def testNegativeDisc(self):
"""
Test negative discriminant.
using Q(sqrt(-1)).
"""
q1i = round2.round2(self.root1i)
self.assertTrue(q1i)
self.assertEqual(2, len(q1i))
self.assertEqual(-4, q1i[1], q1i) # disc K = -4
def testTrivial(self):
"""
Test trivial errorlessness.
using Q(sqrt(2)).
"""
q2 = round2.round2(self.root2)
self.assertTrue(q2)
self.assertEqual(2, len(q2))
self.assertEqual(8, q2[1], q2) # disc K = 8
def field_discriminant(self):
"""
Return the (field) discriminant of self (using round2 module)
"""
if not hasattr(self, "discriminant"):
int_basis, self.discriminant = round2.round2(self.polynomial)
self.integer_basis = matrix.createMatrix(
self.degree, [vector.Vector(int_basis[j]) for j in range(
len(int_basis))])
return self.discriminant
def field_discriminant(self):
"""
Return the (field) discriminant of self (using round2 module)
"""
if not hasattr(self, "discriminant"):
int_basis, self.discriminant = round2.round2(self.polynomial)
self.integer_basis = matrix.createMatrix(
self.degree,
[vector.Vector(int_basis[j]) for j in range(len(int_basis))])
return self.discriminant
def testSeptic(self):
"""
Test an example: X^7 + 2X^6 + ... + 7X + 8
"""
poly_disc = uniutil.polynomial(enumerate(self.septic),
self.Z).discriminant()
self.assertEqual(-2**16 * 3**12, poly_disc)
result = round2.round2(self.septic)
self.assertTrue(result)
self.assertEqual(2, len(result))
self.assertEqual(-2**12 * 3**10, result[1], result)
def testQuartic(self):
"""
Test an example: X^4 - 10X^2 + 1
"""
poly_disc = uniutil.polynomial(enumerate(self.quartic),
self.Z).discriminant()
self.assertEqual(147456, poly_disc)
result = round2.round2(self.quartic)
self.assertTrue(result)
self.assertEqual(2, len(result))
self.assertEqual(2304, result[1], result)
def testCubic(self):
"""
Test an example: X^3 + 9X + 1
"""
poly_disc = uniutil.polynomial(enumerate(self.cubic),
self.Z).discriminant()
self.assertEqual(-3**3 * 109, poly_disc)
result = round2.round2(self.cubic)
self.assertTrue(result)
self.assertEqual(2, len(result))
self.assertEqual(-327, result[1], result) # disc K = -327 = -3 * 109
def testSextic(self):
"""
Test an example: X^6 + 2X^5 + ... + 6X + 7
"""
poly_disc = uniutil.polynomial(enumerate(self.sextic),
self.Z).discriminant()
self.assertEqual(-2**16 * 7**4, poly_disc)
result = round2.round2(self.sextic)
self.assertTrue(result)
self.assertEqual(2, len(result))
self.assertEqual(-9834496, result[1],
result) # disc K = - 2**12 * 7**4
def test6480(self):
coeff = [6480, 1296, -252, 36, -7, 1]
poly_disc = uniutil.polynomial(enumerate(coeff), self.Z).discriminant()
result = round2.round2(coeff)
self.assertTrue(result)
self.assertEqual(2, len(result))
bases, disc = result
self.assertTrue(poly_disc > disc, result)
self.assertFalse(poly_disc % disc.numerator, result)
#(by magma)
#> IntegralBasis(NumberField(PolynomialRing(RationalField())![6480,1296,-252,36,-7,1]));
#[
# 1,
# $.1,
# 1/6*($.1^2 + 5*$.1),
# 1/216*($.1^3 + 11*$.1^2 + 54*$.1 + 36),
# 1/1296*($.1^4 + 5*$.1^3 + 204*$.1^2 + 792*$.1 + 1080)
#]
# check only the last one
self.assertEqual([1080, 792, 204, 5, 1], [1296 * c for c in bases[-1]],
result)