Here is a simple session with maxima, in which im trying to make the simplification (r-r0)=h
(%i1) ax: G*M*m*(r-r0)/r0^2 - G*M*m/r0 ;
G M m (r - r0) G M m
(%o1) -------------- - -----
2 r0
r0
(%i2) let(r-r0,h);
(%o2) r - r0 --> h
(%i3) expand(scanmap(letsimp,ax));
G M m r 2 G M m
(%o3) ------- - -------
2 r0
r0
I was expecting this in the last part:
G M m h 2 G M m
------- - -------
2 r0
r0
Why did maxima replace (r-r0) with r rather than with h? Iv attempted letsimp and letrat as instructed in this other question: common subexpressions
r - r0 is not a form supported by let. From the documentation:
-- Function: let let (, , , , ..., ) let ([, , , , ..., ], )
Defines a substitution rule for 'letsimp' such that <prod> is replaced by <repl>. <prod> is a product of positive or negative powers of the following terms: * Atoms which 'letsimp' will search for literally unless previous to calling 'letsimp' the 'matchdeclare' function is used to associate a predicate with the atom. In this case 'letsimp' will match the atom to any term of a product satisfying the predicate. * Kernels such as 'sin(x)', 'n!', 'f(x,y)', etc. As with atoms above 'letsimp' will look for a literal match unless 'matchdeclare' is used to associate a predicate with the argument of the kernel.
In this case one can start with a syntactic substitution:
(%i1) ax: G*M*m*(r-r0)/r0^2 - G*M*m/r0 $
(%i2) subst(h, r - r0, ax);
G M h m G M m
(%o2) ------- - -----
2 r0
r0