 Fuchsian linear differential system

In a fixed frame, a first-order linear differential equation is Fuchsian at a finite point when its coefficient matrix has at most a simple pole there. Its residue is $R$. The global object is the matrix-valued one-form $A(z)dz$: in the coordinate $t=1/z$ its coefficient is $-t^{-2}A(1/t)$. A Fuchsian system has intrinsic regular singular points, but an intrinsically regular singular system may have higher-order coefficient poles in a different meromorphic frame.