Surely the bug is related to the fact that the last call to resultant returns 256*(sqrt(7)^2-7) instead of 0.
Ahh, doesn't the general simplifier do 256*(sqrt(7)^2-7) --> 0? Really, resultant shouldn't return an
unsimplified expression.
(%i39) algsys(e,[x,y]);
1" Enter "algsys[[y^2+x^2-1,(y-1/2)^2+(x-1/2)^2-1],[x,y]]
.1" Enter "resultant[2*x^2-2*x+2*y^2-2*y-1,x^2+y^2-1,y]
.1" Exit "resultant8*x^2-4*x-3
.1" Enter "resultant[8*y^2+sqrt(7)-4,8*y^2-8*y-sqrt(7)-2,y]
.1" Exit "resultant256*(sqrt(7)^2-7)
.1" Enter "resultant[8*y^2-sqrt(7)-4,8*y^2-8*y+sqrt(7)-2,y]
.1" Exit "resultant256*(sqrt(7)^2-7)
1" Exit "algsys[]
(%o39) []
--Barton