kill(all)$

maxima :intro how construct pde complex theory version1,part 5a.
peter.vlasschaert@gmail.com,27/04/2021

ref :https://petervlaschemeng.weebly.com/
=================================
-----------------------------------------------------------------------------------------------------------------
maxima :intro how construct pde from geometrical shape (p,q),version1,part 1.
maxima :how construct pde(p,q) :eliminating arbitrary (a,b),version1,part 2.
maxima :intro how construct pde from geometrical shape (p,q,r,s,t),version1,part 3.
maxima :intro how construct pde from arbitrary functions version1,part 4.
-----------------------------------------------------------------------------------------------------------------

load packages,option
-------------------------------

load(lrats)$  ratprint :false$

declare(c,constant);

maxima :commands :depends,dependencies,dependency
---------------------------------------------------------------------------------

depends(y,x);

p1:y^2+x;
diff(p1,x);

dependencies;

remove(y,dependency);

diff(p1,x);

=>  given:f(x(u,v),y(u,v))

p2:f(u(x,y),v(x,y));

→ How construct : f

depends(u,[x,y],v,[x,y]);

depends(f,[u,v]);

1e)  step :{df/dx,df/dy}

diff(f,x);

p1a:'diff(f,x)=%;

diff(f,y);

p1b:'diff(f,y)=%;

2e)  step :{df/du,df/dv}

p2a:diff(f,u);

p2b:diff(f,v);

3e) step:{df/df}

p3a:diff(f,f);

→  sum (result :sum of the differentials)
======

=> given:g(x(u,v),y(u,v)),  f→g

m:f(x(u,v),y(u,v))+g(x(u,v),y(u,v));

p1aa:subst([f=g],p1a);
p1bb:subst([f=g],p1b);

p2aa:subst([f=g],p2a);
p2bb:subst([f=g],p2b);

final result :
=========

'diff(m,x)=p1a+p1aa;
'diff(m,y)=p1b+p1bb;

'diff(m,u)=p2a+p2aa;
'diff(m,v)=p2b+p2bb;

given :

1e)  depends(uu,[xx,yy,zz])   →uu(xx,yy,zz), 'math notation'
2e)  depends(  zz,[xx,yy]   )   →zz(xx,yy)     , 'math notation'

p2a:depends(  zz,[xx,yy]   );
p2b:depends(uu,[xx,yy,zz]  );   

del(uu)=diff(uu);