def type_2_bounds(self):
"""generate the type 2 bounds table"""
output_str = (
r"${d}$ & ${Delta_K}$ & ${label}$ & ${rem} \times 10^{{{exp_at_10}}}$\\"
)
latex_output = []
for d in range(2, self.range + 1):
Delta_K, f_K, K, label = get_smallest_good_number_field(d)
type_2_bound = RR(get_type_2_bound(K))
log_type_2_bound = type_2_bound.log10()
exp_at_10 = int(log_type_2_bound)
rem = log_type_2_bound - exp_at_10
rem = 10 ** rem
rem = rem.numerical_approx(digits=3)
lmfdb_link = LMFDB_NF_URL_TRUNK.format(label)
lmfdb_link_latex = r"\href{{{the_link}}}{{{my_text}}}".format(
the_link=lmfdb_link, my_text=label
)
output_here = output_str.format(
d=d,
Delta_K=Delta_K,
label=lmfdb_link_latex,
rem=rem,
exp_at_10=exp_at_10,
)
latex_output.append(output_here)
for one_line in latex_output:
print(one_line)
def dlmv_table(self):
"""generate the dlmv table"""
output_str = (
r"${Delta_K}$ & $\Q(\sqrt{{{D}}})$ & ${rem} \times 10^{{{exp_at_10}}}$\\"
)
for D in range(-self.range, self.range + 1):
if Integer(D).is_squarefree():
if not D in CLASS_NUMBER_ONE_DISCS:
if D != 1:
K = QuadraticField(D)
Delta_K = K.discriminant()
dlmv_bound = RR(DLMV(K))
log_dlmv_bound = dlmv_bound.log10()
exp_at_10 = int(log_dlmv_bound)
rem = log_dlmv_bound - exp_at_10
rem = 10**rem
rem = rem.numerical_approx(digits=3)
output_here = output_str.format(Delta_K=Delta_K,
D=D,
rem=rem,
exp_at_10=exp_at_10)
print(output_here)