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

[esarcush esarcush]

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. ;)
>
> All the best,
> Esa
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> 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/
>>
>