Python PolynomialRing.degree方法代码示例

# 需要导入模块: from sage.all import PolynomialRing [as 别名]
# 或者: from sage.all.PolynomialRing import degree [as 别名]
def pol_string_to_list(pol, deg=None, var=None):
    if var is None:
        from lmfdb.hilbert_modular_forms.hilbert_field import findvar
        var = findvar(pol)
        if not var:
            var = 'a'
    pol = PolynomialRing(QQ, var)(str(pol))
    if deg is None:
        fill = 0
    else:
        fill = deg - pol.degree() - 1
    return [str(c) for c in pol.coefficients(sparse=False)] + ['0']*fill

# 需要导入模块: from sage.all import PolynomialRing [as 别名]
# 或者: from sage.all.PolynomialRing import degree [as 别名]
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

# 需要导入模块: from sage.all import PolynomialRing [as 别名]
# 或者: from sage.all.PolynomialRing import degree [as 别名]
 def check_roots_are_roots(self, rec, verbose=False):
     """
     check that  embedding_root_real, and embedding_root_image  approximate a root of field_poly
     """
     poly = PolynomialRing(ZZ, "x")(rec['field_poly'])
     dpoly = poly.derivative()
     dbroots = db.mf_hecke_cc.search({'hecke_orbit_code': rec['hecke_orbit_code']}, ["embedding_root_real", "embedding_root_imag"])
     dbroots = [CCC(root["embedding_root_real"], root["embedding_root_imag"]) for root in dbroots]
     if len(dbroots) != poly.degree():
         if verbose:
             print "Wrong number of roots"
         return False
     for r in dbroots:
         # f is irreducible, so all roots are simple and checking relative error is the way to go
         if poly(r)/dpoly(r) > 1e-11:
             # It's still possible that the roots are correct; it could just be a problem of numerical instability
             print r, poly(r)/dpoly(r)
             break
     else:
         return True
     roots = poly.roots(CCC, multiplicities=False)
     # greedily match.  The degrees are all at most 20, so it's okay to use a quadratic algorithm
     while len(roots) > 0:
         best_dist = infinity
         r = roots[0]
         for i, s in enumerate(dbroots):
             dist = abs(r-s)
             if dist < best_dist:
                 best_dist, best_i = dist, i
         # The dim 1 case where poly=x is handled correctly in the earlier loop, so r != 0.
         if best_dist/abs(r) > 1e-13:
             if verbose:
                 print "Roots mismatch", sorted(roots), sorted(dbroots)
             return False
         roots.pop(0)
         dbroots.pop(best_i)
     return True

# 需要导入模块: from sage.all import PolynomialRing [as 别名]
# 或者: from sage.all.PolynomialRing import degree [as 别名]
 def field(self):
     if not self.__field:
         f = PolynomialRing(ZZ,name='x')(str(self.__field_poly))
         self.__field = QQ if f.degree() == 1 else NumberField(f,'a')
     return self.__field