Computing the limit of the lognormal density crashes Sage

[EmmanuelCharpentier]

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

[nbruin]

comment:1

It looks to me like a domain:complex error again. I get:

sage: maxima_calculus.eval("domain:real")
'real'
sage: dlnorm(y,mu,sigma).limit(y=0, dir="+")
0

That's to say, if we set domain to real, maxima in sage seems to do the right thing immediately. So I think it's basically the same problem as #14677.

[slel]

Changed keywords from none to limit, maxima