Let $G$ be an abelian group such that there exist two families $\{\psi_g, \phi_g\}_{g \in G}$, not neccessarily disjoint, of homomorphisms $\psi_g, \phi_g : G \to \langle g \rangle$, each mapping onto the corresponding cyclic subgroup; such that $\phi_g(h) = \psi_h(g)$ for all $g,h \in G$. Then ...

In game programming (my profession) it is often necessary to generate all kinds of random things, including random curves (for example, to make a procedural island or for an agent to follow some path). For one dimensional things, we usually use some random generator that generates say floats (w...

Let $K$ be your non-archimedean local field, $\mathcal O_K$ be the ring of integers, $\mathfrak p$ be the maximal ideal of the ring, and $k := \mathcal O_K / \mathfrak p$ be the residue field. If $k$ is a finite field and $|k| = q$, then we assemble $\overline k$ this way: by the classificatio...