Alan Bromborsky | 1 Jan 17:33 2008
Picon
Picon

Geometric Algebra in Python

I trying to determine if you would be interested in adding a geometric 
algebra package to sympy.  Attached are pdf files introducing geometric 
algebra (imag_numbers.pdf) and a description of a python module I am 
developing for symbolic geometric algebra.  Comments would be welcome.  
Also if the attachments don't get through how can I get them to you?

--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "sympy" group.
To post to this group, send email to sympy@...
To unsubscribe from this group, send email to sympy-unsubscribe@...
For more options, visit this group at http://groups.google.com/group/sympy?hl=en
-~----------~----~----~----~------~----~------~--~---

Attachment (imag_numbs.pdf): application/pdf, 379 KiB
Attachment (symbolicGA.pdf): application/pdf, 165 KiB
Ondrej Certik | 1 Jan 18:24 2008
Picon

Re: Geometric Algebra in Python


Hi Alan!

On Jan 1, 2008 5:33 PM, Alan Bromborsky <abrombo@...> wrote:
> I trying to determine if you would be interested in adding a geometric
> algebra package to sympy.  Attached are pdf files introducing geometric

Yes, I am very interested in this becoming part of sympy.

> algebra (imag_numbers.pdf) and a description of a python module I am
> developing for symbolic geometric algebra.  Comments would be welcome.

Which differences did you discover between swiginac and sympy?
Let's try to converge with these. Also we are interested in speed issues -
how much faster is swiginac when compared to sympy?

From the technical side, Kirill has replied in the previous thread:

http://groups.google.com/group/sympy/browse_thread/thread/a37f142aca01e8e8/

Let us know, when you release your code, so that we can play with it and then
we'll discuss how to best incorporate it into sympy.

> Also if the attachments don't get through how can I get them to you?

They went fine. You can always check that your email went through here:

http://groups.google.com/group/sympy/msg/49ee1f907ec7973c

Ondrej
(Continue reading)

David Joyner | 1 Jan 18:26 2008
Picon

Re: Geometric Algebra in Python


Just some ideas: For me, "geometric algebra" refers to material in the
famous book by E Artin. Your usage of the term is apparently
common with mathematical physicists. I would recommend changing the
name to "clifford algebra", which seems to be used by both communities.
Also, I think there is a large package on Clifford algebras in Maple.
It might be worth comparing them, if there is overlap.

My 2 cents.

On Jan 1, 2008 11:33 AM, Alan Bromborsky <abrombo@...> wrote:
> I trying to determine if you would be interested in adding a geometric
> algebra package to sympy.  Attached are pdf files introducing geometric
> algebra (imag_numbers.pdf) and a description of a python module I am
> developing for symbolic geometric algebra.  Comments would be welcome.
> Also if the attachments don't get through how can I get them to you?
>
> >
>

Ondrej Certik | 1 Jan 18:36 2008
Picon

Re: Geometric Algebra in Python


On Jan 1, 2008 6:26 PM, David Joyner <wdjoyner@...> wrote:
>
> Just some ideas: For me, "geometric algebra" refers to material in the
> famous book by E Artin. Your usage of the term is apparently
> common with mathematical physicists. I would recommend changing the
> name to "clifford algebra", which seems to be used by both communities.
> Also, I think there is a large package on Clifford algebras in Maple.
> It might be worth comparing them, if there is overlap.

Yes, both terms are fine with me. But it's true Clifford algebra
means for me just the anticommutation relations of Dirac matrices (and the
algebra it generates), while geometric algebra means for me:

http://en.wikipedia.org/wiki/Geometric_algebra

but now I learned, that the Dirac matrices algebra is actually called
"spacetime algebra":

http://en.wikipedia.org/wiki/Spacetime_algebra

so any name is fine with me.

In any case, Clifford albegras are really cool, I discovered that just
by accident,
but it really shows me more insight into many things in physics.

Ondrej

(Continue reading)

Alan Bromborsky | 1 Jan 18:56 2008
Picon
Picon

Re: Geometric Algebra in Python


One reason Hestenes calls it geometric algebra is because that's what 
Clifford called it, but he died to soon to impose his will upon the 
mathematical community.  Also, to me Clifford algebra as defined by 
mathematicians today is something significantly more abstract than 
Hestenes definition of geometric algebra.  Hestenes also named the 
follow on to geometric algebra, geometric calculus!!!

Ondrej Certik wrote:
> On Jan 1, 2008 6:26 PM, David Joyner <wdjoyner@...> wrote:
>   
>> Just some ideas: For me, "geometric algebra" refers to material in the
>> famous book by E Artin. Your usage of the term is apparently
>> common with mathematical physicists. I would recommend changing the
>> name to "clifford algebra", which seems to be used by both communities.
>> Also, I think there is a large package on Clifford algebras in Maple.
>> It might be worth comparing them, if there is overlap.
>>     
>
>
> Yes, both terms are fine with me. But it's true Clifford algebra
> means for me just the anticommutation relations of Dirac matrices (and the
> algebra it generates), while geometric algebra means for me:
>
> http://en.wikipedia.org/wiki/Geometric_algebra
>
> but now I learned, that the Dirac matrices algebra is actually called
> "spacetime algebra":
>
> http://en.wikipedia.org/wiki/Spacetime_algebra
(Continue reading)

Alan Bromborsky | 1 Jan 19:08 2008
Picon
Picon

Re: Geometric Algebra in Python


David Joyner wrote:
> Just some ideas: For me, "geometric algebra" refers to material in the
> famous book by E Artin. Your usage of the term is apparently
> common with mathematical physicists. I would recommend changing the
> name to "clifford algebra", which seems to be used by both communities.
> Also, I think there is a large package on Clifford algebras in Maple.
> It might be worth comparing them, if there is overlap.
>
> My 2 cents.
>
> On Jan 1, 2008 11:33 AM, Alan Bromborsky <abrombo@...> wrote:
>   
>> I trying to determine if you would be interested in adding a geometric
>> algebra package to sympy.  Attached are pdf files introducing geometric
>> algebra (imag_numbers.pdf) and a description of a python module I am
>> developing for symbolic geometric algebra.  Comments would be welcome.
>> Also if the attachments don't get through how can I get them to you?
>>
>>     
>
> >
>
>   
I don't know anything about Maple or Mathematica (they cost money so I 
don't use them), but I would have two questions about their Clifford 
packages:

1.  Are they truely coordinate free or do they use an orthogonal 
coordinate system with symbolic expressions for the coordinate coefficients?
(Continue reading)

Pearu Peterson | 1 Jan 19:16 2008
Picon

Re: Geometric Algebra in Python


On Jan 1, 6:08 pm, Alan Bromborsky <abro...@...> wrote:
>
> I don't know anything about Maple or Mathematica (they cost money so I
> don't use them)..

Sometimes it is worth of looking at how other CA systems (most of them
have manuals online for free) handle certain problems and what
interfaces they provide. This is useful in a situation when a user of
these
systems tries out sympy and s/he will be more satisfied if the
general structure/user interface of the corresponding sympy package
looks similar (at least) to what s/he has been used to.

Pearu
Ondrej Certik | 1 Jan 19:36 2008
Picon

Re: Geometric Algebra in Python


On Jan 1, 2008 7:16 PM, Pearu Peterson <pearu.peterson@...> wrote:
>
>
>
> On Jan 1, 6:08 pm, Alan Bromborsky <abro...@...> wrote:
> >
> > I don't know anything about Maple or Mathematica (they cost money so I
> > don't use them)..
>
> Sometimes it is worth of looking at how other CA systems (most of them
> have manuals online for free) handle certain problems and what
> interfaces they provide. This is useful in a situation when a user of
> these
> systems tries out sympy and s/he will be more satisfied if the
> general structure/user interface of the corresponding sympy package
> looks similar (at least) to what s/he has been used to.

Exactly. And also all opensource CA systems should have similar or the
same interface,
currently the project with a biggest momentum in this area is Sage
(sagemath.org).

Ondrej

Alan Bromborsky | 1 Jan 20:30 2008
Picon
Picon

Re: Geometric Algebra in Python


Ondrej Certik wrote:
> On Jan 1, 2008 7:16 PM, Pearu Peterson <pearu.peterson@...> wrote:
>   
>>
>> On Jan 1, 6:08 pm, Alan Bromborsky <abro...@...> wrote:
>>     
>>> I don't know anything about Maple or Mathematica (they cost money so I
>>> don't use them)..
>>>       
>> Sometimes it is worth of looking at how other CA systems (most of them
>> have manuals online for free) handle certain problems and what
>> interfaces they provide. This is useful in a situation when a user of
>> these
>> systems tries out sympy and s/he will be more satisfied if the
>> general structure/user interface of the corresponding sympy package
>> looks similar (at least) to what s/he has been used to.
>>     
>
>
> Exactly. And also all opensource CA systems should have similar or the
> same interface,
> currently the project with a biggest momentum in this area is Sage
> (sagemath.org).
>
> Ondrej
>
> >
>   
I looked at a paper on the Maple Clifford package.  The problem I would 
(Continue reading)

Bill Page | 1 Jan 21:23 2008

Re: Geometric Algebra in Python


On 1/1/08, Alan Bromborsky wrote:
> ...
> I looked at a paper on the Maple Clifford package.  The problem
> I would have with it is that it is Clifford algebra for mathematicians,
> not for physicists.

That is peculiar since it was designed by two physicists.

http://www.math.tntech.edu/rafal
http://clifford.physik.uni-konstanz.de/%7Efauser/Welcome.shtml

It is not really a good idea to call it "the Maple Clifford package"
since as far as I know it is a third party application not supported
by MapleSoft

http://math.tntech.edu/rafal/cliff11/index.html

Also I happen to know that both Rafal Ablamowicz and Bertfried Fauser
have never been very happy about the way they had to implement their
Clifford and Bialgebra packages in Maple.

> I would not have a clue as to how to pose the sort of problems
> I want to solve in that package.

I would very strongly recommend that you send an email to Rafal and/or
Bertfried and ask them about how Clifford could be applied to the
problems you want to solve.

You might also be interested to know that Axiom has a basic
(Continue reading)

Bill Page | 2 Jan 04:17 2008

Re: Geometric Algebra in Python


On 1/1/08, Bill Page wrote:
> On 1/1/08, Alan Bromborsky wrote:
> > ...
> > I looked at a paper on the Maple Clifford package.  The problem
> > I would have with it is that it is Clifford algebra for mathematicians,
> > not for physicists.
>
> That is peculiar since it was designed by two physicists.
>...
> I would very strongly recommend that you send an email to Rafal
> and/or Bertfried and ask them about how Clifford could be applied
> to the problems you want to solve.
>

Bertfried Fauser replied the following (in part) today concerning my
request for some information abut the new version of Clifford for
Maple release 11:

---------- Forwarded message ----------
From: Bertfried Fauser <bertfried.fauser@...>
Date: Jan 1, 2008 7:44 PM
Subject: Re: library_M11.zip
To: Bill Page <bill.page@...>
Cc: Ablamowicz <rablamowicz@...>

Hi Bill,
...
I can tell you that Clifford 11 is just the same software as Clifford
10, with the folloing done:
(Continue reading)

Ondrej Certik | 2 Jan 04:23 2008
Picon

Re: Geometric Algebra in Python


On Jan 2, 2008 4:17 AM, Bill Page <bill.page@...> wrote:
>
> On 1/1/08, Bill Page wrote:
> > On 1/1/08, Alan Bromborsky wrote:
> > > ...
> > > I looked at a paper on the Maple Clifford package.  The problem
> > > I would have with it is that it is Clifford algebra for mathematicians,
> > > not for physicists.
> >
> > That is peculiar since it was designed by two physicists.
> >...
> > I would very strongly recommend that you send an email to Rafal
> > and/or Bertfried and ask them about how Clifford could be applied
> > to the problems you want to solve.
> >
>
> Bertfried Fauser replied the following (in part) today concerning my
> request for some information abut the new version of Clifford for
> Maple release 11:

Thanks Bill for posting this! After reading this I realized I also know
B. Fauser, as we were on the RISC workshop together with Mateusz
(another sympy developer). I know they were discussing schur
functions, but I didn't find it interesting then. :)

Ondrej

David Joyner | 1 Jan 19:36 2008
Picon

Re: Geometric Algebra in Python


On Jan 1, 2008 1:08 PM, Alan Bromborsky <abrombo@...> wrote:
>
> David Joyner wrote:
> > Just some ideas: For me, "geometric algebra" refers to material in the
> > famous book by E Artin. Your usage of the term is apparently
> > common with mathematical physicists. I would recommend changing the
> > name to "clifford algebra", which seems to be used by both communities.
> > Also, I think there is a large package on Clifford algebras in Maple.
> > It might be worth comparing them, if there is overlap.
> >
> > My 2 cents.
> >
> > On Jan 1, 2008 11:33 AM, Alan Bromborsky <abrombo@...> wrote:
> >
> >> I trying to determine if you would be interested in adding a geometric
> >> algebra package to sympy.  Attached are pdf files introducing geometric
> >> algebra (imag_numbers.pdf) and a description of a python module I am
> >> developing for symbolic geometric algebra.  Comments would be welcome.
> >> Also if the attachments don't get through how can I get them to you?
> >>
> >>
> >
> > >
> >
> >
> I don't know anything about Maple or Mathematica (they cost money so I
> don't use them), but I would have two questions about their Clifford
> packages:

(Continue reading)

Robert Kern | 2 Jan 18:01 2008
Picon

Re: Geometric Algebra in Python


On Jan 1, 10:33 am, Alan Bromborsky <abro...@...> wrote:
> I trying to determine if you would be interested in adding a geometric
> algebra package to sympy.  Attached are pdf files introducing geometric
> algebra (imag_numbers.pdf) and a description of a python module I am
> developing for symbolic geometric algebra.  Comments would be welcome.

I'd be interested. A long time ago, I wrote a module for numeric
computations in geometric algebra. I have (mostly) updated it to use
numpy, but that conversion may still be a little rough.

  http://www.enthought.com/~rkern/cgi-bin/hgwebdir.cgi/clifford/

You may also be interested in the book _Geometric Algebra for Computer
Science: An Object-oriented Approach to Geometry_ by Leo Dorst, Daniel
Fontijne and Stephen Mann. A substantial chunk of the book is devoted
to discussing implementation, with code, albeit from a numerical
perspective.

  http://www.geometricalgebra.net/

Alan Bromborsky | 2 Jan 18:30 2008
Picon
Picon

Re: Geometric Algebra in Python


Robert Kern wrote:
> On Jan 1, 10:33 am, Alan Bromborsky <abro...@...> wrote:
>   
>> I trying to determine if you would be interested in adding a geometric
>> algebra package to sympy.  Attached are pdf files introducing geometric
>> algebra (imag_numbers.pdf) and a description of a python module I am
>> developing for symbolic geometric algebra.  Comments would be welcome.
>>     
>
> I'd be interested. A long time ago, I wrote a module for numeric
> computations in geometric algebra. I have (mostly) updated it to use
> numpy, but that conversion may still be a little rough.
>
>   http://www.enthought.com/~rkern/cgi-bin/hgwebdir.cgi/clifford/
>
> You may also be interested in the book _Geometric Algebra for Computer
> Science: An Object-oriented Approach to Geometry_ by Leo Dorst, Daniel
> Fontijne and Stephen Mann. A substantial chunk of the book is devoted
> to discussing implementation, with code, albeit from a numerical
> perspective.
>
>   http://www.geometricalgebra.net/
>
> >
>
>   
I got that book recently.  My favorite is "Geometric Algebra for 
Physicists" by Doran and Lazenby!!!!

(Continue reading)


Gmane