search for: compactif

It seems to me that the documentation of R's complex class & R's atan function do not tell us what to expect, so (as others have suggested), some additional notes are needed. I think that mathematically atan(1i) should be NA_complex_, but R seems not to use any mathematically standard compactification of the complex plane (and I'm not sure that IEEE does either). Incidentally, the signature of the complex constructor is confusing. complex(1L) returns zero, but complex(1L, argument=theta) is an element of the unit circle. The defaults suggest ambiguous results in case only length.out...

...re was an IEEE standard with things like NaN, Inf, and signed zeros But there *is* an IEEE standard now, and even IBM mainframes offer IEEE-compliant arithmetic, so worrying about the sign of zero etc is not something we can really overlook these days. You are of course correct that the one-point compactification of the complex numbers involves adjoining just one infinity and that whacking IEEE infinities into complex numbers does not give you anything mathematically interesting (unless you count grief and vexation as "interesting" (:-)). Since R distinguishes between 0+Infi and NaN+Infi,...

>>>>> Richard O'Keefe >>>>> on Fri, 6 Sep 2024 17:24:07 +1200 writes: > The thing is that real*complex, complex*real, and complex/real are not > "complex arithmetic" in the requisite sense. > The complex numbers are a vector space over the reals, Yes, but they _also_ are field (and as others have argued mathematically only