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Questions about Abs[_]


Hi,
 
I define,
 
G0[r_List, r0_List]:=(Exp[I k Norm[r-r0]/(4*Pi*Norm[r-r0]))*((1+(I/(k*Norm[r-r0]))-(1/(k^2*Norm[r-r0]^2)))*IdentityMatrix[3]-(1/Norm[r-r0]^2)*(1+((3*I)/(k*Norm[r-r0]))-(3/(k^2*Norm[r-r0]^2)))*Outer[Times,r-r0,r-r0])
 
where
 
r = {x,y,z}
r0={x0,y0,z0}
ri={x0,y0,-z0}
rsn=r0+{0,0,2*n*d}
rim=ri+{0,0,2*m*d}
 
When i want to compute
 
G0r0rim=G0[r0,rim]
 
I find something odd...
 
1) Why Abs[2*z0-2*d*m] doesn't give 2*Abs[z0-m*d] ?
 
2) Why Abs[2*z0-2*d*m] doesn't simplify with (2*z0-2*d*m)^2 ?
 
Note : all the variables are positive, i.e. : z0>0, d>0 and -Infinity < m_Integer < Infinity.
 
Steeve Brechmann
Physics Department, Laval University
steevebrechmann at yahoo.ca



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