RWG wrote:
What is the conventional name for 1/(1/x+1/y)?
Don't know. Perhaps capacitive sum (since capacitors in series follow that addition law)? Parallel sum (since resistors in parallel follow that addition law)? The paper "Associativity of the Secant Method" by Sam Northshield refers to this sum. Given a function f, define x oplus y = ( x f(y) - y f(x) )/( f(y)-f(x) ) If f has a pole at e, then define p(x) = f(x)(x-e); otherwise p(x)=f(x). If f has a pole at e, then define z=e; otherwise z=+inf. The homomorphism F(x oplus y) = F(x)+F(y) holds if F'=1/p and F(z)=0. oplus is the capacitive sum for f(x)=x^2, and F(x)=-1/x. oplus is the nirmal sum when f(x)=1/x. oplus is multiplication when f(x) = x/(1-x), and F(x) = ln x. atan is a homomorphism for f(x) = (x^2+1)/x. etc. -- Mike Stay staym@clear.net.nz http://www.cs.auckland.ac.nz/~msta039