I think that your code doesn’t do what you think it does. Note for example
that your declarations are self-contradicting :
Pasting code; enter '--' alone on the line to stop or use Ctrl-D.
:function("xp yp zp tp f")
:var("x y z t v c")
:--
(xp, yp, zp, tp, f)
(x, y, z, t, v, c)
sage: xp.parent()
<class
'sage.symbolic.function_factory.function_factory.<locals>.NewSymbolicFunction'>
sage: xp = (x - v * t) / sqrt(1 - v^2 / c^2)
sage: xp.parent()
Symbolic Ring
What you intend to do isn’t really clear… Could you try and clear your
goals ?
HTH,
Le vendredi 22 janvier 2021 à 19:46:35 UTC+1, [email protected] a écrit :
>
> I'm trying to collect all the terms in an expression with the same
> second partial derivative but it doesn't seem to be working.
> I can't figure out why.
>
> Here is my code....
>
> # ============================================================
>
> function("xp yp zp tp f")
> var("x y z t v c")
>
> xp = (x - v * t) / sqrt(1 - v^2 / c^2)
> yp = y
> zp = z
> tp = (t - v * x / c^2) / sqrt(1 - v^2 / c^2)
>
> e = derivative(f(xp, yp, zp, tp), x, 2) + derivative(f(xp, yp, zp, tp), y,
> 2) + derivative(f(xp, yp, zp, tp), z, 2) - derivative(f(xp, yp, zp, tp), t,
> 2) / c^2
>
> e.collect(derivative(f(xp, yp, zp, tp), x, 2))
>
> # ============================================================
>
> Here is the output. I added spaces at a subtraction to make it easy to see
> there are TWO of those D[0, 0](f) terms (each at the beginning of the
> sections).
>
> (D[0, 0](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y, z, (t -
> v*x/c^2)/sqrt(-v^2/c^2 + 1))/sqrt(-v^2/c^2 + 1) - v*D[0, 3](f)(-(t*v -
> x)/sqrt(-v^2/c^2 + 1), y, z, (t - v*x/c^2)/sqrt(-v^2/c^2 +
> 1))/(c^2*sqrt(-v^2/c^2 + 1)))/sqrt(-v^2/c^2 + 1) - v*(D[0, 3](f)(-(t*v -
> x)/sqrt(-v^2/c^2 + 1), y, z, (t - v*x/c^2)/sqrt(-v^2/c^2 +
> 1))/sqrt(-v^2/c^2 + 1) - v*D[3, 3](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y, z,
> (t - v*x/c^2)/sqrt(-v^2/c^2 + 1))/(c^2*sqrt(-v^2/c^2 +
> 1)))/(c^2*sqrt(-v^2/c^2 + 1))
>
> -
>
> ((v*D[0, 0](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y, z, (t -
> v*x/c^2)/sqrt(-v^2/c^2 + 1))/sqrt(-v^2/c^2 + 1) - D[0, 3](f)(-(t*v -
> x)/sqrt(-v^2/c^2 + 1), y, z, (t - v*x/c^2)/sqrt(-v^2/c^2 +
> 1))/sqrt(-v^2/c^2 + 1))*v/sqrt(-v^2/c^2 + 1) - (v*D[0, 3](f)(-(t*v -
> x)/sqrt(-v^2/c^2 + 1), y, z, (t - v*x/c^2)/sqrt(-v^2/c^2 +
> 1))/sqrt(-v^2/c^2 + 1) - D[3, 3](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y, z, (t
> - v*x/c^2)/sqrt(-v^2/c^2 + 1))/sqrt(-v^2/c^2 + 1))/sqrt(-v^2/c^2 + 1))/c^2
> + D[1, 1](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y, z, (t -
> v*x/c^2)/sqrt(-v^2/c^2 + 1)) + D[2, 2](f)(-(t*v - x)/sqrt(-v^2/c^2 + 1), y,
> z, (t - v*x/c^2)/sqrt(-v^2/c^2 + 1))
>
>
>
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