>>>>> "Paul" == Paul Bowyer <pbowyer at olynet.com> writes:
Paul> Hi David:
Paul> I understand the complexity, but I do actually need the symbolic
Paul> solutions, if there are any. So, I'm looking for a response from someone
Paul> who is a Maxima expert that can tell me if there is a problem in solve,
Paul> especially when it just goes off and never returns, or returns with an
Paul> error message. For other expressions I've tried solve returns an empty
Paul> solution rather than an error message and does not seem to compute forever.
It's unfortunate that solve is so slow in this case. But David
Chappaz has given the necessary hints, I think, to get what you want.
roots:solve(a*y^3+b*y^2+c*y+d,y);
will give you the 3 roots you want in terms of a, b, c, and d.
All you need to do is get a, b, c, and d from your original problem.
You can do
a : coeff(expand(det1),y,3);
b : coeff(expand(det1),y,2);
c : coeff(expand(det1),y,1);
d : coeff(expand(det1),y,0);
And then substitute these values into the messy result obtained from
solve.
But maybe just leaving the roots in terms of a, b, c, d is best. You
can easily substitute the desired coefficients in later.
Ray