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, [email protected] 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 <[email protected]>
> 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, [email protected] 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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