def test_sqrt235(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3) + sqrt(5)
r2 = r * r
r4 = r2 * r2
r6 = r2 * r4
r8 = r2 * r6
self.assertTrue(r > 0)
self.assertEqual(r8 - 40 * r6 + 352 * r4 - 960 * r2 + 576, 0)
def test_sqrt235(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3) + sqrt(5)
r2 = r*r
r4 = r2*r2
r6 = r2*r4
r8 = r2*r6
self.assertTrue(r > 0)
self.assertEqual(r8 - 40*r6 + 352*r4 - 960*r2 + 576, 0)
def test_sqrt2(self):
from constructible import sqrt
r = sqrt(2)
two = r*r
self.assertEqual(two, 2)
s = two._try_sqrt()
self.assertEqual(r, s)
def test_comparison_Qsqrt2(self):
''' test comparison operators on instances of Q[sqrt(2)] '''
from constructible import sqrt
from operator import eq, ne, gt, lt, ge, le
s = sqrt(2)
t = 3 - 2 * s
u = s - s
v = -t
self.assertTrue(s.field == t.field == u.field == v.field,
"Precondition")
# numbers is sorted ascending, so the comarison of numbers and therir indices must be same
numbers = [v, u, t, s]
self.assertTrue(s.field == t.field == u.field == v.field,
"Precondition")
for op in (eq, ne, gt, lt, ge, le):
with self.subTest(op=op):
for i, a in enumerate(numbers):
for j, b in enumerate(numbers):
result = op(a, b)
self.assertEqual(result, op(i, j))
self.assertIsInstance(result, bool)
def test_sqrt2(self):
from constructible import sqrt
r = sqrt(2)
two = r * r
self.assertEqual(two, 2)
s = two._try_sqrt()
self.assertEqual(r, s)
def test_sqrt_2(self):
from constructible import sqrt
r = sqrt(2)
self.assertEqual(r.a, 0)
self.assertEqual(r.b, 1)
self.assertEqual(len(r.field), 2)
self.assertEqual(r.field[0], 2)
self.assertEqual(str(r), 'sqrt(2)')
self.assertTrue(r > 0)
def test_sqrt_2(self):
from constructible import sqrt
r = sqrt(2)
self.assertEqual(r.a, 0)
self.assertEqual(r.b, 1)
self.assertEqual(len(r.field), 2)
self.assertEqual(r.field[0], 2)
self.assertEqual(str(r), 'sqrt(2)')
self.assertTrue(r > 0)
def test_equal(self):
'''
hash of multiple representations of the same value must be equal
'''
from constructible import sqrt
from fractions import Fraction as F
for a,b in [(sqrt(2), 2/sqrt(2)),
(sqrt(2), 1/sqrt(F(1,2))),
(sqrt(2) + sqrt(3), sqrt(3) + sqrt(2))]:
with self.subTest(a=a, b=b):
self.assertEqual(a,b, 'precondition for this test')
self.assertEqual(hash(a), hash(b), '%s == %s, but hash is different' % (a,b))
def test_equal(self):
'''
hash of multiple representations of the same value must be equal
'''
from constructible import sqrt
from fractions import Fraction as F
for a, b in [(sqrt(2), 2 / sqrt(2)), (sqrt(2), 1 / sqrt(F(1, 2))),
(sqrt(2) + sqrt(3), sqrt(3) + sqrt(2))]:
with self.subTest(a=a, b=b):
self.assertEqual(a, b, 'precondition for this test')
self.assertEqual(hash(a), hash(b),
'%s == %s, but hash is different' % (a, b))
def test_roots(self):
from constructible import sqrt
r = sqrt(17)
u = sqrt(2 * (17 - r))
v = sqrt(2 * (17 + r))
cos = (-1 + r + u + 2*sqrt(17 + 3*r - u - 2*v)) / 16
sin = sqrt(1 - cos*cos)
s_i = 0
c_i = 1
for i in range(17):
s = sin * c_i + cos * s_i
c = cos * c_i - sin * s_i
self.assertEqual(s*s + c*c, 1, "radius not equal to 1 at i=%d" % i)
s_i = s
c_i = c
self.assertEqual(s_i, 0)
self.assertEqual(c_i, 1)
def test_roots(self):
from constructible import sqrt
r = sqrt(17)
u = sqrt(2 * (17 - r))
v = sqrt(2 * (17 + r))
cos = (-1 + r + u + 2 * sqrt(17 + 3 * r - u - 2 * v)) / 16
sin = sqrt(1 - cos * cos)
s_i = 0
c_i = 1
for i in range(17):
s = sin * c_i + cos * s_i
c = cos * c_i - sin * s_i
self.assertEqual(s * s + c * c, 1,
"radius not equal to 1 at i=%d" % i)
s_i = s
c_i = c
self.assertEqual(s_i, 0)
self.assertEqual(c_i, 1)
def test_expressions_type(self):
from constructible import sqrt, Constructible
s = sqrt(2)
self.assertIsInstance(s, Constructible)
self.assertIsInstance(2 * s, Constructible)
self.assertIsInstance(2 - s, Constructible)
t = 3 - 2 * s
self.assertIsInstance(t, Constructible)
u = s - s
self.assertIsInstance(u, Constructible)
v = -t
self.assertIsInstance(v, Constructible)
def test_expressions_type(self):
from constructible import sqrt, Constructible
s = sqrt(2)
self.assertIsInstance(s, Constructible)
self.assertIsInstance(2 * s, Constructible)
self.assertIsInstance(2 - s, Constructible)
t = 3 - 2 * s
self.assertIsInstance(t, Constructible)
u = s - s
self.assertIsInstance(u, Constructible)
v = -t
self.assertIsInstance(v, Constructible)
def test_degree(self):
''' test that `a.minpoly()` has a certain degree '''
from constructible import sqrt, Constructible
from fractions import Fraction as F
def deg(num):
assert isinstance(num, Constructible)
value = 0
while num.field:
if num.b != 0:
value += 1
num = num.a
return 2**value
for a in [
sqrt(2), 2 / sqrt(5), 1 / sqrt(F(1, 2)),
sqrt(2) + sqrt(3), (sqrt(3) + sqrt(2)) - sqrt(3)
]:
with self.subTest(a=a):
self.assertEqual(
len(a.minpoly()) - 1, deg(a),
'minpoly of %s has the wrong degree' % (a, ))
def test_substitution(self):
''' test that `a` substituted to `a.minpoly()` gives 0 '''
from constructible import sqrt
from fractions import Fraction as F
def eval(poly, arg):
value = 0
for coef in reversed(poly):
value = coef + value * arg
return value
for a in [
sqrt(2), 2 / sqrt(5), 1 / sqrt(F(1, 2)),
sqrt(2) + sqrt(3),
sqrt(3) + sqrt(2)
]:
with self.subTest(a=a):
self.assertEqual(eval(a.minpoly(), a), 0,
'%s is not a root of its minpoly' % (a, ))
def test_comparison_Qsqrt2(self):
''' test comparison operators on instances of Q[sqrt(2)] '''
from constructible import sqrt
from operator import eq, ne, gt, lt, ge, le
s = sqrt(2)
t = 3 - 2 * s
u = s - s
v = -t
self.assertTrue(s.field == t.field == u.field == v.field, "Precondition")
# numbers is sorted ascending, so the comarison of numbers and therir indices must be same
numbers = [v, u, t, s]
self.assertTrue(s.field == t.field == u.field == v.field, "Precondition")
for op in (eq, ne, gt, lt, ge, le):
with self.subTest(op=op):
for i, a in enumerate(numbers):
for j, b in enumerate(numbers):
result = op(a, b)
self.assertEqual(result, op(i, j))
self.assertIsInstance(result, bool)
def test_sqrt_square(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3) + sqrt(5)
self.assertEqual(sqrt(r * r), r)
def test_sqrt623(self):
from constructible import sqrt
r = sqrt(6) / sqrt(3)
self.assertTrue(r > 0)
self.assertEqual(r, sqrt(2))
def test_sqrt23(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3)
self.assertTrue(r > 0)
self.assertEqual(r * r * r * r - 10 * r * r + 1, 0)
def test_double_sqrt(self):
from constructible import sqrt
r = sqrt(2)
s = sqrt(r)
self.assertEqual(str(s), 'sqrt(sqrt(2))')
def test_double_sqrt(self):
from constructible import sqrt
r = sqrt(2)
s = sqrt(r)
self.assertEqual(str(s), 'sqrt(sqrt(2))')
def test_sqrt23(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3)
self.assertTrue(r > 0)
self.assertEqual(r*r*r*r - 10*r*r + 1, 0)
def test_sqrt623(self):
from constructible import sqrt
r = sqrt(6) / sqrt(3)
self.assertTrue(r > 0)
self.assertEqual(r, sqrt(2))
def test_sqrt_square(self):
from constructible import sqrt
r = sqrt(2) + sqrt(3) + sqrt(5)
self.assertEqual(sqrt(r*r), r)