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/*
* This file:
* http://anggtwu.net/MAXIMA/2025-1-s.mac.html
* http://anggtwu.net/MAXIMA/2025-1-s.mac
* (find-angg "MAXIMA/2025-1-s.mac")
* Author: Eduardo Ochs <eduardoochs@gmail.com>
*
* This file defines the infix substitution operator "_s_".
* See: (c2m242introp 6 "manga")
* (c2m242introa "manga")
* http://anggtwu.net/LATEX/2024-2-C2-intro.pdf#page=6
*
* (find-es "maxima" "operator-subst")
* (find-lisptree "lisptree.mac" "lisptree0")
* (find-maximanode "psubst")
* (find-maximanode "sublis")
* (find-telegachat "-1002074960141#3276" "eu acabei de melhorar")
* (find-telegachatm "-1002074960141#3276" "eu acabei de melhorar")
*
* «.load» (to "load")
* «.core» (to "core")
* «.TFC2» (to "TFC2")
* «.TFC2-tests» (to "TFC2-tests")
* «.S_f_g» (to "S_f_g")
* «.S_f_g-tests» (to "S_f_g-tests")
* «.MV» (to "MV")
* «.MV-tests» (to "MV-tests")
* «.DFI» (to "DFI")
* «.DFI-tests» (to "DFI-tests")
* «.EDOVS» (to "EDOVS")
* «.EDOVS-tests» (to "EDOVS-tests")
* «.EDOLCC» (to "EDOLCC")
* «.EDOLCC-tests» (to "EDOLCC-tests")
* «.E5» (to "E5")
* «.E5-tests» (to "E5-tests")
*/
/* «load» (to ".load")
* Based on: (find-myqdraw "myqdraw3.mac" "load")
* See: (find-fline "~/MAXIMA/lazynouns.lisp")
* (find-fline "~/MAXIMA/dim-antideriv.lisp")
*/
_s_dir : pathname_directory(load_pathname);
load(concat(_s_dir, "lazynouns.lisp"));
load(concat(_s_dir, "dim-antideriv.lisp"));
/* «core» (to ".core")
*/
"_s_" (o,oes) := psubst(_s_s(oes), o);
_s_s (oes) := map('_s_1, oes);
_s_1 (oe) := if atom(lhs(oe)) then _s_ae(oe) else _s_fxye(oe);
_s_ae (ae) := (lhs(ae) = rhs(ae));
_s_fxye(fxye) := block(
[fxy,e,f,xy],
fxy : lhs (fxye),
e : rhs (fxye),
f : op (fxy),
xy : args(fxy),
buildq([f,xy,e], f=lambda(xy,e)));
infix("_s_",99,101);
RC : ('diff(f(g(x)),x) = fp(g(x)) *. gp(x));
II : ('integrate(Fp(x), x) = F(x));
II : (integrate_(Fp(x), x) = F(x));
Aipim : (sqrt(a^2 + b^2) = a + b);
Aipim2 : (sqrt(a^2 - b^2) = a - b);
DefAt : 'at(f(x),x=a) = f(a);
DefDeriv : 'at('diff(f(x),x),x=a) = 'limit((f(a+eps)-f(a))/eps,eps,0);
DefDeriv2 : 'at('diff(f(x),x),x=a) = 'limit((f(x)-f(a))/(x-a),x,a);
/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
S1 : '[f (x):=sin(x),
fp(x):=cos(x),
g (x):=42*x,
gp(x):=42];
RC _s_ S1;
RC _s_ S1 _s_ '[x:=t];
_s_1 (g(a,b)=a/b); "becomes a lambda"$
_s_1 (c =a/b); "stays unchanged"$
"_s_"(a/b, [a=c+d]);
"_s_"(a/b, [a=b,b=a]);
"_s_"(a/f(b), '[a:=b,b:=a,f(x):=x^2+x^3]);
(a/f(b)) _s_ '[a:=b, b:=a, f(x):=x^2+x^3];
*/
/* «TFC2» (to ".TFC2")
* See: (find-fline "~/MAXIMA/antideriv.lisp")
* 2jT68: (c2m242exsubstp 9 "uma-integral")
* (c2m242exsubsta "uma-integral")
*/
at2(fx,xa,xb) := matrix(["", "|", xb],
[fx, "|", ""],
["", "|", xa]);
at2(fx,xa,xb) := block([x:lhs(xa), a:rhs(xa), b:rhs(xb)],
antideriv(fx, x, a, b));
DefDif : (at2(F(x),x=a,x=b) = F(b)-F(a));
TFC2 : ('integrate(Fp(x), x, x=a, x=b) = at2(F(x),x=a,x=b));
TFC2 : (integrate_(Fp(x), x, x=a, x=b) = at2(F(x),x=a,x=b));
/* «TFC2-tests» (to ".TFC2-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
DefDif;
TFC2;
*/
/* «S_f_g» (to ".S_f_g")
*/
S_gx (gx) := [g(x)=gx, gp(x)=diff(gx,x)];
S_gx_fu (gx,fu) := [g(x)=gx, gp(x)=diff(gx,x),
f(u)=fu, fp(u)=diff(fu,u)];
S_gx_fpu(gx,fpu) := [g(x)=gx, gp(x)=diff(gx,x),
fp(u)=fpu];
V(viras) := transpose(matrix(viras));
/* «S_f_g-tests» (to ".S_f_g-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
V([a=aa,b=bb]);
[V(S_gx (x^2)),
V(S_gx_fu (x^2, sin(u))),
V(S_gx_fpu(x^2, cos(u)))];
*/
/* «MV» (to ".MV")
* 2jT87: (c2m242dip 7 "MVDs-e-MVIs-color")
* (c2m242dia "MVDs-e-MVIs-color")
*/
MVD1 : ('integrate(fp(g(x)) *. gp(x), x,x=a,x=b) = 'integrate(fp(u), u,u=g(a),u=g(b)));
MVD1 : (_integrate(fp(g(x)) *. gp(x), x,x=a,x=b) = _integrate(fp(u), u,u=g(a),u=g(b)));
MVI1 : ('integrate(fp(g(x)) *. gp(x), x) = 'integrate(fp(u), u));
MVI1 : (_integrate(fp(g(x)) *. gp(x), x) = _integrate(fp(u), u));
MVD4 : align_eqs([_integrate(fp(g(x)) *. gp(x), x,x=a,x=b),
at2(f(g(x)),x=a,x=b),
f(g(b)) - f(g(a)),
at2(f(u),u=g(a),u=g(b)),
_integrate(fp(u), u,u=g(a),u=g(b))]);
MVI3 : align_eqs([_integrate(fp(g(x)) *. gp(x), x),
f(g(x)),
f(u),
_integrate(fp(u), u)]);
MVs : matrix([MVI1, MVD1],
[MVI3, MVD4]);
/* «MV-tests» (to ".MV-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
S4 : S_gx_fu (x^2, sin(u))$
S3 : S_gx_fpu(x^2, cos(u))$
[V(S3), V(S4)];
MVI1 _s_ S3;
MVD4 _s_ S4;
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
S4 : S_gx_fu (sin(x), log(u)^4)$
S3 : S_gx_fpu(sin(x), 4*log(u)^3 / u)$
[V(S3), V(S4)];
MVI1 _s_ S3;
MVD4 _s_ S4;
*/
/* «DFI» (to ".DFI")
* 2jT97: (c2m242fpp 4 "1-sobre-x")
* (c2m242fpa "1-sobre-x")
* 2jT117: (c2m242dfip 3 "introducao")
* (c2m242dfia "introducao")
*/
DFI6 : align_eqss([[f(g(x)), x],
[diff_(f(g(x)),x), diff_(x,x), 1],
[diff_(f(g(x)),x), fp(g(x)) *. gp(x)],
[fp(g(x)) *. gp(x), 1],
[gp(x), 1/fp(g(x))]]);
DFI2 : align_eqss([[f(g(x)), x],
[gp(x), 1/fp(g(x))]]);
/* «DFI-tests» (to ".DFI-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
Sg : '[g(x):=Log(x), gp(x):=Logp(x)];
Sf : '[f(x):=Exp(x), fp(x):=Expp(x)];
DFI6;
DFI6 _s_ Sg;
DFI6 _s_ Sg _s_ Sf;
DFI2;
DFI2 _s_ Sg _s_ Sf;
*/
/* «EDOVS» (to ".EDOVS")
* (find-angg "MAXIMA/2024-2-C2-EDOVS.mac")
*/
EDOVS_M : matrix(
[ _diff(y,x), "=", g(x) /. h(y) ],
[ h(y)*del(x), "=", g(x)*del(x) ],
[ _integrate(h(y),y), "=", _integrate(g(x),x) ],
[ "||", "", "||" ],
[ H(y) +. C1, "=", G(x) +. C2 ],
[ H(y), "=", G(x) +. C3 ],
[ Hinv(H(y)), "=", Hinv(G(x) +. C3) ],
[ "||", "", "" ],
[ y, "", "" ])$
EDOVS_edo : 'diff(y,x) = g(x) / h(y);
EDOVS_imp : H(y) = G(x) + C3;
EDOVS_exp : y = Hinv(G(x) + C3);
EDOVS_f : Hinv(G(x) + C3);
/* «EDOVS-tests» (to ".EDOVS-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
linel : 110;
S4 : [g(x) = -2*x, h(y) = 2*y,
G(x) = -x^2, H(y) = y^2]$
S5p : [g(x) = -2*x, h(y) = 2*y,
G(x) = -x^2, H(y) = y^2,
Hinv(y) = sqrt(y)]$
S5n : [g(x) = -2*x, h(y) = 2*y,
G(x) = -x^2, H(y) = y^2,
Hinv(y) = -sqrt(y)]$
[EDOVS_M, EDOVS_M _s_ S4];
[EDOVS_M _s_ S5p, EDOVS_M _s_ S5n];
EDOVS_edo _s_ S5p;
EDOVS_imp _s_ S5p;
EDOVS_exp _s_ S5p;
EDOVS_f _s_ S5p;
edo : EDOVS_edo _s_ S4;
sol0 : ode2(edo,y,x);
sols0 : solve(sol0, y);
s0 : C3 = -2*%c;
s1 : solve(s0, %c);
sols1 : subst(s1, sols0);
define(fp(x), EDOVS_f _s_ S5p);
define(fn(x), EDOVS_f _s_ S5n);
P1 : [x=3,y=4];
eq1 : subst(P1, y=fp(x));
eq2 : solve(eq1, C3);
define(fp_P1(x), subst(eq2, fp(x)));
subst(P1, y=fp_P1(x));
P2 : [x=3,y=-4];
eq1 : subst(P2, y=fn(x));
eq2 : solve(eq1, C3);
define(fn_P2(x), subst(eq2, fn(x)));
subst(P1, y=fn_P2(x));
*/
/* «EDOLCC» (to ".EDOLCC")
*/
EDOLCC : matrix(
[ "f''" +. (-a-b)*."f'" +. (a*b) * f, "=", 0],
[ D^2*.f +. (-a-b)*.D*.f +. (a*b) * f, "=", 0],
[(D^2 +. (-a-b)*.D +. (a*b))*.f, "=", 0],
[(D-a)*.(D-b)*.f, "=", 0],
[(D-a)*.(D-b)*.exp(b*x), "=", 0],
[(D-a)*.(D-b)*.exp(a*x), "=", 0]);
EDOLCC_edo : 'diff(y,x,2) + (-a-b)*'diff(y,x) + a*b*y = 0;
/* «EDOLCC-tests» (to ".EDOLCC-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
SR : [a=2, b=-3];
SC : [a=2+3*%i, b=2-3*%i];
EDOLCC;
EDOLCC _s_ SR;
expand(EDOLCC _s_ SC);
edo : EDOLCC_edo _s_ SR;
sol : ode2(edo,y,x);
edo : EDOLCC_edo _s_ SC;
sol : ode2(edo,y,x);
*/
/* «E5» (to ".E5")
* (find-angg "MAXIMA/2025-1-exact.mac")
* (c2m251edosexatasp 3 "metodo-e-exemplo")
* (c2m251edosexatasa "metodo-e-exemplo")
*/
E5 : matrix(
[d *. z, "=", z_x *. dx +. z_y *. dy , "=", 0],
[_diff(z,x,1), "=", z_x +. z_y *. _diff(y,x,1), "=", 0],
[z, "=", C , "", ""]);
E5_edo : z_x + z_y*'diff(y,x) = 0;
E5_imp : z = C;
/* «E5-tests» (to ".E5-tests")
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2025-1-s.mac");
S1 : [z=x^2+y^2, z_x=2*x, z_y=2*y];
E5;
E5 _s_ S1;
edo : E5_edo _s_ S1;
imp : E5_imp _s_ S1;
imp2 : ode2(edo,y,x);
solve(imp, y);
solve(imp2,y);
*/
/*
* Local Variables:
* coding: utf-8-unix
* End:
*/