def from_polynomial(cls, pol):
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredbest().polredabs())
return cls.from_coeffs(
[int(c) for c in pol.coefficients(sparse=False)])
def polredabs(self):
if "polredabs" in self._data.keys():
return self._data["polredabs"]
else:
pol = PolynomialRing(QQ, 'x')(self.polynomial())
pol *= pol.denominator()
R = pol.parent()
from sage.all import pari
pol = R(pari(pol).polredabs())
self._data["polredabs"] = pol
return pol
def polredabs(self):
if "polredabs" in self._data.keys():
return self._data["polredabs"]
else:
pol = PolynomialRing(QQ, 'x')(map(str, self.polynomial()))
# Need to map because the coefficients are given as unicode, which does not convert to QQ
pol *= pol.denominator()
R = pol.parent()
from sage.all import pari
pol = R(pari(pol).polredabs())
self._data["polredabs"] = pol
return pol
def polredabs(self):
if "polredabs" in self._data.keys():
return self._data["polredabs"]
else:
pol = PolynomialRing(QQ, 'x')(map(str,self.polynomial()))
# Need to map because the coefficients are given as unicode, which does not convert to QQ
pol *= pol.denominator()
R = pol.parent()
from sage.all import pari
pol = R(pari(pol).polredabs())
self._data["polredabs"] = pol
return pol
def from_polynomial(cls, pol):
try:
# try to cast to ring
pol = PolynomialRing(QQ, 'x')(pol)
except Exception:
# try again as a string
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredbest().polredabs())
return cls.from_coeffs(
[int(c) for c in pol.coefficients(sparse=False)])
def from_polynomial(cls, pol):
try:
# try to cast to ring
pol = PolynomialRing(QQ, 'x')(pol)
except Exception:
# try again as a string
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
# For some reason the error raised by Pari on a constant polynomial is not being caught
if pol.degree() < 1:
raise ValueError("Polynomial cannot be constant")
R = pol.parent()
pol = R(pari(pol).polredbest().polredabs())
return cls.from_coeffs([int(c) for c in pol.coefficients(sparse=False)])
def poly_to_field_label(pol):
try:
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredabs())
except:
return None
coeffs = list2string([int(c) for c in pol.coeffs()])
d = int(pol.degree())
query = {'coeffs': coeffs}
C = base.getDBConnection()
one = C.numberfields.fields.find_one(query)
if one:
return one['label']
return None
def poly_to_field_label(pol):
try:
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredabs())
except:
return None
coeffs = list2string([int(c) for c in pol.coeffs()])
d = int(pol.degree())
query = {'coeffs': coeffs}
C = base.getDBConnection()
one = C.numberfields.fields.find_one(query)
if one:
return one['label']
return None
def from_polynomial(cls, pol):
pol = PolynomialRing(QQ, 'x')(str(pol))
pol *= pol.denominator()
R = pol.parent()
pol = R(pari(pol).polredbest().polredabs())
return cls.from_coeffs([int(c) for c in pol.coefficients(sparse=False)])
def input_to_subfield(inp):
def finish(result):
return '.'.join([str(z) for z in result])
def notq():
raise SearchParsingError(r"The rational numbers $\Q$ cannot be a proper intermediate field.")
# Change unicode dash with minus sign
inp = inp.replace(u'\u2212', '-')
# remove non-ascii characters from inp
# we need to encode and decode for Python 3, as 'str' object has no attribute 'decode'
inp = re.sub(r'[^\x00-\x7f]', r'', inp)
if len(inp) == 0:
return None
# Do we have a nf label
if re.match(r'\d+\.\d+\.[0-9e_]+\.\d+',inp):
from lmfdb import db
myfield = db.nf_fields.lookup(inp)
if myfield:
return finish(myfield['coeffs'])
else:
raise SearchParsingError("It is not the label for a subfield in the database.")
F = inp.lower() # keep original if needed
# Is it a polynomial
if 'x' in F:
F1 = F.replace('^', '**')
R = PolynomialRing(ZZ, 'x')
pol = PolynomialRing(QQ,'x')(str(F1))
pol *= pol.denominator()
if not pol.is_irreducible():
raise SearchParsingError("It is not an irreducible polynomial.")
coeffs = R(pari(pol).polredabs()).coefficients(sparse=False)
if coeffs == [0,1]:
notq()
return finish(coeffs)
# Nicknames
if F == 'q':
notq()
if F in ['qi', 'q(i)']:
return '1.0.1'
if F[0] == 'q':
if '(' in F and ')' in F:
F=F.replace('(','').replace(')','')
inp=inp.replace('(','').replace(')','')
if F[1:5] in ['sqrt', 'root']:
try:
d = ZZ(str(F[5:])).squarefree_part()
except (TypeError, ValueError):
d = 0
if d == 0 or d == 1:
raise SearchParsingError("After {0}, the remainder must be a nonzero integer which is not a perfect square. Use {0}5 or {0}-11 for example.".format(inp[:5]))
# Recursion has it use polredabs to get the polynomial
return input_to_subfield("x^2 - (%s)" % d)
# Look for cyclotomic
if F[0:5] == 'qzeta':
if '_' in F:
F = F.replace('_','')
match_obj = re.match(r'^qzeta(\d+)(\+|plus)?$', F)
if not match_obj:
raise SearchParsingError("After {0}, the remainder must be a positive integer or a positive integer followed by '+'. Use {0}5 or {0}19+, for example.".format(F[:5]))
d = ZZ(str(match_obj.group(1)))
if d % 4 == 2:
d /= 2 # Q(zeta_6)=Q(zeta_3), etc)
if d < 1:
raise SearchParsingError("After {0}, the remainder must be a positive integer or a positive integer followed by '+'. Use {0}5 or {0}19+, for example.".format(F[:5]))
if d==1: # asking for Q
notq()
if match_obj.group(2): # asking for the totally real field
from lmfdb.number_fields.web_number_field import rcyclolookup
if d < 5: # again, asking for subfield Q
notq()
if d in rcyclolookup:
return input_to_subfield(rcyclolookup[d])
else:
raise SearchParsingError("Subfield %s is not available." % F)
f = pari.polcyclo(d)
return input_to_subfield(str(f))
# Want polcyclo here
raise SearchParsingError('%s is not in the database.' % F)
f = pari.polcyclo(d)
return input_to_subfield(str(f))
raise SearchParsingError('It is not a valid field nickname or label, or a defining polynomial.')
