I need to solve the following system of equations. solve([


a\*c\*e=a2\*c2\*e2,
b\*d\*f=t\*b2\*d2\*f2,
t\*a1\*c1\*e1=a3\*c3\*e3,
b1\*d1\*f1=b3\*d3\*f3,


a\*b\*a1\*b1=a2\*b2\*a3\*b3,
c\*d\*c1\*d1=c2\*d2\*c3\*d3,
e\*f\*e1\*f1=e2\*f2\*e3\*f3,


b+c=b2+c2,
d+e=d2+e2,
b1+c1=b3+c3,
d1+e1=d3+e3,


a1\*b1\*(b + c) + c\*d\*(b1 + c1) =
a3\*b3\*(b + c) + c2\*d2\*(b1 + c1),


c1\*d1\*(d + e) + e\*f\*(d1 + e1) =
c3\*d3\*(d + e) + e2\*f2\*(d1 + e1)


], 
[a2,b2,c2,d2,e2,f2,a3,b3,c3,d3,e3,f3], IgnoreSpecialCases,VectorFormat);


I tried to use some software to solve it. I can only solve it in the cases that most of a,b,c,d,e,f,a1,b1,c1,d1,e1,f1 are given by some numbers. Are there some good software which can solve this system of equations symbolically? Thank you very much.



Good software for solving a system of algebraic equations
The Maple command $$sol := SolveTools:-PolynomialSystem({a\*c\*e = a2\*c2\*e2, b\*d\*f = t\*b2\*d2\*f2, b1\*d1\*f1 = b3\*d3\*f3, a\*b\*a1\*b1 = a2\*b2\*a3\*b3, c\*d\*c1\*d1 = c2\*d2\*c3\*d3, e\*f\*e1\*f1 = e2\*f2\*e3\*f3, t\*a1\*c1\*e1 = a3\*c3\*e3, b+c = b2+c2, b1+c1 = b3+c3, d+e = d2+e2, d1+e1 = d3+e3, a1\*b1\*(b+c)+c\*d\*(b1+c1) = a3\*b3\*(b+c)+c2\*d2\*(b1+c1), c1\*d1\*(d+e)+e\*f\*(d1+e1) = c3\*d3\*(d+e)+e2\*f2\*(d1+e1)}, {a2, a3, b2, b3, c2, c3, d2, d3, e2, e3, f2, f3}): $$ produces a long output which consists of $12$ elements. For example, the first one is $a2$ equals a rational function of the $13$ free variables $ a, a1, a2, b, b1, c, c1, d, d1, e, e1, f, t $ of degree $17$. The others are similar. See the Maple output here <https://www.dropbox.com/s/a8t6z5u2ukf0wt6/system.pdf> as an exported PDF file. [The PolynomialSystem](http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools)  command uses [the Groebner basis](http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis) tools.


