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Commutators with boson operators

I need some help.

I want to write code that Mathematica would calculate commutators [A,B], [A,[B,C]] and so on...,

where A,B,C,D,... are functions like

A = a+ b*creat + c*annih + d*creat**annih + e*annih**creat +  f*creat^2+g*annih^2+...

where a,b,c,d,... are usual complex numbers;

and annih & creat are boson noncommutative operators
that satisfy commutation relation:
[annih, creat] = 1.

Thank you in advance!

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