Maurizio wrote:
> I'd like to jump in the conversation, to describe my own experience.
>
> I don't know what about real numbers, but I found out that in that
> same situation you were talking about (symbolic expression where all
> the symbols are substituted by numbers eventually), and the expected
> result is a complex number, using the ComplexField() makes the
> substitution many orders of magnitude faster than doing .n()
>
> Example:
>
> CF = ComplexField()
> evaluated_number = CF(numerical_expression)
>
> In this way, I get the result in the fastest way (I'm not that much
> experienced, though).
>
> Any suggestion is appreciated
>
As a shortcut, you could just use CC, which is the same as
ComplexField() (i.e., CC is ComplexField with the default 53 bits of
precision)
This would be analogous to the RR example below (except using complex
numbers instead of real numbers.
sage: CC is ComplexField()
True
sage: CC(sqrt(-1))
1.00000000000000*I
I'm surprised that this is orders of magnitude faster than using n(),
since I thought they were essentially doing the same thing. My timing
tests seem to indicate that the opposite is true:
sage: a=sqrt(2)
sage: timeit('CC(a)')
625 loops, best of 3: 33 µs per loop
sage: timeit('a.n()')
625 loops, best of 3: 19.2 µs per loop
sage: timeit('RR(a)')
625 loops, best of 3: 20.7 µs per loop
ah, but if the number is complex:
sage: a=sqrt(2)*I
sage: timeit('CC(a)')
625 loops, best of 3: 83.5 µs per loop
sage: timeit('a.n()')
625 loops, best of 3: 213 µs per loop
The code for n() first tries to convert to a real number, and if an
exception is raised, then it tries to convert to a complex number.
Maybe that try/except block is way, way too slow? Comments?
Thanks,
Jason
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