>Now back in sage, sage chose to be compatible with python's behavior in >x^(1/3) for whatever x that represents a number in the complex field, say x >= -1, RR(-1), CC(-1), QQbar(-1). For x = ZZ(-1), QQ(-1), they chose to >return symbolic expression (-1)^(1/3), which again converted to the same >value with QQbar(-1)^(1/3). For x = RBF(-1), it chose to raise an error. >For x = RDF(-1), it chose to return "nan". All these suggest to sage users >that x^(1/3) means the principal cube root of the number x.
For mathematicians who do real algebra and real algebraic geometry, it's extremely unfortunate when reality is not respected by functions which, mathematically, can respect reality. So you suggest that RR(-1)^(1/3), RBF(-1)^(1/3), RDF(-1)^(1/3) all should return -1 and RR(-1)^(1/4), RBF(-1)^(1/4), RDF(-1)^(1/4) raise errors. That also makes perfect mathematical sense. If you believe strongly in it, you may proceed to implement that. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/da43056f-208c-4f86-8d16-642e199da10fn%40googlegroups.com.
