  This work develops a comprehensive algorithm and a Mathematica program to
construct boundary data and compute real and complex critical points in
spinfoam amplitudes. Our approach covers both spacelike tetrahedra and
triangles in the EPRL model and timelike tetrahedra and triangles in the
Conrady-Hnybida extension, aiming at addressing a wide range of physical
scenarios such as cosmology and black holes. Starting with a single 4-simplex,
we explain how to numerically construct boundary data and corresponding real
critical points from any nondegenerate 4-simplex geometry. Extending this to
the simplicial complex, we demonstrate the algorithm for constructing boundary
data and critical points using examples with two 4-simplices sharing an
internal tetrahedron. By revisiting the $\Delta_3$ triangulation with curved
geometry, we demonstrate the numerical computation of the real critical point
corresponding to the flat geometry and the deformation to the complex critical
points. Additionally, the program evaluates the spinfoam action at the critical
points and compare to the Regge action.
