Difficulties with resultants and Tschirnhaus transformations

edit

I'm experimenting with some polynomial equations, and as a test I'm working through the example given here:

http://www.oocities.org/titus_piezas/...

Basically, in order to eliminate the first two terms of the quintic $x^5-x^4-x^3-x^2-x-1$ we need to find a transformation $y=x^2+ax+b$ (such a polynomial transformation is called a Tschirnhaus transformation, after its first discoverer), for which $a$ and $b$ have the effect of producing a quintic equation in $y$ but without $y^4$ or $y^3$ terms. This is as far as I've got so far:

R.<a,b> = QQ[] 
S.<y> = R[] 
T.<x> = S[]
p = x^5-x^4-x^3-x^2-x-1
res = p.resultant(y-x^2-a*x-b) 
rc = res.coefficients() 
solve([rc[-2],rc[-3]],[a,b]) 

TypeError: a is not a valid variable.

Drat! So I have two questions: why is a not a valid variable, and why can I not isolate individual coefficients of res? I can obtain all the coefficients of res, but I can't isolate just one, with something like res.coeff(y,3).