def to_HNFRepresentation(self):
"""
Transform self to the corresponding ideal as HNF representation
"""
int_ring = self.number_field.integer_ring()
n = self.number_field.degree
polynomial = self.number_field.polynomial
k = len(self.generator)
# separate coeff and denom for generators and base
gen_denom = reduce( gcd.lcm,
(self.generator[j].denom for j in range(k)) )
gen_list = [gen_denom * self.generator[j] for j in range(k)]
base_int, base_denom = _toIntegerMatrix(int_ring)
base_alg = [BasicAlgNumber([base_int[j], 1],
polynomial) for j in range(1, n + 1)]
repr_mat_list = []
for gen in gen_list:
for base in base_alg:
new_gen = gen * base
repr_mat_list.append(
vector.Vector([new_gen.coeff[j] for j in range(n)]))
mat_repr = matrix.RingMatrix(n, n * k, repr_mat_list)
new_mat_repr, numer = _toIntegerMatrix(mat_repr, 2)
denom = gen_denom * base_denom
denom_gcd = gcd.gcd(numer, denom)
if denom_gcd != 1:
denom = ring.exact_division(denom, denom_gcd)
numer = ring.exact_division(numer, denom_gcd)
if numer != 1:
new_mat_repr = numer * new_mat_repr
else:
new_mat_repr = mat_repr
return Ideal([new_mat_repr, denom], self.number_field)
def testInit(self):
b2_1 = Module([ [(5, 10), (-3, 3)], 15 ], self.Q_rt_2)
self.assertEqual(self.b2, b2_1)
b2_2 = Module([ matrix.RingMatrix(2, 2,
[vect([5, 10]), vect([-3, 3])]), 15 ], self.Q_rt_2)
self.assertEqual(self.b2, b2_2)
b2_3 = Module(matrix.RingMatrix(2, 2,
[vect([ra(1, 3), ra(2, 3)]), vect([ra(-1, 5), ra(1, 5)])]
), self.Q_rt_2)
self.assertEqual(self.b2, b2_3)
omega_base_1 = [(1, 0), (ra(-1, 2), ra(1, 2))]
self.assertEqual(self.b5,
Module([ [vect([-3, 0]), vect([0, 6])], 4 ],
self.Q_rt_minus_3, omega_base_1))
omega_base_2 = matrix.RingMatrix(2, 2,
[vect([1, 0]), vect([ra(-1, 2), ra(1, 2)])])
self.assertEqual(self.b5,
Module([ [vect([-3, 0]), vect([0, 6])], 4 ],
self.Q_rt_minus_3, omega_base_2))