/*
 * This file:
 *   http://anggtwu.net/MAXIMA/2024-2-C2-partfrac.mac.html
 *   http://anggtwu.net/MAXIMA/2024-2-C2-partfrac.mac
 *          (find-angg "MAXIMA/2024-2-C2-partfrac.mac")
 * Author: Eduardo Ochs <eduardoochs@gmail.com>
 *
 * (defun e () (interactive) (find-angg "MAXIMA/2024-2-C2-partfrac.mac"))
 * (find-es "maxima" "2024.2-C2-P1")
 * (c2m242p1p 9 "gab-2")
 * (c2m242p1a   "gab-2")
 *
 * «.test-solve»	(to "test-solve")
 * «.test-build»	(to "test-build")
 * «.test-solve2»	(to "test-solve2")
 * «.test-ratcoeff»	(to "test-ratcoeff")
*/

partfrac_all() := (
  [q,r] : divide(fup, fdn, x),
  fup2 : fdn*q + r,
  fdn2 : factor(fdn),

  f1 : fup/fdn,
  f2 : fup2/fdn,
  f3 : (fdn*q)/fdn + r/fdn,
  f4 : (fdn*q)/fdn + r/fdn2,
  f5 : (fdn*q)/fdn + partfrac(r/fdn2, x),

  F1 : 'integrate(f1,x),
  F2 : 'integrate(f5,x),
  F3 :  integrate(f5,x),

  M  : align_eqss([[fup, fup2],
                   [fdn, fdn2],
                   [f1,f2,f3,f4,f5],
                   [F1,F2,F3]
                  ]))$

/* «test-solve»  (to ".test-solve")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-partfrac.mac");

f   : (x^3 + 6*x^2 - 22*x - 55) / (x^2 + 4*x - 21);
fup : (x^3 + 6*x^2 - 22*x - 55);
fdn :                             (x^2 + 4*x - 21);

partfrac_all()$
M;

** «test-build»  (to ".test-build")
** (c2m242vrp1p)
** (c2m242vrp1a)
F : 2/(x+7) + 4/(x-3) - 2 + x;
F : radcan(F);
fup : num(F);
fdn : denom(F);
partfrac_all()$
M;

*/

/* «test-solve2»  (to ".test-solve2")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-partfrac.mac");
F : (x^4 -10*x^2 + 3*x + 1) / (x^2 - 4);
F : (2*x^3 - 6*x^2 - 15*x + 55) / (x^2 - 2*x - 15);
fup : num(F);
fdn : denom(F);
partfrac_all()$
M;

*/

/* «test-ratcoeff»  (to ".test-ratcoeff")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-partfrac.mac");
F : (4*x+5) / ((x+2)*(x-3));
G : A/(x+2) + B/(x-3);
F = G;
G2 : radcan(G);
[numF, numG] : [num(F), num(G2)];

eq : numF=numG;
solve(eq, [A,B]);                 "bad: mentions x,%r1,%r2"$

eq1 : ratcoeff(numF=numG, x, 1);
eq0 : ratcoeff(numF=numG, x, 0);
sol : solve([eq1,eq0], [A,B]);    "good"$
sol2 : subst(sol, F=G);
radcan(sol2);

*/