Consider using subs in the following way. You have two sets of
noncommuting bases e_1,...,e_n and h_1,...,h_n and they are related by
(summation convention for repeated indexes):
e_i = a_ij*h_j and h_i = b_ij*e_j where a_ij and b_ij are sympy
scalars (commuting)
so you create the following dictionarys:
e_to_h = {e_i:a_ij*h_h} and h_to_e = {h_i:b_ij*e_j}
so that if you have a expr linear in an e_i representation and you want
to go to an h_i representation you simply:
expr.subs(e_to_h)
or if you have a expr linear in an h_i representation and you want to go
to an e_i representation you simply:
expr.subs(h_to_e)
This works unless you have entries in the dictionaries of the form (for
example the first entry in each dictionary):
e_to_h[e_1] = h_1 and h_to_e[h_1] = e1
If you go back and forth between representations you change the keys in
the dictionaries. Is there anyway to avoid this?
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