Re: Direct tensor algebra

*To*: mathgroup at smc.vnet.net*Subject*: [mg37423] Re: [mg37385] Direct tensor algebra*From*: John Browne <jbrowne at swin.edu.au>*Date*: Mon, 28 Oct 2002 03:40:41 -0500 (EST)*Organization*: Swinburne University of Technology*References*: <200210260603.CAA29470@smc.vnet.net>*Reply-to*: jbrowne at swin.edu.au*Sender*: owner-wri-mathgroup at wolfram.com

Alexey, Below is a link to the draft of a book on Grassmann algebra. Although not the full tensor algebra, it might give you some ideas for what can be achieved in Mathematica. I think you'll find Mathematica is ideal for encoding mathematical systems. The actual Grassmann algebra code is still being finalized, but should be available early next year. http://www.ses.swin.edu.au/homes/browne/grassmannalgebra/book/index.htm John Alexey Skoblikov wrote: > Dear colleagues. > > Can anyone help me with making direct tensor algebra in Mathematica? > > In direct tensor algebra tensors are not components. Tensors are special > objects, that could be presented in the component form in sonme basis, > but even then they dont appear as S_{mn}, but as > S_{mn}r^m r^n > where r^m and r^n - are vectors of reciprocal basis and S_{mn} - > covariant components. NB! Basis vectors, are not columns like {1,0,0}, > but exaclty vectors i.e. "directed line segment" as is. > > Is it possible to make this kind of package in Mathematica, that could > deal with such objects and also go to the component form - on the lower > level of abstraction - on demand. > > In particular such system would calculate that > a . b x a = 0 (mixed product - cross and dot) WITHOUT making the > constructs like > E^{mnk}b_m a_n a_k, where E^{mnk} - Levi-Chivitta symbols. > > The example is on leshakk.chat.ru - file tensor.pdf -- _________________________________ John Browne School of Engineering and Science Swinburne University of Technology John Street, Hawthorn, Victoria, Australia Quantica phone: +613 9431 4007 Quantica fax: +613 9431 0940 Email: jbrowne at swin.edu.au

**References**:**Direct tensor algebra***From:*Alexey Skoblikov <alexey.skoblikov@compusoft.no>