       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>
• 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

```

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