def test_divmod_brute_force(self):
a=EisensteinInt(3,1) # 3 + w
b=EisensteinInt(2, -1) # 3 + w**2
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = d.divmod_brute_force(a)
self.assertTrue(q == b)
self.assertTrue(r1 == r2)
def test_gt_and_lt(self):
a = EisensteinInt(2,0)
b = EisensteinInt(1,0)
self.assertTrue(a > b)
self.assertTrue(b < a)
a = EisensteinInt(-3,-4)
b = EisensteinInt(1,-1)
self.assertTrue(a > b)
self.assertTrue(b < a)
def test_is_even(self):
# Even iff. norm congruent to 0 mod 3
# Not even iff. norm congruent to 1 mod 3
self.assertTrue(EisensteinInt(1,-1).is_even())
self.assertTrue(EisensteinInt(1,-1).norm() % 3 == 0)
self.assertFalse(EisensteinInt(5,2).is_even())
self.assertTrue(EisensteinInt(5,2).norm() % 3 == 1)
self.assertFalse(EisensteinInt(5,8).is_even())
def test_is_prime(self):
# Test whether a number is an Eisenstein prime
self.assertTrue(EisensteinInt(1,-1).is_prime())
self.assertTrue(EisensteinInt(2,0).is_prime())
self.assertTrue(EisensteinInt(2,1).is_prime())
self.assertTrue(EisensteinInt(1,2).is_prime())
self.assertTrue(EisensteinInt(-2,-1).is_prime())
self.assertTrue(EisensteinInt(-3,1).is_prime())
self.assertFalse(EisensteinInt(-2,-2).is_prime())
self.assertFalse(EisensteinInt(1,0).is_prime())
self.assertFalse(EisensteinInt(3,0).is_prime())
self.assertFalse(EisensteinInt(7,0).is_prime())
def test_floor_div_identity(self):
a=EisensteinInt(1,-1)
self.assertEqual(a // a, EisensteinInt(1))
a=EisensteinInt(1,10)
self.assertEqual(a // a, EisensteinInt(1))
a=EisensteinInt(-2,-4)
self.assertEqual(a // a, EisensteinInt(1))
a=EisensteinInt(-5,1)
self.assertEqual(a // a, EisensteinInt(1))
def test_norm_for_units(self):
# Norm of units are 1
self.assertEqual(EisensteinInt(1,0).norm(), 1)
self.assertEqual(EisensteinInt(-1,0).norm(), 1)
self.assertEqual(EisensteinInt(0,1).norm(), 1)
self.assertEqual(EisensteinInt(0,-1).norm(), 1)
self.assertEqual(EisensteinInt(-1,-1).norm(), 1)
self.assertEqual(EisensteinInt(1,1).norm(), 1)
self.assertEqual(EisensteinInt(-2,-2).norm(), 4)
self.assertEqual(EisensteinInt(1,-1).norm(), 3)
def test_norm_and_conjugate(self):
# a * a.conjugate = norm(a)
a = EisensteinInt(3,1)
aa = a * a.conjugate()
norm = a.norm()
self.assertTrue(aa.real == norm)
a = EisensteinInt(13,-21)
aa = a * a.conjugate()
norm = a.norm()
self.assertTrue(aa.real == norm)
def test_associates(self):
associates = EisensteinInt(2,1).associates()
self.assertEqual(EisensteinInt(2,1), associates[0])
self.assertEqual(EisensteinInt(1,2), associates[1])
self.assertEqual(EisensteinInt(-1,1), associates[2])
self.assertEqual(EisensteinInt(-2,-1), associates[3])
self.assertEqual(EisensteinInt(-1,-2), associates[4])
self.assertEqual(EisensteinInt(1,-1), associates[5])
def test_units(self):
# Test that units are generated
units = EisensteinInt.units()
self.assertEqual(EisensteinInt(1,0), units[0])
self.assertEqual(EisensteinInt(1,1), units[1])
self.assertEqual(EisensteinInt(0,1), units[2])
self.assertEqual(EisensteinInt(-1,0), units[3])
self.assertEqual(EisensteinInt(-1,-1), units[4])
self.assertEqual(EisensteinInt(0,-1), units[5])
def test_mult(self):
self.assertEqual(EisensteinInt(1,0) * EisensteinInt(1,0), EisensteinInt(1,0))
self.assertEqual(EisensteinInt(10,0) * EisensteinInt(-1,0), EisensteinInt(-10,0))
self.assertEqual(EisensteinInt(3,1) * EisensteinInt(2,-1), EisensteinInt(7,0))
def test_sub(self):
self.assertEqual(EisensteinInt(1,0) - EisensteinInt(1,0), EisensteinInt(0,0))
self.assertEqual(EisensteinInt(1,-1) - EisensteinInt(1,-1), EisensteinInt(0,0))
self.assertEqual(EisensteinInt(10,-1) - EisensteinInt(1,12), EisensteinInt(9,-13))
self.assertEqual(EisensteinInt(5,-1) - EisensteinInt(10,-10), EisensteinInt(-5,9))
def test_conjugate_is_prime(self):
self.assertTrue(EisensteinInt(-3,1).is_prime())
self.assertTrue(EisensteinInt(-3,1).conjugate().is_prime())
self.assertTrue(EisensteinInt(1,-1).is_prime())
self.assertTrue(EisensteinInt(1,-1).conjugate().is_prime())
def test_norm_multiplicative(self):
# Norm(a)*Norm(b)=Norm(a*b)
a = EisensteinInt(-2,4)
b = EisensteinInt(1,3)
self.assertEqual((a * b).norm(), a.norm() *b.norm())
def test_floor_div_ints(self):
a=EisensteinInt(10,0)
b=EisensteinInt(7,0)
self.assertEqual(a // b , EisensteinInt(1,0))
a=EisensteinInt(17,0)
b=EisensteinInt(9,0)
self.assertEqual(a // b , EisensteinInt(2,0))
a=EisensteinInt(10,0)
b=EisensteinInt(5,0)
self.assertEqual(a // b, EisensteinInt(2,0))
a=EisensteinInt(20,0)
b=EisensteinInt(-10,0)
self.assertEqual(a // b , EisensteinInt(-2,0))
a=EisensteinInt(-20,0)
b=EisensteinInt(-10,0)
self.assertEqual(a // b , EisensteinInt(2,0))
a=EisensteinInt(-20,0)
b=EisensteinInt(10,0)
self.assertEqual(a // b , EisensteinInt(-2,0))
def test_conjugate(self):
self.assertEqual(EisensteinInt(0,1).conjugate(), EisensteinInt(-1,-1))
self.assertEqual(EisensteinInt(1,0).conjugate(), EisensteinInt(1,0))
self.assertEqual(EisensteinInt(3,1).conjugate(), EisensteinInt(2,-1))
def test_add(self):
self.assertEqual(EisensteinInt(1,0) + EisensteinInt(1,0), EisensteinInt(2,0))
self.assertEqual(EisensteinInt(1,-1) + EisensteinInt(1,-1), EisensteinInt(2,-2))
def test_gcd(self):
p=EisensteinInt(3,1)
q=EisensteinInt(1,-1)
r=EisensteinInt(2,-1)
assert(p.is_prime())
assert(q.is_prime())
assert(r.is_prime())
a=p*q
b=p*r
self.assertEqual(a.gcd(b).canonical(),p.canonical())
p=EisensteinInt(-4,-1)
q=EisensteinInt(2,0)
r=EisensteinInt(6,1)
assert(p.is_prime())
assert(q.is_prime())
assert(r.is_prime())
a=p*q
b=p*r
self.assertEqual(a.gcd(b).canonical(),p.canonical())
p=EisensteinInt(3,2)
q=EisensteinInt(-1,3)
r=EisensteinInt(9,1)
assert(p.is_prime())
assert(q.is_prime())
assert(r.is_prime())
a=p*q
b=p*r
self.assertEqual(a.gcd(b).canonical(),p.canonical())
def test_complex_to_eisenstein(self):
a = EisensteinInt(3,5)
c = a.complex_form()
e = EisensteinInt.eisenstein_form(c)
self.assertEqual(a,e)
a = EisensteinInt(-3,-2)
c = a.complex_form()
e = EisensteinInt.eisenstein_form(c)
self.assertEqual(a,e)
a = EisensteinInt(-2,3)
c = a.complex_form()
e = EisensteinInt.eisenstein_form(c)
self.assertEqual(a,e)
a = EisensteinInt(2,-5)
c = a.complex_form()
e = EisensteinInt.eisenstein_form(c)
self.assertEqual(a,e)
def test_str(self):
self.assertEqual(str(EisensteinInt(1,0)), "1")
self.assertEqual(str(EisensteinInt(0,0)), "0")
self.assertEqual(str(EisensteinInt(1,1)), "1 + ω")
self.assertEqual(str(EisensteinInt(1,-1)), "1 - ω")
self.assertEqual(str(EisensteinInt(1,-2)), "1 - 2ω")
self.assertEqual(str(EisensteinInt(-1,-2)), "-1 - 2ω")
self.assertEqual(str(EisensteinInt(-1,2)), "-1 + 2ω")
self.assertEqual(str(EisensteinInt(0, 1)), "ω")
self.assertEqual(str(EisensteinInt(1,2)), "1 + 2ω")
self.assertEqual(str(EisensteinInt(2,0)), "2")
self.assertEqual(str(EisensteinInt(-2,0)), "-2")
def test_floor_div(self):
a=EisensteinInt(8,0)
b=EisensteinInt(3,1)
self.assertEqual(a // b , EisensteinInt(2,-1))
def test_divmod(self):
a=EisensteinInt(3,1) # 3 + w
b=EisensteinInt(2, -1) # 3 + w**2
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(q == b)
self.assertTrue(r1 == r2)
a=EisensteinInt(3,21)
b=EisensteinInt(-34, -1)
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(r1 == r2)
self.assertTrue(q == b)
a=EisensteinInt(-3,21)
b=EisensteinInt(-5, -1)
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(r1 == r2)
self.assertTrue(q == b)
a=EisensteinInt(19,2)
b=EisensteinInt(3, -2)
r1=EisensteinInt(2,1)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(q == b)
self.assertTrue(r1 == r2)
a=EisensteinInt(-1,-3)
b=EisensteinInt(-5, -1)
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(q == b)
self.assertTrue(r1 == r2)
a=EisensteinInt(-3,21)
b=EisensteinInt(5, -1)
r1=EisensteinInt(1,0)
d=(a*b)+r1
q,r2 = divmod(d, a)
self.assertTrue(r1 == r2)
self.assertTrue(q == b)
from eisenstein import EisensteinInt a = EisensteinInt(-2, -2) a.plot_point(file_name="./plots/1") a.plot_multiples(n=1, file_name="./plots/1-1") a = EisensteinInt(-2, 5) a.plot_point(file_name="./plots/2") a.plot_multiples(n=2, file_name="./plots/2-1") a = EisensteinInt(1, -2) a.plot_point(file_name="./plots/3") a.plot_multiples(n=3, file_name="./plots/3-1") a = EisensteinInt(1, 0) a.plot_point(file_name="./plots/4") a.plot_multiples(n=10, labels=False, file_name="./plots/4-1") a = EisensteinInt(2, 19) a.plot_point(file_name="./plots/5") a.plot_multiples(n=15, labels=False, file_name="./plots/5-1") EisensteinInt.plot_all(n=1, primes=True, file_name="./plots/6-1") EisensteinInt.plot_all(n=2, primes=True, file_name="./plots/6-2") EisensteinInt.plot_all(n=3, primes=True, file_name="./plots/6-3") EisensteinInt.plot_all(n=4, primes=True, file_name="./plots/6-4")
def test_gcd_ints(self):
a=EisensteinInt(12,0)
b=EisensteinInt(6,0)
self.assertEqual(a.gcd(b).canonical(), EisensteinInt(6,0).canonical())
a=EisensteinInt(20,0)
b=EisensteinInt(12,0)
self.assertEqual(a.gcd(b).canonical(), EisensteinInt(-4,0).canonical())
a=EisensteinInt(5,0)
b=EisensteinInt(7,0)
self.assertEqual(a.gcd(b).canonical(), EisensteinInt(1,0).canonical())