What are computed operators? Are those the D[0, 0] things? How avoid
those? Is that same as second derivative of 1st variable?
On Sun, Jan 24, 2021, 11:33 AM Emmanuel Charpentier <
emanuel.charpent...@gmail.com> wrote:
> Probably because “the given second derivative” has a “computed operator”…
>
> BTW :
>
> var("x,y,z,t,v,c")
> f=function("f")
> xp=(t-v*x)/sqrt(1-v^2/c^2)
> yp=y
> zp=z
> tp=(t-v*x/c^2)/sqrt(1-v^2/c^2)
> foo=(sum(map(lambda u:derivative(f(xp,yp,zp,tp),u,2), (x, y,
> z)))-derivative(f(xp,yp,zp,tp),t,2)/c^2).factor()
> view(foo.simplify_full())
>
> does partially what you mean…
> Le dimanche 24 janvier 2021 à 17:36:44 UTC+1, cseb...@gmail.com a écrit :
>
>> Emmanuel
>>
>> But my question is more simple than that. I just want to know why the
>> collect method was not able to collect all the terms with the given second
>> derivative.
>>
>> On Sun, Jan 24, 2021, 2:15 AM Emmanuel Charpentier <
>> emanuel.c...@gmail.com> wrote:
>>
>>> Sage has recently acquired a large set of tools relative to manifolds
>>> <https://sagemanifolds.obspm.fr/>. A look at these tools and related
>>> tutorials/references may be in order…
>>>
>>> HTH,
>>>
>>> Le samedi 23 janvier 2021 à 23:17:26 UTC+1, cseb...@gmail.com a écrit :
>>>
>>>> What you intend to do isn’t really clear… Could you try and clear your
>>>>> goals ?
>>>>>
>>>> Emmanuel
>>>>
>>>> Thanks so much for your help. I'm trying to show that the wave
>>>> equation (https://en.wikipedia.org/wiki/Wave_equation)
>>>> is invariant under a certain coordinate transformation called the
>>>> Lorentz transformation (special relativity).
>>>>
>>>> I represent the function that obeys the wave equation in the primed
>>>> coordinate system by f(xp, yp, zp, tp).
>>>>
>>>> I also represent the primed coordinates by the coordinates in the
>>>> unprimed coordinate system.
>>>> Therefore, f(xp, yp, zp, tp) = f(xp(x, y, z, t), yp(x, y, z, t),
>>>> zp(x, y, z, t), tp(x, y, z, t)).
>>>>
>>>> I then find a bunch of derivates of f(xp(x, y, z, t), yp(x, y, z, t),
>>>> zp(x, y, z, t), tp(x, y, z, t)) and try to collect terms.
>>>>
>>>> All the coordinates should be real numbers.
>>>>
>>>> Does that explain everything?
>>>>
>>>>
>>>>
>>>>
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