Least positive Liouville period (source code)

= Least positive Liouville period
{title2=$\gamma(L)=\inf\{a>0:a\in\operatorname{Per}(L)\}$}

For a nonzero discrete Liouville period group, this is its positive generator. In Euclidean symplectic space, the same group is obtained from signed symplectic areas of disks with boundary on $L$, by the <Stokes theorem> and contractibility of the ambient space. A product of circles of common radius $r$ is a <rational Lagrangian submanifold> with $\gamma(L)=\pi r^2$. Translation changes a primitive only by an exact form and hence leaves the period group unchanged.