I'm a beginner with maxima,
I've took it for the sole purpose of solving a system of equations. Here is my result :
(%i30) e1: a*b - c*d + e*f - g*h = i*j - k*l;
(%o30) (- g h) + e f - c d + a b = i j - k l
(%i31) e2:a^2 + c^2 = b^2 + d^2;
2 2 2 2
(%o31) c + a = d + b
(%i32) e3:a^2 + c^2 = e^2 + g^2;
2 2 2 2
(%o32) c + a = g + e
(%i33) e4:a^2 + c^2 = f^2 + h^2;
2 2 2 2
(%o33) c + a = h + f
(%i34) e5:a^2 + c^2 = i^2 + k^2;
2 2 2 2
(%o34) c + a = k + i
(%i35) e6:a^2 + c^2 = j^2 + l^2;
2 2 2 2
(%o35) c + a = l + j
(%i36) algsys([e1,e2,e3,e4,e5,e6], [a]);
(%o36) []
Now, I'm wondering :
How confident can I be that there is no solution ?
How can I know what are the steps used by maxima to prove such a thing ?
I asked a specialist on irc
The answer is that you can't trust an empty result : it doesn't mean that there is no solution, it mean the cas didn't found one
for the step, I've been recommended to use the lisp debug output to get the process of solving