kill(all)$

load(lrats)$

principal: relation integration and list parameters from integration,version 1.0
peter.vlasschaert@gmail.com,05/08/2019

principal: relation integration and list parameters from integration
==================================================

p1:m='integrate(f(x),x,a,b);

p2:args(p1);

p2a:p2[2];
p2b:args(p2[2]);

p4:[sin(x),x,a,b];

p5:subst([x=y],''integrate(f1(x),x,a,b));

p6:fintegr(f1,f2,f3,f4):=ev('integrate(f1,f2,f3,f4),simp:false);

use list :p4
========

p6a:fintegr(p4[1],p4[2],p4[3],p4[4]);

evaluation integration
=================

laplace transformation
-------------------------------

p6b:ev(p6a,integrate);

laplace(f(t),s,t)

maxima,version
============

laplace(sin(t), t, s);

my ,version (laplace)
================

g1:mylaplace(f1,f2,f3,f4):=block(assume(s>0),ev(''integrate(f1*exp(-s*t),t,f3,f4),simp:false));

g1a:mylaplace(f(t),t,0,∞);

g2a:lratsubst([f(t)=sin(a*t)],g1a);

g3a:ev(g2a,nouns);

g4a:g2a=g3a;

g5a:subst([a=1],g4a);

complex: laplace
=============

g6:mylaplace(f(t),t,0,∞);

g6a:lratsubst([f(t) =exp(%i*a*t)],g6);

g6b:ev(g6a,nouns);

def : rt(z)
=======

rt(z):= realpart(z)+%i*imagpart(z);

g6c:v=rt(g6b);

exp(i*θ) = cos(θ) + i*sin(θ)

g6d:g2a=realpart(rhs(g6c));

g6e:subst([sin(a*t)=cos(a*t)],lhs(g6d)) =imagpart(rhs(g6c));

g7e:g6d*%i;

g7f:g6e+g7e;

g7g:args(lhs(g7f));

a)  part :sin(a*t)
---------------------

g7h1:args(g7g[1]);

g7h2:args(g7g[1])[1];
g7h3:args(g7g[1])[2];
g7h4:args(g7h3);

g7h5:[%i*g7h4[1],g7h4[2],g7h4[3],g7h4[4]];

b) part :cos(a*t)
-----------------------

g8h1:g7g[2];

g8h2:args(g8h1);

final list : g7h5+g8h2
================

g9:[g8h2[1]+g7h5[1],t,0,∞];