# Repeated derivatives

0 votes

I computed a variational derivative and arrived to the following expression:

∫(4d{t}(d{t x}(u)) d{x}(p) d{t x}(u) e{p}-4d{t}(p) d{x}(d{t x}(u)) d{t x}(u) e{p} + 4d{t}(p) d{t x}(u) d{t x x}(u) e{p}-4d{x}(p) d{t x}(u) d{t t x}(u) e{p}}

Here

{x,y,z,t}::Coordinate.
d{#}::PartialDerivative.
{x,y,t,u,p,q}::Depends(d{#}).
e{#}::Accent.


This expression equals zero. Is there any way to simplify it have zero explicitly?

If I copy the expression and put it to cadabra

ex:=4d_{t}(d_{t x}(u)) d_{x}(p) d_{t x}(u) e{p}
-4d_{t}(p) d_{x}(d_{t x}(u)) d_{t x}(u) e{p}
+ 4d_{t}(p) d_{t x}(u) d_{t x x}(u) e{p}
-4d_{x}(p) d_{t x}(u) d_{t t x}(u) e{p};


it automatically convert d{x}(d{t x}(u)) to d_{t x x}(u). But how to do this with a command?

asked

## 1 Answer

0 votes

That simplification should have happened automatically. Can you email me (info@cadabra.science) the code that leads to that non-zero result?

answered by (61k points)

Sent, thank you!

While waiting for a real fix, I use the following workaround:

ex:=@(ex).