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 <[EMAIL PROTECTED]> Date: Jan 1, 2008 7:44 PM Subject: Re: library_M11.zip To: Bill Page <[EMAIL PROTECTED]> Cc: Ablamowicz <[EMAIL PROTECTED]> Hi Bill, ... I can tell you that Clifford 11 is just the same software as Clifford 10, with the folloing done: -- Clifford 11 (Octonion, Bigebra, cliplus, code_support, GfG, SP, SchurFkt etc) have helppages which serve as a sort of regression test. Before posting a new file, (library) Rafal runs all helppages and looks at them via occuli if the program produces the expected results. Sometimes, expected results may be errors, though! -- In a second step he produces the pdf's (this cannot be automated which is still a shame for maple, and I demanded such a feature for a long time) So, Clifford 11 will run stable on maple 11, and I guess on maple 12, since no new maple had major library changes rom maple 8 onwards, and Clifford/Bigebra does not interact very deeply with the maple libraries, and just uses stanrard features of the kernel. ... > This email is the result of perhaps the first of my New Year's > resolutions: To discover the status of the computer algebra work > going on in Clifford Algebra's. I was pleasantly surprised to see > that "Clifford" is still being maintained and developed (especially > GfG). Clifford is still a tool used by a variety of people (especially now in engineering, robotics and optimization of geometric problems). It is somehow complete in its functionality, since you will not find mathematics on 'ordinary' Clifford algebras which is not covered by this program (if Bigebra is considered a part of Clifford, for example the restriction to one digit indices is overcome etc.). We got even citations for our patch of maples define routine (define.m and definemore.m come with this library), which is (as far as I can see in maple 10) still malfunctional in the original maple library (even mathematically meaningless, since you cannot define the base field/ring over which say linearity or multilinearity defined). This is needede to be able to define a tensor, which is also used in GfG (corpoducts, implicitely) and heavily in the SchurFkt package (which therefore is bundlered in the library_Mnn.zip files. ... You may want to do the following: 1) Make a new directory where the library files shall be situated. Usually under /usr/local/maple12/Cliffordlib (or the windows equivalent) 2) Unzip the library files in that directory. If you want to use all of the functionality, there should be a zip file called "matdatam_M10.zip" (needs separate download) which contains precomputed results to look up data about clifford algebras and about several representations. You should get the following list of files: define.m maple.hdb maple.lib matquatL.m matrealR.m definemore.m maple.ind matcompL.m matquatR.m mydefs.m maple.ini matcompR.m matrealL.m make sure maple has rights to read (and possibly write) these files. ... 3) produce a maple.ini file (or hardcode in the startup script) so that 'libname' is set to something like: libname; "/usr/local/maple/maple10/Cliffordlib", "/usr/local/maple/maple10/FGblib","/usr/local/maple/maple10/lib" you see that I have installed FGblib by Fauget (in a separate directory) which contains a fast Groebner solver for maple runing externally as a C program. Its really really fast and I guess it was now incorporated into Maple? Do this: > libname:="<your/Clifford/path>",libname: Make sure all custom libraries come before the maple main library, so that maple will use these functionality first. Otherwise, for example 'define' will not work. The library contains the full help browser documentation of all packages: Clifford / Bigebra / Cliplus / GfG (possibly no material there yet) / SP (same status as GfG) / SchurFkt / Octonion / code_support / ... if any. Try > ?Clifford Many helppages of Bigebra and some of Clifford do contain unpublished mathematics, as quite a few pages of SchurFkt do also (especially the Rota-Stein outer product for monomial symmetric functions). The README.txt is posted on the web page and should, of course, be included into the zip file of the library. We had quite a few updates recently and it seems it got lost in course of doing so. If you have problems let me know please! ... > Of course I also remain very interested in the possibility of > developing something like Clifford in Axiom and hope that I > will have some time available this year to pursue this subject. Rafal's and my intention is to merge (in a larger sense) the Clifford/Bigebra/Cliplus/GfG/and SchurFkt packages. Clifford and Bigebra can handle matrix reps etc, while SchurFkt can handle infinite dimesnional objects and such things as tensor products of representations which is simply too slow in Bigebra to be pushed really forward. (A computer is still not able to compute the multiplication table of the Clifford algebra CL(9,0) and store it precomputed. Using Young tableaux techniques you can deal with arbitrary (OK, say reasonably high) weight tensor products, which are light years out of reach by Bigebra(Clifford). Such a merge should (has to!) include super algebras and Hilbert modules, as it has also to contain q-deformed structures which are partly implemented in Clifford (if you know how to activate them) but not yet fully developed/functional (or even documented). I have declined Tim's offer/attempt to recode Clifford for AXIOM. AXIOM deserves a newly designed package, which prevents lots of design errors of Clifford (and SchurFkt). I cannot recommand a port, its just far too big! and would port errors in design, which any would be possibly uncodable in AXIOM due to its typing system :) The projects contain currently: -- Clifford: 84 exporter proceedures -- Bigebra: 33 exported proceedures -- Cliplus: 10 exported proceedures -- Octonion: 12 exported proceedures -- SP: 29 exported proceedures -- GfG: 23 exported proceedures -- SchurFkt: 76 exported proceedures (still growing) -- code_support: 11 exported functuions -- RJgrobner 26 exported proceedures (by Rafal Ablamowicz and Jane Liu) == in toto =============== 304 exported functuions Note that Clifford/Bigebra/ and SchurFkt come with many own types etc which are not counted (!) and several internal helper functuions which are also not exported from the packages, so a 'port' of the main functionality is a formidable task (may be about 500 proceedures!) AXIOMs Clifford package is in my eyes not more than a 'its possible' study. Note that we face the problem that Clifford can handle a much more general class of Clifford algebras defined by providing a _bilinear form_ not a quadratic form, such Clifford algebras are found mandatorially in QFT and where named 'quantum Clifford algebras' since they can mimic q-deformed Clifford algebras (see one of my J.Phys.A papers on that topic). (However to produce (Feynman) graphs, and count them, one is better of with Schur functions!). After the AXIOM workshop at the RISC in 2007, Martin Rubey, Ralf Hemmecke and I discussed the possibility of a Schur function package for AXIOM. This would be a major issue, since Clifford algebras are somehow strongly related with that and the Hopf algebra structure of Schur functions and Clifford algebars is almost perfectly aligned. So there would be only one attempt to achieve this goal in parallel. There are still unsolved mathematical problems coming with Clifford algebras. With Zbigniew I tried quite a while to understand which categorial axioms one needs to set up to define Clifford algebras, (not as a universal object, but in terms of internal logic, say equationally) this is still unsolved, though Zbigniew made some progress. However, some exotic non Clifford algebras remain as models of such a setting and the computations are tremendously cumbersome if a search in model space is performed (unsolved computational problem) I am currently computing heavy duty knot invariant calculations whith the SchurFkt package, and amazingly this leads back to (spinors (anyons (fractional spin) and 'Clifford algebras of a polynomial invariant form, not just a quadratic form), so I may come back to Clifford more seriously later. Hope this helps Ciao BF. -- % PD Dr Bertfried Fauser % Privat Docent: University of Konstanz, Physics Dept <http://www.uni-konstanz.de> % contact |-> URL : http://clifford.physik.uni-konstanz.de/~fauser/ % Phone : +49 7531 693491 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
