def niceideals(F, ideals): #HNF + sage ideal + label
"""Convert a list of ideas from strongs to actual NumberField ideals
F is a Sage NumberField
ideals is a list of strings representing ideals I in the field, of
the form [N,a,alpha] where N is the norm of I, a the least
positive integer in I, and alpha a field element such that I is
generated by a and alpha.
The output is a list
"""
nideals = []
ilabel = 1
norm = ZZ(0)
for i in range(len(ideals)):
N, n, idl, _ = str2ideal(F, ideals[i])
assert idl.norm() == N and idl.smallest_integer() == n
if N != norm:
ilabel = ZZ(1)
norm = N
label = N.str() + '.' + ilabel.str()
hnf = idl.pari_hnf().python()
nideals.append([hnf, idl, label])
ilabel += 1
return nideals
def niceideals(F, ideals): #HNF + sage ideal + label
"""Convert a list of ideas from strongs to actual NumberField ideals
F is a Sage NumberField
ideals is a list of strings representing ideals I in the field, of
the form [N,a,alpha] where N is the norm of I, a the least
positive integer in I, and alpha a field element such that I is
generated by a and alpha.
The output is a list
"""
nideals = []
ilabel = 1
norm = ZZ(0)
for i in range(len(ideals)):
N,n,idl,_ = str2ideal(F,ideals[i])
assert idl.norm() == N and idl.smallest_integer() == n
if N != norm:
ilabel = ZZ(1)
norm = N
label = N.str() + '.' + ilabel.str()
hnf = idl.pari_hnf().python()
nideals.append([hnf, idl, label])
ilabel += 1
return nideals
def _iter_ideals(self, primes=False, number=None):
"""
Iterator through all ideals of self. Delivers dicts with keys
'label' and 'ideal'.
"""
count = 0
ilabel = 1
norm = ZZ(0)
ideals = self.ideals
if primes:
ideals = self.primes
for idlstr in ideals:
N, n, idl, _ = str2ideal(self.K(), idlstr)
assert idl.norm() == N and idl.smallest_integer() == n
if N != norm:
ilabel = ZZ(1)
norm = N
label = N.str() + '.' + ilabel.str()
yield {'label': label, 'ideal': idl}
ilabel += 1
count += 1
if count == number:
raise StopIteration
def _iter_ideals(self, primes=False, number=None):
"""
Iterator through all ideals of self. Delivers dicts with keys
'label' and 'ideal'.
"""
count = 0
ilabel = 1
norm = ZZ(0)
ideals = self.ideals
if primes:
ideals = self.primes
for idlstr in ideals:
N,n,idl,_ = str2ideal(self.K(),idlstr)
assert idl.norm() == N and idl.smallest_integer() == n
if N != norm:
ilabel = ZZ(1)
norm = N
label = N.str() + '.' + ilabel.str()
yield {'label':label, 'ideal':idl}
ilabel += 1
count += 1
if count==number:
raise StopIteration
def read_lfunction_file_old(filename):
"""
reads an .lfunction file
adds to it the order_of_vanishing
and Lhash
expects:
<target accuracy> + 1
ZZ(root_number * 2^<target accuracy>) ???
ZZ(L(1/2) * 2^<target accuracy>)
order_of_vanishing
n = number of zeros computed
z1
z2
z3
...
zn
plot_delta
number of plot_values
plot_value1
plot_value2
...
"""
output = {};
with open(filename, "r") as lfunction_file:
for i, l in enumerate(lfunction_file):
if i == 0:
accuracy = int(l) - 1;
output['accuracy'] = accuracy;
two_power = 2 ** output['accuracy'];
R = ComplexIntervalField(accuracy)
elif i == 1:
root_number = R(*map(ZZ, l.split(" ")))/two_power;
if (root_number - 1).contains_zero():
root_number = R(1);
sign_arg = 0;
elif (root_number + 1).contains_zero():
root_number = R(-1);
sign_arg = 0.5
else:
assert (root_number.abs() - 1).contains_zero(), "%s, %s" % (filename, root_number.abs() )
sign_arg = float(root_number.arg()/(2*pi))
root_number = root_number #.str(style="question").replace('?', '')
output['root_number'] = root_number;
output['sign_arg'] = sign_arg
elif i == 2:
output['leading_term'] = (R(ZZ(l))/two_power).str(style="question").replace('?', '');
elif i == 3:
output['order_of_vanishing'] = int(l);
if output['order_of_vanishing'] > 0:
output['leading_term'] = '\N'
elif i == 4:
number_of_zeros = int(l);
output['positive_zeros'] = [];
elif i < 5 + number_of_zeros:
double_zero, int_zero = l.split(" ");
double_zero = float(double_zero);
int_zero = ZZ(int_zero);
zero = RealNumber(int_zero.str()+".")/two_power;
zero_after_string = (RealNumber(zero.str(truncate=False)) * two_power).round()
assert double_zero == zero, "%s, %s != %s" % (filename, double_zero, zero)
assert zero_after_string == int_zero, "zero_after_field = %s\nint_zero = %s" % (zero_after_string, int_zero,)
if int_zero == 0:
assert 5 + output['order_of_vanishing'] > i, "%s, %s < %s" % (filename, 5 + output['order_of_vanishing'], i);
else:
assert 5 + output['order_of_vanishing'] <= i, "%s, %s >= %s" % (filename, 5 + output['order_of_vanishing'], i);
# they will be converted to strings later on
# during populate_rational_rows
output['positive_zeros'] += [zero];
#Lhash = (first_zero * 2^100).round()
if 'Lhash' not in output:
output['Lhash'] = str( QQ(int_zero*2**(100 - accuracy)).round() )
if accuracy < 100:
output['Lhash'] = "_" + output['Lhash'];
elif i == 5 + number_of_zeros:
output['plot_delta'] = float(l);
elif i == 6 + number_of_zeros:
len_plot_values = int(l);
output['plot_values'] = [];
elif i > 6 + number_of_zeros:
output['plot_values'] += [float(l)];
assert len(output['plot_values']) == len_plot_values, "%s, %s != %s" % (filename, len(output['plot_values']), len_plot_values)
assert len(output['positive_zeros']) == number_of_zeros - output['order_of_vanishing'], "%s, %s != %s" % (filename, len(output['positive_zeros']), output['number_of_zeros'] - output['order_of_vanishing']) ;
assert 'Lhash' in output, "%s" % filename
for i in range(0,3):
output['z' + str(i + 1)] = str(output['positive_zeros'][i])
return output
def read_lfunction_file(filename):
"""
reads an .lfunction file
adds to it the order_of_vanishing
and Lhash
expects:
root_number as acb2, see from_acb2
order_of_vanishing
L(1/2)^r / r! as arb2
n = number of zeros computed
z1 as arb2
z2 as arb2
z3 as arb2
...
zn as arb2
plot_delta
number of plot_values
plot_value1
plot_value2
...
"""
output = {}
with open(filename, "r") as lfunction_file:
for i, l in enumerate(lfunction_file):
if i == 0:
# Root number
vals = map(int, l.split())
if len(vals) == 1:
return read_lfunction_file_old(filename)
assert len(vals) == 6
root_number = from_acb2(*vals)
assert root_number.abs().contains_exact(1), "%s, %s" % (filename, root_number.abs() )
try:
root_number = ZZ(root_number)
if root_number == 1:
sign_arg = 0
elif root_number == -1:
sign_arg = 0.5
else:
assert root_number in [1, -1], "%s %s" % (root_number, from_acb2(*vals))
except Exception:
sign_arg = float(root_number.arg()/(2*pi))
root_number = CIF(root_number) # for conversion to text purposes
output['root_number'] = root_number;
output['sign_arg'] = sign_arg;
elif i == 1:
# Order of vanishing
output['order_of_vanishing'] = int(l);
elif i == 2:
# Leading term
# L^(r)(1/2) / r!
vals = map(int, l.split())
assert len(vals) == 3
output['leading_term'] = RRR(from_arb2(*vals)).str(style="question").replace('?', '')
elif i == 3:
# Number of zeros
number_of_zeros = int(l);
output['positive_zeros'] = [];
elif i < 4 + number_of_zeros:
vals = map(int, l.split())
assert len(vals) == 3
if vals == [0,0,0]:
int_zero = 0
double_zero = 0
assert 4 + output['order_of_vanishing'] > i, "%s, %s < %s" % (filename, 5 + output['order_of_vanishing'], i);
else:
assert 4 + output['order_of_vanishing'] <= i, "%s, %s >= %s" % (filename, 5 + output['order_of_vanishing'], i);
assert vals[1] - vals[0] <= 2, "%s %s %s" % (filename, vals, i)
arb_zero = from_arb2(*vals).real()
double_zero = float(arb_zero)
if 'accuracy' not in output:
# if vals[3] = -101
# then accuracy = 100
output['accuracy'] = -vals[2] - 1
two_power = 2**output['accuracy']
else:
assert -(output['accuracy'] + 1) == vals[2]
try:
int_zero = ZZ(arb_zero*two_power)
except ValueError:
print "%s %s %s" % (filename, vals, i)
raise
zero = RealNumber(int_zero.str()+".")/two_power;
zero_after_string = (RealNumber(zero.str(truncate=False)) * two_power).round()
assert double_zero == zero, "%s, %s != %s" % (filename, double_zero, zero)
assert zero_after_string == int_zero, "zero_after_field = %s\nint_zero = %s" % (zero_after_string, int_zero,)
# will be converted to strings later on
# as zero.str(truncate=False)
# during populate_rational_rows
output['positive_zeros'] += [zero];
#Lhash = (first_zero * 2^100).round()
if 'Lhash' not in output:
output['Lhash'] = str( QQ(int_zero*2**(100 - output['accuracy'])).round() )
if output['accuracy'] < 100:
output['Lhash'] = "_" + output['Lhash'];
elif i == 4 + number_of_zeros:
output['plot_delta'] = float(l);
elif i == 5 + number_of_zeros:
len_plot_values = int(l);
output['plot_values'] = [];
elif i > 5 + number_of_zeros:
output['plot_values'] += [float(l)];
assert len(output['plot_values']) == len_plot_values, "%s, %s != %s" % (filename, len(output['plot_values']), len_plot_values)
assert len(output['positive_zeros']) == number_of_zeros - output['order_of_vanishing'], "%s, %s != %s" % (filename, len(output['positive_zeros']), output['number_of_zeros'] - output['order_of_vanishing']) ;
assert 'Lhash' in output, "%s" % filename
for i in range(0,3):
# were we don't want to truncate
output['z' + str(i + 1)] = str(output['positive_zeros'][i])
return output