July 2017 - GiNaC-list

Re: [GiNaC-list] How to differentiate from a Tensor?
by Vladimir V. Kisil 18 Jul '17

18 Jul '17

>>>>> On Fri, 14 Jul 2017 13:29:37 +0430, esarcush esarcush <esarcush(a)gmail.com> said: EE> E needs to depend on x. So, symbol A("A"), x("x"); symbol EE> i_sym("i"), j_sym("j"); idx i(i_sym, 3), j(j_sym, 3); ex e = EE> indexed(A, i, j); ex de_dx = e.diff(x); cout << de_dx << "\n"; EE> returns 0. Thus, what is the way to depend "e" on "x" like EE> undefined functions? If a dependence of A on x is not defined, try to use the step function (as one without defined derivative): ex e = indexed(step(x), i, j); This keeps track on derivatives. To maintainer: I have run into similar situation working with differential operators. Shall we add "generic" functions to GiNaC with 1, 2, 3, 4 variables? -- 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> All the bests, EE> On 7/14/17, Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk> wrote: >>>>>>> On Fri, 14 Jul 2017 12:15:49 +0430, esarcush esarcush >>>>>>> <esarcush(a)gmail.com> said: >> EE> Dear all, What is right way to have something like \( EE> \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a EE> tensor "A~i.j.k" and want to differentiate from it with respect EE> to "x" e.g. >> >> For a GiNaC object E its derivative with respect to x is obtained >> by E.diff(x) >> -- >> 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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Re: [GiNaC-list] Tricky way to control over dummy indices
by esarcush esarcush 14 Jul '17

14 Jul '17

On 7/15/17, esarcush esarcush <esarcush(a)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(a)maths.leeds.ac.uk> wrote: >>>>>>> On Fri, 14 Jul 2017 22:54:35 +0430, esarcush esarcush >>>>>>> <esarcush(a)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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Tricky way to control over dummy indices
by esarcush esarcush 14 Jul '17

14 Jul '17

Dear all, in expression { indexed(A, i, j) * indexed(B, j, k) } GiNaC is saying that the dummy index is "j" and "i, k" are free. Is there a way to determine dummy indices based on Einstein summation notation; namely all the indices in the latter be free. All the bests, Esa

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Re: [GiNaC-list] How to differentiate from a Tensor?
by esarcush esarcush 14 Jul '17

14 Jul '17

On 7/14/17, Vladimir V. Kisil <kisilv(a)maths.leeds.ac.uk> wrote: >>>>>> On Fri, 14 Jul 2017 12:15:49 +0430, esarcush esarcush >>>>>> <esarcush(a)gmail.com> said: > > EE> Dear all, What is right way to have something like \( > EE> \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a > EE> tensor "A~i.j.k" and want to differentiate from it with respect > EE> to "x" e.g. > > For a GiNaC object E its derivative with respect to x is obtained by > E.diff(x) > -- > 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/ > E needs to depend on x. So, symbol A("A"), x("x"); symbol i_sym("i"), j_sym("j"); idx i(i_sym, 3), j(j_sym, 3); ex e = indexed(A, i, j); ex de_dx = e.diff(x); cout << de_dx << "\n"; returns 0. Thus, what is the way to depend "e" on "x" like undefined functions? All the bests,

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How to differentiate from a Tensor?
by esarcush esarcush 14 Jul '17

14 Jul '17

Dear all, What is right way to have something like \( \frac{\partial A^{i}_{jk}}{\partial x} \)? Indeed, I defined a tensor "A~i.j.k" and want to differentiate from it with respect to "x" e.g. All the bests, Esa

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CAS
by Robert Hai 07 Jul '17

07 Jul '17

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