[Maxima-discuss] (x-2)^2 becomes (x-4)^2

[Eduardo O. <edu...@gm...>]

Hi list,

I was trying to write some programs using `defmatch' but I was getting
some strange behaviors that SEEMED to be related to subexpressions
being modified in ways that I didn't expect... I still don't understand
what is going on but I finally got something that is easy to reproduce.
The program is below, and I tested it both with a recent Maxima with
"maxima --no-init" and with a Maxima 5.44 with "/usr/bin/maxima
--userdir=/tmp" with a /tmp/ that is empty enough, and I got the same
error.

Note that in the last line the

  (x-2)^2+(y+3)^2 = 4

is not only reordered to

  (y+3)^2+(x-2)^2 = 4

but it is also changed to:

  (y+3)^2+(x-4)^2 = 4

I am attaching a screenshot. I edited the whitespace and the line
breaks in the bash/Maxima window a bit, but besides that I didn't
change anything else.

Here is the program:


display2d : false;

matchdeclare(x, all)$
defmatch(isx2_, x^2)$
isx2     (o) := not atom(isx2_(o))$
isx2_body(o) := isx2(o) and rhs(isx2_(o)[1])$
sqrtp_   (o) := if isx2(o) then  isx2_body(o) else sqrt(o)$
sqrtn_   (o) := if isx2(o) then -isx2_body(o) else sqrt(o)$
sqrtp    (o) := map('sqrtp_,o)$
sqrtn    (o) := map('sqrtn_,o)$

o0 : (x-2)^2+(y+3)^2=4;
          part(o0,1,1);
o  : o0 - part(o0,1,1);   /* (x-2)^2   = 4-(y+3)^2 */
o  : sqrtp(o);            /*  x-2 = sqrt(4-(y+3)^2) */
         part(o,1,2);
o  : o - part(o,1,2);     /*    x = sqrt(4-(y+3)^2)+2 */
define(g1(y), rhs(o));    /* g1(y):=sqrt(4-(y+3)^2)+2 */

o0 : (x-2)^2+(y+3)^2=4;   /* (y+3)^2+(x-4)^2 = 4 */


Cheers,
  Eduardo Ochs
  http://anggtwu.net/eev-maxima.html