#4530 limit(floor( 1/2 + sin(1/x)/10), x, 0) returns ind but should be 0

[Dave Morris]

The expression floor(1/2 + sin(1/x)/10) is 0 everywhere (except at x = 0), but maxima evaluates limit(floor(1/2 + sin(1/x)/10), x, 0) to be ind, rather than 0.

I suspect it may not be feasible to fix this, but it came up as sagemath issue #39819, so I thought I should report it.

Maxima-version: "5.47.0"
Maxima build date: "2025-03-01 01:30:07"
Host type: "x86_64-apple-darwin23.6.0"
Lisp implementation type: "SBCL"
Lisp implementation version: "2.5.2"
User dir: "~/.maxima"
Temp dir: "/var/folders/4p/njwqthhs4clb13nx0pn72q6h0000gn/T"
Object dir: "~/.maxima/binary/5_47_0/sbcl/2_5_2"
Frontend: false

[Dave Morris]

Sorry, there is a typo in the title, but I don't know how to edit it. Instead of two right parentheses at the end of the expression, one of them should be immediately after 10.

[Barton Willis]

Thanks for the bug report. A quick fix is:

(defun simplim%floor (expr var val)
  (let* ((arg (cadr expr))
     (b (behavior arg var val))
     (arglimab (limit arg var val 'think)) ; with $zeroa $zerob
     (arglim (ridofab arglimab)))
    (cond 
    ((eq arglim '$ind) (throw 'limit nil))
    ((and (= b -1)
        (maxima-integerp arglim))
       (m- arglim 1))
      ((and (= b 1)
        (maxima-integerp arglim))
       arglim)

      ((and ($constantp arglim)
        (not (maxima-integerp arglim)))
       (simplify (list '($floor) arglim)))
      (t
       (throw 'limit nil)))))

With this putative fix, we have

(%i60) limit(floor( 1/2 + sin(1/x)/10), x, 0);

(%o60) 0
(%i61) limit(floor( 1/2 + sin(1/x)/2), x, 0);

(%o61) 'limit(floor(sin(1/x)/2+1/2),x,0)
(%i62) limit(floor( 1/2 + sin(1/x)/(2+1/10)), x, 0);

(%o62) 0

Other than these two cases, I have not tested my (quick) fix. And I think that some other parts of this function might need improvements.

Notice that maxima-integerp determines that ind is an integer. At the moment, I'm not sure about the call to $constantp.

Again, thanks for the bug report.

[David Scherfgen]

Notice that maxima-integerp determines that ind is an integer.

Hmm, I don't see that: ?maxima\-integerp(ind) gives me false.

[Barton Willis]

OK, I was mistaken about maxima-integerp called on ind.

[Barton Willis]

Fixed by Commit [324e0f] ; test suggested by bug report appended to rtest_limit_extra. Closing this ticket.

[Dave Morris]

Thanks for fixing this!!