Alasdair McAndrew wrote:
> Thanks for your replies. What I really want to do is calculate the
> total variation of some functions f; this being defined as the integral
> of the absolute value of the derivative of f (see
> http://en.wikipedia.org/wiki/Total_variation). The integral of abs was
> just a test case.
>
> I can probably use pmint, but the results it produces aren't really
> useful. For example:
>
> (%i1) pmint(abs(sin(x)),x);
> (%o1) -cos(x)*abs(sin(x))/sin(x)
>
> which is true, but doesn't allow me to enter values for which sin(x)=0.
> This is too restrictive.
>
> I could probably do all this numerically, but I would rather obtain
> closed-form solutions than numerical approximations.
>
> I'll keep fiddling.
Here's one possible way, which is how I would probably do it by hand,
for the total variation problem.
Find all the points where f'(x) = 0. Maxima can do this for some
functions, but not all. Let the roots be called x[n]. Then the
integral you want becomes the sum of integrals of the form
abs(integrate(f'(x),x, x[n],x[n+1))
Maxima might be able to compute this definite integral.
Hope I didn't make any mistakes!
Ray