Thank you, Waldek,
that explains the behaviour much better. I suspected that there must be
some numerics involved, but when I had put debugging output near places
where I saw Float-s, that never appeared, so I got a bit confused and
didn't want to waste more time on this.
Potentially, I would be in favour of letting imag or real fail if the
sign cannot be determined correctly. In that case the error message
should contain a hint that it might be helpful to increase the Float digits.
On the other hand, it looks like FriCAS is anyway spitting out radical
expressions that are more complicated than needed. I tried rsimp on them
but that failed, unfortunately. Seemingly Mathematica is trying harder
in ToRadicals.
https://reference.wolfram.com/language/ref/ToRadicals.html
Side remark. I am actually not so happy with the name rsimp or rootSimp.
Cannot FriCAS stick to the convention that we have full words and no
abbreviations in function names?
Ralf
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