Robert Marik wrote:
> Hello all
>
> the command
>
> changevar('integrate(sqrt(9-x^2),x),x = 3*sin(t),t,x)
>
>
> gives imaginary unit. Is it what we want?
> rootscontract solves this problem but ....
I don't have a solution, but I think the issue is caused by a call to
radcan within changevar. You can see this if you trace(radcan).
Setting radexpand:false doesn't affect this, even though the
documentation for radexpand seems to imply that sqrt(9-9*sin(t)^2)
shouldn't be changed to %i*sqrt(3*sin(t)-3)*sqrt(3+3*sin(t)).
There also seems to be an inconsistency. radcan(sqrt(1-x^2)) is
sqrt(1-x)*sqrt(1+x). But radcan(sqrt(4-4*x^2)) is
2*%i*sqrt(x-1)*sqrt(x+1). And this happens even if radexpand : false.
Ray