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

[Richard F. <fa...@gm...>]

without looking at this in detail, it seems likely that you are using
the name x for two conflicting purposes.  It is not a good idea to use
x as a pattern variable and as a symbol in your expression, since defmatch
not only returns an equation  x=something,  it also binds x globally to
something.

If seems you are trying to define a function something like this:
vv(h):=if atom(h) then false else if op(h)="^" and part(h,2)=2 then
part(h,1)

Good luck
RJF



On Sun, Jul 20, 2025 at 8:36 AM Eduardo Ochs <edu...@gm...> wrote:

> 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
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