def __init__(self, mod, symmetric=True):
if mod <= 0:
raise ValueError('modulus must be a positive integer, got %s' % mod)
self.dtype = ModularIntegerFactory(mod, self.dom, symmetric)
self.zero = self.dtype(0)
self.one = self.dtype(1)
self.mod = mod
def __init__(self, mod, symmetric=True):
from sympy.polys.domains import ZZ
dom = ZZ
if mod <= 0:
raise ValueError('modulus must be a positive integer, got %s' % mod)
self.dtype = ModularIntegerFactory(mod, dom, symmetric, self)
self.zero = self.dtype(0)
self.one = self.dtype(1)
self.dom = dom
self.mod = mod
def test_ModularInteger():
GF = ModularIntegerFactory(3)
a = GF(0)
assert isinstance(a, GF) and a == 0
a = GF(1)
assert isinstance(a, GF) and a == 1
a = GF(2)
assert isinstance(a, GF) and a == 2
a = GF(3)
assert isinstance(a, GF) and a == 0
a = GF(4)
assert isinstance(a, GF) and a == 1
a = GF(GF(0))
assert isinstance(a, GF) and a == 0
a = GF(GF(1))
assert isinstance(a, GF) and a == 1
a = GF(GF(2))
assert isinstance(a, GF) and a == 2
a = GF(GF(3))
assert isinstance(a, GF) and a == 0
a = GF(GF(4))
assert isinstance(a, GF) and a == 1
a = -GF(1)
assert isinstance(a, GF) and a == 2
a = -GF(2)
assert isinstance(a, GF) and a == 1
a = 2 + GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) + 2
assert isinstance(a, GF) and a == 1
a = GF(2) + GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) + GF(2)
assert isinstance(a, GF) and a == 1
a = 3 - GF(2)
assert isinstance(a, GF) and a == 1
a = GF(3) - 2
assert isinstance(a, GF) and a == 1
a = GF(3) - GF(2)
assert isinstance(a, GF) and a == 1
a = GF(3) - GF(2)
assert isinstance(a, GF) and a == 1
a = 2 * GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) * 2
assert isinstance(a, GF) and a == 1
a = GF(2) * GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) * GF(2)
assert isinstance(a, GF) and a == 1
a = 2 / GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) / 2
assert isinstance(a, GF) and a == 1
a = GF(2) / GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2) / GF(2)
assert isinstance(a, GF) and a == 1
a = 1 % GF(2)
assert isinstance(a, GF) and a == 1
a = GF(1) % 2
assert isinstance(a, GF) and a == 1
a = GF(1) % GF(2)
assert isinstance(a, GF) and a == 1
a = GF(1) % GF(2)
assert isinstance(a, GF) and a == 1
a = GF(2)**0
assert isinstance(a, GF) and a == 1
a = GF(2)**1
assert isinstance(a, GF) and a == 2
a = GF(2)**2
assert isinstance(a, GF) and a == 1
assert bool(GF(3)) is False
assert bool(GF(4)) is True
GF = ModularIntegerFactory(5)
a = GF(1)**(-1)
assert isinstance(a, GF) and a == 1
a = GF(2)**(-1)
assert isinstance(a, GF) and a == 3
a = GF(3)**(-1)
assert isinstance(a, GF) and a == 2
a = GF(4)**(-1)
assert isinstance(a, GF) and a == 4
assert (GF(1) < GF(2)) == True
assert (GF(1) <= GF(2)) == True
assert (GF(1) > GF(2)) == False
assert (GF(1) >= GF(2)) == False
assert (GF(3) < GF(2)) == False
assert (GF(3) <= GF(2)) == False
assert (GF(3) > GF(2)) == True
assert (GF(3) >= GF(2)) == True
assert (GF(1) < GF(7)) == True
assert (GF(1) <= GF(7)) == True
assert (GF(1) > GF(7)) == False
assert (GF(1) >= GF(7)) == False
assert (GF(3) < GF(7)) == False
assert (GF(3) <= GF(7)) == False
assert (GF(3) > GF(7)) == True
assert (GF(3) >= GF(7)) == True
assert (GF(1) < 2) == True
assert (GF(1) <= 2) == True
assert (GF(1) > 2) == False
assert (GF(1) >= 2) == False
assert (GF(3) < 2) == False
assert (GF(3) <= 2) == False
assert (GF(3) > 2) == True
assert (GF(3) >= 2) == True
assert (GF(1) < 7) == True
assert (GF(1) <= 7) == True
assert (GF(1) > 7) == False
assert (GF(1) >= 7) == False
assert (GF(3) < 7) == False
assert (GF(3) <= 7) == False
assert (GF(3) > 7) == True
assert (GF(3) >= 7) == True
raises(NotInvertible, "GF(0)**(-1)")
raises(NotInvertible, "GF(5)**(-1)")
raises(ValueError, "ModularIntegerFactory(0)")
raises(ValueError, "ModularIntegerFactory(2.1)")
raises(TypeError, "ModularIntegerFactory(3, QQ)")