I do not know how to automatically commute partial derivatives on a scalar and simplify it. For example, if I have: $$\partial_a \partial_b \partial_c f- \partial_c \partial_a \partial_b f $$ where $f$ is a scalar function, the ToCanonical and Simplification command do not simplify this. I also use CommuteCovdsonScalar command, but it doesn't work as well. Could anybody help me?
1 Answer
The recommended way to do something like this is to use SortCovDs
, which may introduce Christoffel terms if needed:
In[6]:= PD[-a]@PD[-b]@PD[-c]@F[] - PD[-c]@PD[-a]@PD[-b]@F[] // SortCovDs
Out[6]= 0
If you want to automate SortCovDs
for a given derivative, say PD in this case, use:
SortCovDsStart[PD]
Then this will automatically give zero (again, for general covariant derivatives this would produce Christoffel terms):
In[9]:= PD[-a]@PD[-b]@PD[-c]@F[] - PD[-c]@PD[-a]@PD[-b]@F[]
Out[9]= 0
To stop the automatic commutation of derivatives use
SortCovDsStop[PD]