Direct tensor algebra

*To*: mathgroup at smc.vnet.net*Subject*: [mg37385] Direct tensor algebra*From*: Alexey Skoblikov <alexey.skoblikov at compusoft.no>*Date*: Sat, 26 Oct 2002 02:03:08 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Direct tensor algebra***From:*John Browne <jbrowne@swin.edu.au>