Edwin Woollett wrote:
>
>
> The correct value of integrate ( 1/x, x, -1, 2 )
> is log(2) = 0.693147.. when considered as a
> principal value integral, since we can write this
"Correct" depnds on the point of view.
>
> (%i2) integrate(1/x,x,-1,2);
> Principal Value
> (%o2) log(2)+2*%i*%pi
>
> We know the integral must be a real number, so
> we know integrate(..) cannot be trusted here.
> Integrate appears to be closing the complex plane
> contour for a case where Jordan's lemma is not
> satisfied?
....
> ----------------------------------
> Perhaps integrate should check the integrand
> against conditions of Jordan's lemma before
> returning an answer which is wrong.
>
In physics it is traditional, and *very* important to write
1/x = PP 1/x + %i*%pi*Dirac_delta(x)
Where the real part is indeed a principal part, and there is an imaginary
part given by a delta "function". This result is the basis of causality
analysis, Kramers-Kronig relations, etc. and is indeed related to
application of Cauchy relation for complex integrals.
It may well be that the maxima integration routine takes this in view.
--
Michel Talon