def test_Sn(self):
S0 = fg.SymmetricGroup(0)
self.assertEqual(S0.degree, 0)
self.assertEqual(S0.order, 1)
p = S0.identity
self.assertEqual(p^2, p)
self.assertRaises(TypeError, operator.add, p, p)
self.assertRaises(TypeError, operator.mul, p, p)
self.assertRaises(TypeError, operator.mul, 1, p)
S1 = fg.SymmetricGroup(1)
self.assertEqual(S1.degree, 1)
self.assertEqual(S1.order, 1)
p = S1.identity
self.assertEqual(p^2, p^-1)
S3 = fg.SymmetricGroup(3)
self.assertEqual(S3.degree, 3)
self.assertEqual(S3.order, 6)
self.assertEqual(S3.identity, S3([0, 1, 2]))
p = S3([1, 2, 0])
self.assertEqual(p^3, S3.identity)
q = S3([1, 0, 2])
self.assertEqual(q @ q, S3.identity)
self.assertEqual(q, ~q)
self.assertEqual(p @ q, S3([0, 2, 1]))
self.assertEqual(q @ p, S3([2, 1, 0]))
self.assertEqual({p, q, q}, {p, p, q})
self.assertRaises(ValueError, S3, [1, 2])
self.assertRaises(ValueError, S3, [1, 2, 3])
def test_group_caching(self):
S3_cached = fg.SymmetricGroup(3)
self.assertEqual(self.S3, S3_cached)
self.assertEqual(self.S3(), S3_cached())
QR11_cached = fg.QuadraticResidues(l=4)
self.assertEqual(self.QR11, QR11_cached)
Cl23_cached = fg.ClassGroup(Delta=-23)
self.assertEqual(self.Cl23, Cl23_cached)
self.assertEqual(self.Cl23(), Cl23_cached())
Cl23_cached = fg.ClassGroup(l=5)
self.assertEqual(self.Cl23, Cl23_cached)
def test_Sn(self):
group = fg.SymmetricGroup(5)
a = group([3, 4, 2, 1, 0])
b = a @ a
secgrp = mpc.SecGrp(group)
c = secgrp(a)
d = a @ c
self.assertEqual(mpc.run(mpc.output(d)), b)
e = ~c
f = e @ b
self.assertEqual(mpc.run(mpc.output(f)), a)
self.assertTrue(mpc.run(mpc.output(f == c)))
group = fg.SymmetricGroup(11)
secgrp = mpc.SecGrp(group)
a = group([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0])
secfld = mpc.SecFld(11) # ord(a) = 11
a7 = secgrp.repeat(a, secfld(7))
self.assertEqual(mpc.run(mpc.output(a7)), a ^ 7)
a7 = secgrp.repeat_public(a, secfld(7))
self.assertEqual(mpc.run(a7), a ^ 7)
a6 = a ^ 6
a12 = a6 @ a6
self.assertEqual(mpc.run(mpc.output(secgrp(a6).inverse())), a ^ 5)
self.assertEqual(
mpc.run(mpc.output((secgrp(a) ^ 6) @ secgrp.identity)), a6)
self.assertEqual(mpc.run(mpc.output(secgrp.repeat(a6, secfld(2)))),
a12)
self.assertEqual(
mpc.run(mpc.output(secgrp.repeat(secgrp(a), secfld(6)))), a6)
p = secgrp(a)
self.assertRaises(TypeError, operator.add, p, p)
self.assertRaises(TypeError, operator.mul, p, p)
self.assertRaises(TypeError, operator.mul, 1, p)
group.is_multiplicative = True
self.assertTrue(mpc.run(mpc.output(a * p == a ^ 2)))
group.is_multiplicative = False
self.assertRaises(ValueError, secgrp, [0, 1, 2, 3])
def setUp(self):
self.S3 = fg.SymmetricGroup(3)
self.QR11 = fg.QuadraticResidues(11)
self.SG11 = fg.SchnorrGroup(11, 5, 4)
self.Cl23 = fg.ClassGroup(Delta=-23)