On Wednesday, September 12, 2012 4:20:27 PM UTC+1, Jason Grout wrote:

> I think matlab may automatically do the sort of abs(a-b)<eps thing that 
> Volker was talking about, since numbers are assumed to be floating point 
> in matlab. 


Probably, and for a very confusing value of epsilon.

Mathematica always does interval arithmetic, I think. Friendly to newcomers 
but slow and teaches bad habits for computing with floats. 

In Sage, I actually would prefer for interval arithmetic == to mean that 
intervals overlap. Right now it basically means "intervals are the same" 
which is pretty useless. But the application generally is: I have two 
approximate solutions, and I want to know if they are the same. Of course 
that would make == non-transitive, but so what?

sage: RIF(1/10) + RIF(2/10) == RIF(3/10)
False

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