I'm trying to find a formula concerned with some computation about the relative 
position of two ellipses. But some result along the way looks strange when 
evaluated with RDF numbers, and trying to plug in algebaric numbers instead, I 
encounter the following error message:

sage.libs.pari.gen.PariError: ZZ_123633238138850861[y]/(y^2 + 
114948053005503479*y + 71680486823734693) is not a field in FpX_ffintersect

I have no clue what that error message means, and more importantly, how to 
avoid it. I've pasted my code from my norebook worksheet to 
https://gist.github.com/gagern/9320350. I tried to convert all the sage console 
output style back to sage input notation, with output as comments. Hope I 
didn't miss anything.

As you can see in that file, I've encountered quite a number of places where 
the current behavior of sage surprised or even annoyed me. The question I'm 
posting about now is question 6 from the comments in that file. But if anyone 
can contribute some insight to some of the other questions as well, that would 
be highly appreciated. If not, I might end up posting more mails about these as 
well. But right now, my most immediate problem is that about how to perform a 
proper algebraic computation on these expressions.

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