substitute expressions in Maxima

From the Maxima mailing list: Say you want to substitute one expression for another, also dealing with the case in which the expression to be replaced is multiplied by some constant.

(%i1) e : a^2 + b^2 + c^2;
                                  2    2    2
(%o1)                            c  + b  + a
(%i2) ratsubst(r^2, a^2 + b^2 + c^2, e);
                                       2
(%o2)                                 r
(%i3) e : - 3 * a^2 - 3 * b^2 - 3 * c^2;
                                  2      2      2
(%o3)                        - 3 c  - 3 b  - 3 a
(%i4) ratsubst(r^2, a^2 + b^2 + c^2, e);
                                         2
(%o4)                               - 3 r