[GiNaC-devel] Improved dummy index renaming -> clifford exam fails

[Vladimir Kisil]

		Dear All,

		I am going to fix problems pointed out by Chris in
  clifford.cpp. However I looking for developer's advises before that. 

>>>>> "CD" == Chris Dams <Chris.Dams at mi.infn.it> writes:
    CD>  Anyone who writes code like

    CD> 	indexed(squared_metric, alpha, alpha)

    CD> where alpha is a varidx should realize that he is in a state of
    CD> sin and really doing something that might break anytime.

	Please give me a hint why this is wrong.

    CD> By the way. Wouldn't it be a good idea to remove the restriction
    CD> that indices of clifford objects should be varidxes? 

	I am going to remove this if nobody objects.

    CD> varidxes. Doesn't an up-index mean exactly the same as a down
    CD> one in that case?

	In the recent paper (p. 4)
  http://euklid.bauing.uni-weimar.de/templates/papers/f34.pdf the
  following defining identities of a Clifford algebra in a space with
  a metric g.i.j are used:

  e.i e.j + e.j e.i = g.i.j 
  e~i e~j + e~j e~i = g~i~j 

  however 

  e.i e~j + e~j e.i = delta.i~j 

  Does any one object to implementation of the last identity in GiNaC?
  Or   e.i e~j + e~j e.i = g.i~j should be used instead?

    CD> What I also would like to know, is what on earth it means that
    CD> "generators satisfying the identities e~i e~j + e~j e~i = M(i,
    CD> j) for some matrix (metric) M(i, j), which may be
    CD> non-symmetric".

	Where did you see this? My ginac.info tells that

 e~i e~j + e~j e~i = M(i, j) + M(j, i)

 which is meaningful for non-symmetric M.

 Best wishes,
 Vladimir
-- 
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/