about curvilinear coordinates



hi everyone!

im totally new to maxima, buy i've had used maple a couple of times in the 
past. But i can't find a way to handle coordinate transformations in maxima. 
the manual says that you should feed a TTRANSFORM with a transformation 
matrix, then, what i supposed it meant was this:

(C6) MT:matrix([ diff(x(f,g,h,j),f) , diff( y(f,g,h,j),f ) , diff( 
z(f,g,h,j),f ) , diff( w(f,g,h,j),f) ],[ diff(x(f,g,h,j),g) , diff( 
y(f,g,h,j) ,g) , diff( z(f,g,h,j),g) , diff( w(f,g,h,j),g) ],[ 
diff(x(f,g,h,j),h) ,diff( y(f,g,h,j),h ) , diff( z(f,g,h,j),h) , diff( 
w(f,g,h,j),h) ] , [ diff( x(f,g,h,j),j) ,diff( y(f,g,h,j),j) , diff( 
z(f,g,h,j),j) , diff( w(f,g,h,j),j) ] );
	   ]
(C7) coordTrans:TTRANSFORM( MT );

then i want to get the laplacian in one coordinate, ie:

(C9) L(u,x,y,z,w):=diff(u(x,y,z,w),x,2) + diff(u(x,y,z,w),y,2) + diff( 
u(x,y,z,w),z,2) + diff( u(x,y,z,w),w,2) ;
(D9) L(u, x, y, z, w) := DIFF(u(x, y, z, w), x, 2) + DIFF(u(x, y, z, w), y, 
2) + DIFF(u(x, y, z, w), z, 2) + DIFF(u(x, y, z, w), w, 2)

but now i want to transform to another coordinate system (ie: f,g,h,j -> 
x,y,z,w

for this i specified the actual functions:

(C9) x(f,g,h,j):=cos(f)*sin(g)*sin(h);
(D9) 		     x(f, g, h, j) := COS(f) SIN(g) SIN(h)
(C10) y(f,g,h,j):=sin(f)*sin(g)*sin(h);
(D10) 		     y(f, g, h, j) := SIN(f) SIN(g) SIN(h)
(C11) z(f,g,h,j):=cos(g)*sin(h);
(D11) 		        z(f, g, h, j) := COS(g) SIN(h)
(C12) w(f,g,h,j):=cos(h);
(D12) 			    w(f, g, h, j) := COS(h)


but i dont know what else to do to get the laplacian transformed into the 
new coordinate system, please help me out!

Thanks!



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