# Problem extracting free indices

Hello,

I am trying to extract the free indices out of some expression, and the result seems to depend on the order of factors.
For example:

{a,b,c,d#,z}::Indices.

ex:= 1/2 C^{a b c} D_{b} A_{c};
try:
next(ex.top().free_indices())
print("there's at least a free index")
except:
print("no free indices!")

ex:= 1/2 D_{b} C^{a b c} A_{c};
try:
next(ex.top().free_indices())
print("there's at least a free index")
except:
print("no free indices!")

ex:= 1/2 D_{b} A_{c} C^{a b c};
try:
next(ex.top().free_indices())
print("there's at least a free index")
except:
print("no free indices!")


returns

 1/2 C^{a b c} D_{b} A_{c}
there's at least a free index
1/2 D_{b} C^{a b c} A_{c}
no free indices!
1/2 D_{b} A_{c} C^{a b c}
no free indices!


Well spotted, that's a bug indeed. It's fixed on github now.

It works, thank you very much !

However, I still have the following problem:

ex:= 1/2 C^{a b c} D_{b} A_{c} - X_{b} C^{a b c} A_{c};
for i in ex.top().free_indices():
print(i)


returns

 1/2 C^{a b c} D_{b} A_{c}-X_{b} C^{a b c} A_{c}
a
a


That's the expected result: there is one free index 'a' on the first term, and one on the second term. Consider this:

ex:= 1/2 C^{a b c} D_{b} A_{c} - X_{b} C^{a b c} A_{c};
q=0
for i in ex.top().free_indices():
i.name='d'+str(q)
q=q+1

ex;


It turns that expression into

1/2 C^{d0 b c} D_{b} A_{c} - X_{b} C^{d1 b c} A_{c};


(which is invalid, but that's not the point of course).

I see.

That means that if I want to get the name of the actual free index of the tensorial expression I need to do

ex:= 1/2 C^{a b c} D_{b} A_{c} - X_{b} C^{a b c} A_{c};
for i in next(ex.top().terms()).free_indices():
print(i)


right?

In particular, the expand_nabla function always needs a prior distribute, right?

That next(ex.top().terms()) selects the 2nd term, so that's why that loop shows only one index. Yes, as it stands, that expand_nabla requires that you distribute first (it was only meant as an example).

You mean the first term right?
Anyway, thank you very much for the clarifications !

Yes, sorry, I keep messing up python and C++ iterators.