code: def jac_rational_sparse(t, y):
      return csc_matrix(
          [
              [0, 1 / t],
              [
                  -2 * y[1] ** 2 / (t * (y[0] - 1) ** 2),
                  (y[0] + 4 * y[1] - 1) / (t * (y[0] - 1)),
              ],
          ]
      )
  
imports: from itertools import product
  from numpy.testing import assert_, assert_allclose, assert_equal, assert_no_warnings, suppress_warnings
  import pytest
  from pytest import raises
  import numpy
  from scipy.optimize._numdiff import group_columns
  from scipy.integrate import solve_ivp, RK23, RK45, DOP853, Radau, BDF, LSODA
  from scipy.integrate import OdeSolution
  from scipy.integrate._ivp.common import num_jac
  from scipy.integrate._ivp.base import ConstantDenseOutput
  from scipy.sparse import coo_matrix, csc_matrix
label_desc: Use image node_id 8 for calling a global function with example usage: jac_rational_sparse(t, y) and returns: csc_matrix