Dan Bron wrote: > Can you now explain why I was taught, in elementary math, to express %:4 > as (+,-)2 instead of just 2 ? If I have to write (%:4) = (+,-)2 > why do I not have to write (^._1) = 0 j. 1p1 * 1 + 2 * i: _ ? Is it > because the former has only 2 elements, but the latter infinitely many? > > By the way, I'm pretty sure 0 j. 1p1 * 1 + 2 * i: N (scalar positive > integer N ) is the right expression for generating for the logs of _1 > but J doesn't agree: >
Henry's non-mathematician's response is right on the money. Mathematicians used to have a more inclusive idea of function, including "multivalued functions", which are now called "relations" (the terminology being most obvious in relational databases). Square root is the first obvious example of a multivalued function, and it may be treated this way in elementary curricula. Multivalued functions are not functions in modern terminology, and they are systematically eliminated from calculus curricula, except in implicit differentiation. You are absolutely correct that the complex numbers z such that ^z is _1 are given by odd multiples of j.1p1 . This can be seen easily from Euler's formula. J is using a principal domain that is something like the complex numbers r*^j.x where r>0 and x is a real number in the interval (_1p1,1p1) (with possibly one end closed). The complex log is then (^.r)+j.x . As Henry points out, if x is very close to 1p1 (where the cut in the complex plane is made), it may go either way. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
