If you're going to have versions of sqrt in S29 that deal with Complex numbers, you ought to do likewise with a number of other functions:
multi sub abs (: Complex ?$x = $CALLER::_ ) returns Num should return the magnitude of a complex number. abs($x) := $x.magnitude, or whatever the appropriate method for extracting the magnitude of a Complex number is. (I'm unaware of the exact terminology used within Complex, or even if it has been established yet.) multi sub sign (: Complex ?$x = $CALLER::_) returns Complex Since I would expect $x == sign($x) * abs($x) to be true for Nums, the sign of a complex number would logically be a unitary complex number, or zero if $x is zero: sign($x) := ($x == 0) ?? 0 :: $x / abs($x). Thus, this would be distinct from $x.angle, or whatever it's called, which would return a Num representing the direction as measured in radians, degrees, etc. multi sub exp (: Complex ?$exponent = $CALLER::_, Complex +$base) returns Complex multi sub log (: Complex ?$exponent = $CALLER::_, Complex +$base) returns Complex multi sub func (: Complex ?$x = $CALLER::_, +$base) returns Complex (where func is any trig-related function) IIRC, raising a base to a Complex exponent raises the base's absolute value by the real component of the exponent, and rotates its angle (as measured in radians) by the imaginary component. All of the trig functions can be aliased to expressions using exp and log. This may be useful for the purpose of defining the Complex versions. All of these functions, as well as sqrt, need to restrict the range of valid return values: frex, sqrt ought to always return something with either a positive real component or a zero real component and a non-negative imaginary component. (Another possibility would be to return a list of every possible result when in list context, with the result that you'd get in scalar context being element zero of the list. This even has its uses wrt sqrt(Num), providing a two-element list of the positive and negative roots, in that order. This option would apply to sqrt, exp, log, and the trig functions.) This has implications for the infix:<**> operator as well. -- Jonathan "Dataweaver" Lang
