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\start
Date: Thu, 5 Nov 2015 14:57:17 +1100
From: Alasdair McAndrew <amca01@gmail.com>
To: axiom-mail@nongnu.org, fricas-devel@googlegroups.com
Subject: [Axiom-mail] New blog post about (Pan)Axiom

Ya'll might be interested in a new blog post "Re-discovering Axiom":

http://numbersandshapes.net/2015/11/re-discovering-axiom/

cheers,
Alasdair

-- 
[image: http://www.facebook.com/alasdair.mcandrew]
<http://www.facebook.com/alasdair.mcandrew> [image:
https://plus.google.com/+AlasdairMcAndrew/posts]
<https://plus.google.com/+AlasdairMcAndrew/posts> [image:
https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108]
<https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image:
https://twitter.com/amca01] <https://twitter.com/amca01> [image:
http://numbersandshapes.net] <http://numbersandshapes.net>

\start
Date: Wed, 4 Nov 2015 22:05:36 -0600
From: daly@axiom-developer.org
To: Alasdair McAndrew <amca01@gmail.com>
Subject: Re: [Axiom-mail] new blog post....

Interesting. Is this your blog?  -- Tim

\start
Date: Wed, 4 Nov 2015 23:00:03 -0600
From: daly@axiom-developer.org
To: Alasdair McAndrew <amca01@gmail.com>
Subject: Re: [Axiom-mail] blog post

This appears to be a conference stressing teaching mathematics.
(http://atcm.mathandtech.org/)

I would appreciate it if you'd point out that THE key focus of the
Axiom project is to make it possible to understand how to read, write,
and modify computational mathematics.

The whole point is to try to keep Axiom alive and growing beyond the
lifetime of the original authors. Computational Mathematics is the
result of the collision of mathematics and computers. Axiom is the
"Newton's Notebook" of that collision.

In general, Axiom was created as a piece of research software used
only by fellow researchers, usually to complete their thesis work.
Thus, the algorithms are world class. But the documentation isn't.

It is important to document the algorithms. The code is NOT sufficient
since there are design decisions and tradeoffs that have nothing to do
with the algorithms. You can see this clearly in work by Jack Dongarra
(http://netlib.org/utk/people/JackDongarra/etemplates/book.html) where
he raises all kinds of implementation issues like stability and
convergence. In Axiom's case there are even more issues, some of which
are addressed by the new proof machinery being created.

I will grant you that this is a very long term goal which will take a
while to accomplish. Longer now, sadly. The Axiom community used to
have 568 unique contributors. The forks ended that. Now it seems there
are only a few people left. Nevertheless, it is vital that Axiom
becomes easier to understand, maintain, and modify so it can help the
next generation of Computational Mathematicians.

Ideally I would like Axiom to be THE software used as the platform
for teaching computational mathematicians.

Tim

\start
Date: Sat, 07 Nov 2015 18:47:56 +1100
From: Alasdair McAndrew <amca01@gmail.com>
To: fricas-devel@googlegroups.com, axiom-mail@nongnu.org
Subject: [Axiom-mail] Formal polynomials?

A quickie: is there any way of defining a formal polynomial with unknown
coefficients, such as:

a_0+a_1*x+a_2*x^2+a_3*x^3 ?

I want to calculate the values of the coefficients by a system of linear
equations based on integrations whose integrands include that polynomial.

For small polynomials I can write

p:=a+b*x+c*x^2+d*x^3

but this gets clumsy for higher powers.

I can enter, for example

A:=[a[n] for n in 0..10]

for a list of symbols, but neither of

sum(a[i]*x^i, i=0..10)

or

sum(A.i*x^(i-1),i=1..11)

work, nor do they work when "sum" is replaced with "summation".


--

[https://ci6.googleusercontent.com/proxy/2sF0a1ZoLMOPckOBVppCZ4OFi06ffJNGtQadXIhbQiE95NE6m4gM53kVdCiQnVJYlRw380RlZ0tK7XHk4CmM2qy3nTM_ptogovPuXhk2=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/facebook.png] 
[http://www.facebook.com/alasdair.mcandrew][https://ci4.googleusercontent.com/proxy/egLBn4P9MCM5JXRJFUg5fGnVRlWCGBo6zl_hik07VL66K0muLhfGiUf2i_7iymWxqLVLANxJraL5xfbJOTx8akBt9TmFlAIJcVuyk6fs2a9ASV26=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/f-gplus_256-48.png] 
[https://plus.google.com/+AlasdairMcAndrew/posts][https://ci3.googleusercontent.com/proxy/-agz0u1Ac2-yf996SqPviIMbF5L-qAheB2hrZu975cEQB4YOZRFxRLuXLXmoQYBGNsMppMznpOXtgH2hmVu428QgisuXNCqKPzRQf1ZJ=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/linkedin.png] 
[https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108][https://ci5.googleusercontent.com/proxy/V-iov0_6bPsm3W5m1rgoRpRS5HaoNkB_5EbwhbqM_SqKHZOJsrTxalR6JGpq4SaT0gndZYFa2JH92qAJUGe2YVF05zindKPUWLep5js=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/twitter.png] 
[https://twitter.com/amca01][https://ci6.googleusercontent.com/proxy/AMQYVjh54hMGPrzE9x9QAB8CTaI4oJKwlOSjuRnDGBKXOtbQJ9c9nVqOdcEd9fLnc1vtced39dXoWEEJHoJ0SUb2eH6a6wZdyjPMJQY3vw=s0-d-e1-ft#https://dl.dropboxusercontent.com/u/2796170/wordpress.png] 
[http://numbersandshapes.net]

\start
Date: Sun, 8 Nov 2015 20:24:55 +1100
From: Alasdair McAndrew <amca01@gmail.com>
To: axiom-mail@nongnu.org, fricas-devel@googlegroups.com
Subject: [Axiom-mail] A blog post...

Y'all might be interested in a new blog post of mine which uses PanAxiom
for the computations.  (Just doing my tiny bit to get the system "out
there".)

It's at
http://numbersandshapes.net/2015/11/stieltjes-polynomials-and-integration/

-Alasdair

-- 
[image: http://www.facebook.com/alasdair.mcandrew]
<http://www.facebook.com/alasdair.mcandrew> [image:
https://plus.google.com/+AlasdairMcAndrew/posts]
<https://plus.google.com/+AlasdairMcAndrew/posts> [image:
https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108]
<https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image:
https://twitter.com/amca01] <https://twitter.com/amca01> [image:
http://numbersandshapes.net] <http://numbersandshapes.net>

\start
Date: Mon, 09 Nov 2015 17:41:46 +0100
From: panAxiom@first.in-berlin.de
To: axiom-mail@nongnu.org
Subject: Re: [Axiom-mail] A blog post...

To get the system "out there", a better documentation
would be more helpful, I think....

...when going from simpele things into deep details,
there IMHO is a lack of documentation, that helps on this
journey...



Quoting Alasdair McAndrew <amca01@gmail.com>:

> Y'all might be interested in a new blog post of mine which uses PanAxiom
> for the computations.  (Just doing my tiny bit to get the system "out
> there".)
>
> It's at
> http://numbersandshapes.net/2015/11/stieltjes-polynomials-and-integration/
>
> -Alasdair
>
> --
> [image: http://www.facebook.com/alasdair.mcandrew]
> <http://www.facebook.com/alasdair.mcandrew> [image:
> https://plus.google.com/+AlasdairMcAndrew/posts]
> <https://plus.google.com/+AlasdairMcAndrew/posts> [image:
> https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108]
> <https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image:
> https://twitter.com/amca01] <https://twitter.com/amca01> [image:
> http://numbersandshapes.net] <http://numbersandshapes.net>

\start
Date: Thu, 12 Nov 2015 14:10:09 +1100
From: Alasdair McAndrew <amca01@gmail.com>
To: fricas-devel@googlegroups.com, axiom-mail@nongnu.org
Subject: [Axiom-mail] Function inside a function?

I have been experimenting with writing a few little programs to perform
numerical integration, in which I have been running into difficulties.  I
can do all the operations I need from the command line, but I run into
problems when I try to bundle those commands into a program.

As a simple example, suppose I wanted a program to implement the two-point
Gaussian rule, which approximates the integral of f(x) between -1 and 1 by
f(-1/sqrt(3))+f(1/sqrt(3)).

On an interval other than [-1,1], we need a scaling transformation.  So I
might have a file called "gauss2.input" which contains one function:

gauss2(f,a,b)==
  xs:LIST Float := [-1/sqrt(3),1/sqrt(3)]
  g := (x:Float):Float +-> f((b-a)/2*x+(b+a)/2)
  int2 := (b-a)/2*(g(xs.1) + g(xs.2))
  return(int2)

However, the system clams up on the use of the scaling function g(x), and
this gives no results.

I have two questions here: first, how do I get round this?  and second, if
I'm writing programs, should I be writing them in Aldor (that's the
language of ".input" files, isn't it?), or SPAD?

For that matter, how do all the languages Aldor, SPAD, Lisp, Boot link up -
which is used for which purpose, and why?

Thanks,
Alasdair

-- 
[image: http://www.facebook.com/alasdair.mcandrew]
<http://www.facebook.com/alasdair.mcandrew> [image:
https://plus.google.com/+AlasdairMcAndrew/posts]
<https://plus.google.com/+AlasdairMcAndrew/posts> [image:
https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108]
<https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image:
https://twitter.com/amca01] <https://twitter.com/amca01> [image:
http://numbersandshapes.net] <http://numbersandshapes.net>



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