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- from sympy.core import S, Rational
- from sympy.combinatorics.schur_number import schur_partition, SchurNumber
- from sympy.core.random import _randint
- from sympy.testing.pytest import raises
- from sympy.core.symbol import symbols
- def _sum_free_test(subset):
- """
- Checks if subset is sum-free(There are no x,y,z in the subset such that
- x + y = z)
- """
- for i in subset:
- for j in subset:
- assert (i + j in subset) is False
- def test_schur_partition():
- raises(ValueError, lambda: schur_partition(S.Infinity))
- raises(ValueError, lambda: schur_partition(-1))
- raises(ValueError, lambda: schur_partition(0))
- assert schur_partition(2) == [[1, 2]]
- random_number_generator = _randint(1000)
- for _ in range(5):
- n = random_number_generator(1, 1000)
- result = schur_partition(n)
- t = 0
- numbers = []
- for item in result:
- _sum_free_test(item)
- """
- Checks if the occurrence of all numbers is exactly one
- """
- t += len(item)
- for l in item:
- assert (l in numbers) is False
- numbers.append(l)
- assert n == t
- x = symbols("x")
- raises(ValueError, lambda: schur_partition(x))
- def test_schur_number():
- first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160}
- for k in first_known_schur_numbers:
- assert SchurNumber(k) == first_known_schur_numbers[k]
- assert SchurNumber(S.Infinity) == S.Infinity
- assert SchurNumber(0) == 0
- raises(ValueError, lambda: SchurNumber(0.5))
- n = symbols("n")
- assert SchurNumber(n).lower_bound() == 3**n/2 - Rational(1, 2)
- assert SchurNumber(8).lower_bound() == 5039
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