Re: Symbolica package warning: Using rat() heuristics for double-precision input (is this what you wanted?)

[Mike Miller]

On Fri, Feb 17, 2017 at 11:42:26 -0500, Przemek Klosowski wrote:
> I don't understand the symbolic package's precision propagation. It seems to
> know e.g. pi to arbitrary precision:
> 
> vpa(pi,55)
> ans = (sym) 3.141592653589793238462643383279502884197169399375105821
> 
> but calculations seem to be limited to 50 significant digits:
> 
> vpa(pi/2,55)
> ans = (sym) 1.570796326794896557998981734272092580795288085937500000
> 
> Is there something magic about 50?

No, there is something magic about the double value returned by pi.

The function that converts numeric values has special code to test
whether a given double value is exactly pi (to the extent of double
precision), and replaces that with the string value "pi" for SymPy to
evaluate.

To get pi/2 with more digits, use

  vpa (pi, 55) / 2

The doc strings for both sym and vpa mention taking care when
constructing symbolic or variable-precision values from double values
that the user may have intended to represent an exact fraction.

-- 
mike