Entropy function for a q-ary alphabet ($H_q(x)=x{\log }_q(q-1)-x{\log }_{q}x-(1-x){\log }_q(1-x)$)

This is the entropy in base $q$ of the distribution with one symbol of probability $1-x$ and each of the other $q-1$ symbols of probability $x/(q-1)$. It increases on $[0,1-1/q]$ from zero to one, and governs the exponential volume of a Hamming ball. For $q=2$ it is the binary entropy function.

// Target: algebra.bigb