[GiNaC-list] Tricky way to control over dummy indices

[Vladimir V. Kisil]

>>>>> On Sat, 15 Jul 2017 00:06:29 +0430, esarcush esarcush <esarcush at gmail.com> said:

    EE> On 7/15/17, esarcush esarcush <esarcush at gmail.com> wrote:
    >> Agreement: Every dummy index have a hidden sigma.
    >> 
    >> Based on the page you linked (and in common also), there are two
    >> ways to illustrate a dummy index in a term: 1) "j" is a dummy one
    >> iff it appears as superscript and subscript.
    >> 
    >> 2) "j" is a dummy one iff it appears in two (or more that two)
    >> tensor coefficients making that term.
    >> 
    >> GiNaC is using second approach. This makes some troubles to
    >> somebodies that are using first one. For example, I'd like to
    >> deal with some tensorials that have in-common indices as
    >> e.g. subscripts but free (as mentioned example). I think second
    >> approach is more physical vs first one more diff-geometrical. ;)

    Did you notice the existence of GiNaC::idx and GiNaC::varidx
  classes? For the first case you need to use varidx.
-- 
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/

    >> 
    >> All the best, Esa
    >> 
    >> 
    >> 
    >> 
    >> 
    >> 
    >> 
    >> 
    >> On 7/14/17, Vladimir V. Kisil <kisilv at maths.leeds.ac.uk> wrote:
    >>>>>>>> On Fri, 14 Jul 2017 22:54:35 +0430, esarcush esarcush
    >>>>>>>> <esarcush at gmail.com> said:
    >>> 
    EE> Dear all, in expression
    >>> 
    EE> { indexed(A, i, j) * indexed(B, j, k) }
    >>> 
    EE> GiNaC is saying that the dummy index is "j" and "i, k" are
    EE> free. Is there a way to determine dummy indices based on
    EE> Einstein summation notation; namely all the indices in the
    EE> latter be free.
    >>> 
    >>> My understanding of
    >>> 
    >>> https://en.wikipedia.org/wiki/Einstein_notation
    >>> 
    >>> is that in the above expression there is summation over j, thus
    >>> it is not free.
    >>> --
    >>> 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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