def testMonic(self):
t1 = gfp(3, [2, 0, 1])
self.assertEqual(t1.monic(), gfp(3, [1, 0, 2]))
t1 = gfp(3, [0, 0])
self.assertRaises(ValueError, t1.monic)
t1 = gfp(7, [2, 3, 2, 6])
self.assertEqual(t1.monic(), gfp(7, [1, 5, 1, 3]))
def testInvTable(self):
t = gfp(2)
self.assertEqual(t.invTable, [0, 1])
t = gfp(3)
self.assertEqual(t.invTable, [0, 1, 2])
t = gfp(7)
self.assertEqual(t.invTable, [0, 1, 4, 5, 2, 3, 6])
def testInv(self):
t = gfp(2)
self.assertEqual(t.inv(1), 1)
self.assertRaises(ValueError, t.inv, 0)
t = gfp(7)
self.assertEqual(t.inv(6), 6)
self.assertEqual(t.inv(3), 5)
def testPolySub(self):
t1 = gfp(3, [1, 0, 2])
t2 = gfp(3, [1, 1])
self.assertEqual(t1.polySub(t2), gfp(3, [1, 2, 1]))
t1 = gfp(2, [0, 1, 0])
t2 = gfp(2, [1, 0, 0, 1])
self.assertEqual(t1.polySub(t2), gfp(2, [1, 0, 1, 1]))
t1 = gfp(7, [3, 1, 4, 1])
t2 = gfp(7, [5, 2, 6, 0, 2])
self.assertEqual(t1.polySub(t2), gfp(7, [2, 1, 2, 4, 6]))
def testConv(self):
t1 = gfp(2, [1, 0, 1])
t2 = gfp(2, [1, 1, 0])
self.assertEqual(t1.conv(t2), gfp(2, [1, 1, 1, 1, 0]))
t1 = gfp(2, [0, 0, 1])
self.assertEqual(t1.conv(t2), gfp(2, [0, 0, 1, 1, 0]))
t1 = gfp()
t2 = gfp(2, [1, 0, 1])
self.assertEqual(t1.conv(t2), gfp())
def primitivePoly(p, n):
""" primitive polynomials of characteristic-p of order n-1 """
iPoly = irreduciblePoly(p, n + 1)
#print(iPoly)
candidates = [gfp(p, v) for v in iPoly if len(v) == n + 1]
#print(candidates)
fieldPoly = [0 for i in range(p**n)]
fieldPoly[0], fieldPoly[-1] = 1, -1
fieldPoly = gfp(p, fieldPoly)
#print(fieldPoly)
pPoly = []
for i in range(len(candidates)):
q, r = fieldPoly.deconv(candidates[i])
if r == gfp(p):
pPoly.append(candidates[i])
return pPoly
def findPrimitiveElement(p, n, genPoly):
mPoly = [gfp(p, v) for v in enumerateMonicPoly(p, n)]
order = p**n
isPrimitive = [True for i in range(order - 2)]
cyclicGroup = [gfp(p, [1])]
i = 0
while len(cyclicGroup) < order - 1:
cyclicGroup = [gfp(p, [1])]
while not isPrimitive[i]:
i += 1
nextPoly = mPoly[i]
while not nextPoly == cyclicGroup[0]:
isPrimitive[mPoly.index(nextPoly)] = False
cyclicGroup.append(nextPoly)
dummy, nextPoly = nextPoly.conv(mPoly[i]).deconv(genPoly)
return cyclicGroup
def test__init__(self):
t = gfp(2, 1)
#self.assertRaises(ValueError, gfp, 2, [])
t = gfp(2, 0)
t = gfp(3, [1])
t = gfp(3, [1, 2, 0])
t = gfp()
t = gfp(3, [1, -1])
def generateAdditionTable(p, n, genPoly):
cyclicGroup = gf.findPrimitiveElement(p, n, genPoly)
elem = cyclicGroup + [gfp(p)]
# generator = gfp(p, [1, 1])
# elem = [gfp(p, 1), generator]
# order = p**n
# for i in range(2, order - 1):
# nextPoly = elem[-1].conv(generator)
# q, r = nextPoly.deconv(genPoly)
# print(r)
# if r in elem:
# print('stop')
# elem.append(r)
#
# elem.append(gfp(p))
addTab = []
order = p**n
for i in range(order):
addTab.append(
[elem.index(elem[i].polyAdd(elem[j])) for j in range(order)])
return addTab
def testDeconv(self):
t1 = gfp(2, [1, 0, 1, 1])
t2 = gfp(2, [0, 1, 1])
self.assertEqual(t1.deconv(t2), (gfp(2, [1, 1, 0]), gfp(2, [1])))
t1 = gfp(2, [1, 0, 1, 0, 0, 0, 1])
t2 = gfp(2, [1, 0, 1, 0, 1])
self.assertEqual(t1.deconv(t2), (gfp(2, [1, 0, 0]), gfp(2, [1, 0, 1])))
t1 = gfp(2, [1, 1, 0])
t2 = gfp(2, 1)
self.assertEqual(t1.deconv(t2), (gfp(2, [1, 1, 0]), gfp()))
t1 = gfp(2, [1, 1, 0])
t2 = gfp()
self.assertRaises(ZeroDivisionError, t1.deconv, t2)
t1 = gfp(7, [3, 1, 4, 1, 5, 2])
t2 = gfp(7, [2, 3, 5])
self.assertEqual(t1.deconv(t2), (gfp(7, [5, 0, 0, 4]), gfp(7, 3)))
t1 = gfp()
t2 = gfp(2, [1, 1])
self.assertEqual(t1.deconv(t2), (gfp(), gfp()))
def testProper(self):
t1 = gfp(2, [0, 0, 1, 0])
self.assertEqual(t1.proper(), gfp(2, [1, 0]))
t1 = gfp()
self.assertEqual(t1, gfp(2, [0]))
t1 = gfp(2)
self.assertEqual(t1, gfp(2, [0]))
t1 = gfp(2, [0])
self.assertEqual(t1, gfp())
t1 = gfp(2, [0, 0])
self.assertEqual(t1, gfp())
t1 = gfp(3, [1, -1])
t2 = gfp(3, [1, 2])
self.assertEqual(t1, t2)