Re: [Maxima-discuss] Integrate Differential Form Over Manifold "Easily"?

[Francisco C. <fra...@up...>]

I think you are referring to the calculation of the exterior 
anti-differential of a form, not to the integration of a k-form over a 
k-manifold. Sorry if I am wrong.

One closed form is not always the exterior differential of another in 
the domain. It depends on the topology of the domain. Poincaré's lemma 
states that if the domain is a star-shaped set with respect to the 
origin, a closed form has an exterior anti-differential. The method I 
have used is valid under these conditions, and the form you propose is 
not defined on a star-shaped set with respect to the origin. In R^2 for 
example, the domain of its 1-form is R^2-{x-axis} which is not 
star-shaped with respect to the origin.

Best regards

El 6/6/21 a las 11:35, Dimiter Prodanov escribió:
> How can you integrate the from
>
> dy/y
>
> using your method?
> The substitution y -> t *y does not work.
>
> best regards,
>
> Dimiter
>
> On Fri, Jun 4, 2021 at 12:45 PM Francisco Carbajo 
> <fra...@up... <mailto:fra...@up...>> 
> wrote:
>
>     Here is the wxmaxima file that solves the proposed example using
>     the cartan package.
>
>     Regards
>
>     El 4/6/21 a las 10:55, Jeffrey Rolland escribió:
>>     Is there a way to integrate a differential k-form "easily" over a
>>     k-manifold, say using the dii_form package? Here is an example of
>>     integrating over a 3-torus in Mathematica, illustrating Stokes's
>>     Theorem. This would be the last piece to replace Mathematica with
>>     wxMaxima for me. (You need to have the DifferentialForms.m file
>>     in your Mathematica path -- your HOME directory should work --
>>     for the notebook to function properly.)
>>
>>     -- 
>>     Jeffrey Rolland
>>     <air...@gm... <mailto:jro...@gm...>>
>>
>>     "The weed of crime bears bitter fruit; crime does NOT pay! The Shadow
>>     knows!"
>>      - The Shadow, _The Shadow_ (1994)
>>
>>      -----BEGIN GEEK CODE BLOCK-----
>>     Version: 3.1
>>     GM d-- s:+ a+ C++>$ UL+>$
>>     P? L+++>+++++$ E--- W+++>$ N+++>+++$ o? K--? !w--- !O---- !M-
>>     !V-- PS++
>>     PE- Y? PGP+++ t+++ 5? X+ R+>$ tv++ !b DI+++>+++++ !D G+ e++++$ h+ r--
>>     y++
>>     ------END GEEK CODE BLOCK------
>>
>>
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