/*
 * This file:
 *   http://anggtwu.net/MAXIMA/2025-1-C2-P2.mac.html
 *   http://anggtwu.net/MAXIMA/2025-1-C2-P2.mac
 *          (find-angg "MAXIMA/2025-1-C2-P2.mac")
 * Author: Eduardo Ochs <eduardoochs@gmail.com>
 *
 * (defun e () (interactive) (find-angg "MAXIMA/2025-1-C2-P2.mac"))
 * (find-myqdraw "myqdraw3.mac")
 * (find-fline "~/MAXIMA/2025-1-s.mac")
 * (find-fline "~/MAXIMA/2025-1-exact.mac")
 *
 * «.gab-1»		(to "gab-1")
 * «.gab-1-tests»	(to "gab-1-tests")
 * «.gab-2»		(to "gab-2")
 * «.gab-2-tests»	(to "gab-2-tests")
 * «.gab-2d-tests»	(to "gab-2d-tests")
 * «.gab-3»		(to "gab-3")
 * «.gab-3-tests»	(to "gab-3-tests")
*/

load_myqdraw();
load("~/MAXIMA/2025-1-s.mac");
load("~/MAXIMA/2025-1-exact.mac");

/* «gab-1»  (to ".gab-1")
 * (c2m251p2p 3 "questao-1")
 * (c2m251p2a   "questao-1")
*/
S5p : [g(x) = -2*(x+1),     h(y) = 2*(y-1),
       G(x) = -(x+1)^2,     H(y) = (y-1)^2,
                         Hinv(y) = sqrt(y)+1]$
S5n : [g(x) = -2*(x+1),     h(y) = 2*(y-1),
       G(x) = -(x+1)^2,     H(y) = (y-1)^2,
                         Hinv(y) = 1-sqrt(y)]$

item_1a() := (
  define(g(x), g(x) _s_ S5p),
  define(h(y), h(y) _s_ S5p),
  [xmin,ymin, xmax,ymax] : [-2,-2, 2,2],
  myqdrawp(xyrange(), directionfield(h(y),g(x), lc(red)))
  );

item_1b() := matrix(
  [define(fp(x), EDOVS_f _s_ S5p)],
  [define(fn(x), EDOVS_f _s_ S5n)]
  );

item_1c() := (
  star_1 : EDOVS_edo _s_ S5p,
  test   : subst(y=fn(x), star_1)
  );

item_1d() := (
  P1 : [x=-1,y=0],
  P2 : [x= 3,y=4],
  P1_eq : subst(P1, y=fn(x)),
  P2_eq : subst(P2, y=fp(x)),
  P1_C3 : solve(P1_eq, C3),
  P2_C3 : solve(P2_eq, C3),
  define(f_P1(x), subst(P1_C3, fn(x))),
  define(f_P2(x), subst(P2_C3, fp(x))),
  matrix([fundef(f_P1)],
         [fundef(f_P2)])
  );

item_1f_f_P1() := ex1(f_P1(x), x,-2,0, lc(red));
item_1f_f_P2() := ex1(f_P2(x), x,-6,4, lc(orange));
item_1f() := (
  [xmin,ymin, xmax,ymax] : [-6,-6, 6,6],
  myqdrawp(xyrange(), item_1f_f_P1(), item_1f_f_P2())
  );

/* «gab-1-tests»  (to ".gab-1-tests")
** (c2m251p2p 3 "questao-1")
** (c2m251p2a   "questao-1")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-C2-P2.mac");
[transpose(matrix(S5p)),
 transpose(matrix(S5n))];
EDOVS_M   _s_ S5p;
EDOVS_edo _s_ S5p;
EDOVS_imp _s_ S5p;
EDOVS_exp _s_ S5p;
EDOVS_f   _s_ S5p;

item_1a();
item_1b();
item_1c();
  ev(%, diff);

item_1d();
  subst(P1, y=f_P1(x));
  subst(P2, y=f_P2(x));

"item 1e"$
  subst(P1, y=f_P2(x));
  subst(P2, y=f_P1(x));

item_1f();

*/




/* «gab-2»  (to ".gab-2")
*/
 star2 : 'diff(y,x,2) - 3*'diff(y,x) - 10*y = 0;
 star3 : 'diff(y,x,2) - 4*'diff(y,x) + 13*y = 0;
Sstar2 : [a=5,      b=-2];
Sstar3 : [a=2+3*%i, b=2-3*%i];

Lstar3(f) := diff(f,x,2) -4*diff(f,x) + 13*f;

item_2a() := (
  define(f1(x), exp( 5*x)),
  define(f2(x), exp(-2*x)),
  define(f3(x), a*f1(x)+b*f2(x)),
  matrix([fundef(f1)],
         [fundef(f2)],
         [fundef(f3)])
  );

item_2b() := (
  define(gg (x), f3(x)),
  define(ggx(x), diff(gg(x),x)),
  eqs : [gg(0)=2, ggx(0)=3],
  sol : solve(eqs, [a,b]),
  define(g(x), subst(sol, gg(x)))
  );

item_2c() := (
  define(f4(x), exp((2+3*%i)*x)),
  define(f5(x), exp((2-3*%i)*x)),
  define(f6(x), exp(2*x) * sin(3*x)),
  define(f7(x), exp(2*x) * cos(3*x)),
  matrix([fundef(f4)],
         [fundef(f5)],
         [fundef(f6)],
         [fundef(f7)])
  );

/* «gab-2-tests»  (to ".gab-2-tests")
** (find-es "maxima" "postfix-diff")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-C2-P2.mac");
sol_star2 : ode2(star2,y,x);
sol_star3 : ode2(star3,y,x);

       EDOLCC;
       EDOLCC _s_ Sstar2;
expand(EDOLCC _s_ Sstar3);

item_2a();
item_2b();
item_2c();

*/

/*
** «gab-2d-tests»  (to ".gab-2d-tests")
** (c2m251p2p 6 "gab-2d")
** (c2m251p2a   "gab-2d")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-C2-P2.mac");
gradef(h,x, 2*h);
gradef(s,x, 3*c);
gradef(c,x,-3*s);
f6 : h*s;
diff(f6,x);
diff(f6,x,2);
Lstar3(f6);
expand(%);

gradef(h,x, 4*h);
gradef(s,x, 5*c);
gradef(c,x,-5*s);
f8 : h*s;
diff(h*s,x);
diff(h*c,x);
diff(f8,x);
diff(f8,x,2);
Lstar3(f8);
expand(%);

*/



/* «gab-3» (to ".gab-3")
*/
"_x"   (o) := diff(o,x);
"_y"   (o) := diff(o,y);
"_intx"(o) := integrate(o,x);
"_inty"(o) := integrate(o,y);
postfix("_x");
postfix("_y");
postfix("_intx");
postfix("_inty");

/* «gab-3-tests»  (to ".gab-3-tests")
** (c2m251p2p 4 "questao-3")
** (c2m251p2a   "questao-3")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-C2-P2.mac");

"3a:"$
z_x : 20 * x   * y^3;
z_y : 30 * x^2 * y^2;
z_x _y = z_y _x;
[maxxp,maxyp] : [2,3];
[ca(z_x), ca(z_y), ca(z_x _y)];

"3b:"$
z_x : 20 * x^2 * y^3;
z_y : 30 * x^3 * y^2;
z_x _y = z_y _x;
[maxxp,maxyp] : [3,3];
[ca(z_x), ca(z_y), ca(z_x _y), ca(z_y _x)]; 

"3c:"$
z_x : 20 * x   * y^3;
z_y : 30 * x^2 * y^2;
[z_x _intx, z_y _inty];
z : z_x _intx;
[maxxp,maxyp] : [2,3];
S    : ['z=z,     'z_x=z_x,     'z_y=z_y];
Sca  : ['z=ca(z), 'z_x=ca(z_x), 'z_y=ca(z_y)];
E5     _s_ S;
E5     _s_ Sca;
imp  : z = C;
exps : solve(imp, y);
exp  : exps[3];

"3d:"$
edo  : E5_edo _s_ S;
test : subst(exp, edo);
ev(test,diff);

"3e:"$
z_x : 8*x*y^2 + 14*x;
z_y : 8*x^2*y + 5;
z_x _y = z_y _x;

"3f:"$
[maxxp,maxyp] : [2,3];
[z_x, z_y, z_x _intx, z_y _inty];
[ca(z_x), ca(z_y), ca(z_x _intx), ca(z_y _inty)];
z : 4*x^2*y^2 + 5*y + 7*x^2;
ca(z);
S    : ['z=z,     'z_x=z_x,     'z_y=z_y];
Sca  : ['z=ca(z), 'z_x=ca(z_x), 'z_y=ca(z_y)];
E5     _s_ Sca;
imp  : z = C;

*/