[Maxima-discuss] circumventing x^a * x^b --> x^(a+b) simplification with labeled boxes

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

Stavros suggested to me that to_poly_solve should be extended to handle equations that are linear in exp(X), but not explicitly so; for example  exp(x) + exp(x + 1)= 1.


The simple way to do this, of course, is to do exp(x + 1) --> exp(x) * exp(1) at  the top-level of to_poly. But exp(x) * exp(1) automatically simplifies to exp(x + 1), so it's not so easy.  I considered several ways to circumvent the automatic simplification--one possibility is to use labeled boxes. I don't have much (any?) experience with labeled boxes, so if you all have insights, let me know.

Here are two functions that would do this.  The function boxify-mepxt  does x^(a+b) -> box(x^a, tbox) * box(x^b, tbox) and the function if-deboxify removes boxes with a given label.

These  functions could be just as well be written in Maxima, but to_poly is written in CL, so I wrote them in CL.

;; x^(a+b+...) -> box(x^a, tbox) * box(x^b, tbox) * ... This provides a workaround for the automatic
;; simplification x^a * x^b --> x^(a+b).

(defun boxify-mepxt (p tbox)
  (maxima-substitute  #'(lambda (a b)
  (setq b ($expand b))
  (if (mplusp b)
      (reduce 'mul (mapcar
    #'(lambda (s)  (take '(mlabox) (take '(mexpt) a s) tbox)) (margs b)))
    (take '(mlabox) (take '(mexpt) a b) tbox))) 'mexpt  p))

;; remove a box if the label is tbox (temporary box)
(defun if-deboxify (e tbox)
  (maxima-substitute #'(lambda (x z) (if (eq z tbox)  x (take '(mlabox) x z))) 'mlabox e))


And of course, if you all have suggestions for to_poly_solve, send me a note.


--Barton