load("cliffordan")$

Euclidean 3D space

clifford(e,3);

 r:cvect([x,y,z]);

Green function

 G:r/sqrt(-cnorm(r))^3/(4*%pi);

    mvectdiff(G,r)=0;

Potential

P:-1/sqrt(-cnorm(r))/(4*%pi);

mvectdiff(P,r)=G;

Homogeneous Poisson equation 

dependsv(F,[x,y,z])$

mvectdiff(F,r,2)=0;

P solves the equation

mvectdiff(P,r,2)=0;

Define cyclindrical coordinates

declare( [rho, phi], scalar)$

cyl_eq:[x=rho*cos(phi), y=rho*sin(phi)];

r_c:coordsubst(r, cyl_eq);

Green function in cylindrical coordinates

GG_c:coordsubst(G, cyl_eq),factor;

mvectdiff(GG_c,r_c)=0;

dependsv(F,[x,y,z,rho, phi])$

Homogeneous Poisson equation 

 mvectdiff(F,r_c,2)=0;

V:coordsubst(P,cyl_eq);

mvectdiff(V,r_c)=GG_c;

V solves the equation

mvectdiff(V,r_c,2)=0;