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14

The critical issue in the first example is that Mathematica is using significance arithmetic to track precision. This is certainly billed as a feature by Wolfram Research. As we see in this example though, it can be portrayed as a weakness. In truth, you might need to know what you're doing to use it correctly. In this answer, I mentioned that significance ...


12

Without commenting on how much attention one should pay to marketing literature: the second example is somewhat relevant. Mathematica's polynomial factoring algorithm is known to be at least fifteen years behind the state of the art, and things that Maple will factor in seconds will go away (literally) forever in Mathematica. This is, of course, not too ...


22

The first example seems to intentionally set Mathematica up to "fail" by specifying insufficient input accuracy. With additional precision: ClearAll[s] s[i_] := s[i] = 2*s[i - 1] - 3*s[i - 1]^2 s[0] = 0.3`30; s[40] 0.333333 And Mathematica is capable of far greater precision if necessary: ClearAll[s] $RecursionLimit = ∞ s[i_] := s[i] = 2*s[i - 1] - ...



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