/*
 * This file:
 *   http://anggtwu.net/MAXIMA/2024-2-C2-E5.mac.html
 *   http://anggtwu.net/MAXIMA/2024-2-C2-E5.mac
 *          (find-angg "MAXIMA/2024-2-C2-E5.mac")
 * Author: Eduardo Ochs <eduardoochs@gmail.com>
 *    See: (find-es "maxima" "2024.2-C2-E5")
 *         (c2m242edosexatasp 3 "metodo-e-exemplo")
 *         (c2m242edosexatasa   "metodo-e-exemplo")
 *
*/

mkmatrix5(x,xs,y,ys,expr) ::=
  buildq([x,xs,y,ys,expr],
         apply('matrix,
               makelist(makelist(ev(expr),x,xs),y,ys)));

[maxxp,maxyp] : [3,3];
polycoef(poly,xp,yp) := ratcoef(ratcoef(poly, 'x,xp), 'y,yp);
caixinhas0(expr) :=
  mkmatrix5(xp,seq(0,maxxp), yp,seqby(maxyp,0,-1), expr);
caixinhas (poly) :=
  mkmatrix5(xp,seq(0,maxxp), yp,seqby(maxyp,0,-1), polycoef(poly,xp,yp));

caixinhas_3(z__, z__x, z__y) := [caixinhas(z__), caixinhas(z__x), caixinhas(z__y)];
caixinhas_2     (z__x, z__y) :=                 [caixinhas(z__x), caixinhas(z__y)];
caixinhas_1(z__)             := caixinhas_3(z__, diff(z__,x), diff(z__,y));

/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-E5.mac");
polycoef  (x^2*y^3*4, 2,3);
caixinhas0([xp,yp]);
caixinhas  (x^2*y^3*4);
caixinhas_1(x^2*y^3*4);
[maxxp,maxyp] : [2,3];
caixinhas_1(x^2*y^3*4);

*/

E5_3(z,zx,zy) := matrix(
  ['del(z),    "=", zx * 'del(x) + zy * 'del(y) , "=", 0],
  ['diff(z,x), "=", zx + zy*'diff(y,x),           "=", 0],
  [z,          "=", C ,                           "", ""]);

E5_1(z) := E5_3(z, diff(z,x), diff(z,y));

/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-E5.mac");

z__x : 2*x*y^3;
z__y : 3*x^2*y^2;
M    : E5_3(z, z__x, z__y);
eq1  : M[2][3] = 0;
sol  : ode2(eq1, y, x);
sol  : radcan(sol);
eq2  : subst(sol, eq1);
eq3  : ev(eq2, diff);

*/

/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-E5.mac");
[maxxp,maxyp] : [2,2];
z : 4*y^2 + 5*x^2*y^2
  + 6     + 7*x^2;
z : 5*y  + 4*x^2*y^2
  + 6     + 7*x^2;
caixinhas_1(z);
linel : 110;
M : E5_1(z);

solve(z,y);

*/


/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-E5.mac");
[maxxp,maxyp] : [3,3];
z : 4*x*y^3 + 5*y^2
  + 6*x^3*y + 7*x^2;
caixinhas_1(z);
linel : 130;
M : E5_1(z);
M[1];
e1 : M[1][3] = 0;
tex1(e1);


solve(z,y);

*/