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Problem with Around (simplification of sums of Around)

Mario Veruete
Posted 1 month ago

POSTED BY: Mario Veruete
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On my system I get automatic simplification with no need for Simplify. There is also an example in the documentation

In[1]:= Around[1, .1] + Around[2, .4]

Out[1]= Around[3., 0.4123105625617661]
POSTED BY: Gianluca Gorni
Jim Baldwin
Jim Baldwin
Posted 1 month ago

Gianluca: It's when each of those terms are multiplied by an unassigned symbolic value where the automatic simplification does not occur.
POSTED BY: Jim Baldwin

Interesting, the two expressions are not totally equivalent when the variable itself is an Around object:

In[1]:= Around[10, 1]*X + Around[20, 2]*X /. X -> Around[1, 2]

Out[1]= Around[30., 44.77722635447623]

In[2]:= (Around[10, 1] + Around[20, 2])*X /. X -> Around[1, 2]

Out[2]= Around[30., 60.0416522091123]
POSTED BY: Gianluca Gorni

In other words, the distributive law is not valid for Around objects.
POSTED BY: Gianluca Gorni
Jim Baldwin
Jim Baldwin
Posted 1 month ago

I'm not sure that I would call the need to use Simplify a "problem". It is certainly possible in a practical application to have two correlated Around's. In such a case I wouldn't want the automatic simplification.

In fact, I would consider the automatic simplification of Around[12, 2] + Around[10, 1] to be a potential problem.
POSTED BY: Jim Baldwin
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