See answer in text.
Le samedi 19 juillet 2014 18:25:42 UTC+2, Anne Schilling a écrit :
>
> Hi!
>
> [ Bandwidth savings ]
>
> Pulling out e^{2\pi i x} to simplify the integral to a one dimensional
> integral,
>
??? Again, I can't follow you. Care to explain ?
> Sage can solve this numerically:
>
> sage: g = lambda x : (1+e^(2*pi*I*x)).abs()
> sage: numerical_integral(g,0,1)
> (1.2732395447351625, 1.4155343563970746e-14)
> sage: n(4/pi)
> 1.27323954473516
>
> but not symbolically:
>
> sage: integral(g,(x,0,1))
>
Ahem. This is kinda Mathematica-like syntax. In Sage, one should write
integrate((1+e^(2*i*pi*x)).abs(),x,0,1), which gives :
sage: integrate((1+e^(2*i*pi*x)).abs(),x,0,1)
1/2*(2*pi - I)/pi + 1/2*I/pi
sage: integrate((1+e^(2*i*pi*x)).abs(),x,0,1).expand()
1
Yay ! A worse problem ?
But I note that your syntax is *also* accepted by Sage (which I didn't
know) for single variable integration :
sage: integral(x,(x,0,1))
1/2
sage: integral(x*y,(x,0,1),(y,0,1))
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
[ Bandwith savings : lotsa backtrace... ]
TypeError: cannot coerce arguments: no canonical coercion from <type
'tuple'> to Symbolic Ring
A possible enhancement ?
HTH,
--
Emmanuel Charpentier
> Anne
>
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