[GiNaC-list] Tricky way to control over dummy indices
esarcush esarcush
esarcush at gmail.com
Fri Jul 14 21:36:29 CEST 2017
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/
>>
>
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