code: def test_integer_partition():
      # no zeros in partition
      raises(ValueError, lambda: IntegerPartition(list(range(3))))
      # check fails since 1 + 2 != 100
      raises(
          ValueError, lambda: IntegerPartition(100, list(range(1, 3)))
      )
      a = IntegerPartition(8, [1, 3, 4])
      b = a.next_lex()
      c = IntegerPartition([1, 3, 4])
      d = IntegerPartition(8, {1: 3, 3: 1, 2: 1})
      assert a == c
      assert a.integer == d.integer
      assert a.conjugate == [3, 2, 2, 1]
      assert (a == b) is False
      assert a <= b
      assert (a > b) is False
      assert a != b
  
      for i in range(1, 11):
          next = set()
          prev = set()
          a = IntegerPartition([i])
          ans = {IntegerPartition(p) for p in partitions(i)}
          n = len(ans)
          for j in range(n):
              next.add(a)
              a = a.next_lex()
              IntegerPartition(i, a.partition)  # check it by giving i
          for j in range(n):
              prev.add(a)
              a = a.prev_lex()
              IntegerPartition(i, a.partition)  # check it by giving i
          assert next == ans
          assert prev == ans
  
      assert IntegerPartition([1, 2, 3]).as_ferrers() == "###\n##\n#"
      assert IntegerPartition([1, 1, 3]).as_ferrers("o") == "ooo\no\no"
      assert str(IntegerPartition([1, 1, 3])) == "[3, 1, 1]"
      assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1]
  
      raises(ValueError, lambda: random_integer_partition(-1))
      assert random_integer_partition(1) == [1]
      assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1]) == [
          5,
          2,
          1,
          1,
          1,
      ]
  
file_path: sympy/sympy/combinatorics/tests/test_partitions.py
imports: from sympy.core.sorting import ordered, default_sort_key
  from sympy.combinatorics.partitions import Partition, IntegerPartition, RGS_enum, RGS_unrank, RGS_rank, random_integer_partition
  from sympy.testing.pytest import raises
  from sympy.utilities.iterables import partitions
  from sympy.sets.sets import Set, FiniteSet
label_desc: Use image node_id 3 for calling a global function with example usage: test_integer_partition() without return types