Re: [GiNaC-list] Tricky way to control over dummy indices
On 7/15/17, esarcush esarcush <esarcush@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
On 7/14/17, Vladimir V. Kisil <kisilv@maths.leeds.ac.uk> wrote:
> On Fri, 14 Jul 2017 22:54:35 +0430, esarcush esarcush > <esarcush@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/
On Sat, 15 Jul 2017 00:06:29 +0430, esarcush esarcush <esarcush@gmail.com> said:
EE> On 7/15/17, esarcush esarcush <esarcush@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@maths.leeds.ac.uk> wrote: >>>>>>>> On Fri, 14 Jul 2017 22:54:35 +0430, esarcush esarcush >>>>>>>> <esarcush@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/ >>> >> EE> _______________________________________________ GiNaC-list EE> mailing list GiNaC-list@ginac.de EE> https://www.cebix.net/mailman/listinfo/ginac-list
participants (2)
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esarcush esarcush
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Vladimir V. Kisil