code: def christoffels(base_point):
      def coefficients(param_a, param_b):
          """Christoffel coefficients for the beta distributions."""
          poly1a = gs.polygamma(1, param_a)
          poly2a = gs.polygamma(2, param_a)
          poly1b = gs.polygamma(1, param_b)
          poly2b = gs.polygamma(2, param_b)
          poly1ab = gs.polygamma(1, param_a + param_b)
          poly2ab = gs.polygamma(2, param_a + param_b)
          metric_det = 2 * (
              poly1a * poly1b - poly1ab * (poly1a + poly1b)
          )
  
          c1 = (
              poly2a * (poly1b - poly1ab) - poly1b * poly2ab
          ) / metric_det
          c2 = -poly1b * poly2ab / metric_det
          c3 = (poly2b * poly1ab - poly1b * poly2ab) / metric_det
          return c1, c2, c3
  
      param_a, param_b = base_point[..., 0], base_point[..., 1]
      c1, c2, c3 = coefficients(param_a, param_b)
      c4, c5, c6 = coefficients(param_b, param_a)
      vector_0 = gs.stack([c1, c2, c3], axis=-1)
      vector_1 = gs.stack([c6, c5, c4], axis=-1)
      gamma_0 = SymmetricMatrices.matrix_representation(vector_0)
      gamma_1 = SymmetricMatrices.matrix_representation(vector_1)
  
      return gs.stack([gamma_0, gamma_1], axis=-3)
  
file_path: geomstats/geomstats/test_cases/information_geometry/beta.py
imports: import pytest
  import geomstats.backend
  from geomstats.geometry.symmetric_matrices import SymmetricMatrices
  from geomstats.test_cases.information_geometry.dirichlet import DirichletDistributionsTestCase, DirichletMetricTestCase
label_desc: Use image node_id 3 for calling a global function with example usage: christoffels(base_point) and returns: gs, c1,  c2,  c3