Re: [Axiom-mail] Bug in computing a limit?

[Martin Rubey]

Sergio Polini <address@hidden> writes:

> The limit of 3^x * log(x) / x as x -> +oo is +oo, but I get:
>
> (1) -> limit(3^x*log(x)/x,x=%plusInfinity)
>
>    (1)  "failed"
>
> Am I missing anything?

no, axiom (and FriCAS and OpenAxiom), is not particularly strong at
computing limits.  Attached is an experimental package by Waldek for
FriCAS (should work on other flavours of axiom, as well), that
implements a better algorithm.  However, it doesn't seem to like 3^x,
you need to enter it as exp(x*log 3)...

(19) -> mrv__limit(exp(x*log 3)*log x/x, x)

   (19)   + infinity
                           Type: OrderedCompletion(Expression(Integer))

(it is only for real limits, and the direction is always
plusInfinity...)

mrvlimit.spad
Description: Binary data

Martin