function simplimsubst problems

Imported from SourceForge on 2024-07-07 00:14:48 Created by willisbl on 2021-09-21 10:22:22 Original: https://sourceforge.net/p/maxima/bugs/3861

The non-user level function simplimsubst evaluates a limit by direct substitution.

Near the top of simplimsubst there is a check if the expression involves any one of $atan2, $floor, %round, .... And when that's the case, simplimsubst declines direct substitution and returns nil.

There are lots of problems with this scheme. For one, the check only looks to see if these functions are in the expression, but it doesn't look to see if the argument of any of these functions depend on the limit variable. This gives rise to inconsistent results:

(%i9) limit(log(-1+%i*x) * ceiling(a),x,0,minus);
(%o9)                         - %i %pi ceiling(a)
(%i10) limit(log(-1+%i*x) * a,x,0,minus);
(%o10)                            log(- 1) a

For %o9, since the expression involves ceiling, the function simplimsubst declines to use direct substitution and the limit is computed by some other method. But for %o10, simplimsubst decides that uses direct substitution is OK and it returns a wrong value.

Further, the check declines direct substitution for many cases that are OK; for example the limit of floor(x) as x approaches 5/2 for example.

rtoy / maxima

function simplimsubst problems #2881