# This tests whether free, fixed and independent indices
# are treated correctly.

{x,y,z}::Symbol;
{a,b,c}::Indices(name="free_indices", position=free);
{m,n,p}::Indices(name="fixed_indices", position=fixed);
print(properties())

ex:= A_{x} + A_{y};
print("Test 01 passed")

ex:= A_{a} + A^{a};
lower_free_indices(_);
tst:= 2 A_{a} - @(ex);
assert(tst==0)
print("Test 02 passed")

try:
    ex:= A_{m} + A^{m};
    assert(1==0)
except:
    print("Test 03 passed")


\m::LaTeXForm("\mu").
D{#}::Derivative;
{\m,\n}::Indices(s,position=fixed);

{x_\m}::Coordinate;

ex:= D_{x_\m}{A^\m};

print(tree(ex))
    
for i in ex.top().free_indices(): 
   display(i);