[GiNaC-list] How to differentiate from a Tensor?
esarcush esarcush
esarcush at gmail.com
Fri Jul 14 11:34:56 CEST 2017
I think it is not a suitable way. Happening other situations, this
method will lack. For example, consider a case that \( A_{ij} \) is a
two variable function. Moreover, please try your answer (if I
understand it well):
{
symbol x("x");
symbol i_sym("i"), j_sym("j");
idx i(i_sym, 3), j(j_sym, 3);
ex e = indexed(step(x), i, j);
ex de_dx = e.diff(x);
cout << de_dx << "\n";
}
returning 0.
All the best,
On 7/14/17, Vladimir V. Kisil <kisilv at maths.leeds.ac.uk> wrote:
>>>>>> On Fri, 14 Jul 2017 13:29:37 +0430, esarcush esarcush
>>>>>> <esarcush at 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 at maths.leeds.ac.uk> wrote:
> >>>>>>> On Fri, 14 Jul 2017 12:15:49 +0430, esarcush esarcush
> >>>>>>> <esarcush at 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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