2 Maple code to obtain the operators

This is not a free software, and it can be obtained in [3].

2.1 The metric in the chosen coordinate basis

> restart;
> with(DifferentialGeometry):with(Tensor):with(Tools):
> g_c:=array(symmetric,sparse,1..3,1..3):
> g_c[1,1]:=1:
> g_c[2,2]:=1:
> g_c[3,3]:=1:
> g:=create([-1,-1],eval(g_c));

spherical coordinates

> x:=r*cos(phi)*sin(theta);

> y:=r*sin(theta)*sin(phi);

> z:=r*cos(theta);

metric in the chosen coordinate basis

> g_c:=array(symmetric,sparse,1..3,1..3):
> g_c[1,1]:=diff(x,r)*diff(x,r)+diff(y,r)*diff(y,r)+diff(z,r)*diff(z,r):
> g_c[1,2]:=diff(x,r)*diff(x,theta)+diff(y,r)*diff(y,theta)+diff(z,r)*
> diff(z,theta):
> g_c[1,3]:=diff(x,r)*diff(x,phi)+diff(y,r)*diff(y,phi)+diff(z,r)*diff(z,phi):
> g_c[2,2]:=diff(x,theta)*diff(x,theta)+diff(y,theta)*diff(y,theta)+diff(z,theta)*
> diff(z,theta):