Re: [Maxima-discuss] simplimit function vs simplimit%fun property

[Barton W. <wi...@un...>]

I don't that that any simplim%function should return (minf, zerob, zeroa, ind, und, inf, or infinity). And I don't think that a simplifier should have to handle those cases either.  Plus I think that zeroa and zerob should be internal to the limit code, not user-level symbols.

 I didn't try all that much, but I did not discover how Maxima converts elliptic_kc(zeroa) to %pi/2.

The testsuite never calls simplim%elliptic_kc.

I'm not sure about the option variable preserve-direction, but here is a starting point for a better simplim%elliptic_kc function:

(defun simplim%elliptic_kc (expr var val)
  ;; Look for the limit of the argument
  (let ((dir) (m (let ((preserve-direction t)) (limit (cadr expr) var val 'think))))
    (cond ((onep1 m)
           (setq dir (behavior (cadr expr) var val))
           ;; elliptic_kc(1^(-)) = inf; ellitic(1^(+)) = infinity
           (if (eql dir -1) '$inf '$infinity))

          ;; elliptic_kc(minf) = zeroa
          ((eq m '$minf)
            (if preserve-direction '$zeroa 0))

          ;; elliptic_kc(inf) = infinity
          ((eq m '$inf) '$infinity)

          ;; elliptic_kc(und) = und. Or should this throw an error?
          ((eq m '$und) '$und)

          ;; when Maxima can determine that 1 isn't in the range of expr and
          ;; m = ind, return ind; otherwise return und
          ((eq m '$ind)
            (if (eq t (mnqp (cadr expr) 1)) '$ind '$und))

          ;; elliptic_kc is continous and nonzero at 0
          ((or (eq m '$zerob) (eq m '$zeroa))
            (ftake '%elliptic_kc (ridofab m)))

          (t
            ;; All other cases are handled by the simplifier of the function.
            (ftake '%elliptic_kc m)))))



________________________________
From: Raymond Toy <toy...@gm...>
Sent: Monday, April 7, 2025 4:40 PM
To: Barton Willis <wi...@un...>; max...@li... <max...@li...>
Subject: Re: [Maxima-discuss] simplimit function vs simplimit%fun property

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On 4/7/25 10:05 AM, Barton Willis wrote:

The CL function ridofab (get rid of zeroa and zerob) substitutes zero for zerob and zeroa ; example:

(%i17) limit(elliptic_kc(m), m, 0, 'plus);

1 Call   ridofab [elliptic_kc(zeroa)]
1 Return ridofab %pi/2
Yeah, I see that. I guess I’ll have to do some digging to see how ridofab gets called. From my own tracing, it’s called after the simplim for elliptic_kc has returned with a value of elliptic_kc(zeroa).

(%o17) %pi/2

Converting simplim%tan to use the symbol property dispatch mechanism should be fairly easy (and to not use the special variables var and val) .  Converting all the special cases in simplimit to use the symbol property dispatch would be a larger effort—these functions are not written in in a consistent fashion.
Yep. And they use the same simplim function for different functions. I probably won’t convert those for a while.
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