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Proposed fix:

(defmfun $resultant (a b mainvar)

(prog (varlist formflag $ratfac res ans genvar $keepfloat

$algebraic)

(setq varlist (list mainvar) $ratfac t ans 1 $algebraic t)

It seems to fix the problem:

(%o9) [b*c+a^2-a,b*d+a*b-b,c*d+a*c-c,d^2-d+b*c]

(%i10) algsys(%,[a,b,c,d]);

(%o10) [[a=-(sqrt(1-4*%r7*%r8)-1)/2,b=%r7

Barton