Symbolic Calculations



> I am starting to look for freely available programs for mathematical
> applications. I am interested also in the possibilities of symbolic
> calculations. How does Maxima compare to e.g. Maple? Can I use it, for
> instance, to solve parametric linear systems?

I'm afraid I don't know anything about Maple, but Maxima can certainly
solve linear systems with parameters, e.g.
eq1:  a = b*x1 + (b^2-1)*x2 + a/b*x3$
eq2:  0 = x1 + x2 - x3$
eq3:  1=  1/(a+b)*x1 + (1-a)*x2 + x3$
solve([eq1,eq2,eq3],[x1,x2,x3]);

                        4      3     2             2     3      2       2
                       b  + a b  + (a  - 2 a - 1) b  + (a  - 2 a ) b + a
(D10) [[x1 = ----------------------------------------------------------------------,
              4              3     2             2     2                 3    2
             b  + (2 a - 1) b  + (a  - 2 a - 1) b  + (a  - 2 a - 1) b
+ a  - a  + a


                                    3    2      2
                                   b  - a  b + a
x2 = - ----------------------------------------------------------------------, 
        4              3     2             2     2                 3    2
       b  + (2 a - 1) b  + (a  - 2 a - 1) b  + (a  - 2 a - 1) b + a  - a  + a


                4            3     2             2     3    2
               b  + (a - 1) b  + (a  - 2 a - 1) b  + (a  - a ) b
x3 = ---------------------------------------------------------------------- ]]
      4              3     2             2     2                 3    2
     b  + (2 a - 1) b  + (a  - 2 a - 1) b  + (a  - 2 a - 1) b + a  - a  + a