You said before AlgebraicNumber should represent any branch of the root, but here we are talking about the sign of radical.
Does that mean we are taking a specific branch interpretation here? - Qian On 5/15/24 17:42, Waldek Hebisch wrote:
TrigonometricManipulations (which implements imag) is using sign$ElementaryFunctionSign to determine if a root is complex. 'sign' may return "failed" and 'imag' treats this the same as nonnegative, so assumes that root is real. 'sign' for numbers tries interval approximation. If precision it too low, then this fails and 'sign' returns "failed"... Mathematically determining sign of numbers (which is needed to choose form of roots) requires numerical computation potentially of much higher precision than input data. So there will be a cutoff or we would run out of memory (or time) in some cases. So one question is how hard FriCAS should try, currently FriCAS just uses current numeric preciion and do not try to escalate. Another question is what to do in case of failure. Honestly FriCAS should return "failed" or signal error in such case. 'sign' returns "failed" which IMO is OK. Probably 'imag' should signal error. I can guess that possibly users call 'imag' and related functions without real need, so lying (as done now) could be a pragmatic choice. Or simply this is piece of research code that never really get finished.
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