#4373 conjugate doesn't know li[n](x) is complex in general

[Robert Dodier]

Working w/ version 4afc4ab (post-5.47). conjugate(li[n](x)) simplifies to li[n](x) even though li[n](x) can be complex.

Follow-on work for #4368. Thanks to Dan Gildea for pointing it out.

[Barton Willis]

I'll try to fix this bug this week. Something like the following might be better:

(defun conjugate-li (z)
   (let ((s (first z)) (zz (second z)))
          (setq zz (risplit zz))
          (if (and ($featurep s '$integer)
                   (or (eq t (mnqp (cdr zz) 0)) (eq t (mgrp 1 (car zz)))))
              (subftake '$li (list s) (list (ftake '$conjugate (second z))))
              (list (list '$conjugate 'simp)
                 (ftake 'mlist (subftake '$li (list s) (list (second z))))))))

I'm not sure the featurep check is needed--need to think about that.

[Barton Willis]

Here is a fix to the nounform part of the above mentioned code:

;; For z ∈ C \ [1,∞) and a positive integer n, we have 
;;   conjugate(li[n](z) = li[n](conjugate(z)). 
;; For all other cases, return a conjugate nounform.
(defun conjugate-li (z)
   (let ((n (first z)) (zz (risplit (second z))))
          (if (and ($featurep n '$integer)
                   (eq t (mgrp n 0))
                   ;; either the imagpart(z)≠ 0 or the realpart(z) < 1
                   (or (eq t (mnqp (cdr zz) 0)) (eq t (mgrp 1 (car zz)))))
                       (subftake '$li (list n) (list (ftake '$conjugate (second z))))
                       ;; give up and return conjugate nounform
                       (list (list '$conjugate 'simp)
                          (subftake '$li (list n) (list (second z)))))))

[Barton Willis]

Fixed by [4bf14b] . Closing this ticket as fixed.