ex:= A_{m n} B_{n} + C_{m n p} D_{n p};
for i in ex.top().indices():
    print(i)

for i in ex.top().free_indices():
    print(i)

print("---")
for term in ex.top().terms():
    print(str(term)+" has indices:")
    for i in term.indices():
        print(i)
        
    
def expand_nabla(ex):
    for nabla in ex[r'\nabla']:
        nabla.name=r'\partial'
        dindex = nabla.indices().__next__()   # need .index() to give direct single index without __next()__.
        for arg in nabla.args():              # need .arg() to give direct single argument without __next()__.
            ret:=0;
            for index in arg.free_indices():
                t2:= @(arg);
                if index.parent_rel==sub:
                    t1:= -\Gamma^{p}_{@(dindex) @(index)};
                    t2[index]:= _{p};
                else:
                    t1:=  \Gamma^{@(index)}_{@(dindex) p};
                    t2[index]:= ^{p};
                ret += t1 * t2
            nabla += ret
    return ex

\nabla{#}::Derivative;
\hat{#}::Accent;
ex:= \nabla_{a}{ h^{b}_{c} }; 
expand_nabla(ex);

ex:= \nabla_{a}{ v_{b} w^{b} };
expand_nabla(ex);
    
ex:= \nabla_{\hat{a}}{ h_{b c} v_{d} } + \nabla_{b}{ h_{\hat{a} c d } } + T_{\hat{a} b c d};
expand_nabla(ex);