[GiNaC-list] question about lorentz_g contract with sy_anti tensor

[Vladimir V. Kisil]

>>>>> On Sat, 25 May 2019 14:57:54 +0000, Feng Feng <F.Feng at outlook.com> said:

    FF> Thanks very for the reply.  and I have tried the suggestion,
    FF> i.e., using the following expression:

    FF> auto ret = indexed(A, sy_anti(0,1,2,3), ia,ib,ic,id) *
    FF> lorentz_g(ic, id.toggle_variance());

    FF> but I got something like: -delta.d~c*A~d~a~b~c, still a non-zero
    FF> result.

    It looks like you did not call simplified_indexed(). Please see
  attached code which outputs:
  
Not-reduced: delta.d~c*A~b~a~d~c
Anti-symmetry: 0

    FF> BTW, if c’s variance is not toggled in lorentz_g,
    FF>       then these two dummy index c’s variance is not matched,
    FF> and is that allowed?

    This is exactly what you obtain by lowering/raised just one index in
  the metric tensor itself: g_c^d = g_{ce} g^{ed}, see

  https://en.wikipedia.org/wiki/Metric_tensor
-- 
Vladimir V. Kisil                 http://www.maths.leeds.ac.uk/~kisilv/
  Book:     Geometry of Mobius Transformations     http://goo.gl/EaG2Vu
  Software: Geometry of cycles          http://moebinv.sourceforge.net/

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