@nspam.invalid> wrote:
>     Does Python have good mathematical capabilities? I am interested in
> learning a second language for mathematical purposes. I am considering
> looking at python, perl, fortran, Adas out. It looked too complicated to
> learn. Perl looked easy and I haven't really looked into python.

Absolutely it does! In the built-in types, your integer has arbitrary
precision, and there is an arbitrary-precision Decimal type in the
standard library. There is also, naturally, a standard set of trig
functions and so on. With additional libraries, you can get numeric
and scientific functionality (lots of which is written in Fortran, as
I understand it), giving incredibly high performance for a high level
language; look into SciPy and NumPy. Strongly recommend Python for
numeric work.

ChrisA

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#71722

On 05/17/2014 08:13 PM, Bill Cunningham wrote:
>      Does Python have good mathematical capabilities? I am interested in
> learning a second language for mathematical purposes. I am considering
> looking at python, perl, fortran, Adas out. It looked too complicated to
> learn. Perl looked easy and I haven't really looked into python.
>
> Bill

Depends on what you mean by mathematics.  The language itself has a 
reasonable set of numeric types and operations on those types, but what 
really makes Python shine is the libraries built on Python and their 
capabilities.    Beside the several already mentioned, I'll add
     Sage: www.sagemath.org/index.html
which presents a consistent Python interface to nearly 100 OpenSource 
mathematical packages containing symbolic manipulation of all sorts of 
algebra, calculus, linear algebra, plotting, rings and groups, and much 
*much* more.

Gary Herron

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#71723

On Sat, 17 May 2014 23:13:11 -0400, Bill Cunningham wrote:

> Does Python have good mathematical capabilities? I am interested in
> learning a second language for mathematical purposes. I am considering
> looking at python, perl, fortran, Adas out. It looked too complicated to
> learn. Perl looked easy and I haven't really looked into python.

Yes, Python is excellent for mathematics. Python is rapidly taking over 
as the language of choice for scientific computing:

http://www.talyarkoni.org/blog/2013/11/18/the-homogenization-of-scientific-computing-or-why-python-is-steadily-eating-other-languages-lunch/


You say you want to learn a *second* language, but you don't say what 
your first language is. Nor do you say what sort of mathematics you wish 
to do, or at what level. Depending on what you want to do, you might be 
best off with Mathematica, if you can afford it. Otherwise, there's an 
Open Source and free alternative, Sage, which uses Python.

You may find that the IPython interactive interface to Python is useful. 
It presents an interface which should be familiar to anyone with 
experience with Mathematica. 

For symbolic maths, I like Sympy, where you can do things like this:


py> from sympy import *
py> x, y = symbols('x y')
py> diff(cos(3*x+1), x)
-3*sin(3*x + 1)
py> integrate(-3*sin(3*x+1), x)
cos(3*x + 1)


There is also Numpy and Scipy, for heavy-duty numerical mathematics.

I recommend that you start with Python 3.4, as it is the latest version 
of Python, and also because I'm the author of the statistics standard 
library. It's not a full-blown professional statistics language like R, 
Matlab or SAS, but if you need basic scientific calculator level 
statistics it is useful. Feedback on the library is always welcome.

As far as other languages go, I think that Fortran is still an excellent
language if you need to write high-powered, low-level numeric functions,
but if you just want to *use* pre-existing libraries, you are better off
with a high-level language like Python which offers interfaces to Fortran
libraries. Numpy and Scipy are very good for that.

As far as Perl goes, I find that it suffers from the same weakness as R:

http://www.talyarkoni.org/blog/2012/06/08/r-the-master-troll-of-statistical-languages/

that is, the learning curve is far to steep for my liking. I find Perl
too inconsistent, with far too many special cases and tricks, and not
enough of a consistent design. It's not as bad as PHP, but it gives me
the impression of a language where the only design principle is "Oh, 
that looks cool. Hand me the welding iron, and I'll weld it on 
somewhere. Anywhere will do."


-- 
Steven D'Aprano
http://import-that.dreamwidth.org/

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#71725

"Steven D'Aprano" <steve+comp.lang.python@pearwood.info> wrote in message 
news:53783c5f$0$29977$c3e8da3

> You say you want to learn a *second* language, but you don't say what
> your first language is. Nor do you say what sort of mathematics you wish
> to do, or at what level. Depending on what you want to do, you might be
> best off with Mathematica, if you can afford it. Otherwise, there's an
> Open Source and free alternative, Sage, which uses Python.

    I have spent a lot of time with C. But it's hard for me to learn and 
there are various factors there. That sage looked good. But as a language 
for *nixs and their respective APIs sockets, sys calls and such there's C. 
Fortran might still be a choice. Perl looks really easy. But I haven't 
gotten into any of these because I'm still halding out for one that appeals 
to me.

Bill

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#71729

In article <53783c5f$0$29977$c3e8da3$5496439d@news.astraweb.com>,
 Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:

> You may find that the IPython interactive interface to Python is useful. 
> It presents an interface which should be familiar to anyone with 
> experience with Mathematica. 

I second the IPython suggestion.  I don't use it that often, but when 
I'm doing interactive number crunching, it's my tool of choice.  The 
ability to interactively go back and edit some block of code, then 
re-execute it, is really handy when exploring a dataset.  And the tight 
integration of graphing/plotting libraries is awesome.

I tend to use it in the mode where I'm running the compute kernel on a 
remote machine (typically a big machine in a data center somewhere) and 
the display portion in a browser on my desktop.

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#71731

On 18/05/2014 14:25, Roy Smith wrote:
> In article <53783c5f$0$29977$c3e8da3$5496439d@news.astraweb.com>,
>   Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:
>
>> You may find that the IPython interactive interface to Python is useful.
>> It presents an interface which should be familiar to anyone with
>> experience with Mathematica.
>
> I second the IPython suggestion.  I don't use it that often, but when
> I'm doing interactive number crunching, it's my tool of choice.  The
> ability to interactively go back and edit some block of code, then
> re-execute it, is really handy when exploring a dataset.  And the tight
> integration of graphing/plotting libraries is awesome.
>

Big +1 from me.

-- 
My fellow Pythonistas, ask not what our language can do for you, ask 
what you can do for our language.

Mark Lawrence

---
This email is free from viruses and malware because avast! Antivirus protection is active.
http://www.avast.com

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#71730

>     Does Python have good mathematical capabilities? 

SAGE: http://www.sagemath.org/

Sincerely,

Wolfgang

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#71732

On 2014-05-18, Bill Cunningham <nospam@nspam.invalid> 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").

> I am interested in learning a second language for mathematical
> purposes.

If you want to do calculations on numbers (integral, real, complex,
vectors, matrixes), analyze and visualize data (stuff that was
traditionally done in Fortran), then Python is brilliant.

If you want to do "math" (as in the study of number theory,
topologies, proofs, and so on) then no.  Python is not a good choice.

-- 
Grant

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#71733

"Grant Edwards" <invalid@invalid.invalid> wrote in message 
news:llak9u$8rs$1@reader1.panix.com...
> On 2014-05-18, Bill Cunningham <nospam@nspam.invalid> 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").
>
>> I am interested in learning a second language for mathematical
>> purposes.
>
> If you want to do calculations on numbers (integral, real, complex,
> vectors, matrixes), analyze and visualize data (stuff that was
> traditionally done in Fortran), then Python is brilliant.
>
> If you want to do "math" (as in the study of number theory,
> topologies, proofs, and so on) then no.  Python is not a good choice.

    linear algebra, expanding and factoring equations of all degrees. 
Geometry.

Bill

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#71833

On Sun, 18 May 2014 14:09:43 -0400, "Bill Cunningham"
<nospam@nspam.invalid> declaimed the following:

>    linear algebra, expanding and factoring equations of all degrees. 
>Geometry.
>
	Without significant add-in libraries, probably not...

	"Expanding and factoring equations" -- to me -- implies /symbolic
algebra systems/.

	Python can compute results of equations, but it won't, natively,
reformulate equations.

	Linear algebra tends to turn into matrix manipulation, as I recall...
Again, not a native feature.
-- 
	Wulfraed                 Dennis Lee Bieber         AF6VN
    wlfraed@ix.netcom.com    HTTP://wlfraed.home.netcom.com/

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#71834

On Sun, 18 May 2014 14:09:43 -0400, Bill Cunningham wrote:

>     linear algebra, expanding and factoring equations of all degrees.
> Geometry.

Sounds to me like you really want something like Maple, Mathematica, or 
similar. Try http://www.scilab.org/

Can do heaps of stuff, too. For free.


 /Grrr
-- 
          ___                  ___
 (\_--_/)  | _ ._    _|_|_  _   |o _  _ ._
 ( 9  9 )  |(_)| |\/  |_| |(/_  ||(_|(/_|
 stripes are forever - as overripe ferrets

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#71848

On 2014-05-21 01:59, Tony the Tiger wrote:
> On Sun, 18 May 2014 14:09:43 -0400, Bill Cunningham wrote:
>
>>      linear algebra, expanding and factoring equations of all degrees.
>> Geometry.
>
> Sounds to me like you really want something like Maple, Mathematica, or
> similar. Try http://www.scilab.org/
>
> Can do heaps of stuff, too. For free.

And with Python!

   http://sagemath.org/

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco

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#71850

On 2014-05-21 01:40, Dennis Lee Bieber wrote:
> On Sun, 18 May 2014 14:09:43 -0400, "Bill Cunningham"
> <nospam@nspam.invalid> declaimed the following:
>
>>     linear algebra, expanding and factoring equations of all degrees.
>> Geometry.
>>
> 	Without significant add-in libraries, probably not...
>
> 	"Expanding and factoring equations" -- to me -- implies /symbolic
> algebra systems/.
>
> 	Python can compute results of equations, but it won't, natively,
> reformulate equations.
>
> 	Linear algebra tends to turn into matrix manipulation, as I recall...
> Again, not a native feature.

But all easily available with well-established open source packages. Just 
because it's not in the standard library doesn't mean that Python isn't a 
suitable language for doing this stuff.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco

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#71734

On 2014-05-18 16:40, Grant Edwards wrote:
> On 2014-05-18, Bill Cunningham <nospam@nspam.invalid> 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").

Many mathematicians would disagree.

   http://sagemath.org/

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco

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#71750

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 ;-)

Fabien

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#71751

On 19/05/2014 11:15, 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.

Welcome to the Python world, Fabien.

But I'm sure you realise that question as general-purpose as "is Python
good for Maths?" is pretty much *bound* to generate different kinds of
answers. I'm not sure why it should be seen as scary. If anything, the
variety of responses reflects the diversity of Python's userbase.

The casual mathematician sees Python as perfectly adequate using
built-in tools alone. The more advanced mathematician sees it as helpful
with the addition of some specialist libraries. The most advanced user
would prefer some specialised language or toolset more entirely devoted
to this one area of interest.

And you could repeat the same situation with any number of other areas:
Image Processing, Websites, Network-based message passing, Data mining,
financial market management, web-scraping, etc. For some, Python has
more or less useful built-in support. For some, there are
well-established or highly-regarded 3rd-party libraries and communities.
For some, you might be better advised to look at a different toolset,
especially if you want something which comes ready-made.

As I say, though, welcome to Python!

TJG

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#71754

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.

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