[Maxima] integrate(1/x,x,0,1)

Stavros Macrakis macrakis at alum.mit.edu
Mon Jun 2 17:55:11 CDT 2008


On Mon, Jun 2, 2008 at 6:42 PM, Viktor T. Toth <vttoth at vttoth.com> wrote:
> It is difficult to discern the intent of the original e-mail clearly, but it
> seemed to me that the poster was specifically referring to the behavior when
> x+1 was defined as zero or negative:

Ah, I see.

> Anyhow, I note that our handling of inf (and minf, und, and infinity) leaves
> a lot to be desired. .... Perhaps a revamping of the code handling these
> symbols can go a long way towards resolving those concerns that presently
> justify not evaluating the above definite integral to inf?

People have worked on this on and off over the years, but no one has
finished the task. It shouldn't be rocket science, but it does require
careful logical analysis of the simplifier and perhaps other code as
well -- for instance code might assume that if something is constantp,
it is finite and well-defined.... or that diff(ex,ex) = 1 for all ex
(yes, diff(inf,inf) => 1 -- oops), etc. etc.

Even limit, which should "know better", blunders: limit(inf*x,x,0) =>
0 (!!) and 'limit(inf*x,x,0) ('limit(x,x,0)=0) => false (!!!!) though
limit(inf*x) (x>0) => inf (correct).

            -s


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