We did not get time to convert all the comments into code as is done
for some the new categories and domains in the trunk repository.
For example, from
http://sourceforge.net/p/open-axiom/code/2800/tree/trunk/src/algebra/catdef.spad.pamphlet
Is there a way I could help in a pan-Axiom sort
Is there a way I could help in a pan-Axiom sort of way? For instance,
would it be any help if I went through these categories and drew a
diagram of their relationships? I realise diagrams like:
http://www.axiom-developer.org/axiom-website/bookvol10.2full.html
tend to quickly become
On 05/04/13 01:07, Ralf Hemmecke wrote:
I don't quite understand. If you assume myOp1 to be commutative, then
solving equations is quite a different task from when it is
non-commutative. Where would you store all these axioms?
Yes that's an interesting question. For an Axiom category to
On 04/05/2013 10:51 AM, Martin Baker wrote:
It seems a sight irony that Axiom(the program) does not do much about
axioms.
Of course, AXIOM can deal with axioms, but the SPAD language does not
include any way to specify axiom (not even Aldor can do this).
Looks like you aim at a general term
On 05/04/13 10:20, Ralf Hemmecke wrote:
On 04/05/2013 10:51 AM, Martin Baker wrote:
It seems a sight irony that Axiom(the program) does not do much about
axioms.
Of course, AXIOM can deal with axioms, but the SPAD language does not
include any way to specify axiom (not even Aldor can do
On Fri, Apr 5, 2013 at 3:51 AM, Martin Baker ax87...@martinb.com wrote:
Given that there is no resources (or desire, as far as I can see) to change
the structure of Axiom then I was wondering, just for specific domains where
we want a specific equation solver, could we encode the axioms in a
On 05/04/13 12:11, Gabriel Dos Reis wrote:
Your probably know that OpenAxiom started putting the axioms in AXIOM.
See for example:
http://sourceforge.net/p/open-axiom/code/2800/tree/trunk/src/algebra/catdef.spad.pamphlet
In fact, a couple of years ago, a student of mine did experiments on
On Fri, Apr 5, 2013 at 11:05 AM, Martin Baker ax87...@martinb.com wrote:
On 05/04/13 12:11, Gabriel Dos Reis wrote:
Your probably know that OpenAxiom started putting the axioms in AXIOM.
See for example:
Given that there is no resources (or desire, as far as I can see) to
change the structure of Axiom
There is the desire. Axiom has a long term goal of introducing
program-proof technology (either COQ or ACL2). ACL2 runs on the same
lisp as Axiom. The plan is to load it into the Axiom image and
This is probably not very practical, but I was just trying to do a
thought experiment to investigate what would be required to have
variables that range over domains that are not numbers.
Actually, I wrote an NSF proposal to introduce indeterminate integers.
This would be a first example of a
On 03/30/2013 06:25 PM, Martin Baker wrote:
On 30/03/13 12:01, Ralf Hemmecke wrote:
Unless you specify what solver you intend to write, it's probably an
unsolvable task to write a general solver that works for all types of
algebras.
Agreed, but I was thinking more about doing it on a
Would anyone object if I ask a slightly wider question on this topic?
It would be really nice if one could write an equation solver for a
given algebra, I have often wanted to do that and I wonder if there is
any general advise on this topic for Axiom?
I guess what I am looking for is a way
It would be really nice if one could write an equation solver for a
given algebra, I have often wanted to do that and I wonder if there is
any general advise on this topic for Axiom?
Well, would be nice, but think about the following. An algebra, which is
a field. Depending on which equations
On 30/03/13 12:01, Ralf Hemmecke wrote:
Unless you specify what solver you intend to write, it's probably an
unsolvable task to write a general solver that works for all types of
algebras.
Ralf
Agreed, but I was thinking more about doing it on a per-domain basis and
building up gradually.
Dear Tim,
If you look at the matrixcookbook that Mike mentioned, the first 10
equations are:
(A*B)^-1 = B^-1 * A^-1
(A*B*C...)^-1 = ...C^-1 * B^-1 * A^-1
(A^T)^-1 = (A^-1)^T
(A+B)^T = A^T + B^T
(A*B)^T = B^T * A^T
(A*B*C...)^T = C^T * B^T *A^T
: Raoul rao...@bluewin.ch
Date: 29 March 2013 19:42
Subject: Re: [Axiom-mail] A question about Axiom capabilities
To: u1204 d...@axiom-developer.org, axiom-mail@nongnu.org
Dear Tim,
If you look at the matrixcookbook that Mike mentioned, the first 10
equations are:
(A*B)^-1 = B^-1
I've been looking for some CAS that provided significant symbolic matrix
manipulations, including matrix calculus.
Maybe you should look at SymPy. They have some (although limited)
support for symbolic matrix expressions and computations.
SymPy documentation:
Mike,
It would be possible to build a Domain (e.g. SymbolicMatrix) that
had elements which were symbolic, e.g. the symbol A from the Domain
would be considered an uninterpreted SymbolicMatrix. So you could
write something like:
(A*B)^-1
and get the result
B^1 * A^-1
Indeed, the
Raoul,
I will look at your code. Thanks.
Tim Daly
d...@axiom-developer.org
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Raoul,
If you look at the matrixcookbook that Mike mentioned, the first 10
equations are:
(A*B)^-1 = B^-1 * A^-1
(A*B*C...)^-1 = ...C^-1 * B^-1 * A^-1
(A^T)^-1 = (A^-1)^T
(A+B)^T = A^T + B^T
(A*B)^T = B^T * A^T
(A*B*C...)^T = C^T * B^T *A^T
(A^H)^-1
I can send you a copy I have downloaded, but I will send that email just to
you as I don't feel like spamming the mailing list
On Wed, Feb 27, 2013 at 7:58 PM, u1204 d...@axiom-developer.org wrote:
I tried the cookbook link you posted
http://orion.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
Mike,
These are interesting ideas but I don't know how to do what you
want in the current version of Axiom.
Where is this Matrix Cookbook you mention?
Tim Daly
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The Matrix Cookbook is available online at:
http://orion.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
It is simply a collection of matrix properties which are proved elsewhere.
I have done enough matrix calculus to know a basic approach (very similar
to the derivatives for indexed tensors in Maxima)
One other note - I forgot a logarithm in my example:
D( ln( sum(p[k]*multivariate_normal(mu[k], Sigma), k) ) -- ...
On Tue, Feb 26, 2013 at 8:39 PM, Mike Valenzuela mickle.mo...@gmail.comwrote:
The Matrix Cookbook is available online at:
http://orion.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf
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