Modular symbol
= Modular symbol
{title2=$\{\alpha,\beta\}$}
{wiki}
A modular symbol is the <relative homology class> of a path between two <modular cusps>. Oriented paths satisfy $\{\alpha,\beta\}+\{\beta,\gamma\}=\{\alpha,\gamma\}$. <Continued fractions> subdivide rational-endpoint paths into unimodular edges, giving a finite presentation through <Manin symbols>. The <Hecke operators> act by finite sums of transformed paths, so their matrices can be computed by rational linear algebra.