oldk1331 wrote:
>
> I think it's doable.
>
> First, by default, "limit" is for real expression (there are
> accompanying "complexLimit"), so it knows "sqrt(a)" is positive:
>
> (8) -> limit(sqrt(a)*x,x=%plusInfinity)
>
> (8) + infinity
>
> So in theory, it should also compute for "erf(sqrt(a)*x)", but:
>
> (9) -> limit(erf(sqrt(a)*x),x=%plusInfinity)
>
> (9) "failed"
>
> This should be very simple to compute, but we still use Gruntz
> algorithm to compute and we fail at there. This may indicate
> a bug in Gruntz algorithm, and raise another question: shall
> we add a short path to handle simple cases, like "specialLimit"
> in limitps.spad?
Gruntz seem to be close to computing this limit, so I do not
see special reason to add alternate code path. More generaly,
various "short paths" or "special paths" may seem attractive
at first, but they are pain in longer time.
> Another somewhat related problem:
>
> (1) -> limit(sqrt(a^2)*x,x=%plusInfinity)
>
> (1) "failed"
>
> This case fails because "mrv_normalize" will destroy the structure
> of "sqrt(a^2)",
Do not attach too much importance to 'sqrt' in integral that
started this discussion:
+---+
erf(a x)\|%pi
(4) --------------
2 a
Type: Expression(Integer)
is a valid indefinite integral and we should be generating it
instead of version with 'sqrt(a^2)'. Note that for this
expression limit splits into two cases: positive and negative
and _both_ give the same limit. So we would need version of
Gruntz that can split and combine cases.
And for treating 'sqrt(a^2)' as 'abs(x)' we need version of
'normalize' that splits cases.
> so maybe a "assume" system will still be needed.
> But such a system is invasive and not always work in Maxima.
Yes, in longer term we will need "assume" and handling of
conditions.
--
Waldek Hebisch
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