Wow. Thanks everyone for helping me out.

The error message mentioned the equation so that's what I was focusing
on, but basically it seems to be all to do with type coercions and the
various ways there are to persuade FriCAS to 'do the right thing'.

So to summarize: Bill's solution was to lift the polynomial over the
extension field and use the 3-value eval form (which I didn't know
existed), whereas Ralph's was to nudge FriCAS into creating an
equation between  polynomials over the extension field and then let
FriCAS automatically lift the given polynomial over the extension
field.

The FriCAS type system sure is a subtle and complex beast!

Paul

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