code: def test_insufficient_bconditions():
      # Test cases when required number of boundary conditions
      # are not provided to solve the integration constants.
      L = symbols("L", positive=True)
      E, I, P, a3, a4 = symbols("E I P a3 a4")
  
      b = Beam(L, E, I, base_char="a")
      b.apply_load(R2, L, -1)
      b.apply_load(R1, 0, -1)
      b.apply_load(-P, L / 2, -1)
      b.solve_for_reaction_loads(R1, R2)
  
      p = b.slope()
      q = (
          P * SingularityFunction(x, 0, 2) / 4
          - P * SingularityFunction(x, L / 2, 2) / 2
          + P * SingularityFunction(x, L, 2) / 4
      )
      assert p == q / (E * I) + a3
  
      p = b.deflection()
      q = (
          P * SingularityFunction(x, 0, 3) / 12
          - P * SingularityFunction(x, L / 2, 3) / 6
          + P * SingularityFunction(x, L, 3) / 12
      )
      assert p == q / (E * I) + a3 * x + a4
  
      b.bc_deflection = [(0, 0)]
      p = b.deflection()
      q = (
          a3 * x
          + P * SingularityFunction(x, 0, 3) / 12
          - P * SingularityFunction(x, L / 2, 3) / 6
          + P * SingularityFunction(x, L, 3) / 12
      )
      assert p == q / (E * I)
  
      b.bc_deflection = [(0, 0), (L, 0)]
      p = b.deflection()
      q = (
          -(L**2) * P * x / 16
          + P * SingularityFunction(x, 0, 3) / 12
          - P * SingularityFunction(x, L / 2, 3) / 6
          + P * SingularityFunction(x, L, 3) / 12
      )
      assert p == q / (E * I)
  
imports: from sympy.core.function import expand
  from sympy.core.numbers import Rational, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol, symbols
  from sympy.sets.sets import Interval
  from sympy.simplify.simplify import simplify
  from sympy.physics.continuum_mechanics.beam import Beam
  from sympy.functions import SingularityFunction, Piecewise, meijerg, Abs, log
  from sympy.testing.pytest import raises
  from sympy.physics.units import meter, newton, kilo, giga, milli
  from sympy.physics.continuum_mechanics.beam import Beam3D
  from sympy.geometry import Circle, Polygon, Point2D, Triangle
  from sympy.core.sympify import sympify
label_desc: Use image node_id 2 for calling a global function with example usage: test_insufficient_bconditions() without return types