[GiNaC-list] Tricky way to control over dummy indices
Vladimir V. Kisil
kisilv at maths.leeds.ac.uk
Fri Jul 14 21:56:23 CEST 2017
>>>>> 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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