def _question(self):
d = self.difficulty
if d == 1:
# Positive integer solution
a = r_int(5, '+')
b = r_int(10, '-') * a
left_side = '{a}*x+{b}'.format(a=a, b=b)
right_side = '0'
elif d == 2:
# Real solution/no solution/infinite solutions
a = r_int(10, '-+0', weights={0: 2})
b = r_int(10, '-+0', weights={0: 4})
left_side = '{a}*x+{b}'.format(a=a, b=b)
right_side = '0'
else:
# Real solution/no solution/infinite solutions, any number of terms.
left_side, right_side = self._hard_diff_left_and_right(
x_terms=self.x_terms, non_x_terms=self.non_x_terms)
# Add '0' if the side is empty.
left_side = left_side or '0'
right_side = right_side or '0'
final_string = '='.join([left_side, right_side])
final_string = final_string.replace('+-', '-')
return final_string.replace('x', self.var_name)
def test_0_excluded(self):
s = set()
small_n = 1
# Odds of missing the bug for enough reps is extremely small
# (about 10e-200 for 1k reps)
for _ in range(REPETITIONS):
s.update({
r_int(small_n, '+'),
r_int(small_n, '-'),
r_int(small_n, '-+'),
})
self.assertNotIn(0, s)
def test_0_included(self):
s = set()
small_n = 1
# Odds of missing the bug for enough reps is extremely small
# (about 10e-200 for 1k reps)
for _ in range(10 * 4):
s.update({
r_int(small_n, '+0'),
r_int(small_n, '-0'),
r_int(small_n, '-0+'),
r_int(small_n, )
})
self.assertIn(0, s)
def test_weight_effect_on_odds(self):
nums_lst = []
weight_1 = 3
for _ in range(REPETITIONS):
nums_lst.append(r_int((0, 2), weights={1: weight_1}))
ratio_1 = nums_lst.count(1) / len(nums_lst)
weight_ratio_1 = weight_1 / (1 + weight_1 + 1)
self.assertAlmostEqual(weight_ratio_1, ratio_1, delta=.01)
def _non_x_terms_strings(non_x_terms):
return [str(r_int(10, '-+')) for _ in range(non_x_terms)]
def _x_terms_strings(x_terms):
return ['{}*x'.format(r_int(10, '-+')) for _ in range(x_terms)]
def test_weight_of_negative_or_0_doesnt_raise(self):
self.assertIsNotNone(r_int((-1, 2), weights={-1: 4, 0: 4}))
def test_0bound_exactly_0(self):
self.assertEquals(r_int(0), 0)
def test_excluded(self):
for _ in range(REPETITIONS):
bound = 3
excluded_n = randint(-bound, bound)
self.assertNotEqual(excluded_n, r_int(bound,
excluded={excluded_n}))
def test_only_positives(self):
for _ in range(REPETITIONS):
self.assertGreater(r_int(100, '+'), 0)
def test_only_negatives(self):
for _ in range(REPETITIONS):
self.assertLess(r_int(100, '-'), 0)
def test_within_lower_bound(self):
for _ in range(REPETITIONS):
bound = randint(0, 100)
self.assertGreaterEqual(r_int(bound), -bound)
def test_within_upper_bound(self):
for _ in range(REPETITIONS):
bound = randint(0, 100)
self.assertLessEqual(r_int(bound), bound)
def test_is_int(self):
self.assertTrue(isinstance(r_int(10000), int))
def test_XX_bounds_exactly_X(self):
self.assertEquals(r_int((4, 4)), 4)