Computing the limit of the lognormal density crashes Sage #26497
Description
Define the lognormal density starting from the normal:
var("mu", domain="real")
var("y, m, s, sigma", domain="positive")
dnorm(x, mu, sigma) = e^(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*pi))
dlnorm(y, mu, sigma) = (dnorm(x, mu, sigma).subs(x==log(y))*abs(diff(log(y),y))).simplify()
Let's try to prove that the limit is 0 at 0 and oo:
sage: dlnorm(y, mu, sigma).limit(y=oo)
0
So far so good. But:
dlnorm(y, mu, sigma).limit(y=0, dir="+")
;;;
;;; Detected access to protected memory, also kwown as 'bus or segmentation fault'.
;;; Jumping to the outermost toplevel prompt
;;;
## Numerous repetitions...
Process Sage erreur de segmentation
This seems analogous to but different from #14677...
This limit also seems problematic in other subsystems:
- Sympy returns "Not implemented"
- libgiac returns "Infinity" (wrong)
- Mathematica doesn't return (but (correctly) returns 0 when used directly).
- Used directly, Maxima asks a lot of questions, and fails:
limit(dlnorm(y, mu, sigma), y, 0);
Is sigma^2-mu positive, negative or zero?
p;
Is mu positive, negative or zero?
p;
Is 2*sigma^2-mu positive, negative or zero?
p;
(%o10) ('limit(%e^-((log(y)-mu)^2/(2*sigma^2))/y,y,0))/(sqrt(2)*sqrt(%pi)
*sigma)
This failure mode is different from the one seen in Sage; we may have a new bug...
Upstream: Not yet reported upstream; Will do shortly.
CC: @slel
Component: symbolics
Keywords: limit, maxima
Issue created by migration from https://trac.sagemath.org/ticket/26497