Exactly! That's it, mathematically speaking!

However, when I try 
sage: sin(2 / (A((0.99, 1.01)) + dx + 3*dy))
ValueError: Can only apply sin to formal power series with zero constant 
term.

And, I get
sage: A((0.99,1.01))
1.0?
but
sage: sage: A(RIF(0.99,1.01))
1.0? + O(dx, dy)^53

Shouldn't that give the same?

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