Let $f(x)=(x-a_1)(x-a_2)\cdots(x-a_m)$ and $g(x)=(x-a_{m+1})(x-a_{m+2})\cdots(x-a_n)$, where $m,n \in \mathbb{N}$, $m < n$, $a_i \in F$, $F$ is a field of characteristic zero (for example, $k \in \{\mathbb{R},\mathbb{C}\}$). Let $\lambda,\mu \in F$.
How to compute the subresultants of $f(x)-\lambda$ and $g(x)-\mu$?
If, for example, $m=2$ and $n=4$, then I have succeeded to compute it using $a,b,c,d$:
subresultants [(x-a)(x-b) -\lambda, (x-c)(x-d) - \mu].
But it seems that beyond $a,b,c,d,e$ it is not possible? Or just because I have written $f,g$ (which probably denotes functions). Writing the $a_i$'s does not work.
Thank you very much!