code: def test_basic(self):
      j1 = SingletonInt(1, coeff=1)
      j1_copy = SingletonInt(1, coeff=1)
      j2 = SingletonInt(2, coeff=1)
      j1x2 = SingletonInt(1, coeff=2)
  
      def test_eq(a, b, expected):
          self.assertEqual(sympy.Eq(a, b), expected)
          self.assertEqual(sympy.Ne(b, a), not expected)
  
      # eq, ne
      test_eq(j1, j1, True)
      test_eq(j1, j1_copy, True)
      test_eq(j1, j2, False)
      test_eq(j1, j1x2, False)
      test_eq(j1, sympy.Integer(1), False)
      test_eq(j1, sympy.Integer(3), False)
  
      def test_ineq(a, b, expected, *, strict=True):
          greater = (sympy.Gt, is_gt) if strict else (sympy.Ge, is_ge)
          less = (sympy.Lt, is_lt) if strict else (sympy.Le, is_le)
  
          if isinstance(expected, bool):
              # expected is always True
              for fn in greater:
                  self.assertEqual(fn(a, b), expected)
                  self.assertEqual(fn(b, a), not expected)
              for fn in less:
                  self.assertEqual(fn(b, a), expected)
                  self.assertEqual(fn(a, b), not expected)
          else:
              for fn in greater:
                  with self.assertRaisesRegex(ValueError, expected):
                      fn(a, b)
              for fn in less:
                  with self.assertRaisesRegex(ValueError, expected):
                      fn(b, a)
  
      # ge, le, gt, lt
      for strict in (True, False):
          _test_ineq = functools.partial(test_ineq, strict=strict)
          _test_ineq(j1, sympy.Integer(0), True)
          _test_ineq(j1, sympy.Integer(3), "indeterminate")
          _test_ineq(j1, j2, "indeterminate")
          _test_ineq(j1x2, j1, True)
  
      # Special cases for ge, le, gt, lt:
      for ge in (sympy.Ge, is_ge):
          self.assertTrue(ge(j1, j1))
          self.assertTrue(ge(j1, sympy.Integer(2)))
          with self.assertRaisesRegex(ValueError, "indeterminate"):
              ge(sympy.Integer(2), j1)
      for le in (sympy.Le, is_le):
          self.assertTrue(le(j1, j1))
          self.assertTrue(le(sympy.Integer(2), j1))
          with self.assertRaisesRegex(ValueError, "indeterminate"):
              le(j1, sympy.Integer(2))
  
      for gt in (sympy.Gt, is_gt):
          self.assertFalse(gt(j1, j1))
          self.assertFalse(gt(sympy.Integer(2), j1))
          # it is only known to be that j1 >= 2, j1 > 2 is indeterminate
          with self.assertRaisesRegex(ValueError, "indeterminate"):
              gt(j1, sympy.Integer(2))
  
      for lt in (sympy.Lt, is_lt):
          self.assertFalse(lt(j1, j1))
          self.assertFalse(lt(j1, sympy.Integer(2)))
          with self.assertRaisesRegex(ValueError, "indeterminate"):
              lt(sympy.Integer(2), j1)
  
      # mul
      self.assertEqual(j1 * 2, j1x2)
      # Unfortunately, this doesn't not automatically simplify to 2*j1
      # since sympy.Mul doesn't trigger __mul__ unlike the above.
      self.assertIsInstance(sympy.Mul(j1, 2), sympy.core.mul.Mul)
  
      with self.assertRaisesRegex(ValueError, "cannot be multiplied"):
          j1 * j2
  
      self.assertEqual(j1.free_symbols, set())
  
imports: import itertools
  import sys
  import sympy
  from typing import Callable, List, Tuple, Type
  from torch.testing._internal.common_device_type import skipIf
  from torch.testing._internal.common_utils import TEST_Z3, instantiate_parametrized_tests, parametrize, run_tests, TestCase
  from torch.utils._sympy.functions import FloorDiv
  from torch.utils._sympy.solve import INEQUALITY_TYPES, mirror_rel_op, try_solve
  from torch.utils._sympy.value_ranges import ValueRangeAnalysis, ValueRanges
  from torch.utils._sympy.reference import ReferenceAnalysis, PythonReferenceAnalysis
  from torch.utils._sympy.interp import sympy_interp
  from torch.utils._sympy.singleton_int import SingletonInt
  from sympy.core.relational import is_ge, is_le, is_gt, is_lt
  import functools
  import torch.fx
label_desc: Use image node_id 1 for calling the TestSingletonInt obj's underlying member method code with example usage: obj.test_basic() without return types