def test_division_by_integer(self):
a = EisensteinFraction(four=(1, 1, -3, 2)) / 2
self.assertEqual(a, EisensteinFraction(four=(1, 2, -3, 4)))
b = Eisenstein(2, 0) // 2
self.assertEqual(b, EisensteinFraction(four=(1, 1, 0, 1)))
c = Eisenstein(4, 0) // 2
self.assertEqual(c, EisensteinFraction(four=(2, 1, 0, 1)))
def test_both_div_and_modulo(self):
a = Eisenstein(4, 1)
b = Eisenstein(3, 1)
c = Eisenstein(2, 1)
d = a * b + c
e, f = d.div_mod(a)
self.assertEqual(e, Eisenstein(3, 1))
self.assertEqual(f, Eisenstein(7, 2))
def test_multiplication_by_integer(self):
a = 2 * EisensteinFraction(four=(1, 1, -3, 2))
self.assertEqual(a, EisensteinFraction(four=(2, 1, -6, 2)))
b = 2 * Eisenstein(2, 0)
self.assertEqual(b, EisensteinFraction(four=(4, 1, 0, 1)))
a = EisensteinFraction(four=(1, 1, -3, 2)) * 2
self.assertEqual(a, EisensteinFraction(four=(2, 1, -6, 2)))
b = Eisenstein(2, 0) * 2
self.assertEqual(b, EisensteinFraction(four=(4, 1, 0, 1)))
def test_comparison(self):
a = EisensteinFraction(Eisenstein(1, 2))
b = EisensteinFraction(1, 2)
self.assertEqual(a == b, True)
a = Eisenstein(1, 2)
b = EisensteinFraction(1, 2)
self.assertEqual(a == b, True)
self.assertEqual(b == a, True)
def test_substraction_values(self):
"""
TestEisensteinNumbers:
wolframalfa.com
w = ( -1 + i sqrt(3) ) / 2 ; c = ( 1 + 2 w ) - ( 2 + 4 w )
result: -1 - 2w
"""
a = Eisenstein(1, 2)
b = Eisenstein(2, 4)
c = a - b
self.assertEqual(c, Eisenstein(-1, -2))
def test_add_values(self):
# 2 + 2 = 4
a = EisensteinFraction(Fraction(4, 2))
b = EisensteinFraction(Fraction(6, 3))
c = a + b
self.assertEqual(c, EisensteinFraction(four=(4, 1, 0, 1)))
a = EisensteinFraction(Fraction(1, 2))
b = EisensteinFraction(Fraction(1, 4))
c = a + b
self.assertEqual(c, EisensteinFraction(four=(3, 4, 0, 1)))
a = EisensteinFraction(Eisenstein(1, 1))
b = EisensteinFraction(Eisenstein(1, -1))
c = a + b
self.assertEqual(c, EisensteinFraction(Eisenstein(2, 0)))
def test_multiplication(self):
"""
TestEisensteinFractionNumbers:
wolframalfa.com
query: w = ( -1 + i sqrt(3) ) / 2 ; c = ( 1 + 2 w ) * ( 2 + 4 w )
answer: c = -6
"""
a = EisensteinFraction(Fraction(1, 2))
b = EisensteinFraction(2)
c = a * b
self.assertEqual(c, Eisenstein(1))
a = EisensteinFraction(Eisenstein(2, 1))
b = EisensteinFraction(Fraction(1, 2))
c = a * b
self.assertEqual(c, EisensteinFraction(1, Fraction(1, 2)))
def ceil(self) -> Eisenstein:
"""
See clarification in floor comment.
:param var: Eisenstein Fraction
:return: Floor in Eisenstein Sense
"""
return Eisenstein(int(ceil(self.co_real)), int(ceil(self.co_omega)))
def test_gcd(self):
"""
TestEisensteinNumbers:
"""
a = Eisenstein(2, 0)
b = Eisenstein(2, 0)
self.assertEqual(gcd(a, b), Eisenstein(2, 0))
a = Eisenstein(2, 0)
b = Eisenstein(4, 0)
self.assertEqual(gcd(a, b), Eisenstein(2, 0))
a = Eisenstein(2, 1)
b = Eisenstein(4, 2)
self.assertEqual(gcd(a, b), Eisenstein(2, 1))
def ceil2(self) -> Eisenstein:
"""
Euclidean domain
https://en.wikipedia.org/wiki/Eisenstein_integer
:return:
"""
return Eisenstein(
int(ceil(self.co_real + self.co_omega / SQRT_THREE)),
int(ceil(2 * self.co_omega / SQRT_THREE)),
)
def test_div_mod(self):
obj_a = Eisenstein(2, 3)
obj_b = Eisenstein(1, 0)
obj_c = 2
# self.assertEqual(obj_a / obj_b, Eisenstein(2, 3)) Not allowed!
self.assertEqual(obj_a // obj_b, Eisenstein(2, 3))
self.assertEqual(obj_a // obj_c, Eisenstein(1, 1))
obj_a = Eisenstein(4, 8)
obj_b = Eisenstein(2, 2)
obj_c = 2
# self.assertEqual(obj_a / obj_b, Eisenstein(4, 2)) Not allowed!
self.assertEqual(obj_a // obj_b, Eisenstein(4, 2))
self.assertEqual(obj_a // obj_c, Eisenstein(2, 4))
def floor(self) -> Eisenstein:
"""
Floor is not defined well
google: floor complex number
answer1: https://math.stackexchange.com/questions/2095674/floor-function-in-complex-plane
answer2: https://math.stackexchange.com/questions/1764832/what-is-lfloor-i-rfloor
Little unceranity, mess, etc.
This is another example. First, we define Numbers then Fractions, then Floor and rest of stuff
:param var: Eisenstein Fraction
:return: Floor in Eisenstein Sense
"""
return Eisenstein(int(self.co_real), int(self.co_omega))
def test_another_add_values(self):
a = EisensteinFraction(four=(1, 2, 3, 4))
b = EisensteinFraction(four=(1, 3, 3, 4))
c = a + b
self.assertEqual(str(c), "EisensteinFraction(four=(5, 6, 3, 2))")
a = EisensteinFraction(four=(1, 2, 3, 4))
c = a + 2
self.assertEqual(str(c), "EisensteinFraction(four=(5, 2, 3, 4))")
a = EisensteinFraction(four=(1, 2, 3, 4))
c = a + Eisenstein(2)
self.assertEqual(str(c), "EisensteinFraction(four=(5, 2, 3, 4))")
def test_true_div(self):
"""
This code is to better understand meaning of eisenstein division
:return:
"""
selfy = Eisenstein(1, 2)
other = 2
a = selfy.co_real
b = selfy.co_omega
if type(other) is int:
g = a / other
h = b / other
else:
c = other.co_real
d = other.co_omega
bottom = other.get_norm
e = a * c + b * d - a * d
f = b * c - a * d
g = e / bottom
h = f / bottom
result = Eisenstein(int(g), int(h))
self.assertEqual(result, selfy.__floordiv__(other))
def test_division(self):
"""
TestEisensteinFractionNumbers:
wolframalfa.com
query: w = ( -1 + i sqrt(3) ) / 2 ; a = ( 2 + 4 w ); b = ( 2 + 4 w ) ; c = a / b
answer: c = 1
"""
a = EisensteinFraction(Fraction(1, 2))
b = EisensteinFraction(Fraction(4, 2))
c = a / b
self.assertEqual(c, EisensteinFraction(four=(1, 4, 0, 1)))
a = EisensteinFraction(4)
b = EisensteinFraction(2)
c = a / b
self.assertEqual(c, EisensteinFraction(2))
a = EisensteinFraction(0, 2)
b = EisensteinFraction(0, 4)
self.assertEqual(a, EisensteinFraction(Eisenstein(0, 2)))
self.assertEqual(b, EisensteinFraction(Eisenstein(0, 4)))
c = a / b
self.assertEqual(c, EisensteinFraction(four=(1, 2, 0, 1)))
def test_norm(self):
a = Eisenstein(2, 0)
self.assertEqual(a.get_norm, 4)
a = Eisenstein(3, 0)
self.assertEqual(a.get_norm, 9)
a = Eisenstein(0, 5)
self.assertEqual(a.get_norm, 25)
a = Eisenstein(0, 7)
self.assertEqual(a.get_norm, 49)
a = Eisenstein(2, 3)
self.assertEqual(a.get_norm, 7)
a = Eisenstein(-2, -3)
self.assertEqual(a.get_norm, 7)
def test_floor_and_ceil(self):
a = EisensteinFraction(Fraction(1, 2), 2)
self.assertEqual(Eisenstein(0, 2), a.floor)
self.assertEqual(Eisenstein(1, 2), a.ceil)
a = EisensteinFraction(Fraction(1, 3), 2)
self.assertEqual(Eisenstein(0, 2), a.floor)
self.assertEqual(Eisenstein(1, 2), a.ceil)
a = EisensteinFraction(Fraction(3, 4), Fraction(3, 4))
self.assertEqual(Eisenstein(0, 0), a.floor)
self.assertEqual(Eisenstein(1, 1), a.ceil)
def test_types_mix(self):
"""
TestEisensteinFractionNumbers:
"""
# 2 + 2 = 4
a = EisensteinFraction(Fraction(4, 2))
b = EisensteinFraction(Fraction(6, 3))
c = a + b
self.assertEqual(c, EisensteinFraction(four=(4, 1, 0, 1)))
a = EisensteinFraction(Fraction(1, 2))
b = EisensteinFraction(Fraction(1, 4))
c = a + b
self.assertEqual(c, EisensteinFraction(four=(3, 4, 0, 1)))
a = EisensteinFraction(Eisenstein(1, 1))
b = EisensteinFraction(Fraction(1, 2))
c = a + b
self.assertEqual(c, EisensteinFraction(Fraction(3, 2), 1))
def test_add_values(self):
"""
TestEisensteinNumbers:
wolframalfa.com
query: w = ( -1 + i sqrt(3) ) / 2 ; c = ( 1 + 2w ) + ( 20 + 30w )
result: 32w + 21
"""
a = Eisenstein(1, 2)
b = Eisenstein(20, 30)
c = a + b
self.assertEqual(c, Eisenstein(21, 32))
a = Eisenstein(1, 2)
b = 1
c = a + b
self.assertEqual(c, Eisenstein(2, 2))
a = Eisenstein(1, 2)
b = 1
c = b + a
self.assertEqual(c, Eisenstein(2, 2))
def test_multiplication(self):
"""
TestEisensteinNumbers:
wolframalfa.com
query: w = ( -1 + i sqrt(3) ) / 2 ; c = ( 1 + 2 w ) * ( 2 + 4 w )
answer: c = -6
"""
a = Eisenstein(1, 2)
b = Eisenstein(2, 4)
c = a * b
self.assertEqual(c, Eisenstein(-6, 0))
a = Eisenstein(1, 2)
b = 2
c = a * b
self.assertEqual(c, Eisenstein(2, 4))
a = Eisenstein(1, 2)
b = 2
c = b * a
self.assertEqual(c, Eisenstein(2, 4))
def test_modulo_operation(self):
"""
TestEisensteinNumbers:
wolframalfa.com:
query: w = ( -1 + i sqrt(3) ) / 2 ; (2, 0w)(2, 0w) + (1, 0w)
expected: (5, 0w)
query: w = ( -1 + i sqrt(3) ) / 2 ; (3, 0w) (2, 0w) + (-1, 2w)
expected (5, 2w)
query: w = ( -1 + i sqrt(3) ) / 2 ; (5, 1w) (1, 0w)
expected (5, 0w)
"""
a = 5
self.assertEqual(1, a % 2) # int
a = Eisenstein(5, 0)
self.assertEqual(Eisenstein(1, 0), a % Eisenstein(2, 0)) # Eisenstein
a = Eisenstein(5, 2)
self.assertEqual(Eisenstein(1, 0), a % Eisenstein(2, 0)) # Eisenstein
a = Eisenstein(5, 1)
self.assertEqual(Eisenstein(0, 0), a % Eisenstein(1, 0)) # Eisenstein
a = Eisenstein(5, 2)
self.assertEqual(Eisenstein(1, 0), a % 2) # Eisenstein
a = Eisenstein(5, 1)
self.assertEqual(Eisenstein(0, 0), a % 1) # Eisenstein
def test_presentation(self):
a = Eisenstein(2, 2)
self.assertEqual(str(a), "Eisenstein(2, 2)")
def test_floor_div(self):
a = Eisenstein(3, 4)
b = Eisenstein(11, 19)
c = a * b
self.assertEqual(c // a, b)
def test_division_by_eisenstein(self):
a = EisensteinFraction(four=(1, 1, -3, 2))
b = a / Eisenstein(2, 0)
self.assertEqual(b, EisensteinFraction(four=(1, 2, -3, 4)))
c = a / Eisenstein(3, 0)
self.assertEqual(c, EisensteinFraction(four=(1, 3, -1, 2)))
def test_multiply_imag_by_imag(self):
a = Eisenstein(0, 1)
b = Eisenstein(0, 1)
c = a * b
self.assertEqual(c, Eisenstein(-1, -1))
def test_presentation(self):
a = Eisenstein(2, 2)
self.assertEqual(str(a), "Eisenstein(2, 2)")
a = EisensteinFraction(Fraction(1, 2), 2)
self.assertEqual(str(a), "EisensteinFraction(four=(1, 2, 2, 1))")
def test_round(self):
a = EisensteinFraction(Fraction(1, 2), Fraction(3, 4))
self.assertEqual(Eisenstein(0, 1), a.round)
a = EisensteinFraction(Fraction(-3, 4), Fraction(1, 2))
self.assertEqual(Eisenstein(-1, 0), a.round)