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

[Raymond T. <toy...@gm...>]

On 4/8/25 5:54 AM, Barton Willis wrote:

> Make that: don't that that any |simplim%function| should return 
> F|(minf, zerob, zeroa, ind, und, inf, or infinity)|.   So, I don't 
> think that returning elliptic_kc(zeroa) is correct for behavior for 
> simplim%elliptic_kc.

Agreed. The simplim function should return something more reasonable 
than, essentially, the noun form.

This is beyond the current scope of what I’m working on, but will look 
into. Someday.

>
>
>
>
> ------------------------------------------------------------------------
> *From:* Barton Willis
> *Sent:* Tuesday, April 8, 2025 6:14 AM
> *To:* Raymond Toy; Barton Willis; max...@li...
> *Subject:* Re: [Maxima-discuss] simplimit function vs simplimit%fun 
> property
>
> 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
>
> 	
> *Caution:* Non-NU Email
>
>
> 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.
>
> &#8203;
&#8203;