Current File : //lib/python3/dist-packages/sympy/combinatorics/tests/test_schur_number.py
from sympy.core import S, Rational
from sympy.combinatorics.schur_number import schur_partition, SchurNumber
from sympy.testing.randtest 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 occurance 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}
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(6).lower_bound() == 364
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