Answered
There is an interesting difference in behaviour between input
((x-1)^(2)+(y-1)^(2))=0
and
((x-1)^(2)+(y-1)^(2))*((x-2)^(2)+(y-2)^(2))*((x-3)^(2)+(y-3)^(2))=0
I'd expect the latter to be three points, but it isn't!
The same question 
There is an interesting difference in behaviour between input
((x-1)^(2)+(y-1)^(2))=0
and
((x-1)^(2)+(y-1)^(2))*((x-2)^(2)+(y-2)^(2))*((x-3)^(2)+(y-3)^(2))=0
I'd expect the latter to be three points, but it isn't!
Degenerate conics are all covered; degenerate higher orders not so much :)
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