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ReplaceAll / sequential replacements versus joint replacement


Suppose there is an expression e1 which depends, among others, on variables 
a and b.
Replace both a and b by zero:

e1/.{a->0,b->0} Mathematica gives, say, result1.

Next, consider

e2 = e1/.{a->0};
e2/.{b->0} Mathematica gives, say, result2.

How can result 1 differ from result 2?

For my specific problem, I also attach a short Mathematica notebook.
[Contact the author to obtain the notebook - moderator]

I'd appreciate any help.

Many thanks,
Ron 



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