Re: [boost] c2_functions first submission materials uploaded

From: Roland Schwarz (roland.schwarz_at_[hidden])
Date: 2006-03-25 11:43:20

Roland Schwarz wrote:
> But complex of course could also turn out to be handy at times.
Too fast again (._.)
A complex function AFAIK is indefinitely differentiable by definition.

So it obviously belongs to the class of C2 but is there such a thing as 
complex valued splines?

Then what about function composition? For the equivalence of complex 
differentiation rules with real valued ones you need that the complex 
function is identical to its real valued counterpart when evaluated on a 
part of the real line (sloppy speaking). So this will force the function 
class to be C_infinite. Or am I missing something?

I think c2_functions are not so much interesting because they are 
carrying their derivatives with them, but because they are a handsome 
tool to deal with splines in a very readable manner.

Having said this, I think c2_functions should not be used for hiding the 
algorithm developers laziness to modify his/her algorithm to make use of 
whatever is known about the functions (in case of analytic funtions you 
know all derivatives!).

c2_functions in my opinion  is a want-to-have tool to deal with splines 
numerically, while still focusing on it's appearance as a function.

Other directions deviate from numerical use and extend to symbolic 
systems. This would also be desirable to have, but I think it should go 
to a different library.

Just what I think...

Roland