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

[Jeffrey R. <air...@gm...>]

---------- Forwarded message ---------
From: Jeffrey Rolland <air...@gm...>
Date: Sun, Jun 6, 2021 at 11:04 AM
Subject: Re: [Maxima-discuss] Integrate Differential Form Over Manifold
"Easily"?
To: Dimiter Prodanov <dim...@gm...>


A couple of things:

1) I think you may be talking about the antiderivative script; the integral
over k-manifold script works jsut fine (See attached test01.wxmx).

2) I'm not sure how well any of the antiderivative scripts work with
improper integrals (See attached test02, test03, and test04). Test02 and
test 03 do not have the t-integral for the coefficient converge, but test04
does. As you point out, the test02 has additional problems, as, "even if"
the t-integral converged, the script would return a constant for the
antiderivative, not ln|y| possibly times a constant.

I think when the form has a pole of some sort in [0,1] and the integral is
improper, special care may need to be taken. But, then, I think one of the
hypotheses for the theorem on which the script is based is that the form is
smooth. I'll actually defer to someone with more knowledge of chain
homotopy operators for forms with discontinuities at this point.

On Sun, Jun 6, 2021 at 4:36 AM Dimiter Prodanov <dim...@gm...> wrote:

> 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...> 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... <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------
>>
>>
>> _______________________________________________
>> Maxima-discuss mailing lis...@li...://lists.sourceforge.net/lists/listinfo/maxima-discuss
>>
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>

-- 
Jeffrey Rolland
<air...@gm... <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------


-- 
Jeffrey Rolland
<air...@gm... <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------