Using {fa} in nfdisc() computations

[Kurt Foster <drsardonicus@earthlink.net>]

The optional {fa} parameter [factor() matrix]  seems like just the  
thing for speeding up the computations in a situation I'm looking at.   
I've got a parametric family of polynomials.  I want the exact  
nfdisc()s for a whole swarm of them.  I could, of course, just feed  
the polynomials to nfdisc() and let it crunch away.  This does work,  
of course, but  it occurred to me it might be faster if I could take  
advantage of the fact that the poldiscs have a parametric algebraic  
factorization, and the algebraic factors are generally much smaller  
than the poldisc(), in the sense that

log(abs(algebraic factor))/log(abs(poldisc)

will usually be a lot less than 1.  Thus, factoring the algebraic  
factors should be a LOT quicker than tackling the whole poldisc.

But in order to produce the factor() matrix fa for the poldisc, I've  
got to "combine" the factorization matrices of the algebraic factors.   
There's probably a slick way to do this, but I'm a dunce at  
programming.  Would factor()ing the algebraic factors and "combining"  
the results actually be likely to be faster than tackling the whole  
poldisc?  If so, what's an expeditious way to combine the factor()  
matrices of the separate algebraic factors into the correct factor()  
matrix for the poldisc?