/*
 * This file:
 *   http://anggtwu.net/MAXIMA/2025-mysqrt.mac.html
 *   http://anggtwu.net/MAXIMA/2025-mysqrt.mac
 *          (find-angg "MAXIMA/2025-mysqrt.mac")
 * Author: Eduardo Ochs <eduardoochs@gmail.com>
 *
 * (defun e () (interactive) (find-angg "MAXIMA/2025-mysqrt.mac"))
 * (find-es "maxima" "defmatch")
*/

matchdeclare(x, all);
defmatch(isx2__, x^2);
isx2_    (o) := block([x], isx2__(o));
isx2     (o) := not atom(isx2_(o));
isx2_body(o) := if isx2(o) then part(isx2_(o),1,2);
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);

sqrtpn   (o) := [map('sqrtp,o), map('sqrtn,o)];


/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-mysqrt.mac");

makelist(f(3),       f, [isx2,isx2_,isx2_body]);
makelist(f((a+b)^2), f, [isx2,isx2_,isx2_body]);

makelist(f(3),       f, [sqrt,psqrt,nsqrt]);
makelist(f((a+b)^2), f, [sqrt,psqrt,nsqrt]);

*/

V([elts]) := transpose(apply('matrix, [elts]));



/*
** (c2m251edovsp 12 "4-inversas")
** (c2m251edovsa    "4-inversas")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-mysqrt.mac");

display2d : false;

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

o0 : (x-2)^2+(y+3)^2=4;
          part(o0,1,1);
o  : o0 - part(o0,1,1);
o  : sqrtn(o);
o  : - o;
         part(o,1,2);
o  : o - part(o,1,2);
define(g2(y), rhs(o));

*/



/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-mysqrt.mac");
display2d : false;

matchdeclare(x, all);
defmatch(isx2__, x^2);
isx2_    (o) := block([x], isx2__(o));
isx2     (o) := not atom(isx2_(o));
isx2_body(o) := if isx2(o) then part(isx2_(o),1,2);
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);

(x-2)^2+(y+3)^2=4;
% - (x-2)^2;
sqrtp(%);
% - 3;

(x-2)^2+(y+3)^2=4;
% - (x-2)^2;
sqrtn(%);
- %;
% - 3;

*/